Remarks about diffusive shock pave acceleration

Abstract

The topology of the particle transport equation used in particle acceleration theories at astrophysical shocks has been investigated. The popular and widely used transport equation without momentum diffusion results rigorously from first principles only if a drastic simplification of the Alfvén wave propagation directions is made: all waves move with the same phase speed. It is argued that this simplification is never realized in astrophysical objects and therefore is a severe misrepresentation of the physical acceleration process. Discarding this simplification leads to a situation where momentum diffusion of particles by cyclotron damping the Alfvénic turbulence is un avoidable. Solutions to the transport equation with and without the momentum diffusion term are presented which indicate the importance of momentum diffusion, leading to a quite different view on the elementary acceleration process. The acceleration of particles at shocks is primarily due to the cyclotron damping whereas the energy gain by multiple shock crossings is a minor effect. Astrophysical shock waves with large Peclet numbers accelerate particles very efficient.