Beyond the Test-Particle Power Law: Particle Spectra in Diffusive Shock Acceleration

Collisionless shocks are common in astrophysics and the diffusive shock acceleration (DSA) mechanism is believed to accelerate cosmic rays efficiently in these shocks. When this mechanism was introduced thirty-five years ago, the fact that the test-particle theory produced a power law in momentum reasonably consistent with that observed in cosmic rays, lead to the quick acceptance of DSA as the mechanism of choice for shocks throughout the universe. There are, however, a number of factors that can modify the spectrum produced by DSA and caution must be used in applying the test-particle result. I will briefly describe how DSA can produce spectra that vary considerably from the canonical test-particle power law.