On validity of quasi-linear theory for non-resonant pitch-angle diffusion by finite amplitude parallel propagating Alfven waves

Pitch-angle diffusion of charged particles via non-resonant interaction with low-frequency magnetohydrodynamic waves is discussed. Even in the presence of finite amplitude waves, a quasi-linear theory in which the normalization using wave energy is carried out agrees well with numerical results of test particle simulations. The quasi-linear theory for non-resonant diffusion is also in good agreement with the numerical results, even if the spectra of the waves are not broad.