Journal
JOURNAL OF COSMOLOGY AND ASTROPARTICLE PHYSICS
Volume -, Issue 12, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1475-7516/2011/12/010
Keywords
particle acceleration; cosmic ray theory
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A new analytic solution for 2nd-order Fermi acceleration is presented. In particular, we consider time-dependent rates for stochastic acceleration, diffusive and convective escape as well as a diabatic losses. The power law index q of the turbulence spectrum is unconstrained and can therefore account for Kolmogorov (q - 5/3) and Kraichnan (q - 3/2) turbulence, Bohm diffusion (q = 1) as well as the hard-sphere approximation (q = 2). This considerably improves beyond solutions known to date and will prove a useful tool for more realistic modelling of 2nd-order Fermi acceleration in a variety of astrophysical environments.
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