Power requirements for cosmic ray propagation models involving re-acceleration and a comment on second-order Fermi acceleration theory

Abstract

We derive an analytic expression for the power transferred from interstellar turbulence to the Galactic cosmic rays in propagation models which include re-acceleration. This is used to estimate the power required in such models and the relative importance of the primary acceleration as against re-acceleration. The analysis provides a formal mathematical justification for Fermi's heuristic account of second-order acceleration in his classic 1949 paper. © 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.