Diffusive particle acceleration by an ensemble of shock waves

Details Diffusive particle acceleration by an ensemble of shock waves Diffusive particle acceleration by an ensemble of shock waves

Oct 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993a%26a...278..315s&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 278, no. 1, p. 315-327

Astronomy and Astrophysics

Astrophysics

23

Cosmic Rays, Energy Spectra, Particle Acceleration, Shock Wave Interaction, Shock Waves, Active Galactic Nuclei, Adiabatic Conditions, Energy Dissipation

Scientific paper

The theory of diffusive acceleration of cosmic rays by shock waves (first order Fermi acceleration) is generalized to the case that the particles propagate through a medium in which many shocks are present simultaneously. The basic assumption underlying the theory presented here is that the typical time between two shock transitions a particle undergoes is much longer than the time of spectral formation at an individual shock. This allows the separation of the process of shock acceleration from other propagation effects. We consider as such particle escape from the system (catastrophic losses) and continuous energy losses. The interplay of shock acceleration and these other propagation effects leads to the formation of particle spectra with spectral features such as breaks at characteristic momenta, or humps. In particular, for special choices of the parameters describing the propagation of cosmic rays, results derived earlier (such as the spectral slope of particles produced by a periodic shock structure derived by Spruit, or the particle pile-up obtained by Schlickeiser) are reobtained. The approach followed in this paper is then compared with the one used by Blandford & Ostriker where they included an integral operator in the cosmic ray transport equation to describe impulsive acceleration. The theory considered here may find its application in the study of cosmic ray (re)acceleration in our galaxy, but is likely to be as important in other astrophysical environments, such as the central regions of active galactic nuclei, where we expect highly turbulent flows to be present. It can therefore be expected that in such objects there is a region in which many shocks are present. The multiple shock acceleration theory may then be used to study the formation of spectra in such objects.

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