Self-Similar Evolution of Cosmic-Ray-Modified Quasi-Parallel Plane Shocks

TL;DR

This study uses advanced simulations to analyze the self-similar evolution of cosmic-ray-modified shocks, revealing how shock structures and efficiencies depend on Mach number and wave dynamics.

Contribution

It introduces an improved CRASH code to simulate higher energy CRs and incorporates self-consistent Alfven wave effects, advancing understanding of shock evolution and acceleration.

Findings

Postshock CR pressure reaches a steady state quickly.

Shock precursor broadens linearly with time.

Wave effects reduce CR acceleration efficiency.

Abstract

Using an improved version of the previously introduced CRASH (Cosmic Ray Acceleration SHock) code, we have calculated the time evolution of cosmic-ray (CR) modified quasi-parallel plane shocks for Bohm-like diffusion, including self-consistent models of Alfven wave drift and dissipation, along with thermal leakage injection of CRs. The new simulations follow evolution of the CR distribution to much higher energies than our previous study, providing a better examination of evolutionary and asymptotic behaviors. The postshock CR pressure becomes constant after quick initial adjustment, since the evolution of the CR partial pressure expressed in terms of a momentum similarity variable is self-similar. The shock precursor, which scales as the diffusion length of the highest energy CRs, subsequently broadens approximately linearly with time, independent of diffusion model, so long as CRs continue to be accelerated to ever-higher energies. This means the nonlinear shock structure can be described approximately in terms of the similarity variable, x/(u_s t), where u_s is the shock speed once the postshock pressure reaches an approximate time asymptotic state. As before, the shock Mach number is the key parameter determining the evolution and the CR acceleration efficiency, although finite Alfven wave drift and wave energy dissipation in the shock precursor reduce the effective velocity change experienced by CRs, so reduce acceleration efficiency noticeably, thus, providing a second important parameter at low and moderate Mach numbers.