On the acceleration of charged particles at relativistic shock fronts

Details On the acceleration of charged particles at relativistic shock fronts On the acceleration of charged particles at relativistic shock fronts

Apr 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987apj...315..425k&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 315, April 15, 1987, p. 425-433. Research supported by the Max-Planck-Gesel

Statistics

Computation

136

Charged Particles, Computational Astrophysics, Particle Acceleration, Relativistic Velocity, Shock Fronts, Approximation, Cosmic Rays, Kinetic Equations, Particle Diffusion, Radio Sources (Astronomy), Solar Flares

Scientific paper

The diffusive acceleration of highly relativistic particles at a shock is reconsidered. Using the same physical assumptions as Blandford and Ostriker (1978), but dropping the restriction to nonrelativistic shock velocities, the authors find approximate solutions of the particle kinetic equation by generalizing the diffusion approximation to higher order terms in the anisotropy of the particle distribution. The general solution of the transport equation on either side of the shock is constructed, which involves the solution of an eigenvalue problem. By matching the two solutions at the shock, the spectral index of the resulting power law is found by taking into account a sufficiently large number of eigenfunctions. Low-order truncation corresponds to the standard diffusion approximation and to a somewhat more general method described by Peacock (1981). In addition to the energy spectrum, the method yields the angular distribution of the particles and its spatial dependence.

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