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characterization of electrical discharge machining plasmas

THÈSE NO 3542 (2006)
PRÉSENTÉE le 9 juin 2006 à la facult sciences DE BASE Centre de Recherche en Physique des Plasmas SECTION DE PHYSIQUE

ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE
POUR L'OBTENTION DU GRADE DE DOCTEUR ÈS SCIENCES

PAR

Antoine DESCOEUDRES
ingénieur physicien diplômé EPF de nationalité suisse et originaire de La Sagne (NE)

acceptée sur proposition du jury: Prof. R. Schaller, président du jury Dr Ch. Hollenstein, directeur de thèse Prof. M. Rappaz, rapporteur Dr G. Wälder, rapporteur Prof. J. Winter, rapporteur

Lausanne, EPFL 2006

“La frousse, moi ! ... J’aime autant vous dire, mille tonnerres ! que quand je le rencontrerai, votre yéti, ça va faire des étincelles !” le capitaine Haddock

Abstract
Electrical Discharge Machining (EDM) is a well-known machining technique since more than ﬁfty years. Its principle is to use the eroding eﬀect on the electrodes of successive electric spark discharges created in a dielectric liquid. EDM is nowadays widely-used in a large number of industrial areas. Nevertheless, few studies have been done on the discharge itself and on the plasma created during this process. Further improvements of EDM, especially for micro-machining, require a better control and understanding of the discharge and of its interaction with the electrodes. In this work, the diﬀerent phases of the EDM process and the properties of the EDM plasma have been systematically investigated with electrical measurements, with imaging and with time- and spatiallyresolved optical emission spectroscopy. The pre-breakdown phase in water is characterized by the generation of numerous small hydrogen bubbles, created by electrolysis. Since streamers propagate more easily in a gaseous medium, these bubbles can facilitate the breakdown process. In oil, no bubbles are observed. Therefore, the breakdown mechanism in oil could be rather enhanced by particles present in the electrode gap. Fast pulses of current and light are simultaneously measured during the pre-breakdown. These pulses are characteristic of the propagation of streamers in the dielectric liquid. The pre-breakdown duration is not constant for given discharge parameters, but distributed following a Weibull distribution. This shows that the breakdown is of stochastic nature. After the breakdown, the plasma develops very rapidly (< 50 ns) and then remains stable. The plasma light is particularly intense during the ﬁrst 500 ns after the breakdown and weaker during the rest of the discharge, depending on the current intensity. While the gap distance is estimated to be around 10−100 µm, the discharge excites a broad volume around the electrode gap, typically 200 µm in diameter. This volume grows slightly during the discharge. Vapor bubbles are generated in water and in oil by the heat released from the plasma. At the end of the discharge, the plasma implodes and disappears quickly. Light is still emitted after the discharge by incandescent metallic particles coming from the erosion of the workpiece. Their temperature is measured around 2’200 K, demonstrating that they are still in a liquid state in the beginning of the post-discharge. The spectroscopic analysis of the plasma light shows a strong Hα and continuum radiation, with many atomic metallic lines emitted by impurities coming from electrode and workpiece materials. The EDM plasma is thus composed of species coming from the cracking of the dielectric molecules (mainly hydrogen in the case of water and oil), with contamination from the electrodes. The contamination is slightly higher in the vicinity of each electrode, and the contamination from the workpiece increases during the

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ABSTRACT

discharge probably due to vaporization. The electron temperature, measured from copper line intensities with the two-line method, is found to be low. The temperature is around 0.7 eV (∼ 8’100 K) in the whole plasma, slightly higher in the beginning of the discharge. The electron density has been measured from Stark broadening and shift measurements of the Hα line. The density is extremely high, especially at the beginning of the discharge (> 2·1018 cm−3 during the ﬁrst microsecond). Then it decreases with time, remaining nevertheless above 1016 cm−3 after 50 µs. During the whole discharge, the density is slightly higher in the plasma center. The EDM plasma has such a high density because it is formed from a liquid, and because it is constantly submitted to the pressure imposed by the surrounding liquid. This extreme density produces spectra with strongly-broadened spectral lines, especially the Hα line, and with an important continuum. During the ﬁrst microsecond when the density is at its maximum, spectral lines are so broadened that they are all merged into a continuum. The low temperature and the high density of the EDM plasma make it weakly nonideal. Its typical coupling parameter Γ is indeed around 0.3, reaching 0.45 during the ﬁrst microsecond. In this plasma, the Coulomb interactions between the charged particles are thus of the same order as the mean thermal energy of the particles, which produces coupling phenomena. Spectroscopic results conﬁrm the non-ideality of the EDM plasma. The strong broadening and shift of the Hα line and its asymmetric shape and complex structure, the absence of the Hβ line, and the merging of spectral lines are typical of nonideal plasmas. The EDM plasma has thus extreme physical properties, and the physics involved is astonishingly complex.

Keywords: electrical discharge machining, EDM, plasma, spark, discharge, nonideal plasma, optical emission spectroscopy, spectroscopy, imaging, breakdown, dielectric, liquid.

Version abrégée
L’électro-érosion (ou EDM pour Electrical Discharge Machining) est une technique d’usinage bien connue depuis plus de cinquante ans. Son principe est d’utiliser l’eﬀet érosif sur les électrodes d’étincelles électriques successives créées dans un liquide diélectrique. L’électro-érosion est aujourd’hui très utilisée dans un grand nombre de secteurs industriels. Néanmoins, peu d’études ont été menées sur la décharge elle-même et sur le plasma créé pendant ce processus. Les améliorations futures de l’électro-érosion, en particulier pour le micro-usinage, passent par un meilleur contrôle et une meilleure compréhension de la décharge et de ses interactions avec les électrodes. Dans ce travail, les diﬀérentes phases du processus d’électro-érosion et les propriétés du plasma ont été étudiées de manière systématique, à l’aide de mesures électriques, d’imagerie et de spectroscopie d’émission optique résolue en temps et en espace. La phase de pré-décharge dans l’eau est caractérisée par la génération de nombreuses petites bulles d’hydrogène, créées par électrolyse. Puisque les streamers se propagent plus facilement dans un milieu gazeux, ces bulles peuvent faciliter le processus de claquage. Dans l’huile, aucune bulle n’est observée. Ainsi, le mécanisme de claquage dans l’huile pourrait plutôt être facilité par des particules présentes dans l’espace inter-électrodes. Des impulsions rapides de courant et de lumière sont mesurées simultanément durant la pré-décharge. Ces impulsions sont caractéristiques de la propagation de streamers dans le liquide diélectrique. La durée de la pré-décharge n’est pas constante pour des paramètres de décharge donnés, mais elle est distribuée selon une distribution de Weibull. Ceci montre que le claquage est de nature stochastique. Après le claquage, le plasma se développe très rapidement (< 50 ns) et reste ensuite stable. La lumière du plasma est particulièrement intense durant les premières 500 ns suivant le claquage et plus faible pendant le reste de la décharge, et dépend de l’intensité du courant. Alors que l’espace inter-électrodes est estimé à environ 10−100 µm, la décharge excite un large volume autour des électrodes, d’un diamètre typique de 200 µm. Ce volume croît légèrement pendant la décharge. Des bulles de vapeur sont générées aussi bien dans l’eau que dans l’huile, dû à la chaleur libérée par le plasma. A la ﬁn de la décharge, le plasma implose et disparaît rapidement. De la lumière est encore émise après la décharge par des particules métalliques incandescentes, provenant de l’érosion de la pièce. Leur température a été mesurée à environ 2’200 K, ce qui démontre qu’elles sont toujours à l’état liquide au début de la post-décharge. L’analyse spectroscopique de la lumière du plasma montre un forte radiation de la ligne Hα et une forte émission continue, avec la présence de nombreuses lignes atomiques métalliques émises par des impuretés provenant des matériaux de l’électrode et de la

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pièce. Ainsi, le plasma d’électro-érosion est composé d’espèces provenant de la dissociation des molécules du diélectrique (principalement de l’hydrogène dans le cas de l’eau et de l’huile), avec une contamination des électrodes. La contamination est légèrement plus forte au voisinage de chaque électrode, et la contamination venant de la pièce augmente au cours de la décharge, probablement à cause de son évaporation. La température électronique, mesurée à partir des intensités de lignes de cuivre avec la méthode dite two-line method, est basse. La température est autour de 0.7 eV (∼ 8’100 K) dans tout le plasma, légèrement plus haute au début de la décharge. La densité électronique a été mesurée à partir de l’élargissement et du déplacement par eﬀet Stark de la ligne Hα . La densité est extrêmement élevée, particulièrement au début de la décharge (> 2·1018 cm−3 durant la première microseconde). Elle décroît ensuite avec le temps, restant néanmoins toujours au-dessus de 1016 cm−3 après 50 µs. Pendant toute la décharge, la densité est légèrement plus élevée au centre du plasma. Le plasma d’électro-érosion a une densité si élevée car il est formé à partir d’un liquide, et parce qu’il est constamment soumis à la pression imposée par le liquide environnant. Cette densité extrême produit des spectres avec des lignes spectrales très élargies, particulièrement la ligne Hα , et avec une importante radiation continue. Pendant la première microseconde où la densité est à son maximum, les lignes spectrales sont tellement élargies qu’elles fusionnent et ne forment qu’un continu. La basse température et la haute densité du plasma d’électro-érosion le rendent faiblement non-idéal. Son paramètre de couplage Γ typique est en eﬀet autour de 0.3, atteignant 0.45 pendant la première microseconde. Dans ce plasma, les interactions coulombiennes entre les particules chargées sont ainsi du même ordre que l’énergie thermique moyenne des particules, ce qui produit des phénomènes de couplage. Des résultats de spectroscopie conﬁrment la non-idéalité du plasma d’électro-érosion. Le fort élargissement et déplacement de la ligne Hα ainsi que sa forme asymétrique et sa structure complexe, l’absence de la ligne Hβ , et la fusion des lignes spectrales sont en eﬀet typiques des plasmas nonidéaux. Le plasma d’électro-érosion possède ainsi des propriétés physiques extrêmes, et la physique y relative est étonnamment complexe.

Mots-clés: électro-érosion, EDM, plasma, étincelle, décharge, plasma non-idéal, spectroscopie d’émission optique, spectroscopie, imagerie, claquage, diélectrique, liquide.

Contents
Abstract Version abrégée 1 Introduction 1.1 Electrical Discharge Machining (EDM) 1.1.1 Principles . . . . . . . . . . . . 1.1.2 History . . . . . . . . . . . . . . 1.1.3 State of the art . . . . . . . . . 1.2 Purpose and structure of the work . . . 2 EDM plasmas : Background 2.1 Discharges in gases . . . . . . . . . . . 2.1.1 Spark, arc, glow & co. . . . . . 2.1.2 Sparks and streamers . . . . . . 2.1.3 Electric arcs and cathode spots 2.2 Discharges in dielectric liquids . . . . . 2.3 Other similar plasmas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i iii 1 1 2 4 8 8 11 11 11 12 14 18 22 25 25 27 27 28 29 30 32 32 33 35 37 40 40 41

3 Experimental setup and diagnostics 3.1 Electrical discharge machining device . . . . . . . . . . . . . . 3.2 Electrical measurements . . . . . . . . . . . . . . . . . . . . . 3.2.1 Discharge measurements . . . . . . . . . . . . . . . . . 3.2.2 Pre-breakdown measurements . . . . . . . . . . . . . . 3.3 Plasma light intensity measurements . . . . . . . . . . . . . . 3.4 Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Optical emission spectroscopy . . . . . . . . . . . . . . . . . . 3.5.1 Principles . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.2 Electron temperature measurement . . . . . . . . . . . 3.5.3 Electron density measurement . . . . . . . . . . . . . . 3.5.4 General experimental setup . . . . . . . . . . . . . . . 3.5.5 Experimental setup for time-resolved spectroscopy . . . 3.5.6 Experimental setup for spatially-resolved spectroscopy 3.6 Experimental diﬃculties . . . . . . . . . . . . . . . . . . . . .

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4 Pre-breakdown of EDM discharges 45 4.1 Bubbles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.2 Pre-breakdown current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.3 Pre-breakdown duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 5 Imaging diagnostics of EDM discharges 5.1 Imaging of the EDM process . . . . . . . . . . 5.1.1 Erosion . . . . . . . . . . . . . . . . . 5.1.2 Bubbles . . . . . . . . . . . . . . . . . 5.1.3 Short-circuit . . . . . . . . . . . . . . . 5.1.4 Reproducibility . . . . . . . . . . . . . 5.2 Plasma imaging . . . . . . . . . . . . . . . . . 5.2.1 Evolution of the plasma light intensity 5.2.2 Typical plasma image . . . . . . . . . 5.2.3 Plasma evolution . . . . . . . . . . . . 5.2.4 Eﬀect of the discharge current . . . . . 5.2.5 Hα emission . . . . . . . . . . . . . . . 5.3 Beginning of the discharge : Fast imaging . . 5.4 End of the discharge and post-discharge . . . 53 53 53 54 55 56 56 56 58 59 59 60 61 62 67 67 67 69 70 72 73 74 75 76 76 76 77 79 79 80 81 82 82 83 84

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6 Optical emission spectroscopy of EDM plasmas 6.1 Time-integrated emission spectra . . . . . . . . . . . . . . . 6.1.1 Typical spectrum . . . . . . . . . . . . . . . . . . . . 6.1.2 Eﬀect of the dielectric . . . . . . . . . . . . . . . . . 6.1.3 Eﬀect of the electrode material . . . . . . . . . . . . 6.1.4 Eﬀect of the electrode polarity . . . . . . . . . . . . . 6.1.5 Eﬀect of the discharge current . . . . . . . . . . . . . 6.1.6 Eﬀect of the discharge on-time . . . . . . . . . . . . . 6.1.7 First estimation of electron density and temperature 6.2 Time-resolved emission spectra . . . . . . . . . . . . . . . . 6.2.1 Merging of atomic lines . . . . . . . . . . . . . . . . . 6.2.2 Evolution of the electron temperature . . . . . . . . . 6.2.3 Evolution of the electron density . . . . . . . . . . . 6.3 Spatially-resolved emission spectra . . . . . . . . . . . . . . 6.3.1 Asymmetry of the contamination . . . . . . . . . . . 6.3.2 Electron temperature proﬁle . . . . . . . . . . . . . . 6.3.3 Electron density proﬁle . . . . . . . . . . . . . . . . . 6.4 Time- and spatially-resolved emission spectra . . . . . . . . 6.4.1 Evolution of the contamination . . . . . . . . . . . . 6.4.2 Evolution of the electron temperature proﬁles . . . . 6.4.3 Evolution of the electron density proﬁles . . . . . . .

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CONTENTS 7 Non-ideality of EDM plasmas 7.1 Plasma coupling parameter Γ . . . . . . . . . . . . . 7.2 Spectroscopic signs of the non-ideality . . . . . . . . 7.2.1 Broadening and shift of Hα . . . . . . . . . . . 7.2.2 Asymmetry and structure of Hα . . . . . . . . 7.2.3 Absence of Hβ and line merging . . . . . . . . 7.2.4 Inglis-Teller relation . . . . . . . . . . . . . . 7.3 Summary of the physical properties of EDM plasmas 8 Conclusions

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A Stark broadening and shift of hydrogen spectral lines 105 A.1 The Stark eﬀect on hydrogen levels . . . . . . . . . . . . . . . . . . . . . . 105 A.2 Consequences of the Stark eﬀect on Hα emission . . . . . . . . . . . . . . . 107 References Acknowledgments Curriculum Vitae 111 123 125

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Chapter 1 Introduction
1.1 Electrical Discharge Machining (EDM)

Electrical Discharge Machining (EDM) is a well-known machining technique since more than ﬁfty years. Nowadays it is the most widely-used non-traditional machining process, mainly to produce injection molds and dies, for mass production of very common objects. It can also produce ﬁnished parts, such as cutting tools and items with complex shapes. EDM is used in a large number of industrial areas: automotive industry, electronics, domestic appliances, machines, packaging, telecommunications, watches, aeronautic, toys, surgical instruments...

Figure 1.1: Examples of parts machined with EDM: high speed turbine and mold for the screw thread of PET bottles, produced by die-sinking; die for manufacturing plastic cladding and micro-parts, produced by wire-cutting (images c Agie-Charmilles [1, 2]).

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CHAPTER 1. INTRODUCTION

The advantages of EDM over traditional methods such as milling or grinding are multiple. Any material that conducts electricity can be machined, whatever its hardness (hardened steel, tungsten carbide, special alloys for aerospace applications, for example). Furthermore, complex cutting geometry, sharp angles and internal corners can be produced. Final surface state with low rugosity (< 100 nm) and precise machining (∼ 1 µm) are other important advantages. Moreover, there is no mechanical stress on the machined piece, no rotation of workpiece or tool is necessary, and the machines have a high autonomy. On the other hand, the disadvantages are the relatively low material removal rate (order of 100 mm3 /minute), surface modiﬁcation of the machined workpiece (“white layer” and heat aﬀected zone, typical depth ∼ 50 µm), and limited size of workpiece and tool, for example.

1.1.1

Principles

The principle of EDM is to use the eroding eﬀect of controlled electric spark discharges on the electrodes. It is thus a thermal erosion process. The sparks are created in a dielectric liquid, generally water or oil, between the workpiece and an electrode, which can be considered as the cutting tool. There is no mechanical contact between the electrodes during the whole process. Since erosion is produced by electrical discharges, both electrode and workpiece have to be electrically conductive. Thus, the machining process consists in successively removing small volumes of workpiece material, molten or vaporized during a discharge. The volume removed by a single spark is small, in the range of 10−6 −10−4 mm3 , but this basic process is repeated typically 10’000 times per second. Figure 1.2 gives a simple explanation of the erosion process due to a single EDM discharge. First, voltage is applied between the electrodes. This ignition voltage is typically 200 V. The breakdown of the dielectric is initiated by moving the electrode towards the workpiece. This will increase the electric ﬁeld in the gap, until it reaches the necessary value for breakdown. The location of breakdown is generally between the closest points of the electrode and of the workpiece, but it will also depend on particles present in the gap [3]. When the breakdown occurs, the voltage falls and a current rises abruptly. The presence of a current is possible at this stage, because the dielectric has been ionized and a plasma channel has been created between the electrodes. The discharge current is then maintained, assuring a continuous bombardment of ions and electrons on the electrodes. This will cause strong heating of the workpiece material (but also of the electrode material), rapidly creating a small molten metal pool at the surface. A small quantity of metal can even be directly vaporized due to the heating. During the discharge, the plasma channel expands. Therefore, the radius of the molten metal pool increases with time. The distance between the electrode and the workpiece during a discharge is an important parameter. It is estimated to be around 10 to 100 µm (increasing gap with increasing discharge current). At the end of the discharge, current and voltage are shut down. The plasma implodes under the pressure imposed by the surrounding dielectric. Consequently, the molten metal pool is strongly sucked up into the dielectric, leaving a small crater at the workpiece surface (typically 1−500 µm in diameter, depending on the current).

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(a) Pre-breakdown : voltage applied between the electrode and the workpiece (b) Breakdown : dielectric breakdown, creation of the plasma channel (c) Discharge : heating, melting and vaporizing of the workpiece material (d) End of the discharge : plasma implosion, removing of the molten metal pool (a) (b) (c) (d) (e) time (e) Post-discharge : solidifying and flushing of the eroded particles by the dielectric

voltage

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current

Figure 1.2: Principle of the EDM process.

The liquid dielectric plays a crucial role during the whole process: it cools down the electrodes, it guarantees a high plasma pressure and therefore a high removing force on the molten metal when the plasma collapses, it solidiﬁes the molten metal into small spherical particles, and it also ﬂushes away these particles. The post-discharge is in fact a crucial stage, during which the electrode gap is cleaned of the removed particles for the next discharge. If particles stay in the gap, the electrical conductivity of the dielectric liquid increases, leading to a bad control of the process and poor machining quality. To enhance the ﬂushing of particles, the dielectric is generally ﬂowing through the gap. In addition, the electrode movement can be pulsed, typically every second, performing a large retreat movement. This pulsing movement also enhances the cleaning, on a larger scale, by bringing “fresh” dielectric into the gap. The material removal rate can be asymmetrically distributed between the electrode (wear ) and the workpiece (erosion). The asymmetry is mostly due to the diﬀerent materials of the electrodes. But it also depends on the electrode polarity, on the duration of the discharges and on the discharge current. Note that by convention, the polarity is called positive when the electrode is polarized positively towards the workpiece, negative otherwise. By carefully choosing the discharge parameters, 0.1% wear and 99.9% erosion can be achieved.

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Two main types of machining can be distinguished, as shown in ﬁgure 1.3. In diesinking EDM, the electrode is shaped and will produce its negative form into the workpiece. The wear has to be very low, in order to keep the electrode original shape unmodiﬁed during the whole machining process. The asymmetry in the material removal rate is thus crucial for die-sinking. The electrode is generally in copper or graphite, and the dielectric is oil. In wire-cutting EDM, the electrode is a continuously circulating metallic wire (typical diameter 0.1 mm, generally in steel, brass or copper), which cuts the workpiece along a programmed path. Deionized water is used as dielectric, directly injected around the wire. The wire is capable of achieving very small cutting angles. The wear is a lesser problem than in die-sinking, because eroded portions of the wire are continuously replaced by new ones due to the wire circulation. Die-sinking EDM is mainly used to produce injection molds, whereas the main applications of wire-cutting EDM are the production of steel cutting dies and extrusion dies.
(a) die-sinking
electrode

(b) wire-cutting

cutting direction

workpiece wire circulation

Figure 1.3: Main types of EDM: die-sinking and wire-cutting.

The quality of the machining, i.e. precision and surface rugosity, is directly related to the discharge parameters (current, voltage, discharge duration, polarity...), but also on the dielectric cleanliness. Sparks with strong current produce deep craters: a high removal rate is obtained but with a high surface rugosity. On the other hand, sparks with low current will produce small craters: the surface rugosity is low but the removal rate is also low. For a rough preliminary machining in die-sinking for example, high current, long discharge duration and positive polarity will be chosen, typically 50 A and 1 ms. In wire-cutting, current up to 1000 A can be used, but with shorter duration (∼ µs). For surface ﬁnishing and polishing, short discharges with low current and negative polarity are used, typically 2 A and 5 µs.

1.1.2

History

The historical roots of EDM date back to the discovery of electric discharges. Besides the discharges produced by natural phenomena, namely lightning, the production of artiﬁcial discharges has been closely related to the development of electrical energy sources. First investigations of electrostatic phenomena were performed with frictional machines, during the ﬁrst half of the 18th century. After that, the ﬁrst sparks and pulsed arcs were produced with “Leyden jars”, an early form of capacitor invented in Germany and in the Netherlands

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around 1745 [4] (see ﬁgure 1.4 (a)). More powerful discharges were created by putting several Leyden jars in parallel, creating thus a “battery”. Although scientists of this period sensed that the nature of these artiﬁcial discharges was the same as the nature of lightning, the understanding of the observed phenomena was very incomplete. Joseph Priestley (1733−1804), an English theologian and chemist, was the ﬁrst to discover in 1766 erosion craters left by electric discharges on the cathode surface: “June the 13th , 1766. After discharging a battery, of about forty square feet, with a smooth brass knob, I accidentally observed upon it a pretty large circular spot, the center of which seemed to be superﬁcially melted. (...) After an interruption of melted places, there was an intrie and exact circle of shining dots, consisting of places superﬁcially melted, like those at the center.” (see ﬁgure 1.4 (b)) “June the 14th , 1766. (...) Examining the spots with a microscope, both the shining dots that formed the central spot, and those which formed the external circle, appeared evidently to consist of cavities, resembling those on the moon, as they appear through a telescope, the edges projecting shadows into them, when they were held in the sun.” [5] Priestley also investigated the inﬂuence of the electrode material and of the discharge current on the craters size.

Figure 1.4: (a) Engraved plate sent by Alessandro Volta to Joseph Priestley, showing the spark produced by short-circuit of a Leyden jar (1775) [6]; (b) sketches of erosion craters on cathode surface, observed by Joseph Priestley in 1766 [5].

Whereas the discharges studied by Priestley were pulsed and oscillating (because created by short-circuiting of Leyden jars), continuous discharges could only be produced with battery of electrochemical cells, invented later by Alessandro Volta (1745−1827) in 1799. Developing very large voltaic batteries, the ﬁrst continuous carbon arc was produced by Vasilii Petrov in St-Petersburg in 1802 [7]. Published in 1803 but only in Russian, his discovery remained ignored and forgotten for over a century. The discovery of electric

6

CHAPTER 1. INTRODUCTION

arcs is thus often attributed to Humphry Davy (1778−1829). Unaware of Petrov’s work, he re-discovered independently carbon arcs around 1808, using the huge voltaic battery of the Royal Institution of London (see ﬁgure 1.5 (a)). By separating two horizontal carbon electrodes connected to the battery, Davy created a bright and stable discharge. The shape of this discharge was arched, giving its name to the phenomenon. Development of devices using electric arcs for lighting purposes followed quickly. Swiss natural philosopher Auguste-Arthur de la Rive (1801−1873) proved in 1820 that arcs can also burn in vacuum, by creating a discharge in an exhausted glass vessel. Figure 1.5 (b) shows examples of these early carbon arc lamps.

Figure 1.5: (a) Public demonstration of the carbon arc discharge, probably by Humphry Davy in the Royal Institution of London (early 19th century) [7]. The picture below shows the basement ﬁlled with a huge battery, used to create the discharge; (b) early carbon arc lamps in air (left) and in exhausted glass vessel (right), also known as “Davy’s electric eggs” or “de la Rive’s electric eggs” [7].

With sophistication of electric sources and industrialization, Auguste de Meritens (1834−1898) developed in 1881 in France a second major application using electric arcs. He used the heat produced by an arc for joining lead plates, inventing the principle of arc welding. Nowadays, electric arcs are also used for coating deposition, metal processing, plasma spraying and as high power switches, for example [8]. The history of EDM itself begins in 1943, with the invention of its principle by Russian scientists Boris and Natalya Lazarenko in Moscow. The Soviet government assigned them to investigate the wear caused by sparking between tungsten electrical contacts, a problem which was particularly critical for maintenance of automotive engines during the second world war. Putting the electrodes in oil, they found that the sparks were more uniform and predictable than in air. They had then the idea to reverse the phenomenon, and to use controlled sparking as an erosion method [9]. Though they could not solve the original wear problem, the Lazarenkos developed during the war the ﬁrst EDM machines,

1.1. ELECTRICAL DISCHARGE MACHINING (EDM)

7

which were very useful to erode hard metals such as tungsten or tungsten carbide. The “Lazarenko circuit” remained the standard EDM generator for years. In the 1950’s, progress was made on understanding the erosion phenomenon [10–12]. It is also during this period that industries produced the ﬁrst EDM machines. Swiss industries were involved very early in this market, and still remain leaders nowadays. Agie was founded in 1954, and les Ateliers des Charmilles produced their ﬁrst machine in 1955. Due to the poor quality of electronic components, the performances of the machines were limited at this time.

2005

1955

Figure 1.6: 50 years of evolution in EDM machines: Eleroda D1 (1955) and Roboﬁl 2050 TW (2005) from Charmilles (images c Charmilles Technologies [1]).

In the 1960’s, the development of the semi-conductor industry permitted considerable improvements in EDM machines. Die-sinking machines became reliable and produced surfaces with controlled quality, whereas wire-cutting machines were still at their very beginning. With the introduction of numerical position control in the late 1960’s and early 1970’s, the movements of electrodes became much more precise. This major improvement pushed forward the performance of wire-cutting machines. Computer numerical controlled systems (CNC) improved further the performance of EDM in the mid 1970’s. During the following decades, eﬀorts were principally made in generator design, process automatization, servo-control and robotics. Applications in micro-machining became also of interest during the 1980’s [13]. It is also from this period that the world market of EDM began to increase strongly, and that speciﬁc applied EDM research took over basic EDM research [14]. Finally, new methods for EDM process control arose in the 1990’s: fuzzy control and neural networks.

8

CHAPTER 1. INTRODUCTION

1.1.3

State of the art

Fifty years after the ﬁrst industrial machine, EDM has made considerable progress. Recent improvements in machining speed, accuracy and roughness have been achieved mostly with improvements in robotics, automatization, process control, dielectric, ﬂushing and generator design [15–18]. The other main research domains are the machining of nonconductive materials such as ceramics [19, 20], micro-machining [21–24], characterization and improvement in the machined surface quality [25, 26], and modelling of the EDM process [27–29]. But so far, few studies have been done on the discharge itself, which lies at the heart of the process. However, in various ﬁelds, breakdown in dielectric liquids or solids have already been studied: pre-breakdown and breakdown in diﬀerent liquids [30, 31] and condensed matter [32], exploding wires in water [33], laser produced plasma in transformer oil [34], and Teﬂon capillary discharges [35] for example. These plasmas have similar properties to those of the EDM plasma. Though EDM keeps unmatched abilities such as the machining of hard materials and complex geometries, this technique has to evolve constantly in order to stay competitive and economically interesting in the modern tooling market against other traditional or new machining techniques [17, 18, 36].

1.2

Purpose and structure of the work

Further improvements in EDM performances, especially for micro-machining, require a better control and understanding of the discharge, and of its interaction with the electrodes. A better comprehension of the sparking process will also reduce problems related to its stochastic nature. Until now, process optimization relied almost only on empirical methods and recipes. It is necessary to go beyond this empirical optimization, and to use reliable numerical models to predict important parameters, such as the material removal rate and wear for example. Although EDM is quite old, only a few theoretical and numerical studies on the EDM plasma exist [37–40], mainly due to the complex physics involved in this process. The EDM process mixes indeed breakdown of liquids, plasma physics, heat transfer, radiation, hydrodynamics, materials science, electrodynamics... These models still contain several parameters which are empirically determined or artiﬁcially introduced. Furthermore, experimental characterization of the EDM plasma is lacking. Some spectroscopic measurements have already been made but remain very incomplete [41, 42]. As we will see later (section 3.6), the EDM plasma is experimentally diﬃcult to investigate. These diﬃculties are the main cause for the lack of experimental data, which are nevertheless essential as inputs and for the validation of numerical models. The purpose of this work is thus a systematic experimental investigation of the EDM plasma, in order to measure its physical properties and to improve the understanding of its complex basic physics. Besides the industrial aspect, the study of this plasma is

1.2. PURPOSE AND STRUCTURE OF THE WORK

9

also of fundamental interest. Other works on similar plasmas, notably measurements of their density and temperature (see sections 2.2 and 2.3), showed that they can be classed among non-ideal or strongly coupled plasmas. Such plasmas have very interesting physical properties and are still not well known [43–46]. Strongly coupled plasmas produced in the lab are interesting also for astrophysical studies, because deep layers of giant planets and superdense plasmas of the matter of white dwarves are of this kind [43]. This work is one part of a special EDM research project, initiated by the innovation committee of the Technology-Oriented Program NANO 21 (project n◦ 5768.2). This project was a collaboration involving: • Charmilles Technologies, as the industrial partner (Dr G. Wälder); • the Centre de Recherches en Physique des Plasmas (CRPP) of the Ecole Polytechnique Fédérale de Lausanne (EPFL), for the study of the plasma (Dr Ch. Hollenstein); • the Laboratoire de Simulation des Matériaux (LSMX) of the EPFL, for a numerical model of the temperature evolution in the workpiece surface (Prof. M. Rappaz); • the Département de Physique de la Matière Condensée (DPMC) of the Université de Genève, for the study of metallurgical processes occurring at the workpiece surface (Prof. R. Flükiger); • the Electrochemistry group of the Bern Universität, for the study of corrosion aspects of the EDM process (Prof. H. Siegenthaler). The present manuscript is structured as follows: we will ﬁrst present in chapter 2 a general background for the understanding of EDM plasmas, i.e. a brief summary of existing knowledge about similar phenomena and plasmas. The diﬀerent experimental setups and plasma diagnostics used in this work are described in chapter 3, and the experimental results are presented and discussed in chapters 4 (results about pre-breakdown), 5 (imaging results) and 6 (spectroscopy results). Chapter 7 treats the non-ideal character of EDM plasmas, and also gives a summary of their measured physical properties. Finally, general conclusions are given in chapter 8.

10

CHAPTER 1. INTRODUCTION

Chapter 2 EDM plasmas : Background
Although EDM discharges take place in a dielectric liquid, the ﬁrst section of this chapter will deal with discharges in gases. They have been extensively studied [47–49], and have common features with discharges in liquids. After that, a brief review about the speciﬁc characteristics of discharges in liquids will be given in the second section. Finally, other plasmas similar to the EDM plasmas are presented in the last section.

2.1
2.1.1

Discharges in gases
Spark, arc, glow & co.

Depending on the gas pressure, the electrode gap and the electrode conﬁguration, several discharge regimes can be distinguished. They can be classiﬁed according to their currentvoltage characteristics, as shown in ﬁgure 2.1.
atmospheric pressure

corona

voltage

Townsend discharge normal glow

spark abnormal glow

low-pressure

arc

current

Figure 2.1: Schematic current-voltage characteristics of the diﬀerent types of discharges in gases [47, 48].

11

12

CHAPTER 2. EDM PLASMAS : BACKGROUND Four main types of steady or quasi-steady processes exist: • the Townsend’s dark discharge, characterized by a very weak current (∼ 10−8 A); • the glow discharge, widely used in many industrial processes, operating at low current (∼ 10−2 A), fairly high voltage (∼ 1 kV) and low pressure (∼ mbar). The glow plasma is weakly ionized and in a non-equilibrium state, and is visible as a uniform glowing column. As in the Townsend’s discharge, electrons are emitted by ion impacts on the cold cathode; • the corona discharge, also at low current (∼ 10−6 A) but at atmospheric pressure. Corona discharges develop locally (typically around sharp ends of wires) in strongly non-uniform electric ﬁeld; • the arc discharge, characterized by high current (∼ 100 A), low voltage (∼ 10 V) and a bright light emission. The arc discharge diﬀers from the glow discharge in the electron emission mechanism. In arcs, electrons are emitted by thermionic processes, due to the heating of the cathode. The plasma of high pressure arcs can be considered to be in a state of thermodynamic equilibrium.

On the contrary to Townsend, glow, corona and arc discharges, the spark discharge is not a steady process but a transient process, i.e. an unstable transition state of limited lifetime towards a more stable regime (see ﬁgure 2.1). To be perfectly rigorous, it would be more proper to say “spark breakdown” than “spark discharge”, since it is a transition mechanism and not a state resulting from a transition [48]. However, we will keep (abusively but for clarity) the term spark discharge or simply discharge when speaking about the period during which the EDM plasma exists (part c in ﬁgure 1.2), and the term breakdown will refer to the transition from the no-plasma situation to the plasma situation (part b in ﬁgure 1.2).

2.1.2

Sparks and streamers

Since the plasma created during the EDM process is precisely a spark, it is worthwhile to describe this type of discharge in more detail. Note that lightning shows beautiful examples of giant spark discharges. The breakdown phenomenon leading to the creation of a spark is complex. The breakdown is too fast to be explained by repetitive electron avalanches through secondary cathode emission, as in low pressure discharges. It consists rather of a very rapid growth of a thin weakly-ionized channel called a streamer, from one electrode to the other. A streamer is formed from an intensive primary electron avalanche, starting from the cathode (see ﬁgure 2.2 (a)). A space charge ﬁeld is associated with this avalanche, due to the polarization of charges inside it. This electric ﬁeld increases with the avalanche propagation and growth. The avalanche has to reach a certain ampliﬁcation before it can create a streamer. As soon as the space charge ﬁeld is comparable or exceeding the applied external ﬁeld, a weakly ionized region can be created due to this ampliﬁcation of the electric ﬁeld: the streamer is thus initiated.

2.1. DISCHARGES IN GASES
(a) electron avalanche
anode + t1
propagation
space charge field

13
(b) positive streamer
anode +
streamer

(c) negative streamer
anode +

_ +

_ + + _ + _ + +++ + _ +
_ +

+

_ __ ++ t1 +

_ _ _ _ __ _ _ _ + + + + + + + ++ t2 > t1 + cathode -

hn

+

+ _ + _ t2 > t1 _ + + + _ _+ ++ + ++ + + _ _ +_
+ +

_

_ +

_ +

secondary avalanches

t1

__ _ _ __ +_ + + _

__ _ __ _ _ _ + + _ _+ + _ _ t2 > t1 + _ + cathode -

_ +

_ +

_ +

cathode -

Figure 2.2: Breakdown mechanisms leading to a spark discharge. Propagation of: (a) the primary electron avalanche; (b) a positive streamer; (c) a negative streamer [49].

Once the streamer is initiated, it then grows and propagates, following a zigzagging and branched path due to the random nature of the propagation mechanism. The speed of this propagation is extremely high, reaching 106 m/s. The propagation can be directed towards both the anode or the cathode, depending on the gap distance and voltage. • In moderate gaps and with moderate voltages, the avalanche-to-streamer transition occurs only when the primary avalanche has crossed the gap and reached the anode. The avalanche has not grown enough and the space charge ﬁeld is not high enough to create a ionized region, before the avalanche has reached the anode. Then, the streamer starts from the anode and grows towards the cathode. This kind of streamer is called cathode-directed or positive. The streamer growth is caused by secondary avalanches, created near the positive head of the streamer (see ﬁgure 2.2 (b)). These secondary avalanches are initiated by electrons released by photo-ionization. The electrons of the secondary avalanches are rapidly attracted into the streamer, neutralizing the streamer positive head and leaving behind them the positive ions of the secondary avalanches (ions move much slower than electrons). These positive charges become the new head of the extended streamer. This is how the positive streamer grows. • In large gaps and/or with strong gap voltages, the space charge ﬁeld of the primary avalanche can be suﬃciently high to create the streamer even before reaching the anode. Thus, the avalanche-to-streamer transition occurs in the gap. Then, the streamer propagates towards both electrodes at the same time. If the avalanche-tostreamer transition occurs while the avalanche has not yet gone far from the cathode, the streamer grows mostly towards the anode. In this case, the streamer is called anode-directed or negative. The growth mechanism towards the cathode remains the same as described above, but the growth towards the anode is slightly diﬀerent. Here, the electrons of the primary avalanche form a negative head for the streamer. These electrons rapidly neutralize the positive ions of secondary avalanches, also

14

CHAPTER 2. EDM PLASMAS : BACKGROUND initiated near the streamer head by photo-ionization and by moving electrons (see ﬁgure 2.2 (c)). The electrons of the secondary avalanches then form the new head of the extended streamer. Thus, for both positive and negative streamers, the streamer is “feeding” on charges created ahead of its tip by secondary avalanches.

When the electrode gap is closed by a streamer, the breakdown phase is completed and the discharge phase begins. The transition from a weakly-ionized channel (the streamer bridging the gap) to a highly-ionized channel (the spark itself) is poorly understood. It is probably caused by a “back streamer”, similar to the well-known “return stroke” in lightning discharges [49]. If we assume that a streamer is perfectly conducting, the head of a positive streamer, for example, is at the same potential as the anode. When the streamer head is approaching close to the cathode, all the potential fall is located over a very short distance, the distance between the cathode and the streamer head. The electric ﬁeld is so intense in this region that electrons are emitted in great number from the cathode and from atoms near the cathode. Once the gap is closed by the streamer, these electrons, multiplied at enormous intensity, are accelerated towards the anode in the initial streamer channel, causing strong ionization. This ionization front is propagating “backwards” at ∼ 107 m/s. The formation of the true spark channel is thus probably caused by this back streamer, which strongly increases the degree of ionization in the original streamer channel. The plasma composing the spark channel is highly ionized and conductive, capable of sustaining a large current (∼ 104 A). The spark is accompanied by a cracking sound (the thunder in the case of lightning), resulting from the shock wave created by the rapid and localized heating of the gas surrounding the plasma channel. The channel radially expands with time, because the surrounding gas is gradually ionized, by heat conduction and by the shock wave. The temperature of a spark is typically around 1.8 eV (20’000 K), and the electron density around 1017 cm−3 . If the power source is capable of delivering the discharge current over a certain amount of time, the spark will naturally transform into an arc, since the spark is a only a transient process.

2.1.3

Electric arcs and cathode spots

Existing theories, measurements and models about vacuum and atmospheric arcs are abundant [8, 50–56]. It is still a widely studied subject, because cathode phenomena, for example, remain poorly understood due to their extreme complexity. As in the EDM process, it involves solid state, surface and plasma physics, electric and thermal processes. Since arcs erode cathodes by leaving small craters on their surfaces, the knowledge of arc phenomena can be useful to understand the EDM erosion process, although the EDM plasma is not an arc but a spark. Furthermore, the plasma state in a high pressure arc column is found to be relatively similar to that in a spark channel [49].

2.1. DISCHARGES IN GASES Cathode region

15

The cathode is a region of speciﬁc interest, because it has to produce the necessary electron current for the arc to survive. A high current density is indeed one of the characteristic feature of electric arcs. While electrons are simply falling from the plasma into the anode because of its higher electrical potential, the cathode has to develop very eﬃcient emission mechanisms to extract electrons from the metal into the plasma. Electrons of the conduction band in the metal need in fact some energy to overcome the energy gap of the metal−plasma interface, also called work function. The transformation of a spark into an arc is accomplished by the creation of a hot spot on the cathode surface, called cathode spot. This small spot (∼ 10 µm in diameter) has astonishing physical properties and is capable of supplying a great electron current. Electrons are emitted from the cathode spot by: • thermionic emission (emission of the most energetic electrons from a heated metallic surface); • ﬁeld electron emission (emission by tunnel eﬀect due to the lowering of the external potential caused by an electric ﬁeld at the surface); • thermionic ﬁeld emission, also called thermo-ﬁeld emission, which is a combination of the two preceding processes. The electric ﬁeld enhances the thermionic emission by the Schottky eﬀect. This mechanism dominates by far in electric arc cathodes; • “thermal runaway”, a non-stationary explosive emission of electrons and explosive evaporation. A signiﬁcative quantity of cathode material, typically a protrusion at the surface, can be directly evaporated and transformed into a dense plasma. This occurs when there is a suﬃciently rapid heating of the cathode, i.e. when the deposited power grows faster than heat conduction in the cathode can remove it [57]. The discharge organizes itself in a such way as to create a strong electron emission from the cathode by the mechanisms cited above, i.e. by raising its temperature and by creating a strong electric ﬁeld at its surface. The voltage jump is mostly localized near the electrodes, in the so-called anode and cathode layers (see ﬁgure 2.3). Consequently,
V cathode layer

arc column anode layer x C A

Figure 2.3: Schematic proﬁle of electrical potential in an arc [49].

16

CHAPTER 2. EDM PLASMAS : BACKGROUND

the electric ﬁeld is particularly high in these very thin regions. This type of potential proﬁle is due to the presence of space charged regions near the electrodes. The plasma in the cathode layer, usually called cathode spot plasma because it is located in front of the cathode spot, is a small and dense plasma. It remains poorly understood, but its electron temperature is estimated around 5 eV (60’000 K) and its density around 1020 cm−3 . The cathode spot plasma should thus be dense enough to present non-ideal eﬀects [57]. A detailed structure of the cathode layer is given in ﬁgure 2.4. While the plasma of the arc column is assumed to be in thermal equilibrium, the plasma located in the cathode layer is characterized by deviations from equilibrium [53]. First, a deviation of the electron temperature Te from the heavy particles’ temperature Th is present in a layer of thermal relaxation. Then, we have a violation of the ionization equilibrium. In this ionization layer, the production rate of ions is very high due to collisions with energetic electrons strongly accelerated from the cathode. The ion ﬂux leaving this layer towards the cathode is thus much higher than the ﬂux entering from the layer of thermal relaxation. The dense cathode spot plasma is created in this layer. Finally, the quasineutrality is violated in a very thin sheath near the cathode, where the ion density n+ is higher than the electron density ne . This is the space charged region creating the potential proﬁle shown in ﬁgure 2.3, and where almost all the voltage drop is located.
sheath
space charged (n+ > ne) collisionless

ionization layer
quasineutral ionization > recombination

layer of thermal relaxation
quasineutral ionization = recombination Te > Th

arc column

e-

+ + + e-

cathode

+ + +

Local Thermal Equilibrium (LTE)

+

electric potential

x ~ 20 nm
(Debye length)

~ 10 mm

~ 100 mm

Figure 2.4: Schematic structure of the cathode layer (not to scale). The dimensions of the three layers are evaluated for an argon atmospheric pressure arc plasma at 10’000 K and with a charged particle density of 1017 cm−3 [53].

By this plasma structure, the cathode spot is strongly heated by the ion bombardment coming from the ionization layer through the collisionless sheath. This heating leads to evaporation and melting, thermionic emission and thermal runaway in some cases. The electron emission is further increased by the electric ﬁeld produced by the sheath, adding ﬁeld emission and thermionic ﬁeld emission. In return, the electrons coming from the cathode are crucial to create a high ionization rate in the ionization layer, producing

2.1. DISCHARGES IN GASES

17

the ions that will heat the cathode in a self-consistently balanced regime. This coupled ion/electron production is the sustaining mechanism of the arc discharge. The terms involved in the energy balance at the cathode spot are multiple. The energy is mainly brought by ion bombardment, but smaller contributions are also given by Joule heating, atom and electron bombardment, recombination in the cathode, plasma radiation (almost negligible [57]) and Thomson eﬀect (also negligible). Energy is mostly dissipated by electron emission and heat conduction in the electrode (slow process), but also by evaporation, surface radiation and droplet emission. The relative importance of all these energy sources and sinks depend strongly on the arc conditions (pressure, materials, current, etc.). Heating mechanisms of electrodes in EDM sparks should be very similar to those occurring in arcs as described here. The temperature of a cathode spot is typically around 4’000−5’000 K [57], high above the fusion temperatures of metals, which explains the erosive eﬀect of arcs on cathodes. Besides direct evaporation, ejection of cathode melted matter due to the plasma pressure and explosive erosion by thermal runaway, another erosive mechanism can occur also during the discharge. If energy dissipation dominates at the surface due to a high radiation and electron emission (this is the case if the surface temperature is very high), the maximum temperature is located below the surface, in the cathode spot. This will lead to an internal explosion, and consequently to ejection of solid or liquid matter into the plasma, in the form of µm droplets [57]. Anode region At the anode, the situation is also complex, depending strongly on experimental conditions with several diﬀerent modes, and not completely understood. Generally, the current is distributed over a larger surface than at the cathode. The current density is thus lower, and no signiﬁcative erosion is visible. However, anode spots can develop under certain conditions of current, pressure and anode geometry. In this case, matter can also be evaporated and signiﬁcant erosion is observed. The plasma structure near the anode has similarities with that near the cathode. A negative space charged region is located directly near the anode surface (ne > n+ ), because ions are unable to cross the anode potential barrier. The metal vapor coming from the anode can thus be ionized in the anode layer, due to this space charged region. Energy is brought to the anode by the electron ﬂux and by recombination with ions in the anode; energy is dissipated through evaporation and heat conduction. The temperature of the anode spot is slightly lower than that of the cathode spot, still being around 3’000 K [49]. Inter-electrode plasma A large quantity of power is dissipated in the arc column by the Joule eﬀect, heat conduction and radiation. On the axis of the column, the plasma temperature is typically around 5 eV (60’000 K) and the electron density around 1016 cm−3 , but they depend on the gas, the pressure and the current. These values decrease radially, i.e. towards the edges of the column. The plasma of the arc column is thus much less dense than the cathode spot plasma. Due to frequent collisions and thus intensive energy exchange between particles,

18

CHAPTER 2. EDM PLASMAS : BACKGROUND

the plasma of high-pressure arcs is in local thermal equilibrium. The degree of ionization is also very high, close to 100%. Arcs in EDM EDM sparks can sometimes transform into arcs, especially if long discharge durations and graphite electrodes are used. One hot spot is then created on each electrode surface, and the following discharges will systematically take place between these two hot spots and instantly turn into an arc. The result is catastrophic from the erosion point of view, leading to a localized burn of the workpiece surface and to the destruction of the electrode shape. This is particularly problematic when performing smoothing and polishing operations. Hot spots have to be avoided as much as possible during the EDM process, because one of the advantages of this technique is precisely to distribute the erosion spots over the whole workpiece surface. The stochastic change in the localization of the successive spark discharges is thus crucial in EDM. The arcing phenomenon during EDM is well known, and is generally avoided by stopping the discharge as soon as the voltage reaches a value below a ﬁxed threshold, typically 15−20 V. A decrease in the discharge voltage is the sign of a transition into an arc, because arcs burn with lower voltage than sparks (see ﬁgure 2.1). Other arc detection methods exist, based on the measurement of the time lag between the voltage application and the breakdown, on the measurement of the ignition voltage value, or on the measurement of the voltage descending ﬂank at the breakdown [58].

2.2

Discharges in dielectric liquids

The principal diﬀerence between discharges in gases and discharges in liquids is the density of the medium in which the breakdown occurs. The higher density of liquids makes them more diﬃcult to break down, i.e. it requires a higher electric ﬁeld. As described below, the breakdown mechanism is also slightly diﬀerent, and the plasma properties are strongly inﬂuenced by the pressure imposed by the surrounding liquid. Breakdown in dielectric liquids have been widely studied, especially for insulation problems of electric transformers [32]. Published articles on breakdown phenomena in liquids are very numerous, and the existing knowledge is summarized in a few review articles [32, 59–63]. A wide range of liquids have been investigated: water [64], salted water solutions [65], oils with diﬀerent aromatic constituents [30,66,67], silicon ﬂuids [59], liquid argon and nitrogen [31, 68], benzene, toluene, carbon tetrachloride [69], and other hydrocarbon liquids [70–72] such as propane, pentane, cyclopentene, hexane, cyclohexane, isooctane, decane, etc. The inﬂuences of hydrostatic pressure, conductivity [65], viscosity [59], additives [73] and particles [74, 75] on the breakdown mechanism have also been studied. As in high-pressure gases, streamers are involved in breakdown in liquids. Two types of streamer exist: the positive streamer starting from the anode, and the negative streamer starting from the cathode. The use of a point-to-plane geometry permits a separate obser-

2.2. DISCHARGES IN DIELECTRIC LIQUIDS

19

vation of the two types of streamer, depending on the polarity of the electrodes. Contrary to the situation in gases, the structure and propagation speed of positive and negative streamers are diﬀerent. As shown in ﬁgure 2.5, the positive streamer is “ﬁlamentary” and “fast” (∼ 1−10 km/s), and the negative streamer is “bushy” and “slow” (∼ 100 m/s). In point-to-point geometry, the two types of streamer are emitted from both electrodes.

Figure 2.5: Shadowgraphs of negative and positive streamers in oil (taken from [30]).

The sequence of events leading to breakdown can be broken down as follows: 1. Initiation The initiation of the breakdown mechanism diﬀers from that in gases. Direct propagation of electrons into the liquid and impact ionization are diﬃcult, due to the strong collisions between electrons and molecules occurring in this dense medium. An avalanche of electrons in the liquid phase is thus unlikely, or at least only of short range. It is generally accepted that the development of the primary avalanche, which will create the streamer, takes place in a region of lower density, created beforehand near the electrode. If the liquid pressure is not too high, this low density region is a vapor bubble (or a vortex of hot liquid in very viscous liquids [59]). However, this point is controversial. According to [70, 76], the positive streamer would be a purely electronic process occurring in the bulk liquid, while negative streamer would ﬁrst involve the formation of a bubble. This should explain the diﬀerent propagation speed of the two types of streamer. On the other hand, other authors claim that the breakdown process cannot be initiated without the presence of bubbles [77, 78]. The eﬀect of the pressure on streamer initiation, for example, is in good agreement with this second theory. Increasing the pressure inhibits in fact streamer development and increases the breakdown voltage. This shows that the phenomena involved in the breakdown mechanism occur in a gaseous medium. Additional experimental evidence seems to demonstrate that the role of bubbles in the breakdown triggering is indisputable [79]. Micro-bubbles can pre-exist in the liquid [78] or form electrically, i.e. from heat released by small electron avalanches in the liquid or by ﬁeld emission near electrode

20

CHAPTER 2. EDM PLASMAS : BACKGROUND asperities [68, 80]. In salted solutions, ionic currents can also slightly enhance the formation of bubbles [62]. 2. Streamer formation The propagation of the primary electron avalanche is strongly facilitated in the bubble. Since electrons are continuously heating the liquid in the front of the avalanche, and consequently lowering its density, the bubble is growing (time scale ∼ 10 ns). New avalanches are formed and thus new bubbles grow ahead of the preceding ones. The ionization of a channel in the liquid, i.e. the formation of the streamer, is caused by this cycle of heating, density lowering and avalanche growth. 3. Streamer propagation The streamer then grows and propagates according to the mechanism described above, governed by a combination of electrostatic and hydrodynamic forces and even instabilities [32, 59]. This mechanism is quite similar to that in gases, but more complex. The structure of the streamer is systematically branched, more than in gases. This reﬂects the diﬃculty for the ionization front to propagate in a dense medium. It could also be due to other inhomogeneously distributed microbubbles leading the streamer path, or due to electrostatic repulsion between adjacent streamer branches [78]. Small electric currents (in the form of bursts of fast pulses), localized weak light emission and shock waves are associated with the propagation of streamers. 4. Gap completion and breakdown When the streamer reaches the other electrode, a reverse ionizing front is observed as in gases, starting from the reached electrode and going back towards the initial electrode. The ionized channel thus thickens, establishing the spark or arc discharge. With negative streamers, the return stroke can even be emitted before the streamer has reached the anode [76]. Intense emission of light is recorded simultaneously with the gap completion, as shown in ﬁgure 2.6.

This general description of the breakdown mechanism does not take into account the eﬀects of the numerous experimental parameters. The characteristics of the streamers depend on the gap voltage and distance, on the electrode materials, geometry and surface state, on the liquid pressure, viscosity, density, conductivity, temperature, composition, molecular structure, purity, etc. The presence of particles, for example, strongly facilitates the triggering of a breakdown. The contamination of the dielectric is thus as important as its type for the initiation of a breakdown. The addition of so-called “electron scavengers” can also increase the propagation speed of negative streamers by one order of magnitude. This type of additive (e.g. SF6 or C2 H5 Cl [30]) increases the electronic aﬃnity of the dielectric molecules. Though streamers are of gaseous nature (cf. inﬂuence of pressure, shock waves, role of bubbles), this dependence on electron scavenging additives show that electronic processes are also operating. The emission of light is another evidence of this fact.

2.2. DISCHARGES IN DIELECTRIC LIQUIDS

21

Figure 2.6: Propagation of a positive streamer and breakdown in oil (time in microseconds, gap 1.27 cm, 82 kV, taken from [30]).

Spectroscopic analysis of the light emitted by streamers in hydrocarbon liquids and oil shows the presence of C2 , C3 and H2 molecules, but atomic hydrogen as well [34, 70, 81]. In liquid nitrogen, CN molecules are observed, probably produced by recombination of nitrogen atoms with carbon atoms coming from the electrodes [31]. These results indicate that the ﬂuid molecules are decomposed inside the streamers. Temperatures and densities in streamers have also been measured with spectroscopy. The rotational and vibrational temperatures of N2 molecules in streamers in liquid nitrogen are 500 and 4000 K respectively [31]; the electron temperature of streamers in oil are about 5’000−10’000 K [34]. The electron density is very high, about 1017 − 1019 cm−3 for positive streamers, and about 1016 − 1017 cm−3 for negative streamers [31, 34, 81]. As a general rule, streamers and resulting plasmas in liquids have smaller dimensions and higher densities than those in gases, due to the pressure imposed by the liquid. To conclude about discharges in liquids, we mention that speciﬁc applications have already been developed. Streamer discharges can produce chemical reactants in liquids, which will be used, for example, to degrade organic pollutants by oxidation [82]. Another application is the sterilization of microorganisms present in water, with the aid of chemical species (e.g. H2 O2 ) produced by electric discharges [83].

22

CHAPTER 2. EDM PLASMAS : BACKGROUND

Furthermore, bubbles are of great interest since single-bubble sonoluminescence has been discovered. A gas micro-bubble, trapped in a liquid and periodically driven by intense acoustic waves, can emit light when it is violently collapsing. This phenomenon is called sonoluminescence, and still remains puzzling [84]. The emitted light is in the UV range, which implies a high energy density inside the bubble. Recent experiments seem to prove the existence of a plasma inside a sonoluminescing bubble [85]. Its temperature would be above 15’000 K. Thus, these bubbles could possibly be used to produce thermonuclear fusion.

2.3

Other similar plasmas

Besides sparks and high-pressure arcs in gases, other plasmas have similar properties to those created by electric discharges in dielectric liquids and to EDM plasmas. Exploding wires Plasmas in liquids can not only be created by applying high voltage between two immersed electrodes. They can also be formed by exploding wires. In such experiments, a thin metal wire placed in water is rapidly vaporized due to the ﬂow of a strong current (∼ 100 kA on µs time scale). The plasmas produced in this way have extremely high electron densities (1021 − 1022 cm−3 ) and pressure (∼ 10 kbar), and temperatures of a few eV (10’000−30’000 K) [33,86–88]. These high densities are caused by the strong conﬁnement created by the liquid inertia. Such plasmas are so dense that their core is optically highly opaque. Explosives have even been used to further increase the plasma conﬁnement, and consequently increase the plasma pressure and density [89]. Capillary discharges In this type of discharge, the conﬁning medium is a small capillary made of glass or another dielectric (Teﬂon, polyethylene, alumina, BeO for example), typically with an inner diameter of 1 mm. This tube is in contact with two electrodes applying a fast current pulse (∼ 1 kA over 100 ns). The plasma is formed by ablation of the capillary walls. The electron densities reached are also high (1016 − 1019 cm−3 ), and the temperatures are of a few eV [35, 90–92]. Laser-produced plasmas Plasmas of metals and alloys can be created by focusing energetic Nd:YAG laser pulses on solid targets, placed in a vacuum chamber. Typical pulses have a power density of 1010 W/cm2 , a duration of 7 ns, a repetition frequency of 30 Hz, and can be focused on a 300 µm diameter spot. These plasmas have an electron density of 1016 − 1018 cm−3 , and a temperature of about 1−1.5 eV (10’000−15’000 K) [93–95].

2.3. OTHER SIMILAR PLASMAS Shock waves

23

The compression by shock waves of gases or metal vapor is another way to produce a dense plasma. The gas is generally contained in a tube heated by a resistor furnace. The shock wave is generated with a system of chambers at diﬀerent pressures, or with condensed explosives for powerful compression [43, 96]. The gas is then irreversibly compressed and heated. This method produces plasmas with spectacular pressure (∼ 100 kbar) and densities (∼ 1023 cm−3 ), with temperatures around 10 eV (100’000 K). The use of underground explosions and even nuclear (!) explosives permitted Russian scientists to obtain gigantic pressures, up to hundreds of Mbar [43]. Astrophysical plasmas Electron densities of plasmas present in the universe cover an astonishingly broad range: from 1 cm−3 for interstellar matter and solar wind for example, up to 1030 cm−3 for white dwarfs, which are the late evolution stage of stars having a mass comparable or lower than that of the sun. Among the most dense plasmas, let us cite the plasmas of the deep layers of giant planets (hydrogen plasma, 6 · 1024 cm−3 , 1 eV for Jupiter), the interior of the sun (hydrogen plasma, 6 · 1025 cm−3 , 1.5 keV), and other exotic objects such as the matter of brown dwarfs (hydrogen plasma, 1028 cm−3 , 1 keV) and the matter of white dwarfs (carbon plasma, 5 · 1030 cm−3 , 10 keV) [43, 44]. Dense plasmas can also be produced by spacecraft entering the bottom layers of giant planet atmospheres. The atmospheric pressure on these planets is very high, due to their strong gravitational ﬁeld. Thus, a dense plasma will be formed ahead of a travelling spacecraft by heating of the atmosphere. Micro-plasmas In contrast to the plasmas described above, micro-plasmas do not resemble to EDM plasmas by their densities, but by their typical gap distance. Plasmas with micro- and submicrometric gaps have recently been produced in air and other gases, mainly due to progress in scanning probe microscopy (SPM) piezoelectric gap controllers [97, 98], and progress in fabrication of micro-devices by photolithography [99]. Typical electron density is 1012 − 1015 cm−3 , and the electron temperature around 5 eV [99, 100]. Chips creating micro-discharges can be used as ionizing sources for micro-sensors, gas analyzers and mass spectrometers [101, 102], or as integrated plasma chemical vapor deposition (PCVD) apparatus, for example [103]. Micro-plasmas are also studied for plasma display panel (PDP) applications [104]. Recent progress and applications of micro-plasmas have been reviewed in [105]. Moreover, micro-gaps are of fundamental interest and new physical questions are arising. Since the gap distance becomes of the same order as the sheath thicknesses and even as the plasma Debye length, the discharge has perhaps to organize itself diﬀerently from the traditional macro-gap discharges.

24

CHAPTER 2. EDM PLASMAS : BACKGROUND

Chapter 3 Experimental setup and diagnostics
The ﬁrst section of this chapter presents the EDM device used in this work, along with the machining parameters. The various plasma diagnostics are then described in the following sections. Finally, in the last section we address the speciﬁc diﬃculties related to the experimental study of EDM plasmas.

3.1

Electrical discharge machining device

Figure 3.1 presents diﬀerent views of the machining equipment at the CRPP. We use a small and versatile die-sinking EDM machine, equipped with a generator of the Roboform type from Charmilles Technologies. The electrode is cylindrical, with a diameter of 3 or 5 mm. In order to better control the localization of the sparks, its tip is conical. The servo-controlled movement of the electrode is only vertical. The workpiece used in our experiments is generally a ﬂat cylinder, 5 cm in diameter. In order to ﬂush the particles contaminating the electrode gap during machining, the dielectric can be pumped, and re-injected into the gap with a shower. No dielectric cleaning is performed during this closed circuit circulation. The dielectric, the electrode and the workpiece can easily be changed. We use: • deionized water (typical conductivity 1.5 µS/cm), mineral oil (FluX Elf 2, oil for EDM, viscosity 6) or liquid nitrogen as dielectric. With liquid nitrogen, the workpiece is placed in a dewar to avoid boiling as much as possible; • electrodes in copper, tungsten, graphite and zinc; • workpieces in W300 steel (AISI Type H11). The machining process is completely controlled by the generator. It supplies the discharge voltage and current, regulates them, and controls the servomotor for the electrode displacement. The generator uses principally the measurement of the gap voltage to regulate and control the process.

25

26

CHAPTER 3. EXPERIMENTAL SETUP AND DIAGNOSTICS

(b)

electric motor (for servo-controlled electrode displacement)

(a)
EDM machine

dielectric circuit

control pump EDM pulse generator

(c)
electrode

fibre optics (for optical diagnostics)

dielectric shower

workpiece

Figure 3.1: EDM device. (a) General view; (b) EDM machine; (c) electrodes.

Figure 3.2 shows the discharge parameters which can be set with the generator: ignition voltage V , discharge current I, discharge on-time, oﬀ-time (pause between the end of a discharge and the voltage rise for the next one), electrode polarity. It is impossible to control the pre-breakdown duration, i.e. the time lag between the voltage application and the breakdown, because it depends on the electrode gap and on physico-chemical properties of the dielectric. Note that the pre-breakdown duration is also called “ignition delay time” or “breakdown time lag”. The value of the voltage during the discharge can not be set by the generator either. Its value depends on electrode materials, but is typically around 20−25 V. The values that we can choose with our generator for V , I, on-time and oﬀ-time are given in table 3.1. The machining mode schematically presented in ﬁgure 3.2 is called Isopulse, because every discharge has the same on-time, independently of the pre-breakdown duration. This mode is the standard machining mode used in this work. By adding a capacitor in parallel to the gap, it is possible to use the generator in a capacitive mode, generally used for surface ﬁnishing [106]. The sparks are produced by successive discharges of the capacitor. In this mode, the polarity is always chosen negative. The discharge on-time and current are not controlled, and thus can slightly vary from a discharge to the other, in contrary to the Isopulse mode. Typically, with a 10 nF capacitor, the discharge duration is around 1.5 µs and the current around 6 A.

3.2. ELECTRICAL MEASUREMENTS
pre-breakdown (stochastic) ?

27

voltage

V

off-time

time

current

on-time (plasma) I

time breakdown

Figure 3.2: Main adjustable discharge parameters in Isopulse mode: V , I, on-time and oﬀ-time.

Parameter V [V] I [A] on-time [µs] oﬀ-time [µs]

possible values ±80, ±120, ±160, ±200. 0.5, 1, 1.5, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64. 0.4, 0.8, 1.6, 3.2, 6.4, 12.8, 25, 50, 100, 200, 400, 800, 1600, 3200. 0.8, 1.6, 3.2, 6.4, 12.8, 25, 50, 100, 200, 400, 800, 1600, 3200.
Table 3.1: Discharge parameters: possible values.

3.2
3.2.1

Electrical measurements
Discharge measurements

The most basic plasma diagnostics consist in measuring the evolution of voltage and current during a discharge. The voltage is measured with a diﬀerential probe (SI-9002 by Sapphire Instruments, 25 MHz), connected in parallel to the electrode gap, as shown in ﬁgure 3.3. We use two current probes depending on the application: • a fast current transformer (FCT from Bergoz Instrumentation, 1.6 GHz) for fast measurements, typically for the breakdown study; • a DC − 50MHz probe (AP015 from LeCroy), for a general characterization of the discharges. The probe is placed around the current cable, near to the upper electrode. Both voltage and current probes are connected to a fast oscilloscope (WavePro 950 from LeCroy, 1 GHz).

28

CHAPTER 3. EXPERIMENTAL SETUP AND DIAGNOSTICS

current probe voltage probe EDM pulse generator

electrode to photomultiplier (or spectrograph) fibre optics

G

V

servo-controlled displacement

dielectric spark workpiece

Figure 3.3: Schematic drawing of the diagnostics experimental setup.

Figure 3.4 shows a comparison of measurements with the two current probes. Since the FCT probe acts as a passive transformer, it diﬀerentiates DC currents as shown in ﬁgure 3.4 (a). On the other hand, this probe is well suited for fast measurements. One can see in ﬁgure 3.4 (b) that the response of the DC probe is slower than that of the FCT probe.
(a) complete Isopulse discharge
200 200

(b) breakdown phase

voltage [V]

100

100

0

0

current [A]

2 0 -2 0

DC probe FCT probe
50 100 150

6 4 2 0 - 0.1

FCT probe
12 ns

DC probe

0

0.1

0.2

0.3

0.4

time [ms]

time [ms]

Figure 3.4: Comparison of the two current probes. (a) Measurements during a complete Isopulse discharge; (b) measurements at the breakdown.

3.2.2

Pre-breakdown measurements

For pre-breakdown study, the gap voltage is simply supplied by a standard DC source rather than by the EDM generator, as shown in ﬁgure 3.5. Pre-breakdown currents are in

3.3. PLASMA LIGHT INTENSITY MEASUREMENTS

29

fact weak and fast signals (see section 4.2). The EDM generator produces regular electrical interferences due to its current regulation system, even before a discharge. The intensity of these interferences are of the same order of pre-breakdown current and strongly perturb their measurement. Since the interesting point studied here is pre-breakdown phenomena, a DC source is suﬃcient to simply maintain a constant electrode gap voltage, without producing any parasitic signal.
current probe R manual displacement DC source (0 - 1000 V) voltage probe

V
bubbles

Figure 3.5: Experimental setup for pre-breakdown current measurements.

Without the EDM generator, the upper electrode has to be moved manually, with a micro-screw system. An additional resistance (typically R = 12 kΩ) is placed in series, in order to avoid short-circuiting of the DC source when the electrodes come into contact. Both electrodes used are pointed, because this geometry is found to enhance the occurrence of pre-breakdown current and the bubble generation.

3.3

Plasma light intensity measurements

The temporal evolution of the light intensity emitted during a discharge is measured with a fast photomultiplier (H6780 from Hamamatsu, spectral sensitivity 200 − 800 nm, rise time 0.78 ns). The light is transmitted to the photomultiplier by a quartz ﬁbre located near the plasma (see ﬁgure 3.3). Inside the photomultiplier, the photons are transformed into electrons by a photocathode, and then multiplied by dynodes. The photomultiplier delivers an output current, which is proportional to the incoming light intensity. To further improve the sensitivity of the measurement, the output current is ampliﬁed again (with a C6438 ampliﬁer from Hamamatsu, DC − 50 MHz). Finally, the current is measured with the oscilloscope. This measurement is not an absolute intensity measurement, which would require a speciﬁc calibration. This is not necessary, since the interest of this measurement is simply to determine how the emitted light intensity evolves during the discharge.

30

CHAPTER 3. EXPERIMENTAL SETUP AND DIAGNOSTICS

3.4

Imaging

Due to the small size of the electrode gap, close images of the electrode region show details which are not visible to the naked eye. It gives useful information about the EDM process, especially for its control: inﬂuence of bubbles, short-circuit, localization of the discharges, behavior of eroded particles, etc. Imaging of the plasma itself is also interesting, particularly to see the evolution of the plasma size and shape, from the breakdown to the afterglow. Analysis of the plasma development at the breakdown requires a fast camera, because of the rapidity of the phenomenon (< 100 ns). The most convenient way to acquire images of EDM plasmas is to use an endoscope. This instrument, well-known for medical applications, is composed of thousands of individual optical ﬁbres, which make the “sampling” of the studied object image. The ﬂexibility of the endoscope makes it very easy to position near the electrode gap. Here we use an endoscope from Myriad Fiber Imaging, 1.5 mm in diameter, composed of 30’000 quartz ﬁbres. The endoscope is equipped with a small built-in quartz lens at its tip, in order to have a magniﬁcation of the plasma region. To obtain a compact geometry, this lens is not a conventional one, but a gradient index lens. The light rays are bent inside the lens, because it is made of a material with a gradually varying index of refraction. The minimal working distance of the endoscope is 4 mm, the depth of ﬁeld 2.5 − 15 mm, the ﬁeld of view 30◦ in air and 20 − 25◦ in water. An example of an image obtained with the endoscope is given in ﬁgure 3.6. The individual ﬁbres composing the instrument can be seen on the zoomed image.

Figure 3.6: Image of a ruler graduated every 100 µm, taken in air with the endoscope at a distance of 4 mm.

Figure 3.7 shows the experimental arrangement for imaging. The endoscope is directly immersed in the dielectric. Due to its short working distance, it can be placed a few

3.4. IMAGING

31

millimeters from the spark, assuring therefore a good image magniﬁcation and small light absorption by the dielectric. When studying the EDM process in general, the endoscope is placed a few centimeters from the electrode gap and slightly above, in order to have a general view of the electrodes and their surrounding environment. To observe the electrodes, an external lighting is necessary to illuminate them, because our endoscope is not equipped with a source for illumination. We use two halogen lamps for this purpose. For plasma imaging, the endoscope is placed much closer to the plasma (5 mm typically), and the ﬂat workpiece is replaced by a pointed one. With this point-to-point geometry, the plasma is thus localized as much as possible.
(a)
to camera

(b)

lens endoscope

Figure 3.7: Schematic drawing of the experimental setup for imaging. (a) Imaging of the EDM process; (b) plasma imaging.

The endoscope is directly connected to a CCD camera (SensiCam Fast Shutter from PCO Imaging, 12 bit, exposure time 100 ns − 10 ms, 1280 × 768 pixels). The image focusing is done by a lens with adjustable focal length, placed between the end of the endoscope and the CCD camera. For time-resolved imaging, i.e. acquisition of successive images of short exposure time taken at diﬀerent moments of the discharge, the camera can be gated. In this mode, the exposure begins with an external trigger signal, produced by a pulse generator. The delay between the breakdown (t = 0) and the beginning of the exposure is set by the pulse generator. The t = 0 trigger is obtained by measuring the current rise or the voltage drop which occur at the breakdown. For fast imaging, we use another camera, an intensiﬁed CCD camera (ICCD PI-MAX camera from Princeton Instruments, 16 bit, < 2 ns gating, 1024 × 1024 pixels). Since short exposure time implies low measured intensities, light intensiﬁcation is required. This is performed in ICCD cameras by a micro-channel plate (MCP) placed just behind a photocathode. The electrons created in the photocathode are multiplied in the MCP, and then re-transformed into photons by a ﬂuorescent screen. The MCP is also used as a shutter for gated exposure. Since the electrons in the MCP can be abruptly blocked by reversing the electric ﬁeld, fast gating is achievable with ICCD cameras. For time-resolved imaging with the PI-MAX camera, the delay from the breakdown can be set without a pulse generator. The t = 0 trigger is directly sent to the camera controller, and the delay is set by software.

32

CHAPTER 3. EXPERIMENTAL SETUP AND DIAGNOSTICS

3.5

Optical emission spectroscopy

Optical emission spectroscopy (OES) is a classical plasma diagnostic. Several important plasma measurements can be performed with this non-intrusive method: chemical composition, temperatures, densities, electric and magnetic ﬁelds present in the plasma [107–109].

3.5.1

Principles

OES consists in the spectral analysis of the light emitted in the visible region by the plasma. The light is dispersed in a spectrograph, generally by a grating, and detected by photodiodes, a photomultiplier or a CCD camera. Atoms, ions and molecules emit light with a discrete spectrum when they pass from an excited state to a state of lower energy, i.e. when an electron makes a transition from an upper energy level Ei to a lower energy level Ej inside the atom, ion or molecule. The wavelength λ of the spectral line emitted during this transition will be λ= hc Ei − Ej , (3.1)

where h is Planck’s constant and c the speed of light. Since the atomic or molecular quantum energy levels are diﬀerent for every element or molecule, the discrete spectrum emitted by these electronic transitions, called bound-bound transitions, is like a characteristic signature of the emitting species. The plasma composition can thus be determined with OES by identifying the diﬀerent emitted spectral lines. While the wavelength of a spectral line is only determined by the type of the emitting species, the intensity of this line depends on the abundance of the emitter, i.e. on its density, and also on the population of the excited state considered. This means that line intensities are dependent on the plasma temperature. The energy levels of the hydrogen atom can be exactly calculated with quantum mechanics. The main levels are the eigenvalues of the Hamiltonian describing the electron of the hydrogen atom, and are given by En = − 13.6 eV , n2 n = 1, 2, 3 ... (3.2)

The energy E = 0 corresponds to the ionization threshold. A special terminology is used for the lines emitted by atomic hydrogen. They are given in ﬁgure 3.8. A plasma can also emit light with a continuous spectrum. This occurs when free electrons recombine in atoms or molecules: they pass from a state E > 0 in the energy continuum (i.e. with no deﬁned energy) to a discrete level inside an atom or a molecule. These transitions are called free-bound transitions. Continuous light is also emitted when free electrons lose energy by passing near an ion or an atom. This is the well-known Bremsstrahlung, or free-free radiation.

3.5. OPTICAL EMISSION SPECTROSCOPY
Lyman series
∞

33
Paschen series eV
0 - 0.54 - 0.85 - 1.51 … Pα Pβ

Balmer series

n=5 n=4 n=3

n=2 … Hα Hβ Hγ

n=1 … Lα Lβ Lγ Lδ

Figure 3.8: Main quantum levels and emission lines of the hydrogen atom.

…

- 3.39

- 13.6

3.5.2

Electron temperature measurement

To determine the diﬀerent temperatures of the species present in a plasma, several spectroscopic methods exist [107, 108]. In practice, their respective applicability depends on the type of spectrum emitted by the plasma studied: atomic lines, ionic lines, molecular bands, continuum emission... Most of these methods require the assumption of thermal equilibrium, or at least of local thermal equilibrium (LTE). They need a theoretical relation between the populations of the various excited states and the temperature or the pressure, for example. In case of LTE, this relation is simply given by equilibrium statistical mechanics or thermodynamics. In case of non-equilibrium plasmas, it is much more complicated to develop a theoretical model. Here, for the electron temperature determination in EDM plasmas, we use the two-line method. This method, which is a particular case of the Boltzmann plot method, is based on measurements of the intensity ratio of two spectral lines, emitted by atoms or ions of the same element [107, 108]. Since it is a relative and not an absolute intensity measurement, the calibration of the absolute spectral sensitivity of the optical arrangement is not necessary. If we assume that the plasma is in a state of LTE (the validity of this assumption for EDM plasmas will be discussed later, in § 6.1.7), the distribution of atoms and ions in the diﬀerent excited states is described by the Boltzmann distribution. Thus, the density ni of a certain type particle, atom or ion, in an excited state i is given by ni = n0 gi Ei · exp − Z k B Te , (3.3)

where n0 is the total density of the considered particles in the plasma, gi the statistical

34

CHAPTER 3. EXPERIMENTAL SETUP AND DIAGNOSTICS

weight of the excited level and Ei its energy, Z the partition function, kB the Boltzmann constant and Te the electron temperature. In case of LTE, Te is also equal to the ion temperature and to the gas temperature; Te could thus be replaced in (3.3) with a unique plasma temperature T . The emission coeﬃcient ε of the line emitted by the transition from the upper state i to a lower state j is ε= 1 hc · · Aij ni , 4π λ (3.4)

where λ is the line wavelength and Aij the probability for the transition from the state i to the state j. Replacing ni by its expression given in (3.3), we obtain ε= hc n0 gi Aij Ei · · · exp − 4π Z λ kB Te .

Considering now two lines λ1 and λ2 emitted by the same species, i.e. by atoms or even charged ions of the same element, the ratio of their intensities is given by I1 ε1 g1 A1 λ2 = = · · exp I2 ε2 λ1 g2 A2 E2 − E1 k B Te ,

where gi , Aij and Ei for the line k (k = 1, 2) are noted gk , Ak and Ek respectively. Extracting Te from the preceding equation, we ﬁnally obtain E2 − E1 Te = · ln kB I1 λ1 g2 A2 I2 λ2 g1 A1
−1

.

(3.5)

The ratio I1 /I2 is experimentally determined from an emission spectrum. The electron temperature can be thus calculated with equation (3.5) if Ek , λk , gk and Ak are known values for the two lines. Practically, the choice of the two lines is of importance. Since the relative error on the temperature is ∆Te k B Te ∆ (I1 /I2 ) = · Te |E2 − E1 | I1 /I2 according to (3.5), it is crucial to choose two lines with a diﬀerence |E2 − E1 | as large as possible. Moreover, the chosen lines have to be intense and isolated from other lines, in order to avoid overlapping and to minimize ∆ (I1 /I2 ). It is also desirable that λ1 and λ2 are close to each other. In this case, the absorption by the dielectric and the spectral sensitivity of the optical arrangement can be considered equal for the two lines. No spectral correction is then required for the calculation of I1 /I2 . Finally, the lines have to be non-resonant ones, to avoid self-absorption. It has to be emphasized that with the two-line method, a minimum error of 10% on Te is expected [107].

3.5. OPTICAL EMISSION SPECTROSCOPY

35

As we will see in chapter 6, copper lines are emitted by EDM plasmas when using a copper electrode. Three atomic copper lines fulﬁl the conditions cited above. Their parameters are given in table 3.2. Since |E2 − E1 | must be large, we can use the pairs (a)−(b) and (a)−(c) for the determination of Te with the two-line method.
Line (a) (b) (c) λ [nm] 510.554 515.324 521.820 upper state (i) 4p 4d 4d
2P 3/2 2D 3/2 2D 5/2

lower state (j) 4s2 4p 4p
2D 5/2 2P 1/2 2P 3/2

Ei [eV] 3.817 6.191 6.192

Ej [eV] 1.389 3.786 3.817

gi 4 4 6

gj 6 2 4

Aij [108 s−1 ] 0.02 0.6 0.75

Table 3.2: Line parameters of the Cu I lines used for electron temperature determination [110].

In practice, to calculate the line intensities from a spectrum, the background has to be subtracted ﬁrst. Then the line shapes are ﬁtted with Lorentzian functions (see § 3.5.3), and eventually deconvolved if there are adjacent lines. The line intensity I is not simply the maximum value of the peak, but the whole area under the Lorentzian ﬁt.

3.5.3

Electron density measurement

With the electron temperature Te , the electron density ne is another important physical parameter characterizing a plasma, which can also be determined with optical emission spectroscopy. Again, there are several methods based on measurements of line and continuum intensities, but also on measurements of line proﬁle [107, 108, 111]. The electron density has in fact a direct inﬂuence on line shapes, while they are relatively insensitive to electron and ion temperatures. Spectral lines are broadened and shifted from their theoretical position, increasingly with the electron density. The inﬂuence of the density on line broadening can be qualitatively explained as follows: the collision frequency will increase with density, and so the lifetime of atoms in excited states will decrease due to collisions. By the Heisenberg principle, this will increase the uncertainty on the energy levels, i.e. the uncertainty on the emitted wavelength. Spectral lines are thus more broadened in a dense plasma. There are several broadening mechanisms: • the natural broadening, due to the ﬁniteness of the lifetime of an atom in an excited state; • the broadening due to collisions, such as: – the pressure broadening, caused by collisions between emitters and neutral atoms or molecules; – the Stark broadening, caused by collisions between emitters and charged perturbers. The atomic quantum levels of emitters are modiﬁed by the Stark eﬀect, due to the electric ﬁeld created by the colliding ions or electrons;

36

CHAPTER 3. EXPERIMENTAL SETUP AND DIAGNOSTICS • the Doppler broadening, due to the thermal movements of the emitters along the line of sight.

Stark broadened lines are experimentally valuable for the density determination, because the Stark broadening is particularly sensitive to the electron density. In a dense plasma, and this is the case of EDM plasmas as we will see in chapter 6, this broadening mechanism will dominate by far all the others [34, 111]. For more details on the Stark eﬀect and its consequences on line emission, see appendix A. The Doppler broadening leads to a Gaussian line shape, while processes involving particle impacts, such as the Stark broadening, lead to a line shape close to a Lorentzian. If both eﬀects take place, the line proﬁle will be a Voigt proﬁle, i.e. a combination of the two. Since Stark broadening prevails in EDM plasmas, our lines have a shape close to a Lorentzian. In our case, we use the Hα line emitted by atomic hydrogen at 656.28 nm to determine the electron density. Along with Hβ , this line is a classical candidate for density measurement, because the hydrogen atom is particularly sensitive to the Stark eﬀect. Furthermore, Stark broadening and shift of the hydrogen Balmer lines have been well studied since many years, because this type of diagnostic is particularly important in fusion experiments and astrophysics, for example. Thus, numerous theoretical and experimental works have been published about Stark broadening and shift of the Hα line, especially for electron density calculations from full width at half maximum (FWHM) measurements [112–115] and from shift measurements [113–117]. Computation of spectral lineshapes is quite diﬃcult, because collisions of both electrons and ions with the emitter have to be taken into account as the broadening mechanism. But in recent years progress has been made to include several dynamic eﬀects in calculations, especially ion dynamics. Here we used the theories of Gigosos and Cardenoso on broadening [112] and of Oks on shift [115] to calculate the electron density. Figures 3.9 (a) and (b) show respectively the simulation results for the dependence of the FWHM and of the shift of Hα on the electron density. Though the plasma temperature has a weak inﬂuence on the line proﬁle, the simulations of FWHM are calculated for diﬀerent temperatures and for diﬀerent reduced mass µ of the emitter−perturbing particle pair. Here, we use the calculation for a plasma of 10’000 K (which is close to the actual EDM plasma temperature, see chapter 6), and with µ = 1 (i.e. hydrogen atoms perturbed by heavy particles). For the shift simulation, we use calculations made for plasmas with temperatures from 13’000 to 20’000 K. EDM plasmas are cooler, but simulation results for lower temperature are not available. The determination of ne is more precise with the FWHM measurements, because the broadening of Hα is experimentally easily measurable for densities at which the shift is still very low. At 5 · 1017 cm−3 for example, the FWHM is 3 nm but the shift is only 1.7 Å. By ﬁtting the simulation results of the ﬁgure 3.9, we obtain two equations giving the electron density as a function of the Hα FWHM and of the Hα shift. Thus, to calculate ne from our FWHM and shift measurements, we use the following relations: ne = 8.8308 · 1016 · ∆λW
1.6005

(3.6)

3.5. OPTICAL EMISSION SPECTROSCOPY
(a) broadening
5·10
18 18

37
(b) shift
electron density [cm-3]
simulation fit

electron density [cm-3]

10

simulation fit

4·10 3·10 2·10

18

18

10

16

18

10

14

10 0.01 0.1 1 10

18

5

10

15

20

FWHM of the Ha line [nm]

shift of the Ha line [Å]

Figure 3.9: Relation between the electron density and: (a) the full width at half maximum (FWHM) of the Hα line (simulation results for a 10’000 K plasma with µ = 1, according to [112]); (b) the shift of the Hα line (simulation results for plasmas from 13’000 to 20’000 K, according to Oks [115]).

with ne in cm−3 and the FWHM ∆λW in nm, and ne = 1017 · (1.3591 + 2.0757 · ∆λS + 0.0037 · ∆λ2 ) S (3.7)

with ne in cm−3 and the shift ∆λS in Å. In practice, we have to take into account the broadening caused by the spectrograph. This experimental broadening is measured with a laser, which theoretically emits a single wavelength. The Hα line is treated as the copper lines for Te determination: background subtraction and Lorentzian ﬁt. Then, the line FWHM is obtained by subtracting the experimental broadening from the FWHM of the Lorentzian ﬁt.

3.5.4

General experimental setup

The general experimental setup for OES is presented in ﬁgure 3.10. The emitted light is collected by a quartz ﬁbre, 1 mm in diameter. The ﬁbre is immersed in the dielectric, located a few millimeters from the spark to optimize the collected light intensity and to reduce absorption from the dielectric. The light is then dispersed by a spectrograph equipped with gratings, and detected by a CCD camera or photodiodes. Finally, the signal is digitalized and treated with a computer. We use diﬀerent spectrographs and detectors depending on the application: • for time-integrated spectroscopy, a 0.275 m spectrograph (SpectraPro 275 from Acton Research Company) with three gratings (150, 600 and 1200 grooves/mm),

38

CHAPTER 3. EXPERIMENTAL SETUP AND DIAGNOSTICS
spectrograph spectrum

fibre optics

CCD camera

gratings

Figure 3.10: Schematic drawing of the experimental setup for optical emission spectroscopy.

equipped with a CCD camera (TE/CCD-1024E from Princeton Instruments, 16 bit, 1024 × 256 pixels); • for time-resolved spectroscopy, the same spectrograph SP275 as above, equipped with a detector composed of an array of 700 gated photodiodes (OMA III system from EG&G PARC, 14 bit, 100 ns − 10 ms gating); • for spatially-resolved spectroscopy, a 0.75 m imaging spectrograph (SpectraPro 750i from Acton Research Company) with three gratings (150, 600 and 1800 grooves/mm), equipped with a CCD camera (Spec-10:400B from Princeton Instruments, liquid N2 cooled, 16 bit, 1340 × 400 pixels); • for time- and spatially-resolved spectroscopy, the same spectrograph SP750i as above, equipped with the ICCD PI-MAX camera used for fast imaging (see section 3.4). The resolving power and the spectral range for each conﬁguration are given in table 3.3.

spectrograph SP275 CCD camera photodiodes 150 600 1200 150 600 1200 resolving power [nm] spectral range [nm] 1.25 650 0.35 160 0.17 70 2.8 450 0.8 100 0.25 45

spectrograph SP750i CCD camera ICCD camera 150 600 1800 150 600 1800 0.5 240 0.12 60 0.03 15 0.33 120 0.09 30 0.02 10

Table 3.3: Resolving power and spectral range for the diﬀerent experimental conﬁgurations (spectrograph / detector / grating).

The spectral sensitivity of the optical system (ﬁbre + spectrograph + detector) has been measured with a reference light source, whose real emission spectrum is known.

3.5. OPTICAL EMISSION SPECTROSCOPY

39

The sensitivity is calculated by dividing the spectrum of the reference source measured through the optical system by the real spectrum. Figure 3.11 shows the results for the spectrograph SP275 with the CCD camera.
(a) real spectrum
intensity [arb. unit]
150 100 50 1

(c) spectral sensitivity ( = (b) / (a))

spectral sensitivity

0 400 600 800

0.8 0.6 0.4 0.2 0

wavelength [nm]

(b) measured spectrum
intensity [arb. unit]
400

200

300

400

500

600

700

800

900

wavelength [nm]
0 400 600 800

wavelength [nm]

Figure 3.11: Spectral calibration of the optical system composed of the quartz ﬁbre, the spectrograph SP275 and the CCD camera. (a) Real spectrum of the reference light source; (b) spectrum measured through the optical system; (c) spectral sensitivity (normalized).

The spectral sensitivity is maximum between 600 and 750 nm, and falls oﬀ below 500 nm and above 900 nm, mainly due to the quantum eﬃciency of the CCD camera. For all spectrograph-detector conﬁgurations, the optical system is sensitive to light emitted roughly between 300 and 1000 nm. The spectral calibration was made under diﬀerent conditions: without dielectric, with clean oil and with oil contaminated by eroded particles. Though the light absorption by the dielectric increases drastically in contaminated oil, the relative spectral sensitivity remains approximately the same without oil, in clean or contaminated oil. Though the plasma light is intense enough for imaging (even with short exposure time < 1 µs), it is not possible to perform emission spectroscopy of a single spark. For imaging, the total plasma light is concentrated on a few pixels of the CCD chip. But for spectroscopy, the light is dispersed in the spectrograph and spread over the whole chip. The intensity of a single spark is then far too weak to be measured. The light has to be accumulated over thousands of discharges.

40

CHAPTER 3. EXPERIMENTAL SETUP AND DIAGNOSTICS

3.5.5

Experimental setup for time-resolved spectroscopy

Time-resolved spectra are obtained with gated photodiodes. As for time-resolved imaging, a pulse generator is used to generate the detector gate. The light is detected only during a short period of the discharge, which is the time resolution of the measurement. Changing the delay between the beginning of the discharge and the beginning of the light acquisition, we obtain a succession of spectra. Each spectrum is obtained by accumulating the light of the same part of thousands sparks, as shown in ﬁgure 3.12.

voltage

time

current

time

detector gate

delay

exposure time time "t=0" trigger (V or I)

Figure 3.12: Timing diagram for time-resolved spectroscopy.

3.5.6

Experimental setup for spatially-resolved spectroscopy

Figure 3.13 shows the experimental setup for spatially-resolved optical emission spectroscopy. In order to have a spatial sampling of the emitted light, the magniﬁed plasma image captured with the endoscope is projected onto an in-line array of 16 ﬁbres, arranged over 2 mm. In this way, each ﬁbre collects the light coming from a diﬀerent zone of the emitting region. With a typical endoscope-plasma distance of 5 mm, the achievable resolution is ∼ 20 µm/ﬁbre. The ﬁbre bundle brings the sampled light into the imaging spectrograph. The 16 diﬀerent spectra are recorded simultaneously with the CCD camera. Due to the small size of the light emitting region (see section 5.2), this arrangement is the easiest way to perform the spatial sampling. In principle, it could be done directly without the endoscope but with an array of ﬁbres directly located near the plasma, but in this case the miniaturization of the ﬁbres in the bundle is then an issue.

3.6. EXPERIMENTAL DIFFICULTIES
16 spectra endoscope lens imaging spectrograph with CCD camera

41

image bundle of 16 in-line fibres

Figure 3.13: Experimental setup for spatially-resolved spectroscopy.

Since the light acquisition is made over thousands of discharges due to the weak emitted intensity, it is necessary that the successive plasmas stay located, as far as possible, in the same position with respect to the endoscope. Otherwise, one ﬁbre of the bundle would sample light coming from diﬀerent zones of the plasma, and the spatial sampling is no longer valid. As for plasma imaging, we use a point-to-point electrode geometry to localize the sparks as well as possible. Discharges with high current are also avoided, because they produce large craters, and so large variations in the plasma localization already after a few discharges. For time- and spatially-resolved spectroscopy, the setup is the same as shown in ﬁgure 3.13, but the CCD camera is replaced by the ICCD camera, which can be gated.

3.6

Experimental diﬃculties

The experimental investigation of EDM plasmas is not straightforward. Since this work is precisely an experimental characterization of these plasmas, it is important to emphasize the practical problems encountered. The main source of diﬃculties comes from the small size of the plasma. With a typical electrode gap of 10 − 100 µm, moreover in a liquid environment, it is almost impossible to apply all the classical plasma diagnostics: electrostatic probes, mass spectrometry, microwave diagnostics, actinometry... Intrusive and active methods either are not applicable, or too diﬃcult. Optical methods, such as emission spectroscopy and imaging, are almost the only usable diagnostics. Furthermore, even the optical diagnostics are diﬃcult to implement in practice. A spatial characterization of such a small plasma is challenging. In addition to the problems related to the miniaturization of light acquisition instruments (optical ﬁbre, endoscope), the weak intensity emitted by the plasma is also an issue. It is necessary to have sensitive detectors and to make the measurements in a dark environment. Even so, measurements of a single discharge remains extremely diﬃcult. The short duration of the discharges is also problematic. Since the timescale of the discharges is 1 − 100 µs and the timescale of breakdown phenomena is 10 − 100 ns typ-

42

CHAPTER 3. EXPERIMENTAL SETUP AND DIAGNOSTICS

ically, the measuring devices must have a fast response. Related to the rapidity of the phenomena studied, electrical interference is another problem. In a typical discharge, the current rises at breakdown from 0 to 12 A in ∼ 200 ns, for example. The electromagnetic waves associated with this sudden current rise perturb all the electrical measurements, especially weak signals such as photomultiplier signals. Shielding of the measuring instruments becomes of importance. Another major source of diﬃculties is the poor reproducibility of the discharges, even with the same experimental conditions (see § 5.1.4). The localization of the successive plasmas is constantly changing, due to the evolution during machining of the dielectric cleanliness and of the electrodes surface and geometry. Even the plasma properties can vary, also because of the intrinsic stochastic nature of the breakdown process. In such conditions, one spark can be quite diﬀerent from another. Since our spectroscopic measurements have been done over thousands of discharges due to the weak intensity of a single spark, this light accumulation can be viewed as a way to overcome the reproducibility problem. In other words, our spectroscopic results are describing an “average plasma”. Variation in the plasma localization is particularly problematic for time- and spatiallyresolved spectroscopy (section 6.4). For such measurements, we need short exposure times in order to have a ﬁne temporal resolution. At the same time, the plasma has to be localized and as stable as possible for the spatial sampling. For a suﬃcient measured intensity, a short exposure time requires a large number of recorded discharges (typically 100’000 for 2 µs exposure). But a large number of discharges leads to signiﬁcative erosion, and thus to movements of the plasma. After a certain time of machining, the workpiece surface is in fact no longer ﬂat and presents the beginning of a hole. Then the following plasmas begin to “move” around the pointed electrode (they are located where the gap is the smallest, i.e. between the electrode tip and the side of the newly machined hole). Figure 3.14 shows an experimental arrangement which minimizes the plasma movements when performing time- and spatially-resolved spectroscopy.
servo-controlled displacement

endoscope : fixed

to bundle of fibres, spectrograph and camera

slow manual displacement

Figure 3.14: Experimental setup for time- and spatially-resolved spectroscopy.

3.6. EXPERIMENTAL DIFFICULTIES

43

The erosion is considerably reduced by using a workpiece with a large ﬂat surface, which is manually and slowly moved horizontally. Even with a large number of sparks, the erosion is distributed over the whole surface, which remains roughly ﬂat. The plasma movement is thus minimized, permitting a good spatial sampling with a short exposure time.

44

CHAPTER 3. EXPERIMENTAL SETUP AND DIAGNOSTICS

Chapter 4 Pre-breakdown of EDM discharges
The ﬁrst of the four chapters presenting experimental results is dedicated to the prebreakdown phase. The study of the mechanisms leading to breakdown is physically of great interest, but it is also important from the industrial point of view. Since no material removal is performed during this phase, it would be interesting to understand it and to control its duration, in order to reduce this “waste of time” as much as possible. The ﬁrst section of this chapter summarizes some observations made about the bubbles created during the pre-breakdown. Current measurements are presented in the second section, and ﬁnally a short analysis of the pre-breakdown duration is given in the last section. These results are certainly not exhaustive, but they give a ﬁrst insight into pre-breakdown phenomena.

4.1

Bubbles

Depending on the conditions, small bubbles can be generated at the electrodes as soon as the gap voltage is applied. One can observe that: • bubbles are created only in water, and not in oil; • more bubbles are generated when the electric ﬁeld in the gap is increased. A few bubbles are already visible with a gap of 15 mm and 80 V, and the emission is strongly increased by diminishing the gap distance and/or increasing the gap voltage (see § 5.1.2 for images). Note that no bubbles are generated in oil even with a gap of 100 µm and 1 kV; • bubbles are created at the cathode; • the contamination of the water, and consequently its conductivity, has an eﬀect. For example, very few bubbles are generated in clean conditions (water conductivity < 3 µS/cm). These observations suggest that the bubbles are produced by electrolysis of the water. The ﬂow of a small electric current in the water releases gaseous hydrogen and oxygen at the electrode surfaces, according to the following reactions:

45

46

CHAPTER 4. PRE-BREAKDOWN OF EDM DISCHARGES

2 H2 O −→ O2 + 4 H+ + 4 e− 4 H2 O + 4 e− −→ 2 H2 + 4 OH−

(at the anode), (at the cathode).

The observed inﬂuences of the electric ﬁeld and of the water conductivity on bubble generation is a direct sign that bubbles are related to the ﬂow of an electric current. Since we observe only bubbles coming from the cathode, they are bubbles containing hydrogen. The oxygen released at the anode is probably directly consumed for the oxidation of the anode surface. One can in fact observe that the anode, in copper or in steel, is rapidly oxidized after a few minutes. To conﬁrm that electrolysis is really the source of bubbles, a basic analysis of the bubble gas was performed. Bubbles were collected in a test tube as shown in ﬁgure 4.1, and the gas was tested with a detector sensitive to explosive gases (hydrogen, methane or propane for example). The detector was quickly saturated already with a small volume of gas, indicating that the bubbles are certainly made of hydrogen.
collected gas

Figure 4.1: Experimental setup for bubbles collection.

Note that the electric ﬁeld responsible for the electrolysis is much higher than the value simply obtained by dividing the gap voltage by the gap distance. Since we use a point-to-point geometry, the ﬁeld near the electrode tip is strongly enhanced by the point eﬀect. Figure 4.2 shows a calculation for a gap of 5 mm and 200 V, assuming electrode tips with a curvature radius of 100 µm. The ﬁeld at the tip can reach 2’300 V/cm, nearly six times higher than the plane electrode, uniform ﬁeld value of 400 V/cm.

4.2

Pre-breakdown current

Before the breakdown, which is characterized by a large voltage drop and current rise, fast current pulses are sometimes measured. An example of such pre-breakdown current is given in ﬁgure 4.3. The measured current pulses reach a few milliamperes and last about 5−20 ns.

4.2. PRE-BREAKDOWN CURRENT

47

0V 200 V
R = 100 mm 220 V/cm

2300 V/cm

900 V/cm

20 V

1 mm

Figure 4.2: Increase in the electric ﬁeld du to the point eﬀect. Simulation result for a pointto-point geometry, 100 µm curvature radius, 5 mm gap, 200 V, in water: lines of equipotential and electric ﬁeld strength (in grey scale).

200

voltage [V]

100

breakdown

0 2

current [mA]

1

0

-0.6

-0.4

-0.2

0

time [ms]

Figure 4.3: Typical pre-breakdown current (AC component) measured in 1.5 µS/cm water (gap voltage 180 V).

We observe this type of current not necessarily just before a breakdown as in ﬁgure 4.3, but randomly as soon as the gap voltage is applied, provided that the electrode spacing is small enough. The occurrence of these irregularly-spaced pulses increases when moving the electrode towards the workpiece. Figure 4.4 shows, on a longer timescale, the multiplication of these current bursts when reducing the gap distance. A DC component is measured (electrolysis current), because the water used is not a perfect dielectric due to its contamination. The water ﬁlling the gap acts therefore as a resistance, whose value

48

CHAPTER 4. PRE-BREAKDOWN OF EDM DISCHARGES

is roughly proportional to the gap distance. This explains why we measure a decrease in the gap voltage and an increase in the DC current, when the gap distance is reduced.
200 150 100 50 0 20 15

voltage [V]

DC component

current [mA]

10 5

AC component
0 0 5 10 15 20

time [s]

Figure 4.4: Current bursts measured in water when the gap distance is slowly diminished (the electrode is moved manually towards the workpiece).

As mentioned in section 2.2, this type of current signal is typically associated with the propagation of streamers in the gap [31, 34, 63, 66, 72]. Each pulse is due to a sudden growth of the ionized channel. A small current can be measured, because this propagation involves a movement of charged species. The electrode polarity should inﬂuence the shape of the pre-breakdown current signal, since positive and negative streamers propagate slightly diﬀerently. However, no clear eﬀect can be observed in our measurements, because our electrode geometry is symmetric (point-to-point). To clearly diﬀerentiate current signals of the two types of streamer, a strongly asymmetric electrode conﬁguration must be used (point-to-plane, for example [63]). As for the bubble generation, oil and water behave diﬀerently. No AC or DC prebreakdown current are measured in oil, for any condition. This remarkable point emphasizes the crucial role of gaseous bubbles for the propagation of streamers, as shown also in other studies [77–79]. In water, their initiation and propagation are strongly facilitated by the pre-existing bubbles, created by electrolysis. On the other hand, the creation of a bubble in oil is more diﬃcult, because electrolysis does not occur. The initiation of a streamer in oil requires a higher electric ﬁeld than that created with our source (∼ 0.1−10 MV/cm is necessary, according to [30, 60, 63, 72]). This explains the absence of pre-breakdown current in oil in our measurements.

4.2. PRE-BREAKDOWN CURRENT

49

Although the breakdown mechanisms in water and in oil should not be completely diﬀerent and should follow the general sequence described in section 2.2, they can nevertheless be inﬂuenced by diﬀerent parameters. In water, the breakdown triggering is certainly enhanced by the presence of bubbles. In oil, there are rather the contaminating particles that could play this role, by forming a “conductive bridge” [3,75]. Although both bubbles and particles certainly inﬂuence the breakdown in water as in oil, the dominant contribution is not the same in the two types of dielectric. As expected, the conductivity of the water has an inﬂuence on pre-breakdown current [65]. Figure 4.5 presents measurements in clean water, in water contaminated with eroded particles, and in a slightly salted solution.
(a) clean water 1.5 mS/cm
200 200

(b) contaminated water 7 mS/cm
200

(c) salted water 20 mS/cm

voltage [V]

100

100

100

0 30

0 30 20 DC component DC component 10 0 0 1 2 0 5 10

0 30 20 10 0 0 8 16 DC component

current [mA]

20 10 0

time [ms]

time [ms]

time [ms]

Figure 4.5: Eﬀect of the water conductivity on pre-breakdown current: (a) clean water; (b) water contaminated with eroded particles; (c) salted water.

Increasing the conductivity naturally also increases the DC current. Therefore, the bubble generation by electrolysis will be more eﬃcient and pre-breakdown currents more frequent. This is exactly what we observe in our measurements. In clean water, the DC current is almost zero and current pulses are seldom measured (typically < 1 pulse every 10 µs). Then, the average number of current pulses per time unit increases with the conductivity. The addition of external particles or other additives to the dielectric thus certainly inﬂuences and facilitates the breakdown mechanism. But for a stable machining process, these additives should not increase the liquid conductivity too much. The liquid has to keep some of its insulating properties. In the salted solution (c), short-circuits become very frequent. A water conductivity higher than 20 µS/cm will thus lead to an unstable situation, prejudicial to the quality of the machining process. In real conditions of machining, the dielectric is always contaminated with particles, despite continuous ﬁltering

50

CHAPTER 4. PRE-BREAKDOWN OF EDM DISCHARGES

and cleaning of the liquid. Figure 4.5 (b) thus reﬂects a more realistic situation than (a) and (c). Other studies have shown that light is emitted during the propagation of streamers. The light intensity follows the same evolution as the current [31,34,63,66,72]. An example of light emission measured with a photomultiplier during the pre-breakdown is given in ﬁgure 4.6.
140

voltage [V] current [mA] light intensity [arb. unit]

120

100

8

4

0

0.3 0.2 0.1 0 -0.8 -0.6 -0.4 -0.2 0

time [ms]

Figure 4.6: Light emission associated with pre-breakdown current in water (gap voltage 140 V).

Whereas the light at the breakdown is intense (saturation of the detector), the emission associated with streamers is very weak. Therefore, the gain of the photomultiplier has to be set high, and this produces considerable electronic noise on the output signal. This kind of measurement is therefore quite diﬃcult. Nevertheless, one can see that the light emission is clearly correlated with the current, as expected.

4.3

Pre-breakdown duration

Once the gap voltage is applied, it takes a certain amount of time until a breakdown occurs. This duration is not constant from a discharge to another, even if they have the

4.3. PRE-BREAKDOWN DURATION

51

same parameters. Statistics of the pre-breakdown duration have been done for diﬀerent types of discharges. The mean duration diﬀers according to the discharge parameters, but the duration distribution is always of the same kind. Figure 4.7 shows histograms of the pre-breakdown duration measured on two types of discharges.
(a)
500

(b)

Weibull distribution fit
400

3000

Weibull distribution fit

number

number

300

2000

mean = 11.3 ms
200 100 0 0 10 20 30 40 50 60 70

mean = 46.9 ms
1000

0 0 50 100 150 200 250 300

pre-breakdown duration [ms]

pre-breakdown duration [ms]

Figure 4.7: Histograms of the pre-breakdown duration. (a) Statistics on 8’000 similar discharges: 6 A, 8 µs on-time, 8 µs oﬀ-time, −200 V, in water; (b) statistics on 19’000 similar discharges: 6 A, 50 µs on-time, 50 µs oﬀ-time, +200 V, in water.

The distribution of pre-breakdown duration can be well ﬁtted with the Weibull distribution [118]. The probability density function of this type of distribution is P (x|a, b) = a b xb−1 · exp(−axb ) (x > 0) ,

where a and b are constant parameters. The general shape of this distribution is, starting from zero, an increase to a maximum value, followed by an exponential decay. The Weibull distribution is known for describing, among others, the repartition of the pre-breakdown duration in various dielectric liquids [119, 120]. The breakdown process in EDM has thus a strong stochastic nature, which clearly appears in these measurements. Although we can optimize discharge parameters and experimental conditions to reduce the mean prebreakdown duration (addition of electron scavengers in the dielectric for example), we will always have distributed values. The poor reproducibility of EDM discharges can undoubtedly be related to this stochastic aspect of the breakdown. As we will see in the next chapter, the stochastic nature of the breakdown has a practical consequence for plasma imaging. Since it is impossible to predict precisely when the next breakdown will occur, the camera opening for the exposure of a given discharge can only be triggered with the beginning of this very discharge. We cannot anticipate the beginning of the next discharge, as could be done with pulsed RF plasmas, for example.

52

CHAPTER 4. PRE-BREAKDOWN OF EDM DISCHARGES

Chapter 5 Imaging diagnostics of EDM discharges
The ﬁrst section of this chapter presents images taken from ﬁlms that were recorded during the EDM machining process. Images of the plasma itself are analyzed in the second section. Finally, the third and fourth sections are respectively dedicated to images of the plasma at the beginning and at the end of the discharge.

5.1
5.1.1

Imaging of the EDM process
Erosion

Figure 5.1 shows a typical example of what can be observed during machining.
1
electrode

2

3
bubbles

4

workpiece 1 mm

spark

5

6

7

8

eroded cavity

Figure 5.1: Images taken during the machining process (1 ms exposure; Cu electrode, steel workpiece, 8 A, 50 µs on-time, + 200 V, water). Sparks and bubbles are clearly visible. The duration of the whole sequence is approximatively 40 s.

53

54

CHAPTER 5. IMAGING DIAGNOSTICS OF EDM DISCHARGES

The workpiece surface, completely ﬂat on image 1 before machining, is slightly eroded by the successive sparks. After a few tens of seconds of machining, i.e. after a few hundreds of thousands of sparks, a small cavity is formed (image 8). Some of these sparks are visible on images 2, 4, 5 and 7. The heat released by the discharges generates vapor bubbles close to the electrode gap. They can be clearly seen on images 3, 6 and 7 for example.

5.1.2

Bubbles

Diﬀerent types of bubbles can be observed. As mentioned in section 4.1, hydrogen bubbles are released during pre-breakdown in water by electrolysis. During machining, the heat of the plasma is generating vapor bubbles, in water as in oil. Images of these diﬀerent kinds of bubbles are given in ﬁgure 5.2.
(a) H2 bubbles during pre-breakdown in water (b) vapor bubbles during erosion in water
electrode

(c) vapor bubbles during erosion in oil
electrode

1 mm

1 mm

1 mm

Figure 5.2: Diﬀerent types of bubbles generated during the EDM process: (a) small hydrogen bubbles created by electrolysis during pre-breakdown in water (large and small gap, + 200 V); (b) water vapor bubbles thermally induced during machining (8 A, 50 µs); (c) oil vapor bubbles thermally induced during machining (6 A, 6 µs).

By zooming on the images of ﬁgure 5.2 (a), the diameter of the electrolysis bubbles can be roughly estimated around 30 − 100 µm. The generation of these hydrogen bubbles is strongly enhanced with an increase in the electric ﬁeld. With a small gap (bottom image of ﬁgure 5.2 (a)), one can in fact observe numerous bubbles ejected from the gap with high velocity, leading even to turbulent phenomena (vortices).

5.1. IMAGING OF THE EDM PROCESS

55

On the other hand, the thermally-induced vapor bubbles are much larger. Their diameter is ∼ 500 µm, in water as in oil (ﬁgure 5.2 (b) and (c)). When machining in water, both hydrogen and vapor bubbles are created. This can be seen on ﬁgure 5.1, image 6 for example: two large vapor bubbles are visible, along with several small hydrogen bubbles going up on both sides of the pointed electrode. In oil, only large vapor bubbles can be observed.

5.1.3

Short-circuit

Imaging permits also the observation of undesirable phenomena, such as the short-circuit of the electrodes. The phenomenon shown in ﬁgure 5.3 has been observed both in water and in oil.
1
electrode

2
vapor bubble

3
hot spot (arc?)

4

workpiece 500 mm

5

6

7

8

new bubble

Figure 5.3: Short-circuit, creation of a stable hot spot and continuous generation of large growing vapor bubbles in oil. The duration of the whole sequence is approximatively 15 s (images: 9 ms exposure).

A short-circuit occurs when the two electrodes come into contact, or if a conducting debris bridges the gap. If the electrodes are not separated but kept in contact, the current ﬂow heats them by Joule eﬀect. With a point-to-point geometry as in ﬁgure 5.3, a hot spot is easily formed between the electrodes, because the current density becomes very high in this region due to their small contact area. The heat released by this hot spot generates a vapor bubble (image 2), just as the sparks do during machining. On image 3, the inter-electrode distance has been slightly increased. The hot spot becomes bright and is probably a small arc. The heat release is then more intense, leading to a growth of the vapor bubble, which remains “attached” to the hot spot (images 3 and 4). Once the bubble reaches a critical size, the buoyancy force is large enough to detach the bubble from the hot spot (image 5). A new bubble is immediately formed, and grows just like

56

CHAPTER 5. IMAGING DIAGNOSTICS OF EDM DISCHARGES

the preceding one (images 6, 7 and 8). This cycle of bubble generation is very stable and will continue repeatedly, unless the electrodes are clearly separated. On images 7 and 8, the inter-electrode distance is further increased. The arc then grows and becomes very bright (image 8). The arc suddenly disappears as soon as the generator can not sustain it anymore, due to a too large gap distance.

5.1.4

Reproducibility

To illustrate the problem of the reproducibility of the discharges (discussed in section 3.6), ﬁgure 5.4 shows several images of discharges with the same parameters.
electrode

spark

500 mm

workpiece

Figure 5.4: Images of similar discharges, illustrating the problem of reproducibility (9 ms exposure; 12 A, 50 µs, oil). The electrode outlines are drawn.

Even with a point-to-point geometry, the plasma localization strongly changes from one discharge to another. Furthermore, the size of the sparks, and consequently their physical properties, also vary. Therefore, all our measurements were repeated several times. Numerous plasma images were acquired, and the most representative ones are presented in the following sections.

5.2
5.2.1

Plasma imaging
Evolution of the plasma light intensity

Before analyzing images of EDM plasmas, it is important to study the evolution of the plasma light intensity during the discharge. Two examples of such measurements are given in ﬁgure 5.5, along with voltage and current measurements.

5.2. PLASMA IMAGING
(a) short discharge
100 6 80
8 6 4 2 0

57
(b) long discharge
200 150 100 50 0

voltage [V]

current [A]

4

60 40

2 20 0 0

light intensity [arb. unit]

1.6 1.2 1.2 0.8 0.8 0.4 0 0.4 0

0

2

4

6

8

0

20

40

60

80

100

time [ms]

time [ms]

Figure 5.5: Evolution of the plasma light intensity, of the current and of the voltage during a single discharge: (a) short discharge (4 A, 8 µs, water); (b) long discharge (8 A, 100 µs, water).

Two phases can be distinguished: the breakdown phase and the discharge phase. The major part of the light is emitted during the breakdown phase, i.e. approximately during the ﬁrst 500 ns after the breakdown (see ﬁgure 5.5 (a)). During the discharge itself, the light emission is 10 to 150 times less intense. In ﬁgure 5.5 (b), the ﬁrst light peak seems to last much longer than 500 ns. This is an artefact due to the saturation of the photomultiplier. For this measurement, the gain of the detector has in fact been set higher in order to better visualize the light emission during the discharge phase. The intensity of the ﬁrst peak is thus in reality much higher and lasts less than 1 µs. The light emission during the discharge phase becomes much more intense when increasing the discharge current. Furthermore, the oscillations observed on light intensity measurements in ﬁgure 5.5 (b) are correlated to those on current (the current waveform is caused by the regulation system of the generator). This shows that these two physical values are unsurprisingly interdependent. From the erosion point of view, the ﬁrst microsecond seems to be very diﬀerent from the rest of the discharge. The high intensity of the ﬁrst light peak suggests that a massive ﬂow of energy is brought to the workpiece during the breakdown phase. Due to the short duration of this event (< 1 µs), it is probable that only the workpiece surface is aﬀected by this primary energy ﬂow, while the workpiece bulk remains unaﬀected. A burst of energy will in fact directly evaporate only the very superﬁcial layers of the workpiece. The bulk is not aﬀected, because it can not absorb this high amount of energy by conduction on such

58

CHAPTER 5. IMAGING DIAGNOSTICS OF EDM DISCHARGES

a short time scale. The bulk will be heated by the plasma during the discharge phase. Like the workpiece, the electrode is probably also aﬀected by this primary energy ﬂow. A small superﬁcial erosion of the electrode during the breakdown phase could be consistent with the well-known fact that wear mostly occurs at the beginning of the discharge. The fast and superﬁcial erosion process occurring at the breakdown could be similar to the “thermal runaway” of protrusions on arc cathode surfaces (see § 2.1.3). Protrusions can be evaporated or even explode if the input power is higher than what the electrode can evacuate by conduction. The typical time scale of fast evaporation processes is 1−100 ns, and below 1 ns for explosive processes [56]. Interest in using very short discharges could thus arise in EDM, considering that such fast eroding mechanisms will produce surfaces with very low roughness. A new type of machining could perhaps be developed, with generators capable of producing powerful ultra-short discharges.

5.2.2

Typical plasma image

Contrary to the images of the section 5.1, plasma images are acquired without any external lighting. The measured light comes only from the plasma itself. Figure 5.6 shows a typical image of an EDM plasma. The electrodes have been outlined because they are not visible without the external lighting.
(a) image (b) contour plot
intensity [arb. unit]
-200 -100

(c) vertical profile

50 mm

200 mm

0

100

200

distance from center [mm]

Figure 5.6: (a) Typical plasma image (5 µs exposure, 5 µs delay after breakdown; 24 A, 100 µs, oil), the position of the electrodes is drawn; (b) contour plot of (a); (c) intensity proﬁle of (a) along the vertical axis.

The light emitting region is generally round or oval. As we will see later, its diameter increases with the discharge current. The light mostly originates from a broader region than the gap itself, i.e. the discharge excites a broad volume around the electrode gap. In order to better analyze the images, it is useful to view them as contour and proﬁle plot, as shown in ﬁgure 5.6 (b) and (c). The dots in the center of ﬁgure 5.6 (b), and the irregularities in the center of ﬁgure 5.6 (c), are not real but due to the individual sampling by the endoscope ﬁbres. There are indeed small spaces between the ﬁbres in the endoscope which do not bring the light to the camera. The brightest zone is the central

5.2. PLASMA IMAGING

59

region (electrode gap) and the light emission decreases rapidly with distance: at 40 µm from the center, the intensity is halved.

5.2.3

Plasma evolution

The evolution of the plasma size is another delicate point. Care has to be taken for the image treatment and interpretation. First, the light emitting region (excited region) could be broader than the plasma itself (ionized region), and the light could partly be scattered from the liquid in the surrounding of the electrodes. Secondly, the images have to be normalized in intensity. If not, the plasma seems to be bigger during the ﬁrst microsecond, simply because the light intensity at this stage is much higher. Finally, we cannot acquire more than one image during a single discharge, because the readout time of the CCD camera is much longer than the discharge on-time. Thus, each image will be acquired during a diﬀerent discharge. Since the discharges are poorly reproducible, the comparison between the images becomes diﬃcult. However, ﬁgure 5.7 shows plasma images at diﬀerent stages of the discharge.

200 mm

0 to 5 ms

5 to 10 ms

10 to 15 ms

20 to 25 ms

50 to 55 ms

90 to 95 ms

Figure 5.7: Plasma images at diﬀerent times during the discharge (5 µs exposure, variable delay after breakdown; 24 A, 100 µs, water). The images are normalized in intensity. Each image is obtained during a diﬀerent discharge.

There is a slight growth of the emitting region, but its size remains fairly constant during the whole discharge. Similar measurements have been reported elsewhere [27,121]. The emitting region was also found to grow with time. Even if the light emitting region could be larger than the plasma itself, it is likely that these images reﬂect an increase in the plasma size during the discharge, as expected from simulations [40, 122]. Other results conﬁrm this conclusion. Measurements of crater radius on the cathode surface have been made for diﬀerent discharge on-time [123]. The crater radius rc (t), supposed to be close to the plasma radius rp (t), is found to increase with t0.2 . In previous models, rp (t) was assumed to grow with t3/4 [40], or with tanh(t) [124]. We will not propose any relation here. In our opinion, the reproducibility of our images is not good enough to propose any numerical relation, which would be an over-interpretation of the measurements.

5.2.4

Eﬀect of the discharge current

As shown in ﬁgure 5.8, the diameter of the light emitting region increases with the discharge current, being roughly from 150 to 400 µm for a current increase from 3 to 48 A.

60

CHAPTER 5. IMAGING DIAGNOSTICS OF EDM DISCHARGES

Thus, the plasma size most likely also increases with the discharge current. Again, this can be correlated with the fact that discharges with high current produce larger craters than discharges with low current.
3A 6A 12 A 24 A 48 A

200 µm

∅ ≅ 185 µm

∅ ≅ 210 µm

∅ ≅ 270 µm

∅ ≅ 275 µm

∅ ≅ 410 µm

Figure 5.8: Plasma images for diﬀerent discharge currents and estimation of the emitting region diameter (5 µs exposure, 10 µs delay after breakdown; 100 µs, water). The images are normalized in intensity.

5.2.5

Hα emission

As we will see in chapter 6, the hydrogen Hα line is the dominant contribution in EDM plasma line emission. Intensity evolution and imaging of the Hα emission has been measured by using a band-pass ﬁlter centered around 656 nm. The ﬁlter is placed between the optical ﬁbre and the photomultiplier for intensity measurements, and between the endoscope and the camera for imaging. Results are given in ﬁgure 5.9.
(a) intensity evolution
15 200 150 100 50 0

(b) image

voltage [V]

current [A]

10 5 0

100 mm

light intensity [arb. unit]

1.5 1 0.5 0 0 10 20 30 40 50 60 50 mm

intensity [arb. unit]
-200

time [ms]

0

200

distance from center [mm]

Figure 5.9: Emission of the Hα line: (a) intensity evolution; (b) typical image (5 µs exposure, 0 µs delay), contour plot and vertical intensity proﬁle. Discharge parameters: 12 A, 50 µs, water.

5.3. BEGINNING OF THE DISCHARGE : FAST IMAGING

61

The intensity evolution of this line is similar to the evolution of the total emission, given previously in ﬁgure 5.5. The major part of the light is emitted during the breakdown phase. Similarly, the images obtained with the Hα ﬁlter are very similar to those obtained without it (see ﬁgure 5.6). The emitting region has the same shape, size and intensity proﬁles. We can thus conclude that the Hα line is emitted by the whole plasma volume.

5.3

Beginning of the discharge : Fast imaging

Figure 5.10 shows fast imaging of the ﬁrst 300 ns of the discharge, obtained with the ICCD camera. This time interval corresponds to the emission of the ﬁrst light peak and to the ﬁrst fast current rise (see ﬁgure 5.5 (a)). This interval is thus important in the plasma evolution: it is during the very beginning of the discharge that the plasma is forming and that a high amount of energy is brought into it.
exposure I/8 [A]

1

V/200 [V]

50 to 100 ns

0.5 0 1

100 to 150 ns

0.5 0 1

150 to 200 ns

0.5 0 1

200 to 250 ns

0.5 0 1

250 to 300 ns

0.5 0 0 0.5 1

time [ms]

Figure 5.10: Fast imaging of the discharge beginning along with current and voltage evolution (50 ns exposure, variable delay; 6 A, water). The images are normalized in intensity. Each image is obtained during a diﬀerent discharge.

The exposure time is 50 ns for each image, with variable delays. There is always a 50 ns intrinsic delay between the trigger signal (current rise at the breakdown) and the camera opening, due to gating electronics and cables. Since we cannot anticipate the breakdown

62

CHAPTER 5. IMAGING DIAGNOSTICS OF EDM DISCHARGES

for the camera triggering as previously mentioned in section 4.3, the ﬁrst image can only be acquired 50 ns after the breakdown. Between 100 and 200 ns after the breakdown, the current reaches its maximum. The light intensity is also at its maximum. However, on the plasma images, no clear evolution is visible from 50 to 300 ns: size and geometry remain constant. Images obtained with delays longer than 300 ns are not shown here, but they are similar to those of the ﬁgure 5.10. This shows that the plasma develops very rapidly (within 50 ns) after the breakdown, and then remains quite stable.

5.4

End of the discharge and post-discharge

Since the major part of the workpiece material is removed at the end of the discharge when the plasma collapses, the transition from the discharge to the post-discharge is particularly interesting to study. This stage in the EDM process is certainly crucial for the optimization of the material removal rate. The evolution of the light intensity at the transition and during the post-discharge is presented in ﬁgure 5.11.
8 6 4 2 0 1.4 200 150 100 50 0

current [A]

voltage [V]

intensity [arb. unit]

discharge light

0.7

post-discharge light
0 50 150 250 350 450

time [ms]

Figure 5.11: Evolution of the light intensity during a post-discharge (discharge: 6 A, 50 µs, water).

As soon as the current is shut down, it drops rapidly to zero, and the light intensity is simultaneously also dropping fast. But there is still a weak slowly-decaying light emission, typically until 300 µs after the end of the discharge. The corresponding images of the transition are given in ﬁgure 5.12.

5.4. END OF THE DISCHARGE AND POST-DISCHARGE
exposure

63

1

I/8 [A] V/200 [V]

50 to 51 ms

0.5 0 1

discharge (plasma)

51 to 52 ms

0.5 0 1

52 to 53 ms

0.5 0

1

post-discharge (particles)

53 to 54 ms

0.5 0 1

54 to 55 ms

0.5 0 45 50 55

time [ms]

Figure 5.12: Images of the transition between the discharge and the post-discharge, along with current and voltage evolution (1 µs exposure, variable delay; 12 A, 50 µs, water). The images are normalized in intensity. Each image is obtained during a diﬀerent discharge.

As long as the discharge current is established, the plasma is visible as a bright spot. When the current drops down, the disappearance of the plasma is almost immediate. The plasma collapse is thus a very fast phenomenon. Images of the post-discharge in ﬁgure 5.12 are less clear, due to the weak intensity of the light emitted during this period. The objects which are emitting light are diﬃcult to identify. The quality of the images are much improved by setting the sensitivity of the ICCD camera at its maximum and by increasing the exposure time. It is also easier to do the measurements in oil, because the numerous bubbles present in water strongly perturb the acquisition of the light. Some examples of better post-discharge images are shown in ﬁgure 5.13. It becomes clearer that the light emitted after the discharge is due to particles of heated metal. These particles come from the molten metal pool created in the workpiece during the discharge, and are then removed from the workpiece and ejected in the dielectric when the discharge is shut down. We see their path and not only luminous dots, because they are moving during the camera exposure. These explosions of particles were also clearly

64

CHAPTER 5. IMAGING DIAGNOSTICS OF EDM DISCHARGES

200 mm

Figure 5.13: Incandescence of the removed particles after a discharge. Each image is taken during a single post-discharge (100 µs exposure; 12 A, 50 µs, oil).

visible on ﬁgure 5.4. However, on these previous images, the exposure time was long enough to record both the spark and the post-discharge. Therefore, the interpretation of these luminous paths was not obvious. They could have been attributed to bubbles for example, which would scatter the light of the spark. On the other hand, images of ﬁgure 5.13 are time-resolved and the light is acquired only during post-discharges. The interpretation is thus less ambiguous. In order to conﬁrm the hypothesis of the metal particles, optical emission spectroscopy of the post-discharge light has been performed. An example of the spectrum is shown in ﬁgure 5.14.

intensity [arb. unit]

blackbody fit 2300 K

400

500

600

700

800

wavelength [nm]

Figure 5.14: Optical emission spectrum of the post-discharge light, with a 2’300 K blackbody ﬁt. The light measurement is time integrated over thousands of post-discharges (50 µs exposure, 150 g/mm grating; 16 A, 50 µs, oil).

Spectroscopy shows that the post-discharge light emission is close to a blackbody radiation, which conﬁrms that the emitters are hot metal particles. The spectrum in ﬁgure 5.14 is quite noisy, due to the low intensity of the light emission. Fitting several post-discharge spectra with Planck’s law, the temperature of the emitters is found to be around 2’200 K (± 100 K). Since the melting point of steel is ∼ 1’700 K, the particles are still in a liquid state in the very beginning of the post-discharge. The temperature found

5.4. END OF THE DISCHARGE AND POST-DISCHARGE

65

is consistent with metallurgical analyses of the modiﬁed layers of the workpiece [25, 125]. In these studies, the maximum temperature of the workpiece surface reached during the EDM process has been estimated to be around 3’000 K. The particle size can be measured on the images. We found that the largest particles have a diameter of ∼ 30 µm, which is in good agreement with previous work on sparkeroded particles [126, 127]. The particle speed can also be estimated from images. The maximum speed is around 3 m/s. Since the particles move in the liquid, their trajectories and speed can be aﬀected if a liquid ﬂow velocity is imposed.

66

CHAPTER 5. IMAGING DIAGNOSTICS OF EDM DISCHARGES

Chapter 6 Optical emission spectroscopy of EDM plasmas
The inﬂuence of the discharge parameters on the emission spectra are analyzed in the ﬁrst section, which presents measurements integrated over thousands of whole discharges. The evolution of the spectra during the discharge duration is shown in the second section, with time-resolved measurements. Spatially-resolved spectra are presented in the third section. Finally, time- and spatially-resolved measurements are given in the fourth section.

6.1
6.1.1

Time-integrated emission spectra
Typical spectrum

An example of an optical spectrum emitted by the EDM plasma is shown in ﬁgure 6.1.
Ha

intensity [arb. unit]

Cu Cu C2 Fe Fe
300 400 500 600 700 800 900 1000

Cr Cu Fe C Fe + Cr

wavelength [nm]

Figure 6.1: Typical emission spectrum (Cu/steel, 12 A, 2 µs, oil, 150 g/mm grating).

67

68

CHAPTER 6. OPTICAL EMISSION SPECTROSCOPY OF EDM PLASMAS

The dominant line is the Balmer Hα line emitted by atomic hydrogen, which comes from the cracking of the dielectric molecules. Some lines of atomic carbon and C2 molecules (Swan system) are also visible. This indicates that the organic molecules of oil are almost completely cracked by the discharge. As previously mentioned in § 5.2.5, imaging showed that the Hα line is emitted by the whole plasma volume. This can be understood considering the fact that the plasma is formed by cracking and ionizing the dielectric molecules and atoms. Since the hydrogen source is the dielectric, hydrogen atoms are present everywhere in the plasma. Although the Hα line is dominant, the remaining Balmer series lines such as Hβ (486.13 nm) or Hγ (434.05 nm) are not observed. This remarkable point will be discussed later, in section 7.2. The plasma is contaminated by impurities: several lines of atomic copper from the electrode are present, along with many lines originating from atomic iron, chromium and carbon of the removed material of the steel workpiece. These lines can be seen in more detail in ﬁgure 6.2.
Fe

intensity [arb. unit]

Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe

Fe Fe Fe Fe Fe Fe

Fe Fe Fe

Fe

Fe Fe

Fe Fe Fe

Fe

360

380

400

420

440

wavelength [nm]

Cr

intensity [arb. unit]

C C C C

Fe Fe C2 Cr Fe Fe

C2 Fe Cu Cu Fe Fe Cr C2 Cr Fe Fe Cu Cr Fe

Fe C2 C CC

460

480

500

520

540

560

900

920

940

960

wavelength [nm]

wavelength [nm]

Figure 6.2: Typical emission spectrum, details (Cu/steel, 12 A, 100 µs, oil, 600 g/mm grating).

The fact that all observed lines are atomic lines (along with a few neutral molecular lines) and that no ionic lines are visible, is a ﬁrst indication that the plasma is cold. The excitation of ions requires indeed higher energy than the excitation of atoms. Furthermore,

6.1. TIME-INTEGRATED EMISSION SPECTRA

69

atoms and ions of metallic elements are easily excited, more easily than those of nonmetallic elements. For example, the excited state energies of visible transitions of Fe atoms and of Fe+ ions are respectively around 3 and 11 eV (from the ground state of atoms and ions respectively), but for C atoms and for C+ ions they are respectively around 8 and 22 eV [128, 129]. Thus, the absence of ionic lines of iron, copper or chromium indicates clearly that the plasma temperature is low. Since sparks in gases are known to be highly ionized plasmas [49], EDM sparks should nevertheless also be fairly ionized. The low excitation energy of metallic atoms explains the abundance and the relatively high intensity of their lines in the EDM plasma emission (see for example the numerous Fe lines in ﬁgure 6.2). It should be noted that this abundance does not mean that a large amount of metal is present in the plasma. In electric arcs for example, the light emission is dominated by metallic lines already with a contamination of a few percents of metal. It is also well known that metallic impurities strongly cool down fusion plasmas in tokamaks, because of their strong radiation. Thus, a quantitative estimation of the metallic contamination in the EDM plasma from our spectra would be hazardous. An intense broadband continuum radiation is also observed. The origin of this radiation remains unclear. Blackbody ﬁts do not match well with our measurements. Thus, a continuous emission by heated electrodes or metal particles is unlikely. It is more probable that this continuum is due to free-bound transitions, i.e. radiation emitted during recombination processes. Free-free radiation is also another plausible source. Since molecules generally emit a broadband spectrum, molecules or fragments of molecules from the dielectric certainly also participate to the continuum [34, 63].

6.1.2

Eﬀect of the dielectric

Figure 6.3 shows emission spectra obtained in diﬀerent dielectrics.

(a) water
Ha

(b) oil
Ha

(c) liquid nitrogen

intensity [arb. unit]

Cu Cu Cu O Cu O C2 400 500 600 700 800 900 Cu Cu C Cu Cu N Cu N N N 500 600 700 800 N

400 500 600 700 800 900

900 1000

wavelength [nm]

wavelength [nm]

wavelength [nm]

Figure 6.3: Eﬀect of the dielectric on the emission spectrum (Cu/steel, 150 g/mm grating): (a) water, 12 A, 2 µs; (b) oil, 12 A, 2 µs; (c) liquid nitrogen, 48 A, 2 µs.

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CHAPTER 6. OPTICAL EMISSION SPECTROSCOPY OF EDM PLASMAS

As mentioned previously, the discharge cracks the dielectric molecules, even the strong triple bond of nitrogen N2 molecules. We observe atomic hydrogen and oxygen lines from water; atomic hydrogen, atomic carbon and C2 lines from oil; atomic nitrogen lines from liquid nitrogen. The dominant lines in ﬁgure 6.3 (c) are copper lines, because we have more electrode wear than workpiece erosion under these experimental conditions in liquid nitrogen. The dielectric cleanliness has an eﬀect on the emission spectrum, as shown in ﬁgure 6.4. The continuum radiation is found to be more intense in clean dielectric than in dielectric contaminated with eroded particles. Unsurprisingly, lines emitted by Fe, Cr and Cu follow the opposite tendency. The high intensity of the continuum in clean dielectric is not clearly understood. It is probably because the contribution of dielectric molecules (continuous radiation) dominates the radiation of metallic elements in a clean dielectric.
(a) clean oil (b) contaminated oil

intensity [arb. unit]

Fe, Cr, Cu Fe, Cr, Cu

400

500

600

700

800

900 1000

400

500

600

700

800

900 1000

wavelength [nm]

wavelength [nm]

Figure 6.4: Eﬀect of the dielectric cleanliness on the emission spectrum (Cu/steel, 12 A, 50 µs, 150 g/mm grating): (a) clean oil; (b) oil contaminated with eroded particles.

The addition of metallic powders to the dielectric has also been brieﬂy investigated with spectroscopy. The aim of adding powders is to deposit new layers on the workpiece surface and to improve its quality during the machining process. For example, the addition of graphite nano-particles is found to improve the hardness of the white layer and to reduce the number of cracks in it [125]. The addition of aluminium and tungsten powders does not signiﬁcantly modify the emission spectrum. New Al and W atomic lines are simply added. Thus, the plasma properties are certainly not drastically changed by the introduction of powders. It is rather the breakdown process and the surface quality which can be inﬂuenced by the powders, depending on their size and composition.

6.1.3

Eﬀect of the electrode material

Emission spectra obtained with an electrode in copper, in graphite and in tungsten are shown in ﬁgure 6.5. The electrode material contaminates the plasma, and lines of respectively atomic copper, of atomic carbon and C2 , and of atomic tungsten are emitted. With a graphite electrode, the Swan bands of C2 and the C lines are much stronger than

6.1. TIME-INTEGRATED EMISSION SPECTRA

71

in ﬁgure 6.1 for example, because the carbon contamination of the plasma due to the graphite electrode is much greater than the carbon produced by the cracking of the oil. The tungsten lines are very diﬃcult to observe because they are located in the same spectral region as many iron lines, which are more intense.
(a) copper (b) graphite (c) tungsten

intensity [arb. unit]

Cu Cu Cu

C2 C

C W

400 500 600 700 800 900

400 500 600 700 800 900

400 500 600 700 800 900

wavelength [nm]

wavelength [nm]

wavelength [nm]

Figure 6.5: Eﬀect of the electrode material on the emission spectrum (12 A, 5 µs, oil, 150 g/mm grating): (a) Cu/steel; (b) graphite/steel; (c) W/steel.

The use of a zinc electrode produces a spectrum quite diﬀerent from the others, as shown in ﬁgure 6.6. It should be noted that zinc is never used as electrode material in die-sinking machines, but only as a coating layer of the wire in wire-cutting machines.
Zn

intensity [arb. unit]

Zn Ha Zn Zn
+

+

Zn

+

Zn

+

C Zn 300 400 500 600 700 800 900 1000

wavelength [nm]

Figure 6.6: Emission spectrum with a zinc electrode (Zn/steel, 12 A, 12 µs, −200 V, oil, 150 g/mm grating).

In addition to the Hα line and C lines, both atomic Zn lines and ionic Zn+ lines are emitted, with high intensities. Zinc is the only material tested in this work that produces ionic lines. The wavelengths of these lines, along with those of all other main

72

CHAPTER 6. OPTICAL EMISSION SPECTROSCOPY OF EDM PLASMAS

lines observed in EDM spectra, are given in table 6.1. The diﬀerent behavior of zinc comes from its physical properties. Excited states energies of Zn+ transitions already exist from 8 eV [128]. Thus, Zn+ ions are more easily excited than Fe+ , Cu+ or Cr+ ions. Moreover, this material has a low melting and boiling temperature (692 K and 1184 K respectively), much lower than those of copper for example (1356 K and 2839 K respectively). Zinc has also a vapor pressure ∼ 400 times higher than copper. Consequently, the wear of a zinc electrode is high during the EDM process, and that explains why this material is never chosen for real die-sinking EDM operations. A theoretical study based on experimental data showed that the energy balance at the cathode is strongly related to the electrode material properties [28]. It is demonstrated in this work that a zinc cathode creates a higher density current and a lower ionic current fraction than other cathode materials, due to the particular physical properties of zinc. species H C C2 O N Cu W Fe Cr Zn Zn+ wavelengths [nm] 656.3 (Hα ) 833.5, 906.2, 467.9, 468.5, 777.2, 777.4, 746.8, 821.6, 510.6, 515.3, 400.9, 407.4, 358.1, 382.0, 520.5, 520.6, 468.0, 472.2, 491.2, 589.4, 909.5, 469.8, 777.5, 868.0, 521.8, 426.9, 404.6, 520.8, 481.1, 602.1, 911.2, 471.5, 844.6 939.3, 578.2, 429.5 438.4, 529.8, 636.2 610.2, 940.6, 962.1, 965.8 473.7, 512.9, 516.5, 563.6 (Swan system) 1011.5 793.3, 809.3 495.8, 516.7, 527.0, 561.6, 718.7, 751.1, 822.0 541.0, 723.6, 740.0 747.9, 758.9, 773.3

Table 6.1: Wavelengths of the main lines emitted by EDM plasmas [128–132].

6.1.4

Eﬀect of the electrode polarity

The emission spectra also give qualitative information about the electrode wear and the workpiece erosion. Figure 6.7 shows two spectra measured under the same experimental conditions, except for the electrode polarity. In ﬁgure 6.7 (a), the tungsten electrode is positively polarized with respect to the workpiece. In this conﬁguration, the wear of the electrode is very strong. In the other conﬁguration where the workpiece is positively polarized with respect to the electrode (ﬁgure 6.7 (b)), the erosion is more eﬀective and the electrode wears much less. The polarity has a clear inﬂuence on spectra. With negative electrode polarity, the iron lines of the group around 520 nm are much more intense than with positive polarity. If we consider the Hα line as a reference of intensity (its intensity does not depend on erosion or wear but originates only from the dielectric), the iron lines show clearly that the erosion is more eﬃcient with negative polarity. If we look at the region between 350 and 450 nm, it

6.1. TIME-INTEGRATED EMISSION SPECTRA
(a) polarity + (b) polarity -

73

Ha

Fe Fe
350 400

Ha Fe

intensity [arb. unit]

W
450 350

400

450

Fe

300

400

500

600

700

800

900 1000

300

400

500

600

700

800

900 1000

wavelength [nm]

wavelength [nm]

Figure 6.7: Eﬀect of the electrode polarity on the emission spectrum (W/steel, 1 A, 100 µs, water, 150 and 600 g/mm gratings): (a) positive polarity; (b) negative polarity.

is obvious that the wear is stronger with positive polarity: in (a) several tungsten and iron lines are visible with comparable intensities, in (b) the tungsten lines are no longer visible and the iron lines are more intense. Note that these conclusions are only qualitative, since it is diﬃcult to deduce the quantities of materials removed from these spectra.

6.1.5

Eﬀect of the discharge current

Three emission spectra obtained with diﬀerent discharge currents are presented in ﬁgure 6.8.
(a) 6 A
Ha

(b) 12 A
Ha

(c) 48 A
Ha

intensity [arb. unit]

Fe, Cr, Cu Fe, Cr, Cu Fe, Cr, Cu Cu Cu Cu

400 500 600 700 800 900

400 500 600 700 800 900

400 500 600 700 800 900

wavelength [nm]

wavelength [nm]

wavelength [nm]

Figure 6.8: Eﬀect of the discharge current on the emission spectrum (Cu/steel, 12 µs, oil, 150 g/mm grating): (a) 6 A; (b) 12 A; (c) 48 A.

74

CHAPTER 6. OPTICAL EMISSION SPECTROSCOPY OF EDM PLASMAS

Increasing the discharge current strongly enhances the intensity of the emitted light. But from the spectroscopic point of view, the increase in the current has little eﬀect. It only increases the intensities of the metallic lines. This can be understood by considering that discharges with high current produce large craters and remove more material than low current discharges.

6.1.6

Eﬀect of the discharge on-time

The discharge on-time has a signiﬁcant inﬂuence on the emission spectrum. Figure 6.9 (a) and (b) are spectra for two diﬀerent on-times of Isopulse discharges, where the current is controlled and maintained constant during the discharge. To produce shorter discharges, we use the generator in the capacitive mode (see section 3.1). Figure 6.9 (c) is the spectrum of discharges produced in the capacitive mode with a 10 nF capacitor.
(a) 200 ms
Ha

(b) 5 ms
Ha

(c) ~ 1.6 ms (capacitive mode)
Ha

intensity [arb. unit]

O

O

O

O

O

400 500 600 700 800 900

400 500 600 700 800 900

400 500 600 700 800 900

wavelength [nm]

wavelength [nm]

wavelength [nm]

Figure 6.9: Eﬀect of the discharge on-time on the emission spectrum (Cu/steel, water, 150 g/mm grating): (a) 200 µs, 12 A; (b) 5 µs, 12 A; (c) discharges produced in the capacitive mode, ∼ 1.6 µs, ∼ 6 A.

The broadening of the Hα line increases drastically with decreasing on-time as shown in ﬁgures 6.9 (a) and (b). The FWHM of the Hα line reaches almost 10 nm in ﬁgure 6.9 (b). Such an important broadening can only be due to dynamic Stark broadening, which dominates other broadening mechanisms under these conditions. The Hα line is also shifted to higher wavelengths with decreasing on-time. The measured values of FWHM and line shift are a sign of an extremely high electron density, in particular for brief discharges and thus for the beginning of any discharge. Because the presented spectra are time-integrated, the evolution of electron density can not be directly determined from these FWHM measurements. For discharges shorter than 2 µs, the plasma is so dense that almost all the atomic lines are completely merged into one broad continuum. We hardly distinguish on ﬁgure 6.9 (c) the Hα line, two oxygen lines and two copper lines. This continuum is of another nature than the continuum observed on the previous spectra. It is created by a degeneracy of atomic lines, due to the high plasma density. Extreme densities “destroy” the upper

6.1. TIME-INTEGRATED EMISSION SPECTRA

75

energy levels of the atoms, and the free-bound radiation becomes more important than line radiation [133, 134]. This eﬀect will be discussed in more detail later, in section 7.2.

6.1.7

First estimation of electron density and temperature

With a Hα FWHM of almost 10 nm for short discharges (ﬁgure 6.9 (b)), the order of magnitude of the electron density is 1018 cm−3 (equation (3.6)). This is a particularly high value, ∼ 100 times higher than the density of vacuum arcs and 10 times higher than the density of sparks in gases. This ﬁrst estimation is in good agreement with other studies on discharges in liquids (see section 2.2), and is also conﬁrmed by the spectrum of ﬁgure 6.9 (c): this kind of line-merging phenomenon can only occur in extremely dense plasmas. The pressure imposed by the liquid surrounding the plasma is the cause of its high density. With the two-line method applied to copper lines from time-integrated spectra, the electron temperature is estimated around 0.7 eV ± 0.15 eV (∼ 8’100 K ± 1750 K). The errors in intensity measurements are principally due to other overlapping lines located near the copper lines. The value found is a low electron temperature, but consistent with previous studies on EDM plasmas [40, 41] and other similar plasmas [31, 34, 135]. It should be noted that this electron temperature estimation does not give information on the temperature at the electrode surfaces, which would be a useful value to know for simulations and practical applications. This temperature has to be measured diﬀerently. Results can be found in [123, 136]. The two-line method is based on the assumption of LTE. It is not an obvious assumption, especially for non-ideal plasmas such as EDM plasmas (see chapter 7), where coulombian interactions are comparable to thermal interactions. The evolution to the equilibrium state by thermal interactions is thus perturbed by coulombian eﬀects. However, due to the high plasma density, one can assume that the numerous collisions between particles thermalize them rapidly. A density criterion giving the validity of LTE can be derived theoretically [107, 137]. A plasma of temperature T is in complete LTE if its electron density ne is higher than ne ≥ 9.2 · 1017 · kB T · EH E2 − E1 EH
3

[cm−3 ] ,

(6.1)

where EH is the ionization energy of the hydrogen atom, E1 the ground state energy of the atoms present in the plasma and E2 the energy of their ﬁrst excited state. According to this criterion, a hydrogen plasma at 0.7 eV is in LTE if ne ≥ 8.6 · 1016 cm−3 . (6.2)

If we assume that the EDM plasma is mainly composed by hydrogen, its electron density is suﬃciently high for the assumption of LTE to be reasonably accepted. Therefore, even if we have not measured it separately, the ion temperature can be estimated to be of the same order as the electron temperature.

76

CHAPTER 6. OPTICAL EMISSION SPECTROSCOPY OF EDM PLASMAS

6.2
6.2.1

Time-resolved emission spectra
Merging of atomic lines

An example of time-resolved emission spectra taken during the ﬁrst 5 microseconds of the discharge is given in ﬁgure 6.10.

Figure 6.10: Example of time-resolved spectra (Cu/steel, 16 A, water; time resolution 500 ns, 150 g/mm grating).

The intensities of the spectra decrease with time, because the light emission is particularly intense during the ﬁrst microsecond of the discharge, as stated previously in § 5.2.1. No lines are clearly identiﬁable in the very ﬁrst spectrum. The emission is almost continuous. This eﬀect of line merging has already been observed with very short discharges in the preceding section (ﬁgure 6.9). The previous conclusions about the high plasma density at the beginning of the discharge is thus conﬁrmed by time-resolved measurements. The merging can be more clearly seen in ﬁgure 6.11, which presents spectra of the ﬁrst 3 microseconds of the discharge measured with a better time resolution than in ﬁgure 6.10. The spectral region investigated is centered around 520 nm, where the main Cu, Cr and Fe lines are located. All the lines are completely merged during approximately the ﬁrst 400 ns. Their shapes then appear, strongly broadened between ∼ 400 ns and 1 µs, much less afterwards. This is evidence that the electron density is decreasing with time, as we will see later in § 6.2.3.

6.2.2

Evolution of the electron temperature

The evolution of Te during the discharge is measured by applying the two-line method on each time-resolved spectrum. Note that it is impossible to measure Te during the ﬁrst microsecond of the discharge with this method, because of the line merging. The electron

6.2. TIME-RESOLVED EMISSION SPECTRA

77

intensity (normalized)

1

0.8

0.6

0.4 0 1 2 3 460 480 500 520 540 560 580

Figure 6.11: Merging of the Fe, Cu and Cr atomic lines (Cu/steel, 12 A, water; time resolution 200 ns, 600 g/mm grating). The spectra are normalized to the intensity of the Cu line at 521.8 nm.

temperature is slightly higher during the ﬁrst 10 µs than for the rest of the discharge, being from ∼ 0.8 to 0.7 eV (∼ 9’000 to 8’000 K). Then it remains rather constant around 0.7 eV within the margin of error, even after 1 ms.

tim e [m

s]
wavelength [nm]

6.2.3

Evolution of the electron density

Figure 6.12 shows time-resolved emission spectra of the Hα line during the ﬁrst 10 µs of the discharge.
656.28 nm
intensity (norm.)
1 0.8 0.6 0.4 0.2 0

peak position

Figure 6.12: Broadening and shift of the Hα line (Cu/steel, 16 A, water; time resolution 1 µs, 600 g/mm grating). The spectra are normalized to the intensity of the Hα line.

time [ms]

5 10 640 650 660 670

680

wavelength [nm]

78

CHAPTER 6. OPTICAL EMISSION SPECTROSCOPY OF EDM PLASMAS

The very ﬁrst spectra show extremely broadened and shifted Hα lines. Thus, it is quite diﬃcult to ﬁnd a good ﬁt for the ﬁrst spectra, leading to non negligible errors in the FWHM measurements. The black lines on ﬁgure 6.12 represent the theoretical position of the Hα line (656.28 nm) and the measured peak positions. These lines are drawn to easily visualize the line shift. At the beginning of the discharge, we can measure FWHM up to 10 nm and shift up to 10 Å. The evolution of ne is calculated from these time-resolved Hα spectra with equations (3.6) and (3.7). Results are given in ﬁgure 6.13.

electron density [cm-3]

10

18

broadening shift

10

17

1

10

100

time [ms]

Figure 6.13: Evolution of the electron density, deduced from time-resolved broadening and shift measurements of the Hα line (Cu/steel, 16 A, water).

In spite of some diﬀerences, the FWHM and the shift measurements give comparable density values and evolution. As expected, the electron density is extremely high during the ﬁrst microsecond (above 1018 cm−3 ) and then decreases rapidly with time. The EDM plasma is created from a liquid, which is a dense medium (∼ 3·1022 water molecules/cm3 , for example). This is the main reason for the high plasma density. In the very beginning of the discharge, the plasma has to overcome the extreme pressure imposed by the dielectric. Then the plasma expands, which results in a decrease in its density. But during the whole discharge, the density remains high (always above 1016 cm−3 ) due to the constant pressure of the surrounding liquid. The density reduction with time is conﬁrmed by other studies on discharges in liquids [34]. The high electron density measured reinforces the assumption of free-bound and freefree radiation for the explanation of the continuum given in § 6.1.1. Since these two types of radiation processes involve free electrons, the intensity of free-bound and freefree radiation is in fact directly related to ne . Therefore, the continuum is expected to be intense with such high values of ne . Moreover, the measured continuum decreases with the discharge on-time (see ﬁgure 6.9), which is consistent with the decrease of ne with time.

6.3. SPATIALLY-RESOLVED EMISSION SPECTRA

79

6.3

Spatially-resolved emission spectra

Figure 6.14 shows an example of spatially-resolved spectra along the vertical axis. The intensities of the spectra located in the center are higher, because the plasma is brighter in this region (see also ﬁgure 5.6).

intensity [arb. unit]
5 10

# fibre

15 450 500 550 600

650

700

wavelength [nm]

Figure 6.14: Example of spatially-resolved spectra, along the vertical axis (Cu/steel, 12 A, 4 µs, water, 150 g/mm grating).

Note that the spatially-resolved axis is not calibrated in real distance, but simply graduated with the numbers of the ﬁbres making the sampling. In order to make the conversion into real distance, we have to know the spatial resolution obtained with the ﬁbre bundle, i.e. the real distance between two points seen by two consecutive ﬁbres. This spatial resolution depends on the optical arrangement, mostly on the plasma−endoscope distance, which is not constant from one set of measurements to another. After each set of measurements (the simultaneous acquisition of the 16 spectra), the electrodes have to be changed due to their erosion, and the optical arrangement has to be re-aligned. Thus, an exact calibration for each set of measurements is time-consuming and has not been systematically done. The spatial resolution can nevertheless be estimated around 20−30 µm/ﬁbre (gap distance ∼ 100 µm), for all the measurements presented here.

6.3.1

Asymmetry of the contamination

As previously said, the spectral region around 520 nm is interesting for a qualitative characterization of the plasma contamination, because of the presence of three chromium lines at 520.45, 520.6 and 520.84 nm, and of the copper line at 521.82 nm. With a copper electrode and a stainless steel workpiece, the Cu line is emitted by particles coming from the electrode and the Cr lines are emitted by particles coming from the workpiece. Figure 6.15 shows spatially-resolved spectra along the vertical axis of this spectral region.

80

CHAPTER 6. OPTICAL EMISSION SPECTROSCOPY OF EDM PLASMAS
Cr line

1

Cu line (=1) to steel electrode

intensity (normalized)

0.8 0.6 0.4 0.2 0

to copper electrode

500

510

520

530

540

wavelength [nm]

550 11

10

9

8

7

6

# fibre

Figure 6.15: Vertical asymmetry of the plasma contamination (Cu/steel, 6 A, 100 µs, water, 150 g/mm grating). The spectra are normalized to the intensity of the Cu line at 521.8 nm.

An asymmetry of the plasma contamination is clearly visible. Near the Cu electrode, the Cu line is more intense than the Cr lines. On the other hand, the Cr lines are more intense than the Cu line near the steel workpiece. Thus, even if Cu and Cr lines are present everywhere in the plasma, we see that each electrode is contaminating the plasma mostly in a region close to itself. Unsurprisingly, no asymmetry is visible along the horizontal axis (measurement not shown here). Depending on the discharge parameters, material transfer from one electrode to the other can sometimes be observed. In this case, the intensity of lines emitted by both electrode materials are quite constant across the vertical proﬁle. With the discharge conditions of ﬁgure 6.15, no material transfer is macroscopically visible on the electrodes after several minutes of machining. This is qualitatively conﬁrmed by the contamination asymmetry measured by spatially-resolved spectroscopy.

6.3.2

Electron temperature proﬁle

Spatially-resolved spectra of the three Cu lines used for Te calculations are shown in ﬁgure 6.16, along with the electron temperature vertical proﬁle calculated from them. The central spectra have a better signal to noise ratio than the outer ones, because the light intensity is higher in the center. The electron temperature is quite constant over the whole proﬁle. Measurements along the horizontal axis are not shown here but do not show any diﬀerence. The plasma has thus a homogeneous electron temperature around 0.7 eV, as previously measured.

6.3. SPATIALLY-RESOLVED EMISSION SPECTRA
1

81
1 0.8 0.6 0.4 0.2 0 4 6 8 10 12
Te 510-515 Te 510-521

0.8 0.6 0.4 0.2 0 6

515.3 nm

8

# fibre

10

12

505

510

515

520

525

electron temperature [eV]

510.6 nm

521.8 nm (=1)

intensity (norm.)

wavelength [nm]

# fibre

Figure 6.16: Vertical proﬁle of the electron temperature calculated from spatially-resolved Cu lines intensities ratios (Cu/steel, 6 A, 100 µs, water, 1800 g/mm grating). The spectra are normalized to the intensity of the Cu line at 521.8 nm.

6.3.3

Electron density proﬁle

Spatially-resolved Hα spectra, along with the electron density vertical proﬁle calculated from them with equation (3.6), are shown in ﬁgure 6.17. The values found are in good agreement with our previous results (ﬁgure 6.13), around 5·1016 cm−3 for a 100 µs discharge. Despite large error bars, the electron density seems to be slightly higher in the plasma center. The horizontal proﬁle, not shown here, is very similar to the vertical one.

intensity (norm.)

6

electron density [cm-3]
8 10 620 640 660 680 700 10
16

1 0.8 0.6 0.4 0.2 0

10

17

# fibre

4

6

8

10

12

wavelength [nm]

# fibre

Figure 6.17: Vertical proﬁle of the electron density calculated from spatially-resolved Hα broadening measurements (Cu/steel, 6 A, 100 µs, water, 600 g/mm grating). The spectra are normalized to the intensity of the Hα line.

82

CHAPTER 6. OPTICAL EMISSION SPECTROSCOPY OF EDM PLASMAS

6.4
6.4.1

Time- and spatially-resolved emission spectra
Evolution of the contamination

A temporal and spatial characterization of the contamination can be obtained by gating the camera when acquiring spatially-resolved spectra of the Cr and Cu lines. In order to present the contamination results in a convenient way, we have calculated, for each spectrum, the lines intensities ratio R deﬁned by I(520.5 nm) + I(520.6 nm) + I(520.8 nm) . I(Cr) R= = . I(Cu) I(510.6 nm) + I(515.3 nm) + I(521.8 nm) This value represents the relative importance of the contamination coming from the workpiece (Cr lines) with respect to the contamination coming from the electrode (Cu lines). The absolute value of R has no physical signiﬁcance and is not important, but its evolution in space and time is of interest for a description of the contamination. Figure 6.18 shows an example of a spectrum where these lines are located, along with the evolution of R proﬁles. The delay between the beginning of the discharge and the camera exposure is indicated near each proﬁle.
0.8 40 ms

Cu

Cr Cu

R = ratio Cr / Cu

Cu

intensity

0.6

30 ms 20 ms

0.4 4 ms 0.2 5 steel 10 15 0 ms

8 ms

510

515

520

wavelength [nm]

# fibre

copper

Figure 6.18: Evolution of the contamination distribution, deduced from time- and spatiallyresolved spectra of Cu and Cr lines (Cu/steel, 12 A, 50 µs, water; time resolution 2 µs).

The ratio R clearly increases during the discharge, from ∼ 0.35 to 0.7 in 40 µs. It indicates that the plasma contamination from the workpiece material increases with time, probably by direct vaporization of the metal into the plasma. This vaporization is mostly eﬃcient after ∼ 10 µs (R is roughly constant before). Again, it is impossible to quantify the eﬃciency of the vaporization, in terms of material removal rate. But even if some amount of material is vaporized during the discharge, the largest part of the erosion occurs certainly at the end of the discharge, with the implosion of the plasma. The increase in R with time could also be partially due to a small decrease of the contamination from the electrode during the discharge. It is known indeed that wear mostly occurs at the beginning of the discharge.

6.4. TIME- AND SPATIALLY-RESOLVED EMISSION SPECTRA

83

Due to the asymmetry of the contamination observed in the preceding section, the proﬁles of R should be decreasing from the left to the right. The steel workpiece is indeed located towards the left (towards ﬁbre #1) and the copper electrode towards the right (towards ﬁbre #16). This tendency cannot be observed in ﬁgure 6.18. It is mainly due to the large experimental errors (error bars are not shown for clarity). As stated in section 3.6, time- and spatially-resolved measurements are particularly diﬃcult. Contrary to the increase in R with time, the asymmetry is probably an eﬀect too subtle to be detected during these measurements. The eﬀect of the electrode polarity on the contamination distribution and evolution is shown in ﬁgure 6.19.
(a) polarity +
0.8 2.2 2

(b) polarity -

R = ratio Cr / Cu

R = ratio Cr / Cu

0.7

36 ms 28 ms

1.8 1.6 1.4 1.2 1 0.8 0.6 32 ms

44 ms

0.6 20 ms 12 ms 8 ms 0.4 5 steel 10 15 copper

24 ms

0.5

16 ms 8 ms 5 steel 10 15 copper

# fibre

# fibre

Figure 6.19: Eﬀect of the electrode polarity on the evolution of the contamination repartition, deduced from time- and spatially-resolved spectra of Cu and Cr lines (Cu/steel, 6 A, 50 µs, water; time resolution 4 µs): (a) positive polarity; (b) negative polarity.

As in ﬁgure 6.7, the situation where the wear is important (ﬁgure 6.19 (a)) can be distinguished from the situation where the erosion is important (ﬁgure 6.19 (b)). The ratio R is in fact lower with the positive polarity (0.5−0.7) than with the negative polarity (0.8−2). R increases with time, for both polarities: it slightly increases from 0.5 to 0.65 in (a), but doubles from 0.9 to 1.8 in (b). The vaporization is thus more eﬃcient in the latter case. Again, it is diﬃcult to observe the contamination asymmetry. Some of the proﬁles in ﬁgure 6.19 (b) nevertheless slightly decrease from left to right.

6.4.2

Evolution of the electron temperature proﬁles

Spatially-resolved spectra of the Cu lines taken at three diﬀerent times of the discharge are given in ﬁgure 6.20. The decrease in the continuum intensity and in the line broadening with time can be observed. It is remarkable that even the Cu lines show a signiﬁcant broadening during several microseconds, due to the high plasma density. These lines are in fact much less sensitive to Stark broadening than hydrogen lines. Broadening of Cu lines is also observed in laser-produced plasmas with copper targets [94, 138].

84

CHAPTER 6. OPTICAL EMISSION SPECTROSCOPY OF EDM PLASMAS
(a) 0 to 2 ms (b) 4 to 6 ms (c) 48 to 50 ms

5 10 15 510 520

5 10 15 500 510 520 500

5 10 15 500 510 520

# fibre

wavelength [nm]

Figure 6.20: Time- and spatially-resolved spectra of the Cu lines used for electron temperature calculation (Cu/steel, 12 A, 50 µs, water; time resolution 2 µs, 600 g/mm grating): (a) 0 to 2 µs; (b) 4 to 6 µs; (c) 48 to 50 µs.

Figure 6.21 shows the evolution of Te proﬁles calculated from the previous spectra. As previously mentioned, the electron temperature is slightly higher at the beginning, but remains around 0.7 eV. The proﬁles are roughly ﬂat within the margin of errors.
0.9

electron temperature [eV]

0.8 12 ms 0.7 16 ms 0.6

8 ms

48 ms

28 ms

0.5 0 4 8 12 16

# fibre

Figure 6.21: Evolution of the electron temperature proﬁles (Cu/steel, 12 A, 50 µs, water, time resolution 2 µs).

6.4.3

Evolution of the electron density proﬁles

Time- and spatially-resolved Hα spectra are shown in ﬁgure 6.22. The spectra are quite noisy, due to the weak intensity emitted. Nevertheless, the Hα broadening is easily observable. The evolution of the electron density proﬁles is presented in ﬁgure 6.23. These density measurements are consistent with time-resolved and spatially-resolved measurements

6.4. TIME- AND SPATIALLY-RESOLVED EMISSION SPECTRA
(a) 0 to 2 ms (b) 4 to 6 ms (c) 36 to 38 ms

85

5

10 640 650

# fibre 15

660

5

10 15 640

650

660

5

10 15 640 650

660

wavelength [nm]

Figure 6.22: Time- and spatially-resolved spectra of the Hα line (Cu/steel, 12 A, 50 µs, water; time resolution 2 µs, 600 g/mm grating): (a) 0 to 2 µs; (b) 4 to 6 µs; (c) 36 to 38 µs.

previously presented (ﬁgures 6.13 and 6.17). The density diminishes during the discharge, by almost two orders of magnitude in 50 µs. The density is slightly higher in the plasma center, and this tendency is veriﬁed during the whole discharge. This temporal and spatial characterization of ne can be useful for the validation of EDM plasma simulations.
10
18

0 ms 4 ms

electron density [cm-3]

10

17

12 ms

8 ms 16 ms

36 ms 10
16

20 ms

48 ms 4 6 8 10 12 14

# fibre

Figure 6.23: Evolution of the electron density proﬁles (Cu/steel, 12 A, 50 µs, water, time resolution 2 µs).

86

CHAPTER 6. OPTICAL EMISSION SPECTROSCOPY OF EDM PLASMAS

Chapter 7 Non-ideality of EDM plasmas
In this chapter, we will show that EDM plasmas are weakly non-ideal. The deﬁnition of a non-ideal plasma is given in the ﬁrst section. Spectroscopic evidence of the non-ideality of EDM plasmas is discussed in the second section. Finally, the third section presents a general summary of the EDM plasma physical properties, measured in this work.

7.1

Plasma coupling parameter Γ

Natural plasmas and artiﬁcially-produced plasmas are both very diverse. Generally, they are classiﬁed according to their temperature and density, because the properties of a plasma depend mostly on these two parameters. In particular, the density n and temperature T deﬁne whether a plasma is ideal or not. In an ideal plasma, the particles are almost free, i.e. their movement is only weakly inﬂuenced by other particles. In this case, the mean kinetic energy of particles is much higher than the mean Coulomb potential energy between them. Knowing n and T for a given plasma, we can calculate its coupling parameter Γ, which quantiﬁes its “degree of ideality”. This parameter represents the ratio of the potential energy of Coulomb interaction at the mean inter-particle distance divided by the mean thermal energy of the charged particles in the plasma. It is deﬁned by . Γ= Z 2 e2 , 4πε0 a kB T (7.1)

where Z is the charge of the particles (Z=1 for hydrogen ions, for example), e the elementary charge, ε0 the vacuum permittivity, and a the mean inter-particle distance given by 1/3 3 . (7.2) a= 4πn Therefore, we see that Γ∝ n1/3 . T 87 (7.3)

88

CHAPTER 7. NON-IDEALITY OF EDM PLASMAS

The plasma is called: • ideal if Γ 1;

• weakly non-ideal if Γ ≤ 1; • strongly coupled if Γ > 1. According to equation (7.3), we see that ideal plasmas are characterized by a low density and a high temperature. Note that Γ is linked with the Debye length λD , deﬁned by . λD = by the relation Γ 3/2 ∝ ε0 kB T , e2 n 1 . n λ3 D (7.4)

Therefore, we see also that, in an ideal plasma, a very large number of particles is contained in a Debye sphere. Nevertheless, the higher the number of particles in a Debye sphere, the less the particles interact with each other. On the other hand, non-ideal and strongly coupled plasmas are dense and/or cold. In such plasmas, the inter-particle distance is short enough, and the particle velocity small enough, to produce signiﬁcant electrostatic interactions between the charged particles. For a given particle, the microﬁelds created by the others have a signiﬁcant inﬂuence on it. We have seen in the previous chapter that EDM plasmas have a typical electron temperature of 0.7 eV and a typical electron density of 1018 cm−3 . Thus, the typical coupling parameter of EDM plasmas is around Γ 0.33 .

If we consider that ne reaches 2.5 · 1018 cm−3 in the very beginning of the discharge (see ﬁgure 6.13), Γ 0.45 during the ﬁrst microsecond. Thus, EDM discharges produce cold and dense plasmas which are weakly non-ideal. According to equation (7.4), the typical Debye length of EDM plasmas is around 6 nm. The mean inter-particle distance a is also around 6 nm (equation (7.2)). Thus, a Debye sphere is containing roughly only one particle. This is another illustration of the plasma non-ideality. Figure 7.1 shows the classiﬁcation of the main types of natural and artiﬁcial plasmas, including EDM plasmas, in a log density−log temperature diagram. Ideal, weakly nonideal and strongly coupled plasmas can easily be distinguished in such a log-log diagram, because Γ iso-contours are straight lines.

7.1. PLASMA COUPLING PARAMETER Γ
log T [K]
2 30
white dwarf brown dwarf

89

3

4

5

6

7

8

9

10

25

ak l pl y n a s on m -id as e

strongly-coupled plasmas
Jupiter core

al

Sun core

we

ideal plasmas

Laser plasma

Focus

20

10

EDM

Shock tubes

Z-pinches Fusion reactor

G

=

log n [cm-3]

15

G

=

1

1

High pressure arcs

=

10

0.

Alkali metal plasma

Low pressure

G

Fusion experiments

= 01

0.

Glow discharge Flames

Solar corona

active galactic nucleus

5

G
Earth ionosphere

0 -2

Interstellar gas

Solar wind (1 AU)

Earth plasma sheet

-1

0

1

2

3

4

5

6

log T [eV]

Figure 7.1: Classiﬁcation of plasmas according to their density and temperature (adapted from [45, 139]).

One can see in ﬁgure 7.1 that the majority of natural and artiﬁcial plasmas are ideal. Besides extremely dense astrophysical objects, few non-ideal plasmas exist. From the physical point of view, their extreme properties make them particularly interesting to study. The physics of non-ideal plasmas is complex, diﬀering from “classical” plasma

90

CHAPTER 7. NON-IDEALITY OF EDM PLASMAS

physics theories [43–46]. Corrections have to be made because of deviations from the binary collision model due to collective eﬀects. For example, the screening mechanism described by the Debye model has to be modiﬁed in non-ideal plasmas. Theories have been developed quite recently, mainly due to the lack of experimental data before the 1980’s. The creation of dense, and therefore non-ideal plasmas, is in fact diﬃcult and requires considerable experimental resources (see § 2.3). In this context, EDM discharges appear to be a very simple method to produce such plasmas. EDM plasmas are indeed amongst the most dense artiﬁcially-created plasmas. But unfortunately, these plasmas are not the easiest to be investigated experimentally, as repeated several times in this work.

7.2

Spectroscopic signs of the non-ideality

In addition, spectroscopic results indicate also that the EDM plasma is non-ideal.

7.2.1

Broadening and shift of Hα

Since non-ideal plasmas are dense, a strong Stark broadening and shift of spectral lines is naturally a characteristic sign of non-ideality. The microﬁelds deform the energy spectrum of radiating atomic particles, i.e. they perturb the initial and ﬁnal states of radiative transitions. The atomic levels are shifted and split, and this results in line broadening and shift [43, 44]. This eﬀect can be clearly observed on optical spectra emitted by EDM plasmas, especially on the Hα line. This fact has already been discussed in detail in chapter 6. Similar strong broadening and shift of hydrogen lines in dense plasmas have been reported in numerous works [113, 115, 117, 135, 140–144]. It should be noted that the calculation of spectral line shapes emitted by dense plasmas has been recently much improved. Simulations in good agreement with experimental data are obtained with models including several non-ideal eﬀects, such as the eﬀect of the dynamic microﬁeld created by the ions or the inﬂuence of electron collisions [45]. Calculations are mostly done for lines of the hydrogen atom or hydrogen-like ions, because of the “simplicity” of quantum calculations for these species.

7.2.2

Asymmetry and structure of Hα

Besides its broadening and shift, the Hα line gives other useful information. Figure 7.2 shows a typical example of a high resolution spectrum of the Hα line. If a lorentzian ﬁt is applied, it is observed that the shape of the line is slightly asymmetric and deviates from the ﬁt. This asymmetry is also due to interactions between ions and the emitter (hydrogen atom in our case), and is another sign of plasma non-ideality [43, 114, 116]. We also see in ﬁgure 7.2 the complex structures around the Hα line. The arrows mark small bumps which are not due to radiation of other lines. These structures are created by several phenomena, which occur in dense plasmas [145–153]. Figure 7.3 gives a simple explanation for the origin of these structures.

7.2. SPECTROSCOPIC SIGNS OF THE NON-IDEALITY

91

intensity [arb. unit]

Lorentzian fit
650 655 660 665

wavelength [nm]

Figure 7.2: Complex structure of the Hα line (C/steel, 24 A, 12 µs, oil, 1200 g/mm grating).
0s 1s

3p 2p

4p

(a) Stark components

D/ħ 5s 6s 8p

w
0 1 2

(b) satellites
W

3 4 5

w

(c) combination of (a) and (b)

w

Figure 7.3: Theoretical structure of the Hα line in a non-ideal plasma [147]: (a) Stark components of Hα (see appendix A.2); (b) satellite lines due to plasma waves or turbulence; (c) resulting Hα structure. The frequency ω = 0 corresponds to the Hα unperturbed position (λ0 = 656.28 nm). The components on the other side of the line are symmetrically positioned.

First, the quasistatic ion microﬁelds cause splitting of energy levels in hydrogen atoms by the Stark eﬀect. The Hα emission is formed by several lines, due to transitions be-

92

CHAPTER 7. NON-IDEALITY OF EDM PLASMAS

tween these new levels (see appendix A for more details). These lines are represented in ﬁgure 7.3 (a), where σ and π denote the polarization of each component. Moreover, low frequency electrostatic waves can also produce a substantial quasistatic ﬁeld, with the same eﬀect as the ion microﬁeld. Furthermore, if plasma waves or turbulence are present in the plasma, a high frequency electric ﬁeld is superimposed on the quasistatic microﬁeld. This dynamic ﬁeld, oscillating with a frequency Ω, produces satellite lines as shown in ﬁgure 7.3 (b). In the case of Langmuir waves for example, the frequency of the dynamic ﬁeld is Ω ωpe ,

where ωpe is the electron plasma frequency deﬁned by . ωpe = e2 ne . ε0 me (7.5)

For EDM plasmas, ωpe 5 · 1013 s−1 . The ﬁeld associated with Langmuir waves will create satellite lines located at λk = λ0 ± k · λpe , k = 1, 2, 3, ...

where λ0 is the unperturbed Hα position, and where ωpe λpe = · λ2 2πc 0 is the wavelength associated with the electron plasma frequency [148, 153]. The combination of the quasistatic and the oscillating ﬁeld produces a spectrum where the Stark components and the satellites are superimposed, as shown in ﬁgure 7.3 (c). Furthermore, if the frequency between the Stark components matches the frequency of the dynamic ﬁeld (i.e. if ∆/ = Ω), resonant interactions occur. As a consequence, depressions or “dips” will appear on the spectrum. The addition of all these eﬀects, typical in non-ideal plasmas, results in multiple modiﬁcations to the Hα proﬁle, as seen in ﬁgure 7.2. The complexity of the emission spectrum reﬂects the complexity of the plasma itself: it is a cold and dense plasma, highly collisional, with strong electric ﬁelds, turbulence and resonance phenomena. In principle, the position of the structures in ﬁgure 7.2 should allow us to estimate the value of the electric ﬁelds present in the plasma. But this estimation can be done only if the structures are completely identiﬁed, which is extremely complex. The Stark components have to be distinguished from the satellites, which can be produced by diﬀerent simultaneous waves or turbulence. In our case, this identiﬁcation is not possible. First, the structures of ﬁgure 7.2 are barely observable, and it is also almost impossible to estimate which waves are present in the EDM plasma. Turbulent phenomena are certainly more likely than “classical” plasma waves. Nevertheless, the ion microﬁeld can be estimated from the mean inter-particle distance [111, 149]. With a density of 1018 cm−3 , the microﬁeld is around 106 V/cm.

7.2. SPECTROSCOPIC SIGNS OF THE NON-IDEALITY

93

7.2.3

Absence of Hβ and line merging

Another important eﬀect of the plasma non-ideality is the transformation of the upper members of a spectral series into a continuous spectrum [43, 44, 134]. This eﬀect is due to: 1. the lowering of the ionization threshold; 2. the merging of spectral lines near the series limit. First, the ionization potential of atoms is lowered in non-ideal plasmas. Inter-particle interactions in high density plasmas “destroy” in fact the upper atomic levels. More precisely, the microﬁelds which are superimposed on the Coulomb electric ﬁeld of an atomic nucleus, transform the upper energy states of this atom into unbound states, as shown in ﬁgure 7.4.
V(r) r unbound states (1) + (2) (1) Coulomb potential (2) microfield

bound states

Figure 7.4: Lowering of the ionization threshold in non-ideal plasmas, due to the eﬀect of microﬁelds (assumed to be uniform on the atomic scale) [44].

The shift in the ionization energy ∆Ui is given by ∆Ui = Z 2 e2 , 4πε0 λD (7.6)

where λD is the Debye length [44,46]. In our case, we found ∆Ui 0.23 eV. This lowering of the ionization threshold modiﬁes the optical spectrum of the plasma. Figure 7.5 explains schematically the consequences in the case of an hydrogen plasma. In an unperturbed atom, all the levels can be populated by electrons (ﬁgure 7.5 (a)). Therefore, the diﬀerent lines of all series can be emitted, in particular those of the Balmer series: Hα , Hβ , Hγ , etc. Continuous radiation by free-bound transitions is emitted by electrons coming from the energy continuum, whose threshold is 13.6 eV above the ground state n = 1 (see ﬁgure 3.8). On the other hand, in a dense plasma, the ionization potential is lowered due to the microﬁelds. If the “new” threshold is located between levels n = 3 and n = 4 for example

94

CHAPTER 7. NON-IDEALITY OF EDM PLASMAS
(a) unperturbed H atom (b) H atom in a dense plasma

continuum ionization threshold n=5 n=4 n=3 ionization threshold n=3

n=2 Ha Hb Hg continuum radiation Ha continuum radiation

n=2

Figure 7.5: Absence of Hβ and increase in the continuum radiation due to the lowering of the ionization threshold in a dense hydrogen plasma.

(ﬁgure 7.5 (b)), the only Balmer line which can still be emitted is the Hα line, because the upper levels of all other Balmer lines are now in the energy continuum. In addition to the disappearance of these lines, another consequence of the lowering of the ionization threshold is an increase in the continuum radiation. Free-bound and free-free transitions become much more likely with a lowered threshold. Secondly, some of the remaining spectral lines, whose upper states are yet below the “new” ionization threshold, can still be “erased”. Although these lines are discrete transitions, they appear as a continuum radiation not because their upper state is in the energy continuum, but because of the Stark broadening. The upper lines of a series are close to each other in the spectrum. If they are signiﬁcantly broadened so that their widths exceed the distance between them, they will overlap with adjacent lines and merge into a continuum. The continuum formed by this degeneracy of lines is the type of continuum observed during the ﬁrst microsecond of the EDM discharge (see § 6.1.6 and § 6.2.1). The Stark broadening of lines near the series limit has thus the same eﬀect as the lowering of the ionization threshold: it transforms the upper members of a spectral series into a continuous spectrum. Therefore, this second eﬀect can be considered as an apparent or optical lowering of the ionization threshold [43, 44]. As showed in chapter 6, the spectra of EDM plasmas are characterized by the absence of the Hβ line and other upper Balmer lines, by an strong continuum radiation and by merging of almost all lines at the beginning of the discharge. All these characteristics can thus be viewed as signs of the non-ideality of the EDM plasma.

7.2.4

Inglis-Teller relation

As previously said, upper spectral lines of a series can be merged if the plasma is dense, due to their overlapping caused by Stark broadening. Since the number of these “erased”

7.3. SUMMARY OF THE PHYSICAL PROPERTIES OF EDM PLASMAS

95

lines depends on the plasma density, the last discernible line gives a rough estimation of the density. For hydrogen Balmer lines, this estimation is given by the Inglis-Teller relation: log n = 23.26 − 7.5 · log nmax , (7.7)

where n is the density expressed in cm−3 and nmax the quantum number of the upper energy level of the last visible transition [43,108,154–156]. This relation is mainly used in astrophysics, to evaluate the electron density in the atmosphere of stars, for example. The coeﬃcients of this relation are sometimes slightly diﬀerent in literature. The uncertainty factor of this relation is about 50% [108]. If we observe on EDM spectra the Hα line (transition from level 3 to 2) but no Hβ line (transition from level 4 to 2), then 3 ≤ nmax < 4 , and the plasma density is at least 6·1018 cm−3 according to relation (7.7). This rough estimation is of the same order of magnitude as our previous density measurements and conﬁrms their validity. Contrary to upper hydrogen Balmer lines which disappear because of their strong broadening, metallic lines do not merge and can be observed in the EDM plasma spectrum, as shown in chapter 6. The metallic lines are much less sensitive to Stark broadening, and this explains why they are still observable. The Stark broadening of non-hydrogenic lines is rather poorly documented, and few data are available [157]. Nevertheless, the FWHM of a few atomic copper lines can be found. For example, in a plasma with an electron density of 1017 cm−3 and at 10’000 K, the FWHM of the Hα line is 10.8 Å, whereas the FWHM of the Cu lines at 510.6, 515.3 and 521.8 nm are 0.43, 1.9 and 2.2 Å respectively [158]. This shows that non-hydrogenic lines are not suﬃciently broadened to merge and disappear into a continuum, as upper hydrogen lines do.

7.3

Summary of the physical properties of EDM plasmas

According to the measurements presented in this work, EDM plasmas have the following characteristics: • The plasma is composed of species coming from the cracking of the dielectric molecules, mainly hydrogen, with contamination from the electrode materials. The contamination is slightly higher in the vicinity of the electrodes, and increases during the discharge. • The electron temperature Te is low, around 0.7 eV (8’100 K), slightly higher at the beginning of the discharge. The temperature is homogeneous in the plasma. The

96

CHAPTER 7. NON-IDEALITY OF EDM PLASMAS assumption of LTE can be accepted due to the high plasma density, and therefore the ion temperature Ti should be similar to the electron temperature. • The electron density ne is extremely high, reaching 2·1018 cm−3 during the ﬁrst microsecond of the discharge, decreasing rapidly afterwards. The density is slightly higher in the plasma center. The ion density ni should be roughly equal to the electron density, since multiple ions are unlikely with such a low electron temperature and since quasineutrality should hold. • The plasma is very dense and cold, and therefore presents several non-ideal eﬀects, especially in the beginning of the discharge. The coupling parameter Γ is around 0.33, and reaches 0.45 during the ﬁrst microsecond. • The Debye length λD is around 6 nm, and the mean inter-particle distance a is also around 6 nm. Therefore, a Debye sphere contains roughly only one particle. Again, this is a sign of the plasma non-ideality. • The light emitted by the plasma is much more intense during the ﬁrst microsecond than during the rest of the discharge. • Due to its high density, the EDM plasma could be not completely optically thin. The opacity of a plasma increases in fact with the density. For example, ultradense plasmas produced by exploding wires in water (ne = 2 · 1021 cm−3 ) are known to be highly opaque and to radiate like a blackbody [33]. Consequently, the light emitted by the very center of the EDM plasma at the beginning of the discharge could be absorbed within the plasma and not be measured. The opacity can be a problem for spectroscopic diagnostics, since the core of an opaque plasma cannot be characterized with such diagnostics. Nevertheless, in our case, the plasma opacity could be critical only during roughly the ﬁrst 500 ns of the discharge, when the density reaches its maximum. But during this period, Te and ne can anyway not be measured with the spectroscopic methods used in this work, because of the line merging. • Energy is dissipated in the plasma by Joule heating, heat conduction, radiation and mechanical work (plasma expansion). Energy is also used for evaporation, dissociation, ionization and excitation of the dielectric molecules and atoms. The energy received by the workpiece is mainly brought by ion bombardment. Thermal runaway of the very superﬁcial layers is also probable in the beginning of the discharge, due to the massive ﬂow of energy at the breakdown. • For a plasma in LTE, the repartition of the densities of the diﬀerent species is described by the Saha equation. For a plasma containing electrons, one type of singly charged ions and one type of atoms, the Saha equation is Ze Zi ne ni = · na Za 2πme kB T h2
3/2

· exp −

Ui − ∆Ui kB T

,

(7.8)

7.3. SUMMARY OF THE PHYSICAL PROPERTIES OF EDM PLASMAS

97

where nk is the density of the species k, Zk its partition function, Ui the ionization energy of the atom, and ∆Ui its correction due to non-ideality (equation (7.6)) [44,159]. In principle, this equation can be used for the calculation of the EDM plasma ionization degree ne /na . For a hydrogen plasma, Ze = 2, Zi = 1 and
nmax

Za =
n=1

En gn exp − kB T

nmax

=
n=1

Ui (1 − 1/n2 ) 2n exp − kB T
2

, 2. Assuming

where Ui = 13.6 eV and n2 = Ui /∆Ui . In our case, we found Za max in addition ne = ni = 1018 cm−3 , we found ne /na = 10−5 .

The ionization degree of the EDM plasma is certainly much higher, probably about 0.1 as for similar discharges [34]. High-pressure arcs have also similar densities as EDM plasmas, and are known to be strongly ionized. The calculation gives ne /na = 10−5 , then we found na = 1023 cm−3 if we assume that ne = 1018 cm−3 . Such a high density of atoms is unlikely, since the density of molecules in the liquid is around 1022 cm−3 . This shows that the ionization degree calculated here is not correct. The assumptions made are probably too strong. In particular, the Saha equation as written in (7.8) does not take into account the complex composition of the EDM plasma. But for a multi-component plasma, the Saha equation has no analytical solution and becomes diﬃcult to solve [159]. • Assuming a temperature of 0.7 eV, a density of 2·1018 cm−3 and that the plasma is a fully ionized hydrogen plasma, the plasma pressure p at the beginning of the discharge is p = p ideal − ∆p = (ne + ni ) kB T − ∆p , where ∆p is a correction due to the plasma non-ideality [44, 46] given by ∆p = e2 · (ne + ni ) . 24πε0 λD

We found that p 4.2 bar. Since the density decreases during the discharge, the pressure is also decreasing. The value found is lower than the pressure calculated with the simulation [40] (∼ 103 bar). But the assumption of a fully ionized hydrogen plasma is obviously a simpliﬁcation. In reality, the plasma composition is more complex and the plasma is partially ionized (the Hα line is emitted by neutral hydrogen atoms). The pressure is thus higher than 4.2 bar, depending on the ionization degree of the plasma. Nevertheless, the pressure is still much lower than the value found with the simulation. • The estimated dimensions of the plasma are summarized in ﬁgure 7.6. The electrode gap is around 100 µm, and the plasma radius in the middle of the gap is also around 100 − 200 µm, growing with time. The contact surface between the plasma

98

CHAPTER 7. NON-IDEALITY OF EDM PLASMAS and the electrodes can be estimated from measurements of crater diameter, and is ∼ 10 µm. Therefore, the current density j ﬂowing through the plasma, and especially through the electrode−plasma interface, is extremely high, in the order of 106 − 107 A/cm2 .
~ 10 µm

anode
sheath (E ≈ MV/cm)

~ 10 nm
hydrogen plasma

plasma column

weakly non-ideal

j ≈ MA / cm2

~ 100 µm

ne = 1018 cm-3 Te = 0.7 eV p ≈ 10 bar E ≈ kV/cm

~ 10 nm

sheath (E ≈ MV/cm)

cathode
~ 100 - 200 µm

Figure 7.6: Schematic image of the general physical properties of the EDM plasma.

• Assuming a potential proﬁle similar to those of electric arcs (see ﬁgure 2.3), most of the voltage jump is located in thin sheaths near the electrodes. The sheath thickness is in the order of the Debye length [53], ∼ 10 nm in our case. The electric ﬁeld is thus very intense in these regions, about 106 V/cm. Consequently, electrons are emitted from the cathode mainly by thermo-ﬁeld emission. The global ﬁeld in the plasma column is lower, about 102 − 103 V/cm. On the other hand, the microﬁeld seen by the particles is also around 106 V/cm, due to the high plasma density. • In a non-ideal plasma, the movement of an electron is mainly inﬂuenced by interactions with ions. The mean free path of an electron λe is thus given by λe = 1 , ni Qei

where Qei is the cross section of thermal electron−ion scattering. This cross section can be theoretically calculated for a strongly ionized non-ideal plasma [44]. The result is

7.3. SUMMARY OF THE PHYSICAL PROPERTIES OF EDM PLASMAS

99

Qei = 4π

Ze2 12πε0 kB T

2

· ln Λ ,

where ln Λ is the Coulomb logarithm. In the case of non-ideal plasma, the usual Coulomb logarithm has to be replaced by 1 ln Λ = · ln 1 + 2 3 ΓD
2

,

(7.9)

where ΓD is a parameter similar to the coupling parameter Γ deﬁned by . ΓD = Z 2 e2 . 4πε0 λD kB T

Note that ΓD ∝ Γ3/2 . For EDM plasmas, ΓD 0.33 and therefore ln Λ 2.2 . −13 2 The cross section is thus Qei 1.3 · 10 cm and the electron mean free path λe 80 nm. • Related to the electron−ion scattering cross section, the plasma electrical conductivity σ can be estimated from the Spitzer conductivity, which is valid for fully ionized plasmas where electron−ion collisions are dominant. The Spitzer conductivity is given by σ = γE · 2 (4πε0 )2 (2 kB T )3/2 π 3/2 Ze2 me ln Λ
1/2

,

(7.10)

where γE is a constant depending on Z, which takes account of electron−electron collisions [44, 46, 160]. For singly charged ions (Z = 1), we have γE = 0.582 and thus σ = 1.53 · 10−2 · T 3/2 ln Λ [Ω−1 m−1 ] ,

with T in K. The Spitzer conductivity holds for ideal plasmas (ln Λ ≥ 10), but can be applied to weakly non-ideal plasmas if the Coulomb logarithm is replaced by the modiﬁed Coulomb logarithm given in equation (7.9) [44]. The value found is σ 5·103 Ω−1 m−1 , much lower than the conductivity of ideal plasmas (∼ 106 Ω−1 m−1 ). • Besides the discharge on-time, the other discharge parameters (current, dielectric, electrode materials, polarity) have roughly no signiﬁcant inﬂuence on the general plasma physical properties enumerated here.

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CHAPTER 7. NON-IDEALITY OF EDM PLASMAS

Chapter 8 Conclusions
Although Electrical Discharge Machining is known, used and studied since the 1950’s, the plasma created during this process remains puzzling. The important lack of knowledge about this plasma is mainly due to the complexity of the phenomena occurring during EDM, but also to the experimental diﬃculties encountered for its characterization. The EDM plasma is small, weakly luminous, of short duration, in a diﬃcult environment, of stochastic nature and poorly reproducible. To our knowledge, this work is the ﬁrst systematic investigation of the EDM plasma with various diagnostics. Considering the signiﬁcant experimental diﬃculties related to it, the ﬁrst success of this work is simply to have shown the applicability of plasma diagnostics to the EDM discharges, particularly optical emission spectroscopy. The eﬀorts made for the application of the diagnostics have been well rewarded. The results obtained are found to be extremely rich, and have permitted us to draw interesting conclusions about the physical properties of this plasma, and also about the diﬀerent phases of the EDM process in general. The pre-breakdown in water is characterized by the generation of numerous small hydrogen bubbles at the cathode, created by electrolysis. These bubbles certainly enhance the triggering of the breakdown, since the propagation of streamers is strongly facilitated in a gaseous medium. On the other hand, no bubbles are observed during the prebreakdown in oil. In this dielectric, the breakdown process can rather be facilitated by the presence of particles in the gap. Fast current pulses have been measured during the pre-breakdown, which are associated with the propagation of streamers. The occurrence of these pulses increases with the liquid conductivity. As expected, a weak light emission is also observable and is correlated with the pre-breakdown current. The duration of the pre-breakdown phase is not constant for given discharge parameters, but the values are distributed following a Weibull distribution. This shows that the breakdown process is of stochastic nature, depending strongly on the dielectric and electrode properties.

101

102

CHAPTER 8. CONCLUSIONS

After the breakdown, the plasma is established very rapidly, in less than 50 ns as observed with fast imaging. The plasma light intensity is particularly high immediately after the breakdown and approximately during the ﬁrst 500 ns. This ﬁrst phase is quite diﬀerent from the rest of the discharge, and the development of generators capable of producing ultra-short discharges could be interesting for a very superﬁcial machining. During the rest of the discharge, the emitted light is weaker, and its intensity depends mostly on the discharge current (more intense with higher current). Imaging shows that the discharge excites a broad volume around the electrode gap, typically 200 µm in diameter, brighter in its center. This volume also clearly increases with the discharge current. The plasma is found to grow slightly during the discharge, as expected according to crater measurements reported elsewhere. Vapor bubbles are generated in water as in oil, by the heat released from the plasma. At the end of the discharge when the current is shut down, the plasma implodes and disappears quickly. The ejection of eroded metallic particles out of the gap is observable with imaging during the post-discharge. These particles emit light by incandescence, which is conﬁrmed by spectroscopic measurements. The spectrum of the post-discharge light is indeed close to a blackbody spectrum at roughly 2’200 K, demonstrating also that the eroded particles are still in a liquid state immediately after the end of the discharge. The spectroscopic analysis of the plasma light gives information about the plasma composition. It is mostly composed by species coming from the cracking of the dielectric molecules, mainly hydrogen in the case of water and oil. Since the plasma is formed from the dielectric, the Hα line, for example, is emitted by the whole plasma volume. The presence of numerous metallic spectral lines indicates that the electrodes are also contaminating the plasma. Time- and spatially-resolved measurements show that the contamination is slightly higher in the vicinity of each electrode, and that the contamination coming from the workpiece increases during the discharge, probably due to vaporization. Workpiece erosion or electrode wear regime can also qualitatively be diﬀerentiated with spectroscopy. Changing the electrode polarity produces in fact very diﬀerent spectra. An increase in the discharge current has also an eﬀect. Since discharges with high current produce larger craters, the metallic spectral lines are more intense with a high discharge current. Almost all the spectral lines observed are atomic lines and not ionic lines, which indicates that the plasma is cold. The electron temperature, determined with the twoline method from copper line intensity measurements, is around 0.7 eV in the whole plasma, slightly higher in the beginning of the discharge. This conﬁrms that the EDM plasma has a low temperature. Discharges with short on-times produce spectra with strongly-broadened lines, especially the Hα line, and with an important continuum radiation. Time-resolved spectroscopy conﬁrms these observations. During the ﬁrst microsecond, spectral lines are so broadened that they are all merged into a continuum. This eﬀect is due to the high plasma density in the very beginning of the discharge. Time- and spatially-resolved measurements of the electron density, based on Stark broadening and shift measurements of the Hα line, show that the density is above 1018 cm−3 in the beginning, and then decreases during

CONCLUSIONS

103

the discharge. But even after 50 µs, the electron density remains high, above 1016 cm−3 . During the whole discharge, the density measured is slightly higher in the plasma center. The EDM plasma has such a high density because it is formed from a liquid, which is a dense medium, and because it is constantly submitted to the pressure imposed by the surrounding liquid. The strong intensity of the continuum radiation can be related to the high electron density. Free-bound and free-free radiations are indeed more likely in a dense plasma. The high electron density also indicates that the plasma is certainly in LTE. As previously mentioned, the EDM plasma is cold and dense. With a typical electron temperature of 0.7 eV and a typical electron density of 1018 cm−3 , its coupling parameter Γ is around 0.3, demonstrating that it is weakly non-ideal. Evaluations of the Debye length, of the mean inter-particle distance and of the Coulomb logarithm, for example, also show the non-ideality of the EDM plasma. Furthermore, spectroscopic results conﬁrm this conclusion. The broadening, the shift, the asymmetrical shape and the structure of the Hα line are characteristic signs of the non-ideality of the plasma. The absence of upper Balmer lines such as the Hβ line, for example, along with the merging of spectral lines in the beginning of the discharge are other demonstrations of this fact. The physical properties of this plasma are quite fascinating. In addition to an extreme electron density, the electric ﬁelds present in the plasma and the current density are particularly high, for example. It is also remarkable that the general plasma physical properties are relatively insensitive to most of the discharge parameters, such as the discharge current, the type of dielectric, the electrode materials and polarity. Whereas these parameters certainly have a signiﬁcant inﬂuence on the machining quality and eﬃciency, they roughly do not change the plasma densities, ﬁelds or temperatures. Although this work has given many interesting and new results, further investigations are necessary to have a complete understanding of the EDM plasma and process. For example, we have only studied discharges used for standard erosion in die-sinking machines. Plasma created during wire-cutting operations could have diﬀerent properties, since very high currents and short on-times are used (up to 1 kA during 2 µs typically). Discharges with low current (< 6 A) have neither been studied, because the plasma intensity with such currents is too weak for our optical diagnostics. These discharges are used for polishing operations, where the workpiece is not signiﬁcantly eroded but just superﬁcially melted. Furthermore, besides density and temperature measurements, optical emission spectroscopy gives mainly only qualitative results. Quantitative estimations of the plasma contamination and of the workpiece vaporization would be useful for example, but can unfortunately not be obtained with this diagnostic. The eﬀective temperature at the workpiece surface is also another important parameter which can not be measured with emission spectroscopy. It should be noted that the other diagnostics which can still be applied to the EDM plasma are few. With miniaturized optical ﬁbres, active spectroscopic methods with lasers could be possibly developed. Measurement of the electron density could thus be

104

CHAPTER 8. CONCLUSIONS

performed with interferometry, and information about bubbles and eroded particles could be obtained with light scattering and absorption measurements. Acoustic diagnostics could also be developed for the study of the formation, expansion and collapse of the plasma and of bubbles [161]. The implementation of spectroscopic diagnostics on industrial machines could be conceivable in the long term. Such diagnostics could be used to control the dielectric cleanliness or to detect transitions into arcs, for example. This ﬁrst investigation of the EDM plasma has emphasized its complexity and has also opened new questions. It will be important in the future to correlate the properties of the plasma with the performances and relevant characteristics of the EDM process, in order to deﬁne the “perfect plasma” for EDM. To have a complete comprehension of the mechanisms of erosion and wear for example, we should understand precisely how the energy is distributed between the plasma, the electrode and the workpiece, and how it is transferred to them during the discharge. Until now, we can only compare with similar situations, such as cathode spots in high-pressure arcs, for example. But we do not have direct measurements of the heating and transfer mechanisms from the plasma to the electrodes. A deep understanding of this could also explain in detail the origin of the asymmetry between wear and erosion, which is a characteristic and crucial feature of the EDM process. Moreover, with a better comprehension and control of the breakdown phenomenon, more reproducible discharges could be obtained, which is also important from the industrial point of view. In conclusion, this work has given a ﬁrst insight into fundamental aspects of the EDM plasma. In our opinion, we are convinced that such a study is necessary for further improvements of the process, and that other investigations should be carried on. Like any other fundamental study, it is clear that this work cannot answer now all the questions related to the EDM process, and that no immediate industrial improvements and direct applications can be obtained from it. Nevertheless, some of the results presented here have already been implemented in a simulation program developed by Charmilles Technologies, which calculates and optimizes the heat exchange during the discharge. This demonstrates that this work is a ﬁrst promising step towards a better understanding of the EDM process, and possibly towards future developments of this technique.

Appendix A Stark broadening and shift of hydrogen spectral lines
The Stark eﬀect is the modiﬁcation of the energy levels of an atom, a molecule or an ion, due to the presence of an external electric ﬁeld. The Zeeman eﬀect is the equivalent of the Stark eﬀect, but for the magnetic ﬁeld. The Stark broadening is the broadening of spectral lines, caused by the modiﬁcation of the emitter energy levels by the Stark eﬀect. In this case, the external electric ﬁeld is a local micro-ﬁeld created by charged particles (ions or electrons) colliding with the emitter. Though the Stark broadening aﬀects every atom, we will present here some results for the hydrogen atom only. Since we use the Stark broadening of the Hα line for the electron density determination, we will focus especially on the levels n = 2 and n = 3.

A.1

The Stark eﬀect on hydrogen levels

The Hamiltonian H describing the electron of the hydrogen atom exposed to an electric ﬁeld is composed of : • the unperturbed Hamiltonian H0 = e2 p2 − , 2me 4πε0 R

where p = −i is the impulsion operator, R the position operator, me and e the mass and the charge of the electron. Note that if we take into account the spin-orbit interaction and relativistic eﬀects, the Hamiltonian becomes H0 = e2 p2 e2 1 − + L · S + relativistic terms , 2me 4πε0 R 2m2 c2 4πε0 R3 e

where L is the angular momentum operator and S the spin operator [162]. This Hamiltonian describes the ﬁne structure of the hydrogen atom.

105

106

APPENDIX A. STARK BROADENING AND SHIFT OF HYDROGEN LINES

• the Stark perturbing term WS due to the electric ﬁeld F WS = − e F · R . Thus we have : e2 p2 − H = H 0 + WS = − eF · R . 2me 4πε0 R (A.1)

Treating WS with the perturbation theory, we found that, to ﬁrst order, the unperturbed (1) energy level En is split into (2n − 1) new levels En given by
(1) En = En + n (n2 − n1 ) · ∆ ,

(A.2)

with 0 ≤ n1 , n2 < n [163]. For example, the level n = 3 will be split into 5 levels : E3 , E3 ± 3∆ and E3 ± 6∆. The diﬀerence in energy between the new levels are multiples of ∆, given by 6π 2 ε0 ∆= ·F . me e (A.3)

We see that ∆ is linear with F . The eﬀect of the electric ﬁeld on the levels given by (A.2) is thus called the linear Stark eﬀect. Taking the ﬁne structure into account, the equation (A.2) has to be modiﬁed as follows:
(1) En = En + n (n2 − n1 )∆ + k ml ms ,

(A.4)

where ml is the magnetic quantum number, ms the spin quantum number and k a constant (for example k = 3 · 10−5 eV for E2 ; 8.9·10−6 eV for E3 − 3∆ ; 1.7·10−6 eV for E3 and E3 + 3∆). The calculation of the energy levels (without the ﬁne structure) at the second order of the perturbation theory modiﬁes equation (A.2) by adding a term quadratic in F . We obtain 3a0 e a3 · F − n4 17n2 − 3(n2 − n1 )2 − 9m2 + 19 0 · F 2 , l 2 16

(2) En = En + n (n2 − n1 ) En
(1)

where a0 is the Bohr radius [163]. The energy shift given by this quadratic term is called the quadratic Stark eﬀect. The linear Stark eﬀect is almost only signiﬁcant for the hydrogen atom and hydrogenlike ions, and with a strong electric ﬁeld (the ﬁeld is called weak when the Stark splitting is small compared with the ﬁne structure splitting, and strong otherwise). The quadratic

A.2. CONSEQUENCES OF THE STARK EFFECT ON Hα EMISSION

107

eﬀect is almost negligible for hydrogen. Other elements are sensitive to the quadratic eﬀect, but the eﬀect is small especially for heavy elements. The hydrogen lines are thus the most broadened ones in a multi-element spectrum.

A.2

Consequences of the Stark eﬀect on Hα emission

As previously mentioned, the Hα line is emitted by the transition from the level n = 3 to n = 2. Figure A.1 shows the splitting of these two levels by the Stark eﬀect, according to equation (A.2).
without electric field with electric field
E3 + 6D E3 + 3D n=3 E3 E3 E3 - 3D E3 - 6D Ha n=3

E2 + 2D n=2 E2 E2 E2 - 2D n=2

Ha emission

D/h

n
-8 p -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 s p s p s 8 p

n

Figure A.1: Splitting of the levels n = 2 and n = 3 of the hydrogen atom due to the Stark eﬀect, and its consequences on Hα emission.

Due to the levels splitting, the possible transitions are multiplied. The Hα emission is not a single line anymore, but it is composed of several lines. Figure A.1 shows also the frequencies emitted by these new transitions (the zero frequency reference is the transition from E3 to E2 ). The letters π and σ denote the polarization of the emitted light. The polarization π corresponds to a transition with ∆ml = 0, with the electric vector parallel to the electric ﬁeld; the polarization σ corresponds to a transition with ∆ml = ±1, with the electric vector perpendicular to the electric ﬁeld [163]. The frequency range covered by the Hα emission is thus larger with an electric ﬁeld than without it. This results in the broadening of the Hα emission: this is the origin of the

108

APPENDIX A. STARK BROADENING AND SHIFT OF HYDROGEN LINES

Stark broadening. If the plasma density increases, the electric ﬁeld seen by the emitter will also increase, because the charged perturbing particles will be closer. As a result, ∆ will be larger according to equation (A.3). So we qualitatively see that the Hα frequency range, i.e. the Stark broadening of Hα , increases with density. Taking into account the ﬁne structure of the hydrogen atom, the Hα emission is composed of several lines even without electric ﬁeld, because a splitting of the levels already exist with F = 0. But the number of lines is also increased by the Stark eﬀect, as shown in ﬁgure A.2 according to equation (A.4).
no field (fine structure) weak field strong field
E3 + 6D D5/2 n=3 P3/2 , D3/2 S1/2 , P1/2 E3 - 3D E3 - 6D E3 + 3D E3

E2 + 2D n=2 P3/2 S1/2 , P1/2 E2 E2 - 2D

Ha lines (strong field)

n
-8 p -6 -5 -4 -3 -2 -1 0 s p s 1 2 3 p 4 5 s 6 8 p

Figure A.2: Fine structure of the levels n = 2 and n = 3 of the hydrogen atom, splitting due to the Stark eﬀect in weak and strong ﬁeld, and Hα emission in strong ﬁeld.

In addition to the broadening, the Hα emission is also shifted to higher wavelengths. Equation (A.4) shows that the center of gravity of the Hα emission (E3 − E2 ) is shifted from its position without ﬁeld, due to the last term. However, this is not suﬃcient to explain the measured shifts of hydrogen lines. While we can give a simple explanation for the Stark broadening, the origin of the Stark shift of spectral lines is much more complicated. It involves several eﬀects such as the quadratic Stark eﬀect, interaction with ﬁeld gradient and emitters-electrons collisions, whereas Stark broadening involves mainly emitter−ion collisions [107].

A.2. CONSEQUENCES OF THE STARK EFFECT ON Hα EMISSION

109

Although the origin of line shape modiﬁcation by Stark eﬀect can be simply understood as presented here, the precise calculations of line broadening and shift require sophisticated models [112–117].

110

APPENDIX A. STARK BROADENING AND SHIFT OF HYDROGEN LINES

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Acknowledgments
This last chapter is undoubtedly the most pleasant one to write. It would have been impossible to complete this thesis without the help of many people. Since they all understand my mother tongue, I wish to warmly thank them en français dans le texte. Mes remerciements vont naturellement tout d’abord au Dr Christoph Hollenstein, directeur du groupe des plasmas industriels du CRPP et directeur de ma thèse, sans qui rien n’aurait été possible et grâce à qui j’ai beaucoup appris. Travailler sous sa supervision, et ainsi pouvoir proﬁter de sa grande expérience et de son sens aigu de la physique, a été un réel plaisir pendant ces cinq ans. Ses qualités scientiﬁques mais aussi humaines ont largement contribué au succès de mon travail de thèse. Merci énormément, Christoph ! Je remercie très sincèrement les personnes de Charmilles Technologies qui ont collaboré à ce projet, spécialement le Dr Georg Wälder qui m’a suivi pendant tout ce travail et qui m’a fait le plaisir d’être membre de mon jury. Un grand merci également à René Demellayer et au Dr Roberto Perez, pour avoir partagé leur grande connaissance de l’électro-érosion et pour leurs précieux conseils. Merci à vous tous pour votre soutien technique et scientiﬁque, ainsi que pour votre enthousiasme face à mon travail. Je tiens aussi à remercier les Drs Ivano Beltrami et Cédric Joseph ainsi que Marco Boccadoro de Agie, pour les discussions fructueuses que j’ai eues avec eux et leur intérêt pour mon projet. Je remercie sincèrement MM. les professeurs Michel Rappaz et Jörg Winter qui ont accepté de faire partie de mon jury de thèse, ainsi que M. le professeur Robert Schaller qui l’a présidé. Si le directeur d’un groupe de recherches est essentiel, ses autres membres ne le sont pas moins. Un très très très grand MERCI au Dr Jean-Luc Dorier, qui a toujours su écouter et trouver des réponses à mes questions tant scientiﬁques que techniques. Merci Jean-Luc de m’avoir fait proﬁter de tes impressionnantes connaissances, et merci de ne jamais être à court de gentillesse et de bonne humeur ! Je remercie également les Drs Alan Howling et Laurent Sansonnens pour leur disponibilité et leurs conseils toujours pertinents. Je suis particulièrement reconnaissant envers Alan qui a relu et corrigé ce manuscrit, et qui a ainsi rendu le texte un peu plus oxfordien. Un grand merci aux doctorants du groupe, Samantha Pavon, Lukas Derendinger, Hannes Schmidt et Benjamin Strahm, mais aussi à il Dottore Raﬀaello Sobbia, pour avoir contribué à l’excellente ambiance de travail. Evidemment, un merci tout particulier à

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Alban Sublet, ambassadeur de Haute-Savoie en Suisse, qui est devenu au ﬁl de ces années bien plus qu’un simple collègue de travail. Merci Alban, collègue physicien, joggeur, fondeur, skieur, vététiste, randonneur, cinéaste, cinéphile, photographe, mélomane, et j’en oublie. T’es un jeune qui n’en veut, moi je dis chapeau. Je tiens également à remercier les anciens doctorants du groupe, tout spécialement les Drs Thierry Delachaux et Malko Gindrat. Merci les gars pour les très nombreux moments de rire passés ensemble, sans vous ce n’est plus pareil... Merci Thierry pour les kilomètres courus en ta compagnie, en particulier ces 26.2 miles de souﬀrance entre Hopkinton et Boston un jour trop chaud d’avril. Et merci Malko, mon voisin de bureau pendant plusieurs années, de m’avoir transmis un peu de ta connaissance inépuisable de l’informatique. Mes remerciements vont bien sûr également aux diﬀérents services techniques du CRPP. Merci aux mécaniciens, électriciens, électroniciens, au service du vide et au service informatique, pour les “p’tits boulots” occasionnels sans lesquels on n’avance pas au labo. Un très grand merci au secrétariat pour toutes les tâches administratives, avec mention spéciale pour Edith Grüter. Merci de tout mon coeur Edith, pour tout et surtout pour tout le reste ! Je tiens aussi à saluer Alexandre Blais, de l’université d’Ottawa certes, mais Québécois avant tout. Merci Alex de ton passage en Suisse, et merci mille fois de m’avoir fait découvrir les richesses de ta belle province. J’ai eu bin d’s’fonne avec toé, mon go ! Enﬁn, je remercie inﬁniment tous les membres de ma famille, les personnes les plus importantes de ma vie, pour leur soutien tout au long de ces années. Merci à la nouvelle génération, Arthur, Gaspard, Anna, Elise et Camille, pour tout le bonheur que vous me transmettez. Merci à mes indispensables soeurs, Véronique, Noémie et Sarah, mais comment diable vivrais-je sans vous ?!? Merci à vous d’avoir choisi Françoise, Antoine et Stephan, je n’aurais pu faire meilleurs choix... Et un merci incommensurable à Maman et à Papa, pour m’avoir soutenu de toutes les manières possibles et m’avoir donné la chance de toujours pouvoir choisir et réaliser ce que j’ai eu envie de faire. Vous m’avez en plus donné l’amour de la Science, merci de m’avoir fait ce si beau cadeau...

Antoine

Curriculum Vitae
Antoine DESCOEUDRES Né le 2 février 1978 à Lausanne (VD), de nationalité suisse et originaire de La Sagne (NE).

FORMATION 2002 - 2006 Thèse de doctorat eﬀectuée dans le groupe des plasmas industriels, Centre de Recherches en Physique des Plasmas (CRPP), Ecole Polytechnique Fédérale de Lausanne (EPFL). Assistant pour divers cours de Physique générale. Diplôme d’ingénieur physicien, EPFL Travail de diplôme eﬀectué au CRPP. Baccalauréat ès lettres (mention latin-mathématiques) et Certiﬁcat de maturité - type A (latin-grec) Gymnase cantonal du Bugnon, Lausanne.

1996 - 2001

1993 - 1996

PUBLICATIONS A. Descoeudres, L. Sansonnens and C. Hollenstein, “Attachment-induced ionization instability in electronegative capacitive RF discharges”, Plasma Sources Sci. Technol., 12(2), 152-157 (2003). A. Descoeudres, C. Hollenstein, R. Demellayer and G. Wälder, “Optical emission spectroscopy of electrical discharge machining plasma”, J. Phys. D: Appl. Phys., 37(6), 875-882 (2004). A. Descoeudres, C. Hollenstein, R. Demellayer and G. Wälder, “Optical emission spectroscopy of electrical discharge machining plasma”, 14th International Symposium for Electromachining (ISEM XIV), April 2004, Edinburgh, Scotland. J. Mater. Process. Technol., 149, 184-190 (2004). A. Descoeudres, C. Hollenstein, G. Wälder and R. Perez, “Time-resolved imaging and spatially-resolved spectroscopy of electrical discharge machining plasma”, J. Phys. D: Appl. Phys., 38(22), 4066-4073 (2005).

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