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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, $M_{f}\!<7$, the angle between the shock normal and average upstream magnetic field, $θ_{Bn}$, is not correlated with the energetic particle pressure; in particular, the partial pressure of energized particles does not decrease for $θ_{Bn} \gtrsim 45^\circ$. The downstream electron-to-proton energy ratio in the range $\gtrsim\!140\,\text{eV}$ for electrons and $\gtrsim\!70\,\text{keV}$ for protons exceeds the expected $\sim\!1\%$ and nears equipartition ($>\!0.1$) for the Wind events.