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.

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Using the recently extended 2D improved Particle Acceleration and Transport in the Heliosphere (iPATH) model, we model an example gradual solar energetic particle event as observed at multiple locations. Protons and ions that are energized via the diffusive shock acceleration mechanism are followed at a 2D coronal mass ejection-driven shock where the shock geometry varies across the shock front. The subsequent transport of energetic particles, including cross-field diffusion, is modeled by a Monte Carlo code that is based on a stochastic differential equation method. Time intensity profiles and particle spectra at multiple locations and different radial distances, separated in longitudes, are presented. The results shown here are relevant to the upcoming Parker Solar Probe mission.

On 2017 September 10, a fast coronal mass ejection (CME) erupted from the active region (AR) 12673, leading to a ground level enhancement (GLE) event at Earth. Using the 2D improved Particle Acceleration and Transport in the Heliosphere (iPATH) model, we model the large solar energetic particle (SEP) event of 2017 September 10 observed at Earth, Mars and STEREO-A. Based on observational evidence, we assume that the CME-driven shock experienced a large lateral expansion shortly after the eruption, which is modeled by a double Gaussian velocity profile in this simulation. We apply the in-situ shock arrival times and the observed CME speeds at multiple spacecraft near Earth and Mars as constraints to adjust the input model parameters. The modeled time intensity profiles and fluence for energetic protons are then compared with observations. Reasonable agreements with observations at Mars and STEREO-A are found. The simulated results at Earth differ from observations of GOES-15. However, the simulated results at a heliocentric longitude 20° west to Earth fit reasonably well with the GOES observation. This can be explained if the pre-event solar wind magnetic field at Earth is not described by a nominal Parker field. Our results suggest that a large lateral expansion of the CME-driven shock and a distorted interplanetary magnetic field due to previous events can be important in understanding this GLE event.

Recent detection of superflares on solar-type stars by Kepler mission raised a possibility that they can be associated with energetic coronal mass ejections (CMEs) and energetic particle events (SEPs). These space weather events can impact habitability of exoplanets around these stars. Here we use the improved Particle Acceleration and Transport in the Heliosphere (iPATH) model, to model the time intensity profile and spectrum of SEPs accelerated at CME-driven shocks from stars of different ages traced by their rotation rates. We consider a solar-like (G-type) star with 6 different rotation rates varying from 0.5Ω to 3.0Ω . In all 6 cases, a fast CME is launched with the same speed of ∼ 1500 km/sec and the resulting time intensity profiles at 3 locations and and energy spectra at 5 locations at 1 AU are obtained. The maximum particle energy at the shock front as a function of r is also shown. Our results suggest that within 0.8 AU the maximum particle energy at the shock front increases with the rotation rate of the star. However, event integrated spectra for the five selected locations along the CME path show complicated patterns. This is because the Parker magnetic field for rapidly rotating stars is more tightly winded. Our results can be used in estimating the radiation environments of terrestrial-type exoplanets around solar-type stars.