The paper is devoted to the exact non-linear calculation, to lowest order in the wave amplitude, of the electromagnetic power absorption by a uniform plasma in the small-collision-frequency limit. The absorption is determined by the average rate of irreversible entropy increase as produced by the full Fokker-Planck operator including both like- and unlike- species collisions. The explicit form of the velocity distribution function of the resonant particles is directly obtained from the relevant non-linear Vlasov equation. The paper treats the case of a purely electrostatic wave in straight geometry, the case of compression and shear magnetic waves in toroidal geometry for electron heating, and makes two corrections to previous results on ion TTMP heating. The limits of validity of the collisionless linear calculations of power absorption in the above problems as a function of the collision frequency are established in an intrinsically more exact way than in any previous evaluation.
Nonlinear oscillations of rarified plasma