ContentsVI PLASMA PHYSICS 219 The Particle Kinetics of Plasma 119.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119.2 Examples of Plasmas and their Density-Temperature Regimes . . . . . . . . 219.2.1 Ionization boundary ........................... 219.2.2 Degeneracy boundary ........................... 419.2.3 Relativistic boundary ........................... 419.2.4 Pair-production boundary . . . ..................... 519.2.5 Examples of natural and man-made plasmas . . . . . . . . . . . . . . 519.3 Collective Effects in Plasmas – Debye Shielding and Plasma Oscillations . . . 719.3.1 Debye Shielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 719.3.2 Collective behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . 819.3.3 Plasma Oscillations and Plasma Frequency ............... 819.4 Coulomb Collisions ................................ 919.4.1 Collision frequency ............................ 1019.4.2 The Coulomb logarithm ......................... 1219.4.3 Thermal Equilibration Times in a Plasma ............... 1219.4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1419.5 Transport Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1619.5.1 Anomalous Resistivity and Anomalous Equilibration ......... 1719.6 Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1919.6.1 Cyclotron frequency and Larmor radius. . . . . . . . . . . . . . . . . 1919.6.2 Validity of the F luid Approximation. . . . . . . . . . . . . . . . . . . 2019.6.3 Conductivity Tensor ........................... 2119.7 Adiabatic Invariants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2419.7.1 Homogeneous, time-independent magnetic field . . . . . . . . . . . . 2419.7.2 Homogeneous time-independent electric and magnetic fields . . . . . 2419.7.3 Inhomogeneous, time-independent magnetic field . . . . . . . . . . . . 2519.7.4 A slowly time varying magnetic field . . . . . . . . . . . . . . . . . . 271Part VIPLASMA PHYSICS2Plasma PhysicsVersion 1019.1.K.pdf, April 1, 2009.A plasma is a gas that is significantly ionized (through heating or photoionization) andthus is composed of electrons and ions, and that has a low enough density to behave clas-sically, i.e. to obey Maxwell-Boltzmann statistics rather than Fermi-Dirac or Bose-Einstein.Plasma physics originated in the nineteenth century, in the study of gas discharges (Crookes1879). However, it was soon realised that plasma is also the key to understanding the prop-agation of radio waves across the Atlantic (Heaviside 1902). The subject received a furtherboost in the early 1950s, with the start of the controlled (and the uncontrolled) thermonu-clear fusion program. The various confinement devices described in the preceding chapterare intended to hold plasma at temperatures as high as ∼108K; the difficulty of this taskhas turned out to be an issue of plasma physics as much as MHD. After fusion, the next newvenue for plasma research was extraterrestrial. Although itwasalreadyunderstoodthatthe Earth was immersed in a tenuous outflow of ionized hydrogen known as the solar wind,the dawn of the space age in 1957 also initiated experimental space plasma physics.Morerecently, the interstellar and intergalactic media beyond the solar system as well as exoticastronomical objects like quasars and pulsars have allowed us to observe plasmas under quiteextreme conditions, unreproducible in any laboratory experiment.The dynamical behavior of a plasma is more complex than the dynamics of the gases andfluids we have met so far. This dynamical complexity has two main origins:(i) The dominant form of interparticle interaction in a plasma, Coulomb scattering, isso weak that the mean free paths of the electrons and ions are often larger than theplasma’s macroscopic length scales. This allows the particles’ momentum distribu-tion functions to deviate seriously from their equilibrium Maxwellian forms and, inparticular, to be highly anisotropic.(ii) The electromagnetic fields in a plasma are of long range. This allows charged particlesto couple to each other electromagnetically and act in concert as modes of excitation(plasma waves or plasmons) that behave like single dynamical entities. Much of plasmaphysics consists of the study of the properties and interactions of these modes.The dynamical behavior of a plasma depends markedly on frequency. At the lowest offrequencies the ions and electrons are locked together by electrostatic forces and behavelike an electrically conducting fluid; this is the regime of magnetohydrodynamics (MHD;Chap. 17). At somewhat higher frequencies the electrons and the ions can mo ve relative to34each other, behaving like two separate, interpenetrating fluids; we shall study this two-fluidregime in Chap. 19. At still higher frequencies, complex dynamics is supported by momentumspace anisotropies and can be analyzed using a variant of the kinetic-theory collisionlessBoltzmann equation that we introduced in Chap. 2. We shall study such dynamics inChap. 20. In the two-fluid and collisionless-Boltzmann analyses of Chaps. 19 and 20 wefocus on phenomena that can be treated as linear perturbations of an equilibrium state.However, the complexities and long mean free paths of plasmas also produce rich nonlinearphenomena; we shall study some of these in Chap. 21. As a foundation for the dynamicalstudies in Chaps. 19, 20, and 21, w e dev elop in Chap. 18 detailed insights in to the microscopicstructure of a plasma.Chapter 19The Particle Kinetics of PlasmaVersion 1019.1.K.pdf, April 1, 2009.Please send comments, suggestions, and errata via email to [email protected] or on paper toKip Thorne, 350-17 Caltech, Pasadena CA 91125Box 19.1Reader’s Guide• This chapter relies significantly on portionsofnonrelativistickinetictheoryasde-veloped in Chap. 2.• It also relies a bit but not greatly on portions of magnetohydrodynamics as devel-oped in Chap. 18.• The remaining chapters 19-21 of Part V, Plasma Physics rely heavily on this chap-ter.19.1 OverviewThe preceding chapter, Chap. 17, can be regarded as a transition from fluid mechanicstoward plasma physics: It described equilibrium and low-frequency dynamical phenomena inamagnetizedplasmausingfluid-mechanicstechniques. In this chapter, we prepare for moresophisticated descriptions of plasma by introducing a number of elementary foundationalconcepts peculiar to
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