Stochastic Acceleration

Abstract

Charged particles moving under the influence of randomly time-varying electromagnetic fields may be expected to experience a net acceleration. This process is analyzed for the special case of nonrelativistic motion in a static uniform magnetic field and time-varying electric field. Acceleration parallel and transverse to the magnetic field are considered separately. In the weak-field approximation, the motion may be described by a Fokker-Planck equation. The coefficients of this equation are expressible in terms of the correlation functions for the electric fields. In certain cases, the coefficients may be expressed in terms of the energy spectrum of the field. The Fokker-Planck equation derived for motion along the magnetic field is closely related to an equation of the quasilinear theory of plasma instability. One may also show that the equation is closely related to the phenomenon of Landau damping. Longitudinal acceleration is effected by waves with phase velocities slightly greater than the particle velocity. A similar statement is true for transverse acceleration, except that the "resonant" waves are in addition shifted by the particle gyrofrequency. In the absence of any other effects (such as "loading" of the accelerating field by the accelerated particles), the transverse energy distribution tends to a Maxwellian form with a temperature which increases linearly with time. The same is true for longitudinal acceleration if the spectrum of the electric field is flat over the range of phase velocities of interest. The equations related to transverse acceleration show that the high-energy electrons observed in the transition region outside the earth's magnetosphere may have been accelerated by quite weak random or quasirandom electric fields.