Self-Consistent Modification of a Fast Tail Distribution by Resonant Fields in Nonuniform Plasmas,

An analytic study is made of the second order modifications produced on the fast tail electron distribution function of a nonuniform plasma subjected to resonant excitation by wave sources. The source models considered can represent excitation by external electromagnetic waves propagating obliquely to the plasma density gradient, mode-conversion of electrostatic whistlers. beat of two transparent electromagnetic waves, and direct conversion from ripples in the density profile. The calculation treats the Landau damping provided by fast tail electrons self-consistently and is applicable to plasmas having a long density scale length L, i.e., kDL to the 13 power 1, where kD is the Debye wave number of the warm background electrons. A threshold condition is found for the formation of a positive slope in the tail distribution by the various excitation mechanisms.