The acceleration of cosmic rays in shock fronts - I

TLDR

Fast particles are confined upstream of a shock by self‑generated Alfvén wave scattering, and the study focuses on already relativistic particles, ignoring initial thermal acceleration. Scattering confines particles near the shock, enabling first‑order Fermi acceleration as they repeatedly cross the shock. Charged particles are accelerated to high energies in shock fronts, producing a power‑law spectrum whose index matches that of galactic cosmic rays.

Abstract

It is shown that charged particles can be accelerated to high energies in astrophysical shock fronts. Fast particles are prevented from streaming away upstream of a shock front by scattering off Alfvén waves which they themselves generate. This scattering confines the particles to the region around the shock and results in first-order Fermi acceleration due to the particles crossing the shock many times. The consequent energy spectrum is a power law with an index close to that observed for galactic cosmic rays. The discussion relates to particles which are already relativistic, and their initial acceleration from thermal energies is not considered.