Diffusion, Scattering, and Acceleration of Particles by Stochastic Electromagnetic Fields

The behavior of charged particles in an electromagnetic field composed of two parts is treated. The first is an unperturbed part, for which the solution of the Vlasov equation is assumed to be known; the second part is a perturbation which is assumed to be random and of small amplitude. Such a ``stochastic'' or ``turbulent'' electromagnetic field leads to diffusion, pitch-angle scattering, and acceleration. Equations governing these processes may be derived by test-particle calculations. The problem is first posed in a general way, and solved by a method similar to that used in quasi-linear theory. The connection of this method with the Fokker-Planck formulation is discussed. The case which is analyzed in detail is that of relativistic particles moving in a uniform magnetic field under the influence of a steady homogeneous spectrum of electromagnetic fluctuations. Results are given which are valid for any (weak) fluctuation spectrum and for finite test-particle gyroradii. The physical meaning of the results is discussed, and it is shown that in certain limits there is agreement with earlier, less general analyses.