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

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 Letter addresses this general problem, in particular in solar flares, where in addition to scattering by turbulence, the magnetic field convergence from the acceleration region toward 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 & Kulsrud, valid for both strong and weak diffusion limits and isotropic pitch-angle distributions 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 in the 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.