The Physics of Plasmas

by T. J. M. Boyd , J. J. Sanderson

• ISBN13: 9780521459129
• ISBN10: 0521459125
• Format: Paperback
• Copyright: 2003-02-03
• Publisher: Cambridge University Press

Summary

The Physics of Plasmas provides a comprehensive introduction to the subject, illustrating the basic theory with examples drawn from fusion, space and astrophysical plasmas. Various aspects of plasma physics are discussed, beginning with particle orbit theory, and including fluid equations, a variety of magnetohydrodynamic (MHD) models, wave equations and kinetic theory. The relationships between these distinct approaches are discussed. In this way, the reader gains a firm grounding in the fundamentals, leading to an understanding of some of the more specialized topics. Throughout the text, there is an emphasis on the physical interpretation of plasma phenomena; Exercises are included.

Table of Contents

Preface	xi
Introduction	1	(11)
Introduction	1	(1)
Thermonuclear fusion	2	(4)
The Lawson criterion	3	(1)
Plasma containment	4	(2)
Plasmas in space	6	(1)
Plasma characteristics	7	(5)
Collisions and the plasma parameter	10	(2)
Particle orbit theory	12	(36)
Introduction	12	(2)
Constant homogeneous magnetic field	14	(2)
Magnetic moment and plasma diamagnetism	16	(1)
Constant homogeneous electric and magnetic fields	16	(3)
Constant non-electromagnetic forces	18	(1)
Inhomogeneous magnetic field	19	(3)
Gradient drift	19	(2)
Curvature drift	21	(1)
Particle drifts and plasma currents	22	(2)
Time-varying magnetic field and adiabatic invariance	24	(2)
Invariance of the magnetic moment in an inhomogeneous field	25	(1)
Magnetic mirrors	26	(2)
The longitudinal adiabatic invariant	28	(3)
Mirror traps	30	(1)
Magnetic flux as an adiabatic invariant	31	(2)
Particle orbits in tokamaks	33	(2)
Adiabatic invariance and particle acceleration	35	(2)
Polarization drift	37	(1)
Particle motion at relativistic energies	38	(2)
Motion in a monochromatic plane-polarized electromagnetic wave	38	(2)
The ponderomotive force	40	(1)
The guiding centre approximation: a postscript	41	(7)
Exercises	43	(5)
Macroscopic equations	48	(29)
Introduction	48	(1)
Fluid description of a plasma	49	(9)
The MHD equations	58	(3)
Resistive MHD	59	(1)
Ideal MHD	60	(1)
Applicability of the MHD equations	61	(10)
Anisotropic plasmas	67	(2)
Collisionless MHD	69	(2)
Plasma wave equations	71	(3)
Generalized Ohm's law	73	(1)
Boundary conditions	74	(3)
Exercises	76	(1)
Ideal magnetohydrodynamics	77	(63)
Introduction	77	(1)
Conservation relations	78	(4)
Static equilibria	82	(23)
Cylindrical configurations	85	(4)
Toroidal configurations	89	(11)
Numerical solution of the Grad--Shafranov equation	100	(2)
Force-free fields and magnetic helicity	102	(3)
Solar MHD equilibria	105	(3)
Magnetic buoyancy	106	(2)
Stability of ideal MHD equilibria	108	(11)
Stability of a cylindrical plasma column	111	(8)
The energy principle	119	(5)
Finite element analysis of ideal MHD stability	123	(1)
Interchange instabilities	124	(6)
Rayleigh--Taylor instability	124	(4)
Pressure-driven instabilities	128	(2)
Ideal MHD waves	130	(10)
Exercises	133	(7)
Resistive magnetohydrodynamics	140	(57)
Introduction	140	(2)
Magnetic relaxation and reconnection	142	(6)
Driven reconnection	145	(3)
Resistive instabilities	148	(14)
Tearing instability	151	(4)
Driven resistive instabilities	155	(2)
Tokamak instabilities	157	(5)
Magnetic field generation	162	(7)
The kinematic dynamo	163	(6)
The solar wind	169	(10)
Interaction with the geomagnetic field	177	(2)
MHD shocks	179	(18)
Shock equations	182	(4)
Parallel shocks	186	(2)
Perpendicular shocks	188	(1)
Oblique shocks	189	(1)
Shock thickness	190	(3)
Exercises	193	(4)
Waves in unbounded homogeneous plasmas	197	(55)
Introduction	197	(1)
Some basic wave concepts	198	(4)
Energy flux	200	(1)
Dispersive media	200	(2)
Waves in cold plasmas	202	(25)
Field-free plasma (B0 = 0)	209	(1)
Parallel propagation (k || B0)	210	(4)
Perpendicular propagation (k T B0)	214	(3)
Wave normal surfaces	217	(5)
Dispersion relations for oblique propagation	222	(5)
Waves in warm plasmas	227	(11)
Longitudinal waves	228	(2)
General dispersion relation	230	(8)
Instabilities in beam--plasma systems	238	(6)
Two-stream instability	240	(1)
Beam--plasma instability	241	(3)
Absolute and convective instabilities	244	(8)
Absolute and convective instabilities in systems with weakly coupled modes	245	(3)
Exercises	248	(4)
Collisionless kinetic theory	252	(44)
Introduction	252	(2)
Vlasov equation	254	(2)
Landau damping	256	(12)
Experimental verification of Landau damping	263	(2)
Landau damping of ion acoustic waves	265	(3)
Micro-instabilities	268	(8)
Kinetic beam--plasma and bump-on-tail instabilities	273	(1)
Ion acoustic instability in a current-carrying plasma	274	(2)
Amplifying waves	276	(1)
The Bernstein modes	277	(6)
Inhomogeneous plasma	283	(4)
Test particle in a Vlasov plasma	287	(9)
Fluctuations in thermal equilibrium	288	(1)
Exercises	289	(7)
Collisional kinetic theory	296	(28)
Introduction	296	(1)
Simple transport coefficients	297	(7)
Ambipolar diffusion	300	(1)
Diffusion in a magnetic field	301	(3)
Neoclassical transport	304	(3)
Fokker--Planck equation	307	(6)
Collisional parameters	313	(4)
Collisional relaxation	317	(7)
Exercises	321	(3)
Plasma radiation	324	(52)
Introduction	324	(1)
Electrodynamics of radiation fields	325	(5)
Power radiated by an accelerated charge	326	(2)
Frequency spectrum of radiation from an accelerated charge	328	(2)
Radiation transport in a plasma	330	(4)
Plasma bremsstrahlung	334	(10)
Plasma bremsstrahlung spectrum: classical picture	336	(2)
Plasma bremsstrahlung spectrum: quantum mechanical picture	338	(1)
Recombination radiation	339	(2)
Inverse bremsstrahlung: free--free absorption	341	(1)
Plasma corrections to bremsstrahlung	342	(1)
Bremsstrahlung as plasma diagnostic	343	(1)
Electron cyclotron radiation	344	(4)
Plasma cyclotron emissivity	346	(1)
ECE as tokamak diagnostic	347	(1)
Synchrotron radiation	348	(7)
Synchrotron radiation from hot plasmas	348	(3)
Synchrotron emission by ultra-relativistic electrons	351	(4)
Scattering of radiation by plasmas	355	(6)
Incoherent Thomson scattering	355	(3)
Electron temperature measurements from Thomson scattering	358	(2)
Effect of a magnetic field on the spectrum of scattered light	360	(1)
Coherent Thomson scattering	361	(4)
Dressed test particle approach to collective scattering	361	(4)
Coherent Thomson scattering: experimental verification	365	(11)
Deviations from the Salpeter form factor for the ion feature: impurity ions	366	(3)
Deviations from the Salpeter form factor for the ion feature: collisions	369	(1)
Exercises	370	(6)
Non-linear plasma physics	376	(49)
Introduction	376	(1)
Non-linear Landau theory	377	(12)
Quasi-linear theory	377	(5)
Particle trapping	382	(2)
Particle trapping in the beam--plasma instability	384	(4)
Plasma echoes	388	(1)
Wave--wave interactions	389	(8)
Parametric instabilities	392	(5)
Zakharov equations	397	(8)
Modulational instability	402	(3)
Collisionless shocks	405	(20)
Shock classification	408	(3)
Perpendicular, laminar shocks	411	(10)
Particle acceleration at shocks	421	(2)
Exercises	423	(2)
Aspects of inhomogeneous plasmas	425	(39)
Introduction	425	(1)
WKBJ model of inhomogeneous plasma	426	(7)
Behaviour near a cut-off	429	(3)
Plasma reflectometry	432	(1)
Behaviour near a resonance	433	(2)
Linear mode conversion	435	(6)
Radiofrequency heating of tokamak plasma	439	(2)
Stimulated Raman scattering	441	(9)
SRS in homogeneous plasmas	441	(1)
SRS in inhomogeneous plasmas	442	(5)
Numerical solution of the SRS equations	447	(3)
Radiation from Langmuir waves	450	(3)
Effects in bounded plasmas	453	(11)
Plasma sheaths	453	(3)
Langmuir probe characteristics	456	(2)
Exercises	458	(6)
The classical theory of plasmas	464	(43)
Introduction	464	(1)
Dynamics of a many-body system	465	(7)
Cluster expansion	469	(3)
Equilibrium pair correlation function	472	(4)
The Landau equation	476	(4)
Moment equations	480	(7)
One-fluid variables	485	(2)
Classical transport theory	487	(14)
Closure of the moment equations	488	(3)
Derivation of the transport equations	491	(4)
Classical transport coefficients	495	(6)
MHD equations	501	(6)
Resistive MHD	503	(2)
Exercises	505	(2)
Appendix 1 Numerical values of physical constants and plasma parameters	507	(2)
Appendix 2 List of symbols	509	(8)
References	517	(6)
Index	523