  Energetic particles in a turbulent medium can be subject to second-order
Fermi acceleration due to scattering on moving plasma waves. This mechanism
leads to growing particle momentum dispersion and, at the same time, increases
the mean particle energy. In the most frequently met situations both processes
can be represented by a single momentum diffusion term in the particle kinetic
equation. In the present paper we discuss the conditions allowing the
additional term for regular acceleration to arise. For forward-backward
asymmetric scattering centres, besides the diffusive term one should explicitly
consider the regular acceleration term in momentum space, which can consist of
the first-order ($\propto V$), as well as the second-order ($\propto V^2$) part
in the wave velocity V . We derive the condition for the scattering probability
in the wave rest frame required for vanishing the regular acceleration term and
provide a simple mechanical example illustrating the theoretical concepts.
Finally, we address its possible role in cosmic ray acceleration processes.

Astrophysics