We assess the impact of non-thermally shock-accelerated particles on the magnetohydrodynamic (MHD) jump conditions of relativistic shocks. The adiabatic constant is calculated directly from first-principles particle-in-cell simulation data, enabling a semi-kinetic approach to improve the standard fluid model and allowing for an identification of the key parameters that define the shock structure. We find that the evolving upstream parameters have a stronger impact than the corrections due to non-thermal particles. We find that the decrease in the upstream bulk speed result in deviations from the standard MHD model up to 10%. Furthermore, we obtain a quantitative definition of the shock transition region from our analysis. For Weibel-mediated shocks the inclusion of a magnetic field in the MHD conservation equations is addressed for the first time.

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• Physical Sciences - Natural Sciences