Efficient particle acceleration in shocks

Open Access
Publisher Website
Google Scholar
Abstract
A self-consistent non-linear theory of acceleration of particles by shock waves is developed, using an extension of the two-fluid hydrodynamical model by Drury & Völk. The transport of the accelerated particles is governed by a diffusion coefficient which is initially assumed to be independent of particle momentum, to obtain exact solutions for the spectrum. It is found that steady-state shock structures with high acceleration efficiency are only possible for shocks with Mach numbers (defined by the ratio of the shock speed to the conventional sound speed, measured in the unshocked gas) less than about 12. A more realistic diffusion coefficient is then considered, and this maximum Mach number is reduced to about 6. The analysis differs from that of Drury & Völk in that the effective specific heat ratio of the accelerated particles is not taken to be a fixed value. The efficiency of the acceleration process determines the relative importance of the non-relativistic and relativistic particles in the distribution of accelerated particles, and this determines the effective specific heat ratio. The variable specific heat ratio allows families of solutions to be found, in contrast to the conclusions of Drury and Völk. It is assumed that a discontinuity in the gas velocity (a subshock) exists. It is also found that, unless the rate of injection of particles into the acceleration process is very low, high-Mach-number shocks can accelerate particles so efficiently that no shock structure involving a subshock exists.

This publication has 0 references indexed in Scilit: