This text is an introduction to the physics of collisional plasmas, as opposed to plasmas in space. It is intended for graduate students in physics and engineering . The first chapter introduces with progressively increasing detail, the fundamental concepts of plasma physic. The motion of individual charged particles in various configurations of electric and magnetic fields is detailed in the second chapter while the third chapter considers the collective motion of the plasma particles described according to a hydrodynamic model. The fourth chapter is most original in that it introduces a general approach to energy balance, valid for all types of discharges comprising direct current(DC) and high frequency (HF) discharges, including an applied static magnetic field. The basic concepts required in this fourth chapter have been progressively introduced in the previous chapters. The text is enriched with approx. 100 figures, and alphabetical index and 45 fully resolved problems. Mathematical and physical appendices provide complementary information or allow to go deeper in a given subject.

scihub/10.1007/978-94-007-4558-2.pdf

zlib/no-category/Michel Moisan ; Jacques Pelletier/Physics of Collisional Plasmas: Introduction to High-Frequency Discharges_25656052.pdf

Springer Science + Business Media BV

Springer Nature (Textbooks & Major Reference Works), Dordrecht, 2012

Grenoble sciences, Dordrecht ; New York, ©2012

Netherlands, Netherlands

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Physics of Collisional Plasmas 4
Preface 6
Acknowledgements 9
Contents 10
Symbols 16
Acronyms 20
Physical constants 21
1 The Plasma State: Definition and Orders of Magnitude of Principal Quantities 22
1.1 Definition and essential nature of plasma 22
1.1.1 A plasma behaves as a collective medium 22
1.1.2 A plasma is a macroscopically neutral medium 23
1.1.3 First examples of plasmas 24
1.2 Areas of research and applications (examples) 26
1.2.1 Controlled thermonuclear fusion 26
1.2.2 Astrophysics and environmental physics 28
1.2.3 Laser pumping 29
1.2.4 Plasma chemistry 30
1.2.5 Surface treatment 31
1.2.6 Sterilisation of medical devices 32
1.2.7 Elemental analysis (analytical chemistry) 33
1.2.8 Lighting 34
1.2.9 Plasma display panels 34
1.2.10 Ion sources 35
1.2.11 Ion propulsion thrusters 35
1.2.12 Further applications 36
1.3 Different types of laboratory plasmas 36
1.3.1 Discharges with continuous current or alternative current at low frequency 36
1.3.2 High frequency (HF) discharges 37
1.3.3 Laser induced discharges 37
1.4 Electron density and temperature of a plasma 38
1.4.1 Range of electron density values in a plasma 38
1.4.2 Definition of plasma ``temperature'' and the concept of thermodynamic equilibrium (TE) 38
1.4.3 Different levels of departure from complete thermodynamic equilibrium 42
1.5 Natural oscillation frequency of electrons in a plasma 44
1.5.1 Origin and description of the phenomenon 44
1.5.2 Calculation of the electron plasma frequency 45
1.6 Debye length: effect of screening in the plasma 48
1.6.1 Description of the phenomenon 48
1.6.2 Calculation of the potential exerted by an ion in a two-temperature plasma: definition of the Debye length 49
1.7 Collision phenomena in plasmas 53
1.7.1 Types of collision 54
1.7.2 Momentum exchange and energy transfer during a collision between two particles 57
1.7.3 Microscopic differential cross-section 65
1.7.4 Total (integrated) microscopic cross-section 69
1.7.5 Total macroscopic cross-section 70
1.7.6 Expression for the temperature of a plasma in electron-volt 74
1.7.7 Collision frequency and mean free path between two collisions 75
1.7.8 Average collision frequency and mean free path 77
1.7.9 Examples of collision cross-sections 79
1.8 Mechanisms for creation and loss of charged particles in a plasma and their conservation equation 85
1.8.1 Loss mechanisms 85
1.8.2 Creation mechanisms 87
1.8.3 Conservation equation for charged particles 88
Problems 89
2 Individual Motion of a Charged Particle in Electric and Magnetic Fields 122
2.1 The general equation of motion of a charged particle in E and B fields and properties of that equation 124
2.1.1 The equation of motion 124
2.1.2 The kinetic energy equation 125
2.2 Analysis of particular cases of E and B 125
2.2.1 Electric field only (B =0) 126
2.2.2 Uniform static magnetic field 134
2.2.3 Magnetic field either (slightly) non uniform or (slightly) varying in time 156
Problems 176
3 Hydrodynamic Description of a Plasma 224
3.1 Fundamental aspects of the Boltzmann equation 226
3.1.1 Formal derivation of the Boltzmann equation 226
3.1.2 Approximation to the Boltzmann elastic collision term: relaxation of the distribution function towards an isotropic state 229
3.1.3 Two classical methods to find an analytic solution to the Boltzmann equation 231
3.2 Velocity distribution functions and the notion of correlation between particles 232
3.2.1 Probability density of finding a particle in phase space 232
3.2.2 Single-point distribution function (the case of correlated particles) 233
3.2.3 Single-point distribution function (uncorrelated particles) 234
3.2.4 Two-point distribution function (correlated particles) 234
3.2.5 Two-point distribution function (uncorrelated particles) 235
3.2.6 N-point distribution functions 236
3.3 Distribution functions and hydrodynamic quantities 236
3.4 Kinetic and hydrodynamic conductivities of electrons in a plasma in the presence of a HF electromagnetic field 239
3.4.1 Kinetic form of the electrical conductivity due to electrons in an HF field 240
3.4.2 Hydrodynamic form of the electrical conductivity due to electrons in an HF field 242
3.5 Transport equations 245
3.5.1 The continuity equation (1st hydrodynamic moment, of zero order in w) 247
3.5.2 The momentum transport equation (2nd hydrodynamic moment, 1st order in w) 248
3.5.3 Moment equations of second order in w 255
3.5.4 Higher order moment equations 260
3.6 Closure of the transport equations 261
3.7 The Lorentz electron plasma model 264
3.8 Diffusion and mobility of charged particles 266
3.8.1 The concepts of diffusion and mobility 266
3.8.2 Solution of the Langevin equation with zero total derivative 267
3.9 Normal modes of diffusion and spatial density distribution of charged particles 274
3.9.1 Concept of normal modes of diffusion: study of a time varying post-discharge 276
3.9.2 Spatial distribution of charged particle density in the stationary diffusion regime 280
3.10 The ambipolar diffusion regime 282
3.10.1 Assumptions required for a completely analytic description of the ambipolar diffusion regime 283
3.10.2 Equations governing the ambipolar diffusion regime and the transition from the free diffusion to the ambipolar regime 284
3.10.3 The value of the space-charge electric field intensity 286
3.10.4 The expression for the charge density 0 on the axis: limits to the validity of the analytic calculation 288
3.10.5 Necessary conditions for a discharge to be in the ambipolar regime 289
3.11 Ambipolar diffusion in a static magnetic field 292
3.12 Diffusion regime or free fall regime 295
3.13 Electron temperature of a long plasma column governed by ambipolar diffusion: scaling law Te(pR) 296
3.13.1 Assumptions of the model 297
3.13.2 Derivation of the relation Te(p0R) 297
3.14 Formation and nature of sheaths at the plasma-wall interface: particle flux to the walls and the Bohm criterion 303
3.14.1 Positive wall-potential with respect to the plasma potential: electron sheath 304
3.14.2 Negative wall-potential with respect to the plasma potential: ion sheath 305
3.14.3 Floating potential 309
Problems 309
4 Introduction to the Physics of HF Discharges 357
4.1 Preamble 357
4.2 Power transfer from the electric field to the discharge 359
4.2.1 Direct current discharges 359
4.2.2 HF discharges 363
4.2.3 HF discharges in the presence of a static magnetic field 365
4.2.4 Variation of the value of as a function of e for different plasma conditions 372
4.3 Influence of the frequency of the HF field on some plasma properties and on particular processes 374
4.3.1 Posing of the problem 375
4.3.2 The EEDF in the non-stationary regime 376
4.3.3 EEDF in the stationary regime 378
4.3.4 Three limit cases of the influence of on a stationary EEDF 380
4.3.5 Influence of on the power 382
4.3.6 Density of species produced per second for a constant absorbed power density: energy efficency of the discharge 383
4.3.7 Experimental and modelling results 384
4.3.8 Summary of the properties of low-pressure HF plasmas 388
4.4 High-pressure HF sustained plasmas 389
4.4.1 Experimental observation of contraction and filamentation at atmospheric pressure 390
4.4.2 Modelling contraction at atmospheric pressure 396
4.4.3 Validation of the basic assumptions of contraction at atmospheric pressure, using a self-consistent model 399
4.4.4 Kinetics of expanded discharges at atmospheric pressure as a result of adding traces of rare gases with a lower ionisation potential 402
4.4.5 Summary of the properties of high-pressure HF plasmas 405
I Properties of the Maxwell-Boltzman Velocity Distribution 406
II The Complete Saha Equation 411
III Partial Local Thermodynamic Equilibrium 413
IV Representation of Binary Collisions in the Centre of Mass and Laboratory Frames 415
V Limiting the Range of the Coulomb Collisional Interactions: the Coulomb Logarithm 417
VI Stepwise Ionisation 430
VII Basic Notions of Tensors 434
VIII Operations on Tensors 438
IX Orientation of w 2 in the Reference Triad with Cartesian Axes (E 0B, E 0, B) 445
X Force Acting on a Charged Particle in the Direction of a Magnetic Field B Weakly Non-uniform Axially 446
XI The Magnetic Moment 447
XII Drift Velocity wd of a Charged Particle Subjected to an Arbitrary Force Fd in a Field B: the Magnetic Field Drift 449
XIII Magnetic-Field Drift Velocity wdm in the Frenet Frame Associated with the Lines of Force of a Magnetic Field with Weak Curvature 451
XIV Spherical Harmonics 455
XV Expressions for the Terms M and R in the Kinetic Pressure Transport Equation 457
XVI Closure of the Hydrodynamic Transport Equation for Kinetic Pressure in the Case of Adiabatic Compression 459
XVII Complementary Calculations to the Expression for Te(pR) (Sect. 3.13) 460
XVIII Propagation of an Electromagnetic Plane Wave in a Plasma and the Skin Depth 463
XIX Surface-Wave Plasmas (SWP) 467
XX Useful Integrals and Expressions for the Differential Operators in Various Coordinate Systems 471
References 477
Recommended Reading 479
Index 482

2014-05-18