Particle Injection at the Mediated Shock

Collisionless shock waves can produce energetic particles via diffusive shock acceleration (DSA). DSA theory dictates that seed particles, which have sufficient energy to cross the shock wave, gain energy by bouncing off turbulence upstream and downstream. Seed particles can be recognized as pre-accelerated thermal component, which exceed injection energy. The produced energetic particles can mediate the shock structure when the pressure of energetic particles (derived from fluid perspective) dominates over the thermal and magnetic pressure. The dominant energetic particle pressure can decelerate the incoming plasma flow, which leads to a modified shock structure profile with a smooth transition. Although it is rare, the modified shock has been observed in the heliosphere. As a result, the mediated shock transition region is usually broader than the non-mediated shock. Although It's been discussed how thermal particles are injected at the standard non-mediated shock waves, the particle injection process is still unclear at the mediated shock waves. If the injection process at the mediated shock waves is less efficient to produce enough high energies, there could be no further acceleration by diffusive shock accelerations (DSA).

In this work, we perform a test particle simulation. In the simulation, the shock profile is given as a tangent hyperbolic function. The underlying Alfven turbulence upstream and downstream of the shock follows a Kolmogorov - 5/3 power spectrum. We vary the thickness of the shockwave to study the differences in particle behavior at the mediated shock and compare with the non-mediated shock. Specifically, we measure the energy distribution function of particles, to check how many particles exceed the injection energy. This serves as an important step for studying particle acceleration and transport by the mediated shock waves.