NON-LINEAR SOLUTIONS OF FOKKER-PLANCK EQUATIONS,
GENERAL DYNAMICS/CONVAIR SAN DIEGO CALIF
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Mathematical statements of the presumed nature of the interaction between a plasma and electromagnetic waves are re-examined for possible methods of exploiting the effects of nonlinear terms in the heretofore linearized versions of magnetohydrodynamic equations. A procedure is studied for orthogonal polynomial expansion of the velocity dependence of the particle distribution functions. The procedure consists of substituting the expansion into the transport equation whose result yields an infinite set of linked equations for the coefficients of the expansion. The set of equations to be studied consists of a finite number of the linked equations combined with the electromagnetic field equations. The important assumptions made are 1 the plasma is fully ionized, 2 the ions have a Maxwellian distribution, 3 electron-electron interactions can be ignored, 4 electron-ion interactions may be described by the Fokker-Planck collision terms used by Grad Comm. on Pure and Applied Math., 2325, 2331, 1949. The proposed solution method contains implicitly the assumptions that 5 the electron distribution is in some sense close to a Maxwellian distribution, 6 coefficients of third products of velocity components taken three at a time and higher order terms can be ignored.