Stochastic acceleration in strong random fields
  Diffusion of particles in velocity space undergoing turbulent field was extensively studied in the problem of warm beam relaxation. Under low field intensities the diffusion is described by the Fokker-Planck equation with the diffusion coefficient given by quasilinear theory. This diffusion coefficient is calculated on the free particle propagator and for weak fields its renormalization due to orbit diffusion is not necessary. To study effects which should be taken into account when the intensity of the turbulent field is increased a numerical simulation of particle motion in the external field of Langmuir waves with given k-spectrum and random phases is done. For strong fields meansquare velocity evolution shows that ballistic regime in the very beginning is changed for oscillatory one in the intermediate stage and later for diffusion. Asymptotically it behaves like fractional power of elapsed time with the exponent dependent on the particular field spectrum. Such evolution in the whole temporal interval of simulation is recovered from the numerical solution of generalized Fokker-Planck equation with time dependent diffusion coefficient obtained from the microscopic approach. The analytical approximation for this solution is also given. 
Anatoly Zagorodny, Volodymyr Zasenko, Jan Weiland