MHD-PIC simulations find that the non-thermal particle spectral index alpha steepens as alpha proportional to beta to the power 0.5 in the relativistic regime, due to inertial mass density acting as an energy sink that reduces Alfven velocity.
L., Lazarian, A., & Vishniac, E
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The $\beta$-Dependence of Particle Spectra in Relativistic Turbulent Reconnection
MHD-PIC simulations find that the non-thermal particle spectral index alpha steepens as alpha proportional to beta to the power 0.5 in the relativistic regime, due to inertial mass density acting as an energy sink that reduces Alfven velocity.