Cosmic-ray shock acceleration in the presence of self-excited waves

Details Cosmic-ray shock acceleration in the presence of self-excited waves Cosmic-ray shock acceleration in the presence of self-excited waves

Feb 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983a%26a...118..223l&link_type=abstract

Astronomy and Astrophysics, vol. 118, no. 2, Feb. 1983, p. 223-228.

Astronomy and Astrophysics

Astrophysics

184

Cosmic Rays, Particle Acceleration, Self Excitation, Shock Wave Propagation, Asymptotic Methods, Diffusion Coefficient, Laplace Transformation, Magnetohydrodynamic Waves, Plane Waves, Random Walk

Scientific paper

The effect of the spatial dependence of the diffusion coefficients on the acceleration rate of particles by diffusive plane shock waves are examined. Upstream, hydromagnetic waves are generated by cosmic rays diffusing away from the shock. Cosmic rays are scattered by these waves, and by the underlying turbulence; thus the diffusion coefficient increases away from the shock. Downstream, the diffusion coefficient may be taken as uniform. The problem is solved using two methods: first, an approximate solution to the transport equation is derived, which makes it possible to evaluate the time of establishment of the equilibrium spectrum; second, a random walk approach is used which emphasizes the stochastic nature of the acceleration mechanism. It is shown that the spatial dependence of the diffusion coefficient considered leads to an increment of the acceleration time with respect to that obtained if the diffusion coefficient had everywhere the value it has at the shock. This effect has to be considered when determining the energy that can be attained by particles accelerated throughout the lifetime of a supernova remnant.

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