Plasmadynamics is concerned with the emission, absorption and scattering of waves by particles, with the scattering of particles by waves, and with wavewave interactions in plasmas. A single-particle approach is usually used in treating spontaneous emission, and absorption may be treated either using a collective-medium approach, with dissipation included in the anithermitian part of the response tensor, or by relating absorption to emission. The link between the single-particle and collective-medium approaches is subtle, involving causality, the second law of thermodynamics, and the optical theorem. In quantum treatments the single-particle approach is strongly preferred, with emission and absorption being related on a microscopic level through detailed balance (or the Einstein coefficients). A semiclassical theory allows one to appeal to this powerful principle while all the detailed calculations remain classical. The Einstein coefficients relate spontaneous emission, stimulated emission and absorption, and they ensure conservation of energy and momentum at the microscopic scale. This overcomes a serious weakness in classical electrodynamics, which does not automatically conserve these quantities, requiring one to invent a radiation reaction force to restore the conservation law. The derivation of the kinetic equations that describe the evolution of the waves and particles is particularly simple in the semiclassical approach. In a collective-medium approach, the derivation of the kinetic equations involves various statistical approaches. In this chapter covariant versions of both single-particle and collective-medium techniques are used, with the emphasis on the semiclassical approach.
KeywordsSpontaneous Emission Quasilinear Equation Wave Quantum Nonlinear Scattering Inverse Compton Scattering
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