Basic Bell-MHD Turbulence

TL;DR

This paper investigates the nonlinear evolution of Bell-MHD turbulence, revealing a scale-energy relationship that impacts cosmic ray acceleration in supernova remnants.

Contribution

It demonstrates that magnetic turbulence from Bell instability behaves like large-scale turbulence and establishes a scale-energy relation relevant for cosmic ray acceleration.

Findings

Magnetic turbulence evolution resembles large-scale turbulence.

The energy-containing scale is proportional to the square root of magnetic energy density.

Maximum particle energy estimates are below average particle energies.

Abstract

Nonresonant current instability was identified by Bell (2004) as an important mechanism for magnetic field amplification in supernova remnants. In this paper we focus on studying the nonlinear stage of this instability using the incompressible MHD formulation. We demonstrate that the evolution of magnetic turbulence driven by the Bell instability resembles turbulence driven on large scales. More importantly, we demonstrate that the energy-containing scale for magnetic fields is proportional to the square root of magnetic energy density. Given the observational constraints of the possible field amplification, this new relation allows us to directly estimate the maximum energy of particles scattered by such fields and this estimate is normally below the average particle energy. This implies that, without taking into account the feedback to cosmic rays, the typical scales of Bell fields, in either linear or nonlinear regime, will be too small to affect high energy particle acceleration. We mention several scenarios of back-reaction to cosmic rays that could be important.