Resonant interaction of hydromagnetic waves with charged particles

The effect of the resonant interaction of a distribution of hydromagnetic waves on a distribution of particles is described by a diffusion equation in momentum space. The diffusion coefficients and other coefficients describing systematic acceleration and diffusion in energy space are derived in general and for a number of particular cases. It is shown that the resonant acceleration of slow ions by hydromagnetic waves is ineffective. The time evolution of the energy spectrum for ultrarelativistic particles due to interaction with hydromagnetic waves is found and applied to the case of the Crab Nebula in an accompanying article.