A Fokker–Planck operator for the emission and absorption of electron plasma waves in a magnetized plasma

Abstract

For slab geometry the perturbation of the electrostatic wake of a superthermal test electron in a magnetized plasma (ωce ≫ ωpe) due to moderate magnetic shear is determined. Allowing for the spherical symmetry of the surfaces of constant phase to the rear of the test electron, the ‘‘resonant’’ field electrons causing the damping of the wave in a magnetic surface at a distance x from the test electron are those with parallel velocity v′∥ = v∥cosβ/cos(β + γ). Here β is the angle between the emitted ray and B(0), γ is the angle between B(0) and B(x) and v∥ is the velocity of the test electron. As a result the damping in the WKB approximation for the wave emission is a function of both the angle of emission and γ. A Fokker–Planck equation is derived for the rate of change of the electron distribution function (f) due to the emission and absorption of the waves under these conditions; f is assumed approximately Maxwellian for v∥ ≲ vT but with an arbitrary tail for v∥ ≳ vT.