Modeling Particle Acceleration and Transport at a 2‐D CME‐Driven Shock

Abstract

We extend our earlier Particle Acceleration and Transport in the Heliosphere (PATH) model to study particle acceleration and transport at a coronal mass ejection (CME)‐driven shock. We model the propagation of a CME‐driven shock in the ecliptic plane using the ZEUS‐3D code from 20 solar radii to 2 AU. As in the previous PATH model, the initiation of the CME‐driven shock is simplified and modeled as a disturbance at the inner boundary. Different from the earlier PATH model, the disturbance is now longitudinally dependent. Particles are accelerated at the 2‐D shock via the diffusive shock acceleration mechanism. The acceleration depends on both the parallel and perpendicular diffusion coefficients κ|| and κ⊥ and is therefore shock‐obliquity dependent. Following the procedure used in Li, Shalchi, et al. (), we obtain the particle injection energy, the maximum energy, and the accelerated particle spectra at the shock front. Once accelerated, particles diffuse and convect in the shock complex. The diffusion and convection of these particles are treated using a refined 2‐D shell model in an approach similar to Zank et al. (). When particles escape from the shock, they propagate along and across the interplanetary magnetic field. The propagation is modeled using a focused transport equation with the addition of perpendicular diffusion. We solve the transport equation using a backward stochastic differential equation method where adiabatic cooling, focusing, pitch angle scattering, and cross‐field diffusion effects are all included. Time intensity profiles and instantaneous particle spectra as well as particle pitch angle distributions are shown for two example CME shocks.

Statistical Study on Multispacecraft Widespread Solar Energetic Particle Events During Solar Cycle 24

“…For example, Lario et al (2013) found an asymmetry of 16 • to the east for 35 STEREO 71-to 112-keV electron events. An asymmetric distribution of SEPs with an eastern offset was also supported in numerical simulations (e.g., Ablaßmayer et al, 2016;He & Wan, 2015;Hu et al, 2017). In contrast, Dresing et al (2014) found an asymmetry of 11 • to the west for 21 widespread 55-to 105-keV electron events.…”

“…In contrast, Dresing et al (2014) found an asymmetry of 11 • to the west for 21 widespread 55-to 105-keV electron events. Hu et al (2017) used a 2-D numerical model to study particle acceleration and transport at a CME-driven shock. In He and Wan (2015, Figure 3), they plotted the simulated peak intensities of SEPs originating from different heliolongitudes with CAs ranging from −140 • to 140 • and showed that the peak intensities of the SEP events originating from solar sources located on the eastern side of the observer footpoint (negative CAs) are systematically larger than those of the SEP events originating from sources located on the western side (positive CAs).…”

“…Furthermore, detailed examination showed that the SEP intensity distribution cannot be fit with a single Gaussian width, and the SEP distribution width increases with the absolute value of CA. Hu et al (2017) used a 2-D numerical model to study particle acceleration and transport at a CME-driven shock. They found that strong perpendicular diffusion is required for the observed asymmetric distribution of SEP intensities.…”

“…Several mechanisms have been proposed to explain such a large spread of SEP events. Cross-field transport in the corona and interplanetary (IP) space is another mechanism that results in widespread SEP events (Hu et al, 2017;Zhang et al, 2009;Zhang & Zhao, 2017). Cross-field transport in the corona and interplanetary (IP) space is another mechanism that results in widespread SEP events (Hu et al, 2017;Zhang et al, 2009;Zhang & Zhao, 2017).…”

“…Coronal shocks driven by fast and wide coronal mass ejections (CMEs) are generally considered to be spatially extended particle sources that accelerate and inject particles into large regions in the heliosphere (Cliver et al, 1995). Cross-field transport in the corona and interplanetary (IP) space is another mechanism that results in widespread SEP events (Hu et al, 2017;Zhang et al, 2009;Zhang & Zhao, 2017). In addition, concurrence of multiple solar eruptions, large magnetic loops, and IP transient structures can also lead to widespread SEP events (e.g., Klein et al, 2008;Leske et al, 2012;Richardson et al, 1991;Schrijver et al, 2013).…”