Fokker–Planck electron diffusion caused by an obliquely propagating electromagnetic wave packet of narrow bandwidth

Abstract

The relativistic motion of electrons in an intense electromagnetic wave packet propagating obliquely to a uniform magnetic field is analytically studied on the basis of the Fokker–Planck–Kolmogorov (FPK) approach. The wave packet consists of circularly polarized electron-cyclotron waves. The dynamical system in question is shown to be reducible to one with three degrees of freedom. Within the framework of the Hamiltonian analysis the nonlinear diffusion tensor is derived, and it is shown that this tensor can be separated into zeroth-, first-, and second- order parts with respect to the relative bandwidth. The zeroth order part describes diffusive acceleration along lines of constant unperturbed Hamiltonian. The second order part, which corresponds to the longest time scale, describes diffusion across those lines. A possible transport theory is outlined on the basis of this separation of the time scales.