The Ruhr University of Bochum, Germany
Focused acceleration of cosmic rays: A new universal first-order Fermi mechanism
The Fokker-Planck equation for cosmic-ray particles in a spatially varying guide magnetic field in a turbulent plasma is analyzed. An expression is derived for the mean rate of change of particle momentum, caused by the effect of adiabatic focusing in a non-uniform guide field. Results of an earlier diffusion-limit analysis are confirmed, and the physical picture is clarified by working directly with the Fokker-Planck equation. A distributed first-order Fermi acceleration mechanism is identified, which can be termed focused acceleration. If the forward- and backward-propagating waves have equal polarizations, focused acceleration operates when the net cross helicity of Alfvénic slab turbulence is either negative in a diverging guide field or positive in a converging guide field. Focused acceleration can contribute to the formation of the anomalous cosmic-ray spectrum at the heliospheric termination shock, and quantitatively modifies the physics of diffusive shock acceleration of cosmic ray particles.