In-situ Measurement of the Energy Fraction in Supra-thermal and Energetic Particles at ACE, Wind, and PSP Interplanetary Shocks

The acceleration of charged particles by interplanetary shocks (IPs) can drain a non-negligible fraction of the plasma pressure. In this study, we have selected 17 IPs observed in-situ at \(1\,\text{au}\) by the Advanced Composition Explorer (ACE) and the Wind spacecraft, and 1 shock at \(0.8\,\text{au}\) observed by Parker Solar Probe (PSP). We have calculated the time-dependent partial pressure of supra-thermal and energetic particles (smaller and greater than \(50\,\text{keV}\) for protons and \(30\,\text{keV}\) for electrons, respectively) in both the upstream and downstream regions. The particle fluxes were averaged for 1 hour before and 1 hour after the shock time to remove short time scale effects. Using the MHD Rankine-Hugoniot jump conditions, we find that the fraction of the total upstream energy flux transferred to supra-thermal and energetic downstream particles is typically \(\lesssim\!16\%\), in agreement with previous observations and simulations. Notably, by accounting for errors on all measured shock parameters, we have found that for any given fast magnetosonic Mach number, \(M_{f}\!\!0.1\)) for the Wind events.