Litvinenko, Yuri E.Schlickeiser, Reinhard2011-08-102011-08-102011Litvinenko, Y.E. & Schlickeiser, R. (2011). Focused acceleration of cosmic-ray particles in non-uniform magnetic fields. The Astrophysical Journal Letters, 732 (L31).https://hdl.handle.net/10289/5558The 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 an Alfvenic slab turbulence is either negative in a diverging guide field or positive in a converging guide field. It is suggested that focused acceleration can contribute to the formation of the anomalous cosmic-ray spectrum at the heliospheric termination shock.application/pdfenThis article has been published in the journal: The Astrophysical Journal Letters. © 2011 The American Astronomical Society.acceleration of particlescosmic raysturbulenceJournal Article10.1088/2041-8205/732/2/L31