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Abstract
Numerical algorithms to load relativistic Maxwell distributions in particle-in-cell (PIC) and Monte-Carlo simulations are presented. For stationary relativistic Maxwellian, the inverse transform method and the Sobol algorithm are reviewed. To boost particles to obtain relativistic shifted-Maxwellian, two rejection methods are proposed in a physically transparent manner. Their acceptance efficiencies are ≈50% for generic cases and 100% for symmetric distributions. They can be combined with arbitrary base algorithms.
Highlights
Because of an increasing demand in high-energy astrophysics, numerical modeling of relativistic kinetic plasmas has been growing in importance
In addition to the simple inverse transform method, we have formally reviewed the Sobol algorithm
The inverse transform method is faster than the Sobol method, because it only requires 3 random variables
Summary
Because of an increasing demand in high-energy astrophysics, numerical modeling of relativistic kinetic plasmas has been growing in importance. Many simulations on relativistic kinetic processes have been performed, such as the Rankine-Hugoniot problem across a relativistic shock, magnetic reconnection and kinetic instabilities in a relativistically hot current sheet, and the kinetic KelvinHelmholtz instability in a relativistic flow shear.. Many simulations on relativistic kinetic processes have been performed, such as the Rankine-Hugoniot problem across a relativistic shock, magnetic reconnection and kinetic instabilities in a relativistically hot current sheet, and the kinetic KelvinHelmholtz instability in a relativistic flow shear.1 In these simulations, one has to carefully set up ultrarelativistic bulk flows and/or relativistically hot plasmas in their rest frame. I.e., initializing particle velocities by using random variables according to a relativistic distribution function, is essentially important. Melzani et al. utilized a numerical cumulative distribution function and cylindrical transformation
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