The Relation Between Escape and Scattering Times of Energetic Particles in a Turbulent Magnetized Plasma: Application to Solar Flares

TL;DR

This study investigates the relationship between escape and scattering times of energetic particles in turbulent magnetized plasmas, with applications to solar flares, using both analytical relations and numerical models to improve understanding of particle transport.

Contribution

It tests and validates an approximate analytic relation between escape and scattering times considering magnetic field convergence, using a kinetic Fokker-Planck model with stochastic differential equations.

Findings

Numerical results agree with the analytic relation for isotropic cases.

Significant differences observed in weak diffusion and non-isotropic cases.

Results aid in interpreting solar flare particle observations and determining transport coefficients.

Abstract

A knowledge of the particle escape time from the acceleration regions of many space and astrophysical sources is of critical importance in the analysis of emission signatures produced by these particles and in the determination of the acceleration and transport mechanisms at work. This paper addresses this general problem, in particular in solar flares, where in addition to scattering by turbulence, the magnetic field convergence from the acceleration region towards its boundaries also influences the particle escape. We test an (approximate) analytic relation between escape and scattering times, and the field convergence rate, based on the work of Malyshkin and Kulsrud (2001), valid for both strong and weak diffusion limits and isotropic pitch angle distribution of the injected particles, with a numerical model of particle transport. To this end, a kinetic Fokker-Planck transport model of particles is solved with a stochastic differential equation scheme assuming different initial pitch angle distributions. This approach enables further insights into the phase-space dynamics of the transport process, which would otherwise not be accessible. We find that in general the numerical results agree well with the analytic equation for the isotropic case, however, there are significant differences weak diffusion regime for non-isotopic cases, especially for distributions beamed along the magnetic field lines. The results are important in the interpretation of observations of energetic particles in solar flares, and other similar space and astrophysical acceleration sites and for the determination of acceleration-transport coefficients, commonly used in Fokker-Planck type kinetic equations.