# Monte Carlo modelling of particle acceleration in collisionless shocks with an effective mean electric field

## TL;DR

This paper introduces a nonlinear Monte Carlo model for particle acceleration in collisionless shocks, incorporating an effective mean electric field and backreaction effects, to better understand cosmic ray acceleration in supernova remnants.

## Contribution

It presents a novel Monte Carlo simulation that explicitly includes an effective mean electric field and backreaction, advancing the modeling of shock acceleration processes.

## Key findings

- Demonstrates the impact of mean electric field on particle acceleration efficiency
- Shows nonlinear feedback effects modify shock structure and acceleration dynamics
- Provides insights into magnetic field amplification mechanisms in supernova remnants

## Abstract

Relativistic particle acceleration in collisionless shocks of supernova remnants is accompanied by magnetic field amplification from cosmic ray (CR) driven plasma instabilities. Bell's fast CR-current instability is predicted to produce turbulence with a non-zero mean electric field in the shock precursor. We present a Monte Carlo model of Fermi shock acceleration explicitly taking into account an effective mean upstream electric field. Our model is nonlinear and includes the backreaction effects of efficient Fermi acceleration on the shock structure.