Comparison between particle acceleration at a continuous compression and at a shock

Abstract

The charged particles in an astrophysical plasma can be accelerated to become energetic particles (cosmic rays) by the first-order Fermi acceleration mechanism. In addition to a shock, a continuous compression is another site where this mechanism can accelerate the particles. We simulate the particle transport near a shock or compression by using a Fokker-Planck equation and choosing an oblique magnetic field. To study this numerically, we solve the equation of particle transport by the finite difference method, interpolation, a TVD method, and the operator splitting technique. From the simulations, we found that there is a peak in intensity vs. distance profiles at the center of a narrow compression region, where the compression width divided by the scattering mean free path (b/lambdaII) is small. Such a peak is not found in models that neglect pitch angle processes. Therefore, we conclude that this feature is associated with magnetic mirroring at anoblique shock or compression, and we call this the "mirroring peak." In association with the mirroring peak, a harder particle spectrum is found in the steady-state (in comparison with the standard diffusion approximation that neglects the pitch angle distribution). This indicates more efficient acceleration for an oblique shock or compression at low energy and low b/lambdaII values, because of magnetic mirroring.