Magnetic field amplification in nonlinear diffusive shock acceleration including resonant and non-resonant cosmic-ray driven instabilities

TL;DR

This paper develops a comprehensive nonlinear Monte Carlo model for diffusive shock acceleration that self-consistently incorporates resonant and non-resonant cosmic-ray driven instabilities, magnetic field amplification, and turbulence cascading, providing insights into particle acceleration and shock structure.

Contribution

It introduces a multi-scale, steady-state model that integrates the full particle spectrum with magnetic turbulence generation and cascade effects, advancing understanding of shock acceleration mechanisms.

Findings

Scaling relations for maximum particle momentum and magnetic field amplification.

Impact of turbulence cascading on shock compression and particle spectra.

Dependence of magnetic field amplification on shock parameters.

Abstract

We present a nonlinear Monte Carlo model of efficient diffusive shock acceleration (DSA) where the magnetic turbulence responsible for particle diffusion is calculated self-consistently from the resonant cosmic-ray (CR) streaming instability, together with non-resonant short- and long-wavelength CR-current-driven instabilities. We include the backpressure from CRs interacting with the strongly amplified magnetic turbulence which decelerates and heats the super-alfvenic flow in the extended shock precursor. Uniquely, in our plane-parallel, steady-state, multi-scale model, the full range of particles, from thermal (~eV) injected at the viscous subshock, to the escape of the highest energy CRs (~PeV) from the shock precursor, are calculated consistently with the shock structure, precursor heating, magnetic field amplification (MFA), and scattering center drift relative to the background plasma. In addition, we show how the cascade of turbulence to shorter wavelengths influences the total shock compression, the downstream proton temperature, the magnetic fluctuation spectra, and accelerated particle spectra. A parameter survey is included where we vary shock parameters, the mode of magnetic turbulence generation, and turbulence cascading. From our survey results, we obtain scaling relations for the maximum particle momentum and amplified magnetic field as functions of shock speed, ambient density, and shock size.