Simulation of Energetic Particle Transport and Acceleration at Shock Waves in a Focused Transport Model: Implications for Mixed Solar Particle Events

Abstract

We use numerical solutions of the focused transport equation obtained by an implicit stochastic differential equation scheme to study the evolution of the pitch-angle dependent distribution function of protons in the vicinity of shock waves. For a planar stationary parallel shock, the effects of anisotropic distribution functions, pitch-angle dependent spatial diffusion, and first-order Fermi acceleration at the shock are examined, including the timescales on which the energy spectrum approaches the predictions of diffusive shock acceleration theory. We then consider the case that a flare-accelerated population of ions is released close to the Sun simultaneously with a traveling interplanetary shock for which we assume a simplified geometry. We investigate the consequences of adiabatic focusing in the diverging magnetic field on the particle transport at the shock, and of the competing effects of acceleration at the shock and adiabatic energy losses in the expanding solar wind. We analyze the resulting intensities, anisotropies, and energy spectra as a function of time and find that our simulations can naturallyreproducethe morphologies of so-called mixed particle events in which sometimes the prompt and sometimes the shock component is more prominent, by assuming parameter values which are typically observed for scattering mean free paths of ions in the inner heliosphere and energy spectra of the flare particles which are injected simultaneously with the release of the shock.

A Model for AR Scorpii: Emission from Relativistic Electrons Trapped by Closed Magnetic Field Lines of Magnetic White Dwarfs

“…As we discussed in section 3.1, the evolution of the Lorentz factor and the perpendicular momentum of the injected electrons depend on the initial pitch angle. The distribution of the pitch angle of the particles for different acceleration processes has been investigated by the previous authors (Achterberg et al 2001;Kartavykh et al 2016), but it is still under investigation with a more realistic situation. In this study, therefore, we assume an isotropic distribution in the initial pitch angle θ p,0 , that is, dṄ e dθ p,0 = constant.…”

Numerical Modeling of Energetic Electron Acceleration, Transport, and Emission in Solar Flares: Connecting Loop-top and Footpoint Hard X-Ray Sources

“…In addition to similar terms in the Parker equation, the focused transport equation contains other terms, e.g., streaming along the magnetic field and variation of pitch angle. It has been widely applied to the transport of solar energetic particles (SEPs) in the corona and interplanetary space (e.g., Wang et al 2012;Zhao et al 2016;Hu et al 2017;Zhang & Zhao 2017;Wei et al 2019;Wijsen et al 2019) and particle acceleration at shocks (e.g., Zuo et al 2011;le Roux & Webb 2012;Zuo et al 2013;Kartavykh et al 2016).…”

The Energetic Particle Detector

“…Some SEP events may exhibit mixed or hybrid (Kallenrode et al 1992) composition, that is, with contribution of particles accelerated both at flares and at CME-driven shocks. The different scenarios proposed to explain the presence of flareaccelerated particles in large SEP events are detailed in the re-cent papers by Desai & Giacalone (2016) and Kartavykh et al (2016).…”

“…Among possible mechanisms that may play a role in perpendicular transport are turbulence-associated cross field motion (e.g. Zhang et al 2009;Schwadron et al 2010;Dröge et al 2010;Kartavykh et al 2016;Laitinen et al 2016;Wijsen, N. et al 2019), charged particle drifts (Dalla et al 2017), and the influence of the heliospheric current sheet (e.g. Agueda et al 2013;Battarbee et al 2018).…”