INTRODUCTION TO PLASMA PHYSICS AND CONTROLLED FUSION SECOND EDITION Volume 1: Plasma Physics ---------------,-----------------~----------------- ··-··-··-· ~ ol~pua~in hblic..ac. O.a Qea. rrt.~~at P , IJ&- 1~ ......... ~...;~.__, ........ .,._......_ __ ,.._~lt14, ---· ....... ~ c...-.., • I "-,.,....... t rt-( ........ ~)LOc., f~f. ,l929- lactOCMt1M • ,.a-,.,... 11.. Tldt. QC11fC»f Ito ).)0.4'4 ll-17666 IUHO.~U32·9 109 n... ""*- •• b.-' Ofl c::a...,._n J ·f GldM: lira edihotl ol "'"'*'·-. ....,_ ,.,, ... ,...~ in 1914 "19114 Pk•t.~m Jl'm,., Ntw Vorl A Diri'*oa of P'k~t~tiYI P\lbl"hin1 Corpoo~ticiEI 233 .s,rit~l Sll'ftl, New Yuri.. N.Y. IOOIJ AU~· ._.td No pan ol1hl. boola IMY bt rqnoctuud, fUftiCI ift a rart'ness of 1hc imponant applications of pluma ph)"sics to ene-rgy produccion and to the understanding of our space environment. In magnetic confinement fusior~. this pe-riod has ~en the attainment of a l.aw&on rw rnber nr« of 2 x 101, ern ... , JJC': in the Alawr toklunak1 at MIT: neutral-beam he;uing of the PLT tok:un:ak at l,rim:cton to KT, • 6.5 kcV; inc-rc:Mc of average /J IO 3"-59& in toka m01ks ;ll Q~lt. Ridge and Ccneral Atorn ic: :md the stabilization of mirror-confined phumas at l..i'o'ermore. together with injection of ion curr-ent to near field-reversal conditionl in the 2Xll8 dc,·ic~. hwcnlion of the t-andem mirror has ghcn magnetic confinement a new and exciting di.mC'ruion. New ide;;tJ ha .. ·c l"mcrgcd. such as the compact torus. su rfac~ficld dc .. -ic:H. and the EBT mirror-toruJ h)·btid. and some old ideas. such as tM- stdlarator and the rc .. ·cfWd·,field pinch. hal'c been revived. R.adiof-n:qucncy heat· ing has become a nC"W a1ar with ill promi$e of dt: curren1 drh·c. Pcrhapt most importantly. grc-ar progru:s las been made in the u_ndentandinx of the MHO beha,ior of 1oroid:al pla$m~ : tD.ring modn. magnet:k viii Prt(ace 141 lilt St.cond .F.Jitlort islands. :md di.srupUont. Concurrently. che problems or rtactor design. rusion ccchnolo~n·, and fission--Fusion hybrids ha,·e rtteived ~riousau~n cion for 1he l'irsc1ime. lncrdal cunlinement fusion has grown from inf-ancy to a research effon onc-fourd1 as large as magnt'lic: fusion. With the 25-TW Shi,,.. lasera1 [..i,·ermc:m:. ~ x 10 10thennonudear neutrontha,·ebecn produced in a ~ingle t>C'IIcc impiletion of 1he tecond edition by about three rean:. Volume I, whith incoqwrat.« the firs1 eight chapters of the first edition, re1alns ita origin:;tl simplidty but has been corrected and expanded. A number or subtle errors pointed out by students and pro ft:JSOI'I hnve ~en rectified. In re.tponse to their requests. the .system o£ units has been c.hanged, rc.-h•ctantl)'• 10 mks (SI). To physicisu of my c)wn gcncrntion, H1)' apologie:s: but tak(' cornJor1 in the thought that the first edhion has bc<.'Omc a collector's item. TI1c dielectric tcnJOr for cold plasm:u hat now ~n irtdud~; it was placed in Appendix 8 to a'·oid oomplicatiug an already long ~nd dHilcuh chapter for the beginner. but it i& there for ready rdere-nce. The chapter on k.in~dc theory h:u ~n e:xpanded to i.ndude ion Landau damping of acGUJ:Ik wa\'el, th~ plasma dispersion funa.ioo. and Bern· s:tcin w:n-es. The cbapter on nonlinnr efrecu now incorporates a treat· menc or soli10ru "ia the KoncweM-dcVrics and n0111incar SchrOdinger equations. This se:e1ion containJ more detail than the rc.s1 of Volume I. but purposel)• SO, tO whet the appelite or the ad\·~m:ed l CUdcnL Hdpful him.s from C. Morales and K. Ni~hikaw~ are hereby ackm;,\\•lcdged. For 1he be:nefit or teachcn, new problems from a decade or examt have been added, and the solutions LO the: old probJe:ms an- gh·en. A sample three·hOUr final exam for undergraduat.et will be found in Append.ix C. The probicrn anlwcn ha,•e: been check~ b)• Da,•id B~·er: a.ny errort are his, not mine. Finally. in regard 10 my cry-ptic dedtcat.ion. I ha'e: good news and bad n.,.... The bad news is that th~ pool (my fath<:r) lw mo'-ed on to tho bnd of 1 song. Tho good now. iJ tbatth< otunal5dlolor (my mo notes for a.n undergradu.atr courx in pwma ph)~ia ch>l ha• ~n ol!e h can also sen·e as a painless way for scitntisu in other llddt-401id a:tate or laser physics, for instance- to become acquailued wid1 J>l\!lrnas. Two guiding principles were followed: Do not lea\'C algebraic steps as an exercise for the reader. and do not let 1hc algebra ot»cure the ph)·sics. The C)(tcnt to which these oppOSing aims could bernet i; largely due IO the utument or plouma as two interpc:nc-Lraling nuid!. The t~fluki picture is both r.u~r to understand and more accurate than the singf.c..fluKI 3pproach, a.t kaJt £or low..deruity ~a.sma phenomena~ The initial chapte:rs a.uu~ ~"e'ry little prepar.uton on the part of the stuckm. but the later chapters are meant to keep pace with his increuing degree of tophistica.tion~ In a nine- or ten-'\llli·celt qu;;art.er, it i.s pos.sibk to CO\"er the 6nt six and one-haJf chapt.us. The m.aterial for xii Preface to the First Edition these chapters was carefully selected to contain only what is essential. The last two and one-half chapters may be used in a semester course or as additional reading. Considerable effort was made to give a clear explanation of Landau damping-one that does not depend on a knowl- edge of contour integration. I am indebted to Tom O'Neil and George Schmidt for help in simplifying the physical picture originally given by John Dawson. Some readers will be distressed by the use of cgs electrostatic units. It is, of course, senseless to argue about units; any experienced physicist can defend his favorite system eloquently and with faultless logic. The system here is explained in Appendix I and was chosen to avoid unnecessary writing of c, ILo exp (-J xl /An) [1-16] The quantity An, called the Debye length, is a measure of the shielding distance or thickness of the sheath. Note that as the density is increased, An decreases, as one would expect, since each layer of plasma contains more electrons. Furthermore, An increases with increasing KT,. Without thermal agitation, the charge cloud would collapse to an infinitely thin layer. Finally, it is the electron temperature which is used in the definition of An because the electrons, being more mobile than the ions, generally do the shielding by moving so as to create a surplus or deficit of negative charge. Only in special situations is this not true (see Problem 1-5). The following are useful forms of Eq. [1-15]: An= 69(T/n) 112 m, An= 7430(KT/n) 112 m, [1-17] KTineV We are now in a position to define "quasineutrality." If the dimensions L of a system are much larger than A0 , then whenever local concentrations of charge arise or external potentials are introduced into the system, these are shielded out in a distance short compared with L, leaving the bulk of the plasma free of large electric potentials or fields. Outside of the sheath on the wall or on an obstacle, V2c/> is very small, and n; is equal to n, typically, to better than one part in 106 • It takes only a small charge imbalance to give rise to potentials of the order of KT/e. The plasma is "quasineutral"; that is, neutral enough so that one can take n; = n, = n, where n is a common density called the plasma density, but not so neutral that all the interesting electromagnetic forces vanish. A criterion for an ionized gas to be a plasma is that it be dense enough that An is much smaller than L. The phenomenon of Debye shielding also occurs-in modified form-in single-species systems, such as the electron streams in klystrons and magnetrons or the proton beam in a cyclotron. In such cases, any local bunching of particles causes a large unshielded electric field unless the density is extremely low (which it often is). An externally imposed potential-from a \vire probe, for instance-would be shielded out by an adjustment of the density near the electrode. Single-species systems, or unneutralized plasmas, are not strictly plasmas; but the mathematical tools of plasma physics can be used to study such systems. THE PLASMA PARAMETER 1.5 The picture of Debye shielding that we have given above is valid only if there are enough particles in the charge cloud. Clearly, if there are only one or two particles in the sheath region, Debye shielding would not be a statistically valid concept. Using Eq. [1-17], we can compute the number N 0 of particles in a "Debye sphere": (Tin°K) [1-18] In addition to An« L, "collective behavior" requires N 0 >» 1 [1-19] CRITERIA FOR PLASMAS 1.6 We have given two condi~ions that an ionized gas must satisfy to be called a plasma. A third condition has to do with collisions. The weakly ionized gas in a jet exhaust, for example, does not qualify as a plasma because the charged particles collide so frequently with neutral atoms that their motion is controlled by ordinary hydrodynamic forces rather than by electromagnetic forces. If w is the frequency of typical plasma oscillations and T is the mean time between collisions with neutral atoms, we require wT > I for the gas to behave like a plasma rather than a neutral gas. 11 Introduction 12 Chapter One PROBLEMS The three conditions a plasma must satisfy are therefore: l. Ao « L. 2. No>»l. 3. WT > l. 1-3. On a log-log plot of n, vs. KT, with n, from I06 to 1025 m-3 , and KT, from 0.01 to I05 eV, draw lines of constant A0 and N 0 . On this graph, place the following points (n in m-', KT in eV): I. Typical fusion reactor: n = 1021 , KT = 10,000. 2. Typical fusion experiments: n = I0 19, KT = IOO (torus); n = I02", KT = I 000 (pinch). 3. Typicalionosphere: n = 10 11 , KT = 0.05. 4. Typical glow discharge: n = 10 15 , KT = 2. 5. Typical flame: n = 10 14 , KT = 0.1. 6. Typical Cs plasma; n = 10 17 , KT = 0.2. 7. Interplanetary space: n = 106 , KT = 0.01. Convince yourself that these are plasmas. 1-4. Compute the pressure, in atmospheres and in tons/ft2 , exerted by ather- monuclear plasma on its container. Assume KT, = KT, = 20 keV, n = 1021 m-', and p = nKT, where T = T, + T,. 1-5. In a strictly steady state situation, both the ions and the e~ctrons will follow the Boltzmann relation n; = n 0 exp (-q; A0 , the energy needed to transport a particle from a plate to the midplane is greater than the average kinetic energy of the particles. 1-7. Compute A0 and N 0 for the following cases: (a) A glow discharge. with n = 10 16 m-", KT, = 2 eV. (b) The earth's ionosphere, with n = I0 12 m-", KT, = 0. I eV. (c) AO-pinch,withn = I02"m-",KT,=800eV. APPLICATIONS OF PLASMA PHYSICS Plasmas can be characterized by the two parameters n and KT,. Plasma applications cover an extremely wide range of n and KT,: n varies over 28 orders of magnitude from 106 to 1034 m-3 , and KT can vary over seven orders from 0.1 to 106 eV. Some of these applications are discussed very briefly below. The tremendous range of density can be appreciated when one realizes that air and water differ in density by only 103 , while water and white dwarf stars are separated by only a factor of 105 • Even neutron stars are only 10 15 times denser than water. Yet gaseous plasmas in the entire density range of 10 28 can be described by the same set of equations, since only the classical (non-quantum mechanical) laws of physics are needed. 1.7 Gas Discharges (Gaseous Electronics) 1. 7.1 The earliest work with plasmas was that of Langmuir, Tonks, and their collaborators in the 1920's. This research was inspired by the need to develop vacuum tubes that could carry large currents, and therefore had to be filled with ionized gases. The research was done with weakly ionized glow discharges and positive columns typically with KT, = 2 eV and 10 14 < n < 10 18 m-3 . It was here that the shielding phenomenon was discovered; the sheath surrounding an electrode could be seen visually as a dark layer. Gas discharges are encountered nowadays in mercury rectifiers, hydrogen thyratrons, ignitrons, spark gaps, welding arcs, neon and fluorescent lights, and lightning discharges. Controlled Thermonuclear Fusion 1. 7.2 Modern plasma physics had it beginnings around 1952, when it was proposed that the hydrogen bomb fusion reaction be controlled to make a reactor. The principal reactions, which involve deuterium (D) and 13 Introduction

Introduction to plasma physics and controlled fusion. Volume 1, Plasma physics

Similar Introduction to plasma physics and controlled fusion. Volume 1, Plasma physics