The energy analysis for the monte carlo simulations of a diffusive shock

TL;DR

This paper uses Monte Carlo simulations to analyze energy conservation and spectrum formation in diffusive shock scenarios, highlighting the impact of energy losses on spectral hardness.

Contribution

It introduces a detailed energy analysis method for Monte Carlo simulations of diffusive shocks, emphasizing the role of scattering law in energy loss and spectrum shape.

Findings

Smaller energy losses lead to harder energy spectra.

Energy conservation is verified through simulation monitoring.

The scattering law influences the spectral characteristics.

Abstract

According to the shock jump conditions, the total fluid's mass, momentum, and energy should be conserved in the entire simulation box. We perform the dynamical Monte Carlo simulations with the multiple scattering law for energy analysis. The various energy functions of time are obtained by monitoring the total particles' mass, momentum, and energy in the simulation box. In conclusion, the energy analysis indicates that the smaller energy losses in the prescribed scattering law are, the harder the energy spectrum produced is.