A stochastic model for non-relativistic particle acceleration

TL;DR

This paper introduces a stochastic model based on a second order Fermi mechanism that explains the energy spectra of non-relativistic particles accelerated at collisionless shock waves, supported by observational data.

Contribution

The paper presents a new stochastic model deriving Weibull-shaped energy spectra for particles, incorporating anomalous diffusion within a second order Fermi acceleration framework.

Findings

The model produces Weibull-shaped energy spectra as stationary solutions.

Observational data from STEREO B supports the model's applicability.

Second order Fermi mechanism explains energetic particle acceleration at shocks.

Abstract

A stochastic model is proposed for the acceleration of non-relativistic particles yielding to energy spectra with a shape of a Weibull\textquoteright s function. Such particle distribution is found as the stationary solution of a diffusion-loss equation in the framework of a second order Fermi\textquoteright s mechanism producing anomalous diffusion for particle velocity. The present model is supported by in situ observations of energetic particle enhancements at interplanetary shocks, as here illustrated by means of an event seen by STEREO B instruments in the heliosphere. Results indicate that the second order Fermi\textquoteright s mechanism provides a viable explanation for the acceleration of energetic particles at collisioness shock waves.