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Karl-Heinz Spatschek: High Temperature Plasmas — 2011/9/1 — page 625 — le-tex

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625

Index

aacoustic branch 129–130adiabatic heating 60adiabatic invariant 58

– first 58– second 60– third 63

Alfvén current 68Alfvén wave 183alpha particle 34α particle heating 38ARCTURUS 414asymptotic stability 581average relative speed 270

bbad curvature 332Balescu–Lenard–Guernsey equation 110ballooning mode 322, 331BBGKY hierarchy 105Bernstein mode 296Bethe–Weizsäcker cycle 34binary collision 22binding energy 32binormal 51Biot–Savart law 42black hole 37black soliton 369blow up 408Bohr radius 12Boltzmann entropy 103Boltzmann equation 97, 154breaking of wake fields 499Brueckner parameter 16bump on tail instability 300Buneman instability 300burning stars 32

ccanonical momentum

– plane wave 69center manifold 565center manifold theory 561center of mass system 25Chandrasekhar mass 37Chapman–Enskog method 155charge density conservation 176chemical potential 10, 86chirp 413CNO cycle 34collapse 408collective effects 21collision frequency 18

– electron-electron 26– electron-ion 24, 26– ion-electron 26– ion-ion 26

collision probability 269complementary variational principles 589Compton length 419conductivity 144confinement time 38corona equilibrium 13correlation function 108Corrsin approximation 272Coulomb logarithm 139CPA 413critical density 426cross section

– momentum transfer 23curvature drift 44curvature vector 51, 331cyclotron waves 296

dDavey–Stewartson equation 372de Broglie wavelength 8

High Temperature Plasmas, Theory and Mathematical Tools for Laser and Fusion Plasmas, First Edition.Karl-Heinz Spatschek.© 2012 WILEY-VCH Verlag GmbH & Co. KGaA. Published 2012 by WILEY-VCH Verlag GmbH & Co. KGaA.

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Karl-Heinz Spatschek: High Temperature Plasmas — 2011/9/1 — page 626 — le-tex

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626 Index

Debye length 2, 17Delta function 273density depression 465diamagnetic 42diffusion 78

– parallel 81, 265– perpendicular 81

diffusion coefficient 76dispersion relation 119dispersive broadening 341distribution function 105drift

– centrifugal 51– electric 51– gradient 51

drift-cyclotron instability 316drift instability 315drift kinetic equation 147drift model 166drift velocity 43

eeigenzeit 72Einstein relation 70, 75Einstein–Smoluchowski relation 269electric charge density 171electric current density 171electric permittivity 514electromagnetic soliton 465electromagnetic wave 67, 165electron cyclotron emission 64electron MHD 176electron plasma oscillations 129, 163ELM mitigation 209Elwert formula 13empiric eigenfunction 557energy density 170–171energy flux density 152energy loss rate 38ensemble

– canonical 86– grand canonical 86

entropy 85–86envelope water soliton 371equation of state 156escape rate 209Euler equation 155–156Euler–Lagrange equations 69Euler potential 178–179extraordinary mode 296

fFarina–Bulanov model 466

Fermi acceleration mechanism 67Fermi momentum 16Fick’s second law 269figure-8 trajectory 74finite amplitude solitons 390finite Larmor radius correction 46firehose instability 303fluid description 149flux surface 64flux tube 332Fokker–Planck equation 97force-free equilibrium 178Fourier transform 4free energy 85friction 74friction force 27, 143fusion plasma

– typical parameters 17

gG-function 126Galerkin approximation 553Gardner equation 524Gaussian system 513Gaussian units 514Gel’fand–Levitan–Marchenko equation 531Ginzburg–Landau equation 576good confinement 332good curvature 332grad B drift 44Grad–Shafranov equation 180gray soliton 368great wave of translation 339guiding center approximation 43guiding center soliton 552gyration 43gyrofrequency 18gyrokinetic equation 148

hH-theorem 102Hall MHD 175Hall term 175Hamiltonian wave formulation 442Hawking radiation 420heat capacity 86heat exchange 143heat flow pattern 209heat flux density 152helium 3 33helium burning 37Hermite polynomial 187Holtsmark distribution 93

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Karl-Heinz Spatschek: High Temperature Plasmas — 2011/9/1 — page 627 — le-tex

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Index 627

hydrogen burning 36hydromagnetic variational principle 599hypergeometric equation 532

iideal gas approximation 15, 86ideal instability 321ideal MHD 173, 177ignition 38–39individual effects 22information entropy 558interchange instability 331internal energy 85internal kink 322inverse scattering transform (IST) 355, 523ion-acoustic instability 300ion-acoustic mode 294ion-acoustic soliton 351ion acoustic velocity 130ion Landau damping 130ion-sound oscillations 165ion sound velocity 129, 165ion sound waves 130ionization 8

– collisional 6, 13– degree 6– photo 13– thermal 6

ionization energy 7irreversibility 102

kKarhunen–Loève expansion 554kinetic equation 105kinetic regime 111kink instability 322, 326Klimontovich equations 113Korteweg–deVries equation 355KP equation 356, 358Krook collision term 158Kruskal–Shafranov criterion 329

lLagrange coordinates 500Lagrange function

– relativistic particle 69Landau contour 118Landau damping 120, 129, 294

– electron 129Landau–Fokker–Planck equation 95Langevin equation 74Langmuir collapse 408Langmuir oscillations 294Langmuir soliton 375, 383, 410

Larmor radius 42Lawson criterion 14, 38Lax equation 531Legendre transform 70Liapunov stability 410Lie bracket 52, 543Lie transform 541Liouville equation 84, 105Liouville operator 106lithium 33longitudinal stability 386Lorentz force 513low-mass stars 34

mmacroscopic description 149magnetic axis 180magnetic bottle 45magnetic field

– inhomogeneous 43magnetic mirror 65magnetic moment 45magnetic surface 178magneto-hydrostatics 178magnetohydrodynamic model 171magnetosonic waves 296mass defect 32mass density 170massive stars 34Maxwell electron fluid model 422Maxwell equations 513–514Maxwell two-fluid model 423Maxwellian 27, 105mean field approximation 111mean free path 18, 268mean velocity 170–171Mercier instability 322MHD ordering 171microfield distribution 91MKSA system 515mobility 76modulational instability 369moment approximation

– 13 moments 190– 21 moments 190– 29 moments 190

moments 149multiple scale analysis 155, 572

nNavier–Stokes equation 157neutrino 36neutron star 37, 421

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Karl-Heinz Spatschek: High Temperature Plasmas — 2011/9/1 — page 628 — le-tex

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628 Index

Newell–Whitehead procedure 571NLS equation 363non-Markovian behavior 111nonlinear dispersion relation 374nonlinear oscillator 505nonlinear Schrödinger equation 363nonrelativistic limit 435normal form 561normal mode analysis 115nuclear fusion 32numerical stability analysis 475

oOhm’s law 174one-field model 435OPCPA 413optical branch 129, 375optimal projection 557ordinary mode 295ordinary-mode electromagnetic

instability 304

pparticle density 169partition function 6, 85Penrose criterion 285pinch discharge 181pinch instability 326pitch angle 66pitch angle diffusion 265, 272plasma

– applications 2– classical 16– definition 1– fully ionized 1– hot 14– ideal 16– quantum 15– relativistic 14

plasma � 175, 303plasma cavity 466plasma dispersion function 126plasma frequency 21

– electron 21plasmadynamical moments 169plasmadynamical variables 161Plemelj formula 117Poisson–Boltzmann equation 3Poisson bracket 52polarization

– circular 67– linear 67

polarization drift 47

ponderomotive force 379, 491ponderomotive pressure 465positron generation 419postsolitons 480Poynting vector 67presolitons 476pressure 86

– kinetic 178– magnetic 178

pressure tensor 151, 170– dissipative part 152

proton-proton reaction 34pseudocanonical transformation 52pulsar field 421purely growing mode 304

qQ-factor 39Q-theorem 477QED regime 419quasilinear diffusion 279quasineutrality 3

rradial electric field 209radioactive products 33rapid perturbations 541Rationalized MKSA system 513Rayleigh–Jeans law 64recombination

– photo 13– three-body 14

red giant 37relativistic optics 413relativistic threshold 68resistive MHD 175resistive mode 321resistivity 144Richtmyer–Meshkov instability 337run away particles 30runaways 32

ssafety factor 329Sagdeev potential 353Saha equation 6, 8sausage instability 326scalar pressure 170scattering 22

– energy 26– momentum 26

Schrödinger scattering problem 523Schwarz inequality 319Schwinger field 419

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Karl-Heinz Spatschek: High Temperature Plasmas — 2011/9/1 — page 629 — le-tex

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Index 629

self-adjoint operator 599separatrix 180shielding 4SI system 513SI units 515single-humped solitons 466slab approximation 310slaving principle 561slow soliton 466solar wind 2solitary envelope solution 465solitary wave 339soliton 339

– conservative 339– dissipative 339

sound wave 156spectroscopy 93stability in inhomogeneous systems 309stability theorem 581statistical physics 83statistical thermodynamics 86stellar fusion 34Stirling formula 7, 104Stoßzahlansatz 99stress tensor 151sun 19

– age 19– mass 19– radius 19– temperature 19

surface wave 339

ttearing instability 322temperature 170test charge 4thermal energy density 170thermodynamic equilibrium 83, 86thermodynamics 85thermoelectric current 201Thomson cross section 10, 123D soliton 489

tokamak 65tracer particles 270transition probability 96transverse instability 391, 484trapping of radiation 465two-beam instability 287two-fluid equations 163two-particle distribution function 108two-soliton solution 537

uultrarelativistic regime 416units

– Gauss 514– MKSA 514– SI 513

Unruh radiation 420upper hybrid frequency 296

vvacuum impedance 69Vakhitov–Kolokolov criterion 474van Allen belt 66variation of action method 405variational principle 403, 589Vlasov approximation 110Vlasov equation 112

wwake field 489wave-breaking 341, 498

– relativistic 502weak coupling approximation 109–110Weibel instability 302whistler waves 297white dwarf 37white noise 75

zZ-function 126Zakharov equations 383, 435ZK equation 359, 589