Proton acceleration at interplanetary shocks: A numerical study for the HENON mission
The ESA-ASI HENON CubeSat mission will operate in a distant retrograde orbit about 0.08 au upstream of Earth to provide advance space-weather monitoring. Its instruments include an energetic particle detector measuring protons from 2 MeV to hundreds of MeV. Early detection of energetic particles is crucial for protecting technological infrastructure. To investigate proton acceleration at interplanetary shocks, we developed a test-particle numerical simulation in which protons move in the drift approximation around a parallel shock transition and gain energy through a first-order Fermi process at each crossing. They can propagate around the shock either diffusively or superdiffusively; particle transport 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. We varied the pitch-angle scattering time, upstream and downstream plasma speeds, and the type of transport. In the superdiffusive case, a power-law distribution of scattering times was generated by mimicking a Lévy walk. Multiple runs identify the parameter ranges that yield efficient acceleration and higher energies. For typical parameters, superdiffusive acceleration turns out to be somewhat faster than normal diffusive acceleration. We find that the main control parameter 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 $V_1 \leq 150$ km/s the proton energy reaches only a few hundred keV. These results help explain why many interplanetary shocks accelerate ions only to moderate energies. They also suggest that when the HENON particle instrument is able to detect energetic protons above 2 MeV, the shock speed in the spacecraft frame is of the order of 800 km/s or more.