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

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.

arXiv comment8 pages, 2 figures, submitted

References in corpus (32)

• Stochastic Acceleration of Electrons and Protons. I. Acceleration by Parallel Propagating Waves
• Plasmoid Ejections and Loop Contractions in an Eruptive M7.7 Solar Flare: Evidence of Particle Acceleration and Heating in Magnetic Reconnection Outflows
• Stochastic Acceleration by Turbulence
• Double Coronal Hard and Soft X-ray Source Observed by RHESSI: Evidence for Magnetic Reconnection and Particle Acceleration in Solar Flares
• Looptop Hard X-Ray Emission in Solar Flares: Images and Statistics
• Impulsive and Long Duration High-Energy Gamma-ray Emission From the Very Bright 2012 March 7 Solar Flares
• The Formation of Kappa-Distribution Accelerated Electron Populations in Solar Flares
• Kappa Distribution Model for Hard X-Ray Coronal Sources of Solar Flares
• A Hitch-hiker's Guide to Stochastic Differential Equations: Solution Methods for Energetic Particle Transport in Space Physics and Astrophysics
• Electron Power-Law Spectra in Solar and Space Plasmas
• RHESSI Observation of Chromospheric Evaporation
• Fermi-LAT Observations of High-energy Behind-the-limb Solar Flares
• Turbulent pitch-angle scattering and diffusive transport of hard-X-ray producing electrons in flaring coronal loops
• First detection of >100 MeV gamma rays associated with a behind-the-limb solar flare
• Kappa distribution and hard X-ray emission of solar flares
• Collisional relaxation of electrons in a warm plasma and accelerated nonthermal electron spectra in solar flares
• Transport phenomena in stochastic magnetic mirrors
• On the Spatial Distribution of Hard X-Rays from Solar Flare Loops
• Heating and Acceleration of Intracluster Medium Electrons by Turbulence
• Probing the Puzzle of Behind-the-Limb $\gamma$-ray Flares: Data-driven Simulations of Magnetic Connectivity and CME-driven Shock Evolution
• The Diffusion Approximation vs. the Telegraph Equation for Modeling Solar Energetic Particle Transport with Adiabatic Focusing. I. Isotropic Pitch-angle Scattering
• Hard X-Ray Emission from Partially Occulted Solar Flares: RHESSI Observations in Two Solar Cycles
• On the variation of solar flare coronal x-ray source sizes with energy
• Determination of Stochastic Acceleration Model Characteristics in Solar Flares
• A Generalized Diffusion Tensor for Fully Anisotropic Diffusion of Energetic Particles in the Heliospheric Magnetic Field
• Derivation of Stochastic Acceleration Model Characteristics for Solar Flares From RHESSI Hard X-Ray Observations
• Particle Acceleration in Solar Flares and Associated CME Shocks
• A more accurate numerical scheme for diffusive shock acceleration
• Acceleration of Thermal Protons By Generic Phenomenological Mechanisms
• Hard X-ray morphology of the X1.3 April 25, 2014 partially occulted limb solar flare
• Determination of Acceleration Mechanism Characteristics Directly and Non-Parametrically from Observations: Application to Supernova Remnants
• Hybrid simulations of chromospheric HXR flare sources

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