Stochastic energy diffusion of electrons in a plasma by an electron cyclotron wave

The investigation of the energy diffusion process of the electrons in a magnetized plasma due to an electron cyclotron wave in perpendicular propagation with respect to the magnetic field is performed. Starting from the description of the relativistic electron motion by means of an actionâ angle Hamiltonian H(I,θ,t), the Fokker–Planck–Kolmogorov (FPK) approach to the diffusion is considered for a globally stochastic regime of the system. In this regime, the phase correlation process is analyzed, and the characteristic decay time is estimated analytically. The action diffusion coefficient D(I) is derived and compared with a local quasilinear expression. With explicit reference to the lowâ density regime, where D increases with I, and is very close to the quasilinear coefficient, the solution of the diffusion equation is compared with the results obtained by direct numerical integration of the motion equations for a statistically significant ensemble of particles. A good agreement with the local quasilinear FPK diffusion is observed. In addition, when the amplitude of the perturbation is varied, oscillations of the average action values around the quasilinear results are found on the long time scale.