Proton acceleration at interplanetary shocks: A numerical study for the HENON mission

Abstract

The HENON CubeSat mission of ESA-ASI is designed to fly on a distant retrograde orbit at around 0.08 au upstream of Earth, for advance-time space-weather monitoring. The mission has a set of instruments that include an energetic particle detector measuring protons from 2 MeV to hundreds of MeV. Detecting energetic particle fluxes well in advance with respect to their impact on Earth is of pivotal importance for protecting technological infrastructures. In order to assess the features of energetic protons being accelerated at interplanetary shocks, we aim to set up a test-particle numerical simulation in which protons move in the drift approximation around a parallel shock transition and are accelerated each time they cross the shock according to a first-order Fermi process. During their motion they can propagate around the shock either diffusively or superdiffusively; particle transport indeed affects shock acceleration. Protons were injected at the shock with an energy distribution of about 10 keV and scattered in pitch angle by a collision operator. In the simulations, we varied the pitch-angle scattering time, the plasma speeds upstream and downstream of the shock, and the type of transport. In the superdiffusive case, a power-law distribution of scattering times was generated by mimicking a Lévy walk. Several runs were carried out in order to determine the parameter domain, which led to efficient acceleration and thus higher energies. For typical parameters, superdiffusive acceleration turns out to be somewhat faster than normal diffusive acceleration. We find that the main control parameter, which determines the maximum energy, appears to be the upstream shock speed, and that energies in the range of 2--10 MeV can be reached for upstream speeds in the shock frame, V_1, of the order of 300 km/s or more. Conversely, for a speed of V_1 łeq 150 km/s the proton energy reaches only a few hundred keV. These results facilitate our understanding of why many interplanetary shocks only accelerate ions up to moderate energies. Furthermore, the present study indicates that when the HENON particle instrument is able to detect energetic protons above 2 MeV, the shock speed in the spacecraft frame is relatively high, i.e. of the order of 800 km/s or more.