A Novel Approach to Non linear Shock Acceleration

First order Fermi acceleration at astrophysical shocks is often invoked as a mechanism for the generation of non-thermal particles. This mechanism is especially simple in the approximation that the accelerated particles behave like test particles, not affecting the shocked fluid. Many complications enter the calculations when the accelerated particles have a backreaction on the fluid, in which case we may enter the non linear regime of shock acceleration. In this paper we summarize the main features of a semi-analytical approach to the study of the non linearity in shock acceleration, and compare some of the results with previous attempts and with the output of numerical simulations.Comment: To appear in the proceedings of the TAUP conference, September 8-12, 2001 - Gran Sasso Laboratory, Ital

Nonlinear Particle Acceleration in Relativistic Shocks

Monte Carlo techniques are used to model nonlinear particle acceleration in parallel collisionless shocks of various speeds, including mildly relativistic ones. When the acceleration is efficient, the backreaction of accelerated particles modifies the shock structure and causes the compression ratio, r, to increase above test-particle values. Modified shocks with Lorentz factors less than about 3 can have compression ratios considerably greater than 3 and the momentum distribution of energetic particles no longer follows a power law relation. These results may be important for the interpretation of gamma-ray bursts if mildly relativistic internal and/or afterglow shocks play an important role accelerating particles that produce the observed radiation. For shock Lorentz factors greater than about 10, r approaches 3 and the so-called `universal' test-particle result of N(E) proportional to E^{-2.3} is obtained for sufficiently energetic particles. In all cases, the absolute normalization of the particle distribution follows directly from our model assumptions and is explicitly determined.Comment: Updated version, Astroparticle Physics, in press, 29 pages, 13 figure

Non linear particle acceleration at non-relativistic shock waves in the presence of self-generated turbulence

Particle acceleration at astrophysical shocks may be very efficient if magnetic scattering is self-generated by the same particles. This nonlinear process adds to the nonlinear modification of the shock due to the dynamical reaction of the accelerated particles on the shock. Building on a previous general solution of the problem of particle acceleration with arbitrary diffusion coefficients (Amato & Blasi, 2005), we present here the first semi-analytical calculation of particle acceleration with both effects taken into account at the same time: charged particles are accelerated in the background of Alfven waves that they generate due to the streaming instability, and modify the dynamics of the plasma in the shock vicinity.Comment: submitted to MNRA