# The Acceleration of Energetic Particles at Coronal Shocks and Emergence of a Double Power Law Feature in Particle Energy Spectra

## TL;DR

This study models particle acceleration at coronal shocks in streamer-like magnetic fields, revealing a double power law in energy spectra and highlighting the streamer’s role in large solar energetic particle events.

## Contribution

It demonstrates how streamer-like magnetic fields influence particle acceleration and produce a double power law energy spectrum, a novel insight into solar energetic particle events.

## Key findings

- High-energy particle acceleration occurs mainly in shock-streamer interaction regions.
- The energy spectrum shows a double power law, indicating two distinct populations.
- Streamer magnetic fields significantly enhance particle intensities at high energies.

## Abstract

We present numerical modelling of particle acceleration at coronal shocks propagating through a streamer-like magnetic field by solving the Parker transport equation with spatial diffusion both along and across the magnetic field. We show that the location on the shock where the high-energy particle intensity is the largest, depends on the energy of the particles and on time. The acceleration of particles to more than 100 MeV mainly occurs in the shock-streamer interaction region, due to perpendicular shock geometry and the trapping effect of closed magnetic fields. A comparison of the particle spectra to that in a radial magnetic field shows that the intensity at 100 MeV (200 MeV) is enhanced by more than one order (two orders) of magnitude. This indicates that the streamer-like magnetic field can be an important factor in producing large solar energetic particle events. We also show that the energy spectrum integrated over the simulation domain consists of two different power laws. Further analysis suggests that it may be a mixture of two distinct populations accelerated in the streamer and open field regions, where the acceleration rate differs substantially. Our calculations also show that the particle spectra are affected considerably by a number of parameters, such as the streamer tilt angle, particle spatial diffusion coefficient, and shock compression ratio. While the low-energy spectra agree well with standard diffusive shock acceleration theory, the break energy ranges from $\sim$1 MeV to $\sim$90 MeV and the high-energy spectra can extend to $\sim$1 GeV with a slope of $\sim$2-3.