SIMULATIONS OF ION ACCELERATION AT NON-RELATIVISTIC SHOCKS. II. MAGNETIC FIELD AMPLIFICATION

Abstract

We use large hybrid simulations to study ion acceleration and generation of\nmagnetic turbulence due to the streaming of particles that are\nself-consistently accelerated at non-relativistic shocks. When acceleration is\nefficient, we find that the upstream magnetic field is significantly amplified.\nThe total amplification factor is larger than 10 for shocks with Alfv\\'enic\nMach number $M=100$, and scales with the square root of $M$. The spectral\nenergy density of excited magnetic turbulence is determined by the energy\ndistribution of accelerated particles, and for moderately-strong shocks\n($M\\lesssim30$) agrees well with the prediction of resonant streaming\ninstability, in the framework of quasilinear theory of diffusive shock\nacceleration. For $M\\gtrsim30$, instead, Bell's non-resonant hybrid (NRH)\ninstability is predicted and found to grow faster than resonant instability.\nNRH modes are excited far upstream by escaping particles, and initially grow\nwithout disrupting the current, their typical wavelengths being much shorter\nthan the current ions' gyroradii. Then, in the nonlinear stage, most unstable\nmodes migrate to larger and larger wavelengths, eventually becoming resonant in\nwavelength with the driving ions, which start diffuse. Ahead of strong shocks\nwe distinguish two regions, separated by the free-escape boundary: the far\nupstream, where field amplification is provided by the current of escaping ions\nvia NRH instability, and the shock precursor, where energetic particles are\neffectively magnetized, and field amplification is provided by the current in\ndiffusing ions. The presented scalings of magnetic field amplification enable\nthe inclusion of self-consistent microphysics into phenomenological models of\nion acceleration at non-relativistic shocks.\n