Introduction to Plasma Physics Copyright © 1995 IOP Publishing Ltd INTRODUCTION TO PLASMA PHYSICS Robert J Goldston and Paul H Rutherford Plasma Physics Laboratory Princeton University Institute of Physics Publishing Bristol and Philadelphia Copyright © 1995 IOP Publishing Ltd @ IOP Publishing Ltd 1995 All rights reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publisher Multiple copying is permitted in accordance with the terms of licences issued by the Copyright Licensing Agency under the terms of its agreement with the Committee of Vice-Chancellors and Principals British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library ISBN 7503 0325 7503 0183 X hardback paperback Library of Congress Cataloging-in-PublicationData Goldston, R J Introduction to plasma physics / Robert J Goldston and Paul H Rutherford P cm Includes bibliographical references and index ISBN 0-7503-0325-5 (hardcover) ISBN 0-7503-0183-X (pbk.) Plasma (Ionized gases) I Rutherford, P H (Paul Harding), 1938- 11 Title QC718.G63 1995 530.4'4 dc20 95-371 17 CIP Published by Institute of Physics Publishing, wholly owned by The Institute of Physics, London Institute of Physics Publishing, Techno House, Redcliffe Way, Bristol BSI 6NX, UK US Editorial Office: Institute of Physics Publishing, The Public Ledger Building, Suite 1035, 150 South Independence Mall West, Philadelphia, PA 19106, USA 'Qpeset in T S using the IOP Bookmaker Macros UK Publishing by J W Arrowsmith Ltd, Bristol BS3 2NT Printed©in1995 the IOP Copyright Ltd Dedicated to Ruth Berger Goldston and Audrey Rutherford Copyright © 1995 IOP Publishing Ltd Contents Preface Introduction Introduction to plasmas 1.1 What is a plasma? 1.2 How are plasmas made? 1.3 What are plasmas used for? 1.4 Electron current flow in a vacuum tube 1.5 The arc discharge 1.6 Thermal distribution of velicities in a plasma 1.7 Debye shielding 1.8 Material probes in a plasma UNIT SINGLE-PARTICLE MOTION 2 13 16 19 Particle drifts in uniform fields 2.1 Gyro-motion 2.2 Uniform E field and uniform B field: E x B drift 2.3 Gravitational drift 21 21 24 21 Particle drifts in non-uniform magnetic fields 3.1 VB drift 3.2 Curvature drift 3.3 Static B field; conservation of magnetic moment at zeroth order 3.4 Magnetic mirrors 3.5 Energy and magnetic-moment conservation to first order for static fields* 3.6 Derivation of drifts: general case* 29 29 33 36 Copyright © 1995 IOP Publishing Ltd 39 41 45 vii VI11 Contents Particle drifts in time-dependent fields 4.1 Time-varying B field 4.2 Adiabatic compression 4.3 Time-varying E field 4.4 Adiabatic invariants 4.5 Second adiabatic invariant: J conservation 4.6 Proof of J conservation in time-independent fields* 49 Mappings 5.1 Non-conservation of J : a simple mapping 5.2 Experimenting with mappings 5.3 Scaling in maps 5.4 Hamiltonian maps and area preservation 5.5 Particle trajectories 5.6 Resonances and islands 5.7 Onset of stochasticity 69 69 70 72 73 76 78 79 UNIT PLASMAS AS FLUIDS Fluid equations for a plasma 6.1 Continuity equation 6.2 Momentum balance equation 6.3 Equations of state 6.4 Two-fluid equations 6.5 Plasma resistivity 49 51 52 57 58 61 83 85 85 86 91 93 94 Relation between fluid equations and guiding-center drifts 7.1 Diamagnetic drift 7.2 Fluid drifts and guiding-center drifts 7.3 Anisotropic-pressure case 7.4 Diamagnetic drift in non-uniform B fields* 7.5 Polarization current in the fluid model 7.6 Parallel pressure balance 97 97 101 103 105 110 111 Single-fluid magnetohydrodynamics 8.1 The magnetohydrodynamic equations 8.2 The quasi-neutrality approximation 8.3 The ‘small Larmor radius’ approximation 8.4 The approximation of-‘infinite conductivity’ 8.5 Conservation of magnetic flux 8.6 Conservation of energy 8.7 Magnetic Reynolds number 115 Copyright © 1995 IOP Publishing Ltd 115 118 120 121 124 125 127 Contents Magnetohydrodynamic equilibrium 9.1 Magnetohydrodynamic equilibrium equations 9.2 Magnetic pressure: the concept of beta 9.3 The cylindrical pinch 9.4 Force-free equilibria: the ‘cylindrical’ tokamak 9.5 Anisotropic pressure: mirror equilibria* 9.6 Resistive dissipation in plasma equilibria UNIT COLLISIONAL PROCESSES IN PLASMAS ix 129 129 131 132 134 136 139 145 147 10 Fully and partially ionized plasmas 147 10.1 Degree of ionization of a plasma 10.2 Collision cross sections, mean-free paths and collision 149 frequencies 151 10.3 Degree of ionization: coronal equilibrium 155 10.4 Penetration of neutrals into plasmas 158 10.5 Penetration of neutrals into plasmas: quantitative treatment* 161 10.6 Radiation 10.7 Collisions with neutrals and with charged particles: relative 163 importance 11 Collisions in fully ionized plasmas 11.1 Coulomb collisions 11.2 Electron and ion collision frequencies 11.3 Plasma resistivity 11.4 Energy transfer 11.5 Bremsstrahlung* 165 165 171 174 177 180 12 Diffusion in plasmas 12.1 Diffusion as a random walk 12.2 Probability theory for the random walk* 12.3 The diffusion equation 12.4 Diffusion in weakly ionized gases 12.5 Diffusion in fully ionized plasmas 12.6 Diffusion due to like and unlike charged-particle collisions 12.7 Diffusion as stochastic motion* 12.8 Diffusion of energy (heat conduction) 185 185 186 187 192 196 200 206 215 13 The Fokker-Planck equation for Coulomb collisions* 13.1 The Fokker-Planck equation: general form 13.2 The Fokker-Planck equation for electron-ion collisions 13.3 The ‘Lorentz-gas’ approximation 13.4 Plasma resistivity in the Lorentz-gas approximation 219 220 222 224 225 Copyright © 1995 IOP Publishing Ltd X Contents 14 Collisions of fast ions in a plasma* 229 14.1 Fast ions in fusion plasmas 229 14.2 Slowing-down of beam ions due to collisions with electrons 230 14.3 Slowing-down of beam ions due to collisions with background ions 235 14.4 ‘Critical’ beam-ion energy 238 14.5 The Fokker-Planck equation for energetic ions 239 14.6 Pitch-angle scattering of beam ions 243 14.7 ‘Two-component’ fusion reactions 245 UNIT WAVES IN A FLUID PLASMA 15 Basic concepts of small-amplitude waves in anisotropic dispersive media 15.1 Exponential notation 15.2 Group velocities 15.3 Ray-tracing equations 16 Waves in an unmagnetized plasma 16.1 Langmuir waves and oscillations 16.2 Ion sound waves 16.3 High-frequency electromagnetic waves in an unmagnetized plasma 247 249 249 252 254 257 257 262 264 17 High-frequency waves in a magnetized plasma 269 17.1 High-frequency electromagnetic waves propagating perpendicular to the magnetic field 269 17.2 High-frequency electromagnetic waves propagating parallel to the magnetic field 277 18 Low-frequency waves in a magnetized plasma 285 18.1 A broader perspective-the dielectric tensor 285 18.2 The cold-plasma dispersion relation 288 290 18.3 COLDWAVE 29 18.4 The shear AlfvBn wave 298 18.5 The magnetosonic wave 18.6 Low-frequency AlfvBn waves, finite T , arbitrary angle k, > 0, and - n i times the residue for the case kz < 0) We obtain x exp (-02 k : ~ :j~ (26.67) For large Iw1 (i.e for w values approaching either -CO or +CO), the imaginary part of D ( w ) is extremely small, and its sign is the same as the sign of the product VikyUdi (determined by the sign of the term in w2 in the imaginary part of 0) We will limit our analysis to the case vi > 0, and we recall that we chose k,udi < for consistency with Figure 26.2 Thus, Im(D) e for large JwJ, which tells us that the Nyquist contour in the vicinity of the point D = must lie just below the real axis, again as shown in all three cases of Figure 26.3 The Nyquist contour in the D plane can cross the real axis only if there are values of w for which the imaginary part of D ( o ) vanishes From equation (26.67), we see that this will occur only if there are real roots w of the quadratic equation (26.68) Using the usual formula for the roots of a quadratic equation, the roots of Copyright © 1995 IOP Publishing Ltd The ‘ion temperature gradient’ instability 473 equation (26.68) are given by -w =- kyudi A { f [ l - A (2 - (26.69) (26.70) In order to determine the shape of the Nyquist curve, it is now important to determine the value of Re(D) where the Nyquist contour crosses the real axis in the D plane (Of course, if there are no real roots of equation (26.68), the contour does not cross the real axis anywhere.) This can be done by substituting into the principal-value integral in equation (26.67) the value of w at which the imaginary part vanishes The simplest approach algebraically is to rearrange equation (26.68) as an equation for w in terms of w2, and substitute this form into the principal-value integral in equation (26.67), noting the various cancellations which then occur We obtain = { f [l - A (2 - vi)]”2} (26.71) where, in the final form, we have substituted for w from equation (26.69) By comparing equation (26.71) with equation (26.69), we see that the values of Re(D) at crossings of the real-D axis are closely related to the corresponding values of w at these points There are three cases to be considered The first is where A(2 - vi) > , in which case equation (26.69) shows that there are no real roots of the quadratic equation, equation (26.68), and therefore no crossings of the realD axis by the Nyquist contour: the Nyquist contour must be of the form illustrated in Figure 26.3(a) Clearly, the area to the left of the Nyquist contour does not contain the point D = + ~ O / Twhich ~ , is the dispersion relation, equation (26.63), and so there can be no unstable mode The second case is where < h(2 - vi) < 1, in which case there are two real roots of the quadratic equation, equation (26.68), given in equation (26.69), both of which have w/kyvd > However, equation (26.71) shows that the values of Re(D) at these w values are both less than unity, with the more negative root w corresponding to the larger value of Re(D), remembering that we have chosen Copyright © 1995 IOP Publishing Ltd 474 The drift-kinetic equation and kinetic drift waves* kyu& < For this case, the Nyquist contour must cross the real axis twice to the left of the point D = and must be of the form illustrated in Figure 26.3(b) Again we see that the area encircled to the left of the Nyquist contour does not contain the point D = Tjo/T,o, and so again there can be no unstable mode The third case is where qi =- 2, in which case equation (26.69) shows that there are two real roots with opposite signs for w/k,udi Equation (26.71) shows that the root with a positive value of w/k,udi (negative w value) has Re(D) > 1, whereas the root with a negative value of w / k y u & (positive w value) has Re(D) e For this case, the Nyquist contour (as w travels along the real axis from -w to +w) crosses the real axis in the D-plane first to the right of the point D = and subsequently crosses it again to the left of the origin: the contour must be of the form illustrated in Figure 26.3(c) This contour encloses to its left an area that includes the point D = + Tjo/T,o if the first (i.e rightmost) crossing of the real axis occurs to the right of this point Using equation (26.71) for the value of D at each crossing of the real axis, this occurs when + { + [ l - A(2 - Vi)I”2} > Ti0 + T,o (26.72) which is therefore the condition that an unstable mode exists By some straightforward manipulation, inequality (26.72) can be expressed as a condition (26.73) For a plane plasma slab that is infinite in both y and z directions, it is possible to choose the wave-vector components k, and k, at will, so that the parameter A given in equation (26.70) takes on all values In particular, choosing sufficiently small values of the ratio k , / k , that the parameter A greatly exceeds unity, the condition for instability will approach a limiting case qi > (26.74) However, since the diamagnetic drift speed is generally much less than the ion thermal speed, specifically U d i / V t , i rLi/LI > In cases where arbitrarily small k, values are not allowed, such as a torus which is approximated as a finite-length cylinder with ‘periodic boundary conditions’, the condition for instability could be significantly more demanding than that given by equation (26.74) The addition of ‘magnetic shear’, i.e where a small field B,(x) is added to the main field B,, also serves effectively to impose a lower limit on the component of the k-vector along the magnetic field In this case also, stability is improved On the other had, inclusion of shorter wavelength modes, - Copyright © 1995 IOP Publishing Ltd The ‘ion temperature gradient’ instability - 475 specifically these with klrLi 1, is found to lower the instability threshold for vi to values close to unity The effect of V B and curvature drifts in geometries other than the plane slab is also found to be destabilizing This ‘ion temperature gradient’ instability poses a significant threat to confinement in high-temperature fusion plasmas-€or which the present ‘collisionless’ approximation is applicable As we saw in Chapter 10, neutral atoms will not penetrate far into a fusion-reactor plasma There will thus be no source of deuterium-tritium ‘fuel’, except at the very edge of the plasma Thus, unless turbulent flows drive net inward convection, the process of turbulent internal diffusion will establish an equilibrium density that is approximately uniform over almost all of the plasma, falling to zero only in a narrow edge layer The density gradient will therefore be very small in the main part of the plasma (with gradient scale-length much greater than the plasma linear dimension) Thermal conduction will carry the heat that is generated from the charged particles produced by the fusion reactions from the central part of the plasma (where the temperature will be highest) to the edge of the plasma (where the temperature will be lowest) Thus the temperature gradient will be substantial in the main part of the plasma (with gradient scale-length of order the plasma linear dimension) It follows from these general considerations that vi values may be quite large in the main part of a fusion-reactor plasma, implying that ion temperature gradient instabilities might arise and cause turbulence and perhaps a highly enhanced rate of heat conduction Indeed this has been a longstanding concern in fusion research Fortunately, however, effects not considered in the present simple analysis tend to stabilize the ion temperature gradient mode Moreover, even when the instability does arise, the enhanced thermal conduction caused by it may not exceed the ‘anomalous’ transport produced by a variety of drift-wave-like and other small-scale instabilities and turbulent processesall of which are predicted to still allow an acceptable overall level of plasma confinement for fusion power production There is an extensive literature on low-frequency drift waves and other related small-scale instabilities in magnetically confined plasmas A review article, which describes all of the basic modes and their linear growth rates and gives simple estimates of the level of turbulent transport to be expected from them, has been written by two of the most prolific contributors to this field, B B Kadomtsev and P Pogutse (1972 Review of Plasma Physics edited by M A Leontovich, pp 249-400, New York: Consultants Bureau) More recently, this field has been developed to include linear calculations in very realistic plasma geometries, as distinct from the ‘plane plasma slab’ considered here, and to nonlinear calculations of the plasma turbulence produced by drift-wavelike instabilities As might be expected, both of these developments involve extensive numerical computation Over the years, many authors have attempted to explain experimental results Copyright © 1995 IOP Publishing Ltd 476 The drifr-kinetic equation and kinetic drifr waves* on anomalous transport in tokamaks using theoretical modes of drift wave turbulence, generally with only limited success However, it is encouraging to note that, as the field becomes more sophisticated in its use of realistic geometries and advanced computational techniques, the level of agreement with experimental data appears to be improving markedly - The development of computational techniques for following the kinetics of gyrating ions into regimes of nonlinear perturbations has been responsible for some of the most notable recent advances Copyright © 1995 IOP Publishing Ltd Appendix A Physical quantities and their SI units SI unit Conversion formula Quantity Symbol Name Abbrev to Gaussian units Length Time Velocity Mass Mass density L , a , r, R meter second meter per second kilogram kilogram per cubic meter newton joule watt (J s-') pascal kelvin coulomb coulomb per cubic meter coulomb per square meter ampere (C s-l) ampere per square meter volt per meter volt tesla weber (T m2) ohm ohm-meter m m = IO2 cm Force Energy Power Pressure Temperature Charge Charge density Surface charge density Current Current density Electric field Electric potential Magnetic field Magnetic flux Electric resistance Resistivity Copyright © 1995 IOP Publishing Ltd S m s-l kg kg m-3 N J W Pa K C C m-3 C m-2 A A m-2 V m-l V T Wb R Rm I m s-' = IO2 cm s-' kg = lo3 g kg m-3 = g~ m - ~ N = IO5 dyne J = lo7 erg W = io7 erg s-I Pa = 10 dyne c m eV = 1.16 x lo4 K C = xlOy esu C m-3 = x io3 esu C m2 = x io5 esu cm-2 A = x 10' esu A m-2 = x io5 esu V m-' = 10-4/3 esu V = 10-2/3 esu T = lo4 gauss Wb = lo8 maxwell a = (IO-"/9) s cm-I a m = (10-'/9) s 477 Appendix B Equations in the SI system Maxwell’s equations (SI units): V.B=O V (EoE)= cr (Poisson’s equation) V x E = -aB/at V x B = poj + (1/c2)8E/at Lorentz force on charge q (SI units): F = q (E (Faraday’s law) + v x B) 478 Copyright © 1995 IOP Publishing Ltd (Ampere’s law) Appendix C Physical constants Physical constant Symbol Value in SI units Elementary charge Electron mass Proton mass Boltzmann constant; e 1.60 x 9.11 x 1.67 x 1.38 x 1.60 x 3.00 x 1.05 8.85 x Speed of light in vacuum Planck constant ( h / n ) Permittivity of free space Permeability of free space m M k c h E(] 10-19c kg loWz7kg 10-23 J K - J eV-' 10' m s-' 10-34 J lo-'* C m-l V-' 4n x = 1.26 x 10-6TmA-1 * Throughout this book, for simplicity of notation, the plasma temperature T is always in 'energy units', i.e joules, so that the Boltzmann constant k never appears The two values of k given here will allow a temperature in kelvin (K) or electron-volts (eV) to be converted into joules (J) Note that the quantities T / e and W / e , where W is an energy, have units of volts Thus, for example, the value of T / e for a lOeV temperature is 1OV 479 Copyright © 1995 IOP Publishing Ltd Appendix D Useful vector formulae D.l VECTOR IDENTITIES A * (B x C) = (A x B) * C A x (B x C) = (A * C)B - (A B)C V-($A)=$(V*A)+A.V$ V x ($A) = $(V x A ) + V $ x A V * (A x B) = B * V x A - A * V x B V x (A x B) = A(V B) - B(V * A ) (B * V)A - ( A V)B A x (V x B) = (VB) * A - (A * V ) B v x (V X A ) = V ( V A ) - V ~ A - + D.2 MATRIX NOTATION Note that we employ the Einstein convention, in which repeated suffices are to be summed over the values 1, 2, D.2.1 Kronecker deltas D.2.2 Levi-Civita symbols ~ i , k3 480 I i # j # k cyclic permutation of 1, 2, -1 i # j # k anti - cyclic permutation of 1,2, i=jorj=kori=k Copyright © 1995 IOP Publishing Ltd Appendix D 481 Matrix notation with the Einstein convention can be used to derive all of the vector identities given in Section D.l of this Appendix For example, we derive the expression for V x ( A x B ) by proceeding as follows which, after rearranging terms on the right-hand side, is the desired expression Copyright © 1995 IOP Publishing Ltd Appendix E Differential operators in Cartesian and curvilinear coordinates E.l CARTESIAN COORDINATES (2,y, z ) Gradient: Divergence: V A = - aA, + - + - aA, ay ax Curl: aA, VxA=(!!$ Laplacian: aAx az ' az v + = -a2+ + - + -a2+ ax2 ay2 aA, az aA, aA, -ax ' ax ay a2+ a22 Laplacian of a vector: V2A = (V2Ax, V2A,, V2A,) Divergence of a tensor: aPxx apYx ap,, (V P ) x= ax ay az ap,, ap,, ap,, (V* P ) , = ax ay az aPx, ap,, ap,, (V P ) , = ax ay az a - Copyright © 1995 IOP Publishing Ltd +- +++-+- Appendix E E.2 CYLINDRICAL COORDINATES ( T , 8, z) Gradient: Divergence: i a V A = (rAr)+ r ar aAe aA, +rae az Curl: Laplacian: Laplacian of a vector: aAe A, V2A = V A r - - -, V Ae r2 ae r2 ( aA, Ae + -, r2 ae r2 V2A,> Divergence of a tensor: i a ( V * P)r = (rPrr) r ar i a ( V P)e = (rPre) r ar i a ( V P ) , = (rPrz) r ar - aper apzr Pee + -+ r a9 az r aPee aP,e Per + -+-r a9 az r ape, ap,, + -+r ae az E.3 SPHERICAL COORDINATES ( T , 8,qh) Gradient: Copyright © 1995 IOP Publishing Ltd 483 Differential operators in Cartesian and curvilinear coordinates 484 Divergence: - i a r2 a r V A = (r2Ar) aA# i a + -(sinOAe) + -rsine 80 rsine a# Curl: VXA= aAe aAr 1a (sin @Ao)- - - -(rA#), r ar rsine a# ' rsine a# (r s L i a - -(rAe) - -r ar r ae Laplacian: Copyright © 1995 IOP Publishing Ltd Appendix F Suggestions for further reading There are many textbooks on plasma physics that go into greater detail and cover somewhat more advanced material than has been possible in the present text In particular, students at the graduate level specializing in plasma physics have found N A Krall and A W Trivelpiece (1963) Principles of Plasma Physics (New York: McGraw-Hill, reprinted 1986 by San Francisco Press), particularly useful Similar material, with a stronger emphasis on fusion applications, can be found in K Miyamoto (1989) Plasma Physics for Nuclear Fusion (Cambridge, MA: MIT Press) A recent graduate-level text, which provides a good introduction to astrophysical, geophysical as well as fusion plasmas is P A Sturrock (1994) P l a s m Physics (Cambridge: Cambridge University Press) Textbooks that take a kinetic, or statistical, approach to the formulation of basic plasma theory include S Ichimaru (1973) Basic Principles of Plasma Physics (Reading, MA: BenjamidCummings), D R Nicholson (1983) Introduction to Plasma Theory (New York: Wiley) and K Nishikawa and M Wakatani (1990) Plasma Physics (Berlin: Springer) A recent treatment that emphasizes the theoretical foundations of the subject from a fusion perspective can be found in R D Hazeltine and J D Meiss (1992) P l a s m Confinement (New York: Addison-Wesley) A more advanced text that focuses on developing and applying the magnetohydrodynamic model is J P Freidberg (1987) Ideal Magnetohydrodynamics (New York: Plenum Press) The topic of waves in plasmas, including also instabilities such as drift waves etc, is treated extensively in T H Stix (1992) Waves in Plasmas (New York: American Institute of Physics) Students interested in the experimental techniques used for measuring plasma quantities in laboratory and fusion plasmas are referred to I H Hutchinson (1987) Principles of Plasma Diagnostics (Cambridge: Cambridge University Press) Those interested primarily in astrophysical and solar plasmas should first develop an overall understanding of modern astrophysics, for example by 485 Copyright © 1995 IOP Publishing Ltd 486 Suggestions for further reading studying F H Shu (1991, 1992) The Physics ofAstrophysics Volumes I and I1 (Mill Valley, CA: University Science Books) They are then encouraged to read D B Melrose (1980) Plasma Astrophysics Volumes and (New York: Gordon and Breach) and H K Moffatt (1978) Magnetic Field Generation in Electrically Conducting Fluids (Cambridge: Cambridge University Press) Geophysical and space plasmas are described in G K Parks (1991) Physics of Space Plasmas (New York: Addison-Wesley) A series of articles outlining the fundamentals of magnetically confined fusion plasmas and the status (circa 1980) of fusion experiments can be found in Fusion Volume I, Parts A and B, ed E Teller (1981, New York: Academic) Fusion reactors from a more engineering perspective are described in R A Gross (1984) Fusion Energy (New York: Wiley) and in W M Stacey (1984) Fusion (New York: Wiley) Those who are interested in pursuing further the theory of plasma confinement and stability in tokamak configurations are referred to J Wesson (1989) Tokamaks (Oxford: Clarendon Press), to R B White (1989) Theory of Tokamak Plasmas (Amsterdam: North-Holland), to B B Kadomtsev (1992) Tokamak Plasma: A Complex Physical System (Bristol: Institute of Physics Publishing) and to D Biskamp (1993) Nonlinear Magnetohydrodynamics (Cambridge: Cambridge University Press) Copyright © 1995 IOP Publishing Ltd .. .INTRODUCTION TO PLASMA PHYSICS Robert J Goldston and Paul H Rutherford Plasma Physics Laboratory Princeton University Institute of Physics Publishing Bristol and Philadelphia Copyright ©... hold the plasma together long enough to create the highly ionized states A whole field of ? ?plasma chemistry’ exists where the chemical processes that can be accessed through highly excited atomic... DE-AC0276-CHO-3073 Robert J Goldston Paul H Rutherford Princeton, 1995 Copyright © 1995 IOP Publishing Ltd Introduction After an initial Chapter, which introduces plasmas, both in the laboratory and