An introduction to the theory of diffusive shock acceleration of energetic particles in tenuous plasmas

Details An introduction to the theory of diffusive shock acceleration of energetic particles in tenuous plasmas An introduction to the theory of diffusive shock acceleration of energetic particles in tenuous plasmas

Aug 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983rpph...46..973d&link_type=abstract

Reports on Progress in Physics (ISSN 0034-4885), vol. 46, Aug. 1983, p. 973-1027.

Physics

805

Energetic Particles, Particle Acceleration, Plasma-Particle Interactions, Rarefied Plasmas, Shock Wave Propagation, Kinematics, Nonlinear Systems, Oblique Shock Waves, Plane Waves, Rankine-Hugoniot Relation, Time Dependence

Scientific paper

The central idea of diffusive shock acceleration is presented from microscopic and macroscopic viewpoints; applied to reactionless test particles in a steady plane shock the mechanism is shown to produce a power law spectrum in momentum with a slope which, to lowest order in the ratio of plasma to particle speed, depends only on the compression in the shock. The associated time scale is found (also by a macroscopic and a microscopic method) and the problems of spherical shocks, as exemplified by a point explosion and a stellar-wind terminator, are treated by singular perturbation theory. The effect of including the particle reaction is then studied. It is shown that if the scattering is due to resonant waves these can rapidly grow with unknown consequences. The possible steady modified shock structures are classified and generalised Rankine-Hugoniot conditions found. Modifications of the spectrum are discussed on the basis of an exact, if rather artificial, solution, a high-energy asymptotic expansion and a perturbation expansion due to Blandford. It is pointed out that no steady solution can exist for very strong shocks; the possible time dependence is briefly discussed.

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