A Plasma Formulary for Physics, Technology, and Astrophysics / Edition 1

A Plasma Formulary for Physics, Technology, and Astrophysics / Edition 1

ISBN-10:
3527402942
ISBN-13:
9783527402946
Pub. Date:
01/28/2002
Publisher:
Wiley, John & Sons, Incorporated

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Overview

A Plasma Formulary for Physics, Technology, and Astrophysics / Edition 1

Plasma physics has matured rapidly as a discipline, and now touches on many different research areas, including manufacturing processes. This collection of fundamental formulae and definitions in plasma physics is vital to anyone with an interest in plasmas or ionized gases, whether in physics, astronomy or engineering.
Both theorists and experimentalists will find this book useful, as it incorporates the latest results and findings.
The text treats astrophysical plasmas, fusion plasmas, industrial plasmas and low temperature plasmas as aspects of the same discipline - a unique approach made possible by the abbreviated nature of a formulary.

Product Details

ISBN-13: 9783527402946
Publisher: Wiley, John & Sons, Incorporated
Publication date: 01/28/2002
Edition description: FIRST
Pages: 220
Product dimensions: 6.96(w) x 9.52(h) x 0.63(d)

Table of Contents

Prefacexv
1Basic Physical Data1
1.1Basic Physical Units2
1.1.1SI Units2
1.1.2cgs-Gaussian Units3
1.2Maxwell's Electromagnetic Equations3
1.3Special Relativity4
1.4Physical Constants5
1.5Dimensional Analysis7
1.6Ionization Energies of Gas-Phase Molecules9
1.7Characteristic Parameters for Typical Plasmas10
2Basic Plasma Parameters13
2.1Notation14
2.2Natural Timescales15
2.2.1Characteristic Frequencies15
2.2.2Characteristic Times16
2.3Natural Scalelengths17
2.3.1Debye Length17
2.3.2Mean Free Path17
2.3.3Plasma Skin Depth17
2.3.4Larmor Radius17
2.4Natural Speeds18
2.4.1Alfven Speed18
2.4.2Sound Speed18
2.5Miscellaneous Parameters19
2.5.1Collision Cross-Section19
2.5.2Differential Scattering Cross-Section19
2.5.3Magnetic Moment19
2.5.4Mobility19
2.6Non-Dimensional Parameters20
2.6.1Dielectric Constant20
2.6.2Hartmann Number21
2.6.3Knudsen Number21
2.6.4Lundquist Number21
2.6.5Mach Number21
2.6.6Magnetic Reynolds Number21
2.6.7Plasma Beta22
3Discharge Plasmas and Elementary Processes23
3.1Notation24
3.2Plasma Sheath25
3.2.1Planar Sheath Equation25
3.2.2Child-Langmuir Law26
3.2.3Collisional Sheaths27
3.3Double-Layer28
3.4Diffusion Parameters29
3.4.1Free Diffusion29
3.4.2Mobility30
3.4.3Ambipolar Diffusion30
3.4.4Ambipolar Diffusion in a Magnetic Field32
3.5Ionization32
3.5.1Townsend Breakdown32
3.5.2Alfven Ionization37
3.5.3Secondary Electron Emission37
3.5.4Townsend Breakdown Criterion39
3.5.5Paschen Curve39
3.6Ionization Equilibrium40
3.6.1Local Thermodynamic Equilibrium40
3.6.2Saha Equation41
4Radiation43
4.1Notation44
4.2Radiation from a Moving Point Charge45
4.2.1Lienard-Wiechert Potentials45
4.2.2Electric and Magnetic Fields of a Moving Charge45
4.2.3Power Radiated by an Accelerating Point Charge46
4.2.4Frequency Spectrum of Radiation from an Accelerating Charge50
4.3Cyclotron and Synchrotron Radiation50
4.3.1Spectral Power Density51
4.3.2Power in Each Harmonic52
4.3.3Total Radiated Power53
4.3.4[beta subscript v] [double less-than sign] 1: Cyclotron Emission53
4.3.5[beta subscript v] [similar] 1: Synchrotron Emission53
4.4Bremsstrahlung54
4.5Radiation Scattering55
4.5.1Thomson Scattering56
4.5.2Incoherent Thomson Scattering from an Unmagnetized Plasma58
4.5.3Coherent Thomson Scattering from an Unmagnetized Plasma60
4.5.4Compton Scattering61
4.5.5Klein-Nishina Cross-Section61
5Kinetic Theory63
5.1Notation64
5.2Fundamentals64
5.3Boltzmann Equation65
5.4Maxwellian Distribution65
5.5Vlasov Description67
5.5.1Equilibrium Solutions67
5.6Collisional Modelling68
5.6.1Boltzmann Collision Term68
5.6.2Simplified Boltzmann Collision Term69
5.6.3Fokker-Planck69
5.6.4Fokker-Planck Potentials70
5.7Driven Systems71
5.7.1Generalized Distribution71
6Plasma Transport75
6.1Notation76
6.2Basic Definitions76
6.3Binary Collisions77
6.3.1Elastic Collisions Between Charged Particles77
6.4Particle Dynamics80
6.4.1Drifts81
6.4.2Adiabatic Invariants83
6.4.3Magnetic Mirror84
6.5Transport Coefficients85
6.5.1Fully Ionised Plasma, Zero Magnetic Field, Krook Operator85
6.5.2Lorentzian and Spitzer Conductivity85
6.5.3Fully Ionized and Magnetized Plasma: Braginskii Coefficients86
6.5.4Corrections to Braginskii Coefficients90
6.5.5Equal Mass Plasma Transport91
7Plasma Waves93
7.1Notation94
7.2Waves in Cold Plasmas95
7.2.1Model Equations95
7.2.2Cold Plasma Variable Dependencies96
7.2.3Dielectric Tensor for a Cold Magnetised Plasma96
7.2.4General Dispersion Relation97
7.2.5Equal-Mass Cold Plasmas103
7.3Fluid Plasmas103
7.3.1Hydromagnetic Equations104
7.3.2Single Fluid MHD Plasma105
7.3.3Variable Dependencies in Ideal MHD106
7.3.4General Dispersion Relation: Ideal MHD107
7.4Waves in Hot Plasmas109
7.4.1Dielectric Function for an Unmagnetized Plasma109
7.4.2Langmuir Waves109
7.4.3Ion-Acoustic Waves110
7.4.4Dielectric Tensor for a Hot Plasma111
8Flows117
8.1Notation118
8.2Fundamental Results118
8.2.1Alfven's Theorem118
8.2.2Cowling's Anti-Dynamo Theorem119
8.2.3Ferraro's Law of Isorotation119
8.2.4Kelvin's Vorticity Theorem119
8.3Hydromagnetic Flows120
8.3.1Hartmann Flow121
8.3.2Couette Flow123
8.3.3Field-Aligned Flows123
8.4Solar Wind125
8.5Neutral Gas/Magnetized Plasma Flows127
8.6Beams128
8.6.1Beam Parameters128
8.6.2Special Cases131
8.7Hydromagnetic Shocks134
8.7.1Further Notation135
8.7.2Shock Classification136
8.7.3Shock Propagation Parallel to B[subscript 1]137
8.7.4Shock Propagation Perpendicular to B[subscript 1]139
8.7.5General Case: Fast Magnetic Shocks140
8.7.6General Case: Slow Magnetic Shocks141
8.7.7Further Reading142
8.8Ion-Acoustic Shock142
9Equilibria and Instabilities145
9.1Notation146
9.2General Considerations147
9.3Fluid Equilibria147
9.3.1Ideal MHD147
9.3.2Cylindrical Equilibria149
9.4Fluid Instabilities152
9.4.1Firehose Instability152
9.4.2Gravitational Instability153
9.4.3Kelvin-Helmholtz Instability155
9.4.4Cylindrical Pinch Instabilities155
9.4.5Generalized Pinch Instabilities157
9.4.6Resistive Drift Wave Instability161
9.4.7MHD Resistive Wall Instability161
9.4.8MHD Resistive Tearing Mode162
9.4.9Streaming Instability163
9.5Kinetic Instabilities164
9.5.1Bump-in-Tail Instability164
9.5.2Electron Runaway165
9.5.3Ion-Acoustic Instability165
10Mathematics167
10.1Vector Algebra168
10.2Vector Calculus168
10.2.1Cartesian Co-ordinates169
10.2.2Cylindrical Co-ordinates170
10.2.3Spherical Co-ordinates172
10.3Integral Theorems174
10.3.1Stokes' Theorems174
10.3.2Gauss' Theorems175
10.3.3Green's Theorems175
10.4Matrices175
10.4.1Matrix Transpose176
10.4.2Complex Conjugate176
10.4.3Symmetric176
10.4.4Orthogonal176
10.4.5Nilpotent176
10.4.6Idempotent176
10.4.7Triangular177
10.4.8Trace177
10.4.9Determinant and Inverse177
10.4.10Partitioned Matrices178
10.4.11Eigenvalues and Eigenvectors178
10.4.12Hermitian Matrix179
10.4.13Unitary Matrix179
10.5Eigenfunctions of the Curl Operator179
10.6Wave Scattering180
10.6.1Simple Constant Barrier180
10.6.2Phase Integral Method182
10.6.3Mode Conversion183
10.7Plasma Dispersion Function185
AppendixA Guide to Notation187
References193
Index199

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