Statistical kinetic treatment of relativistic binary collisions

Details Statistical kinetic treatment of relativistic binary collisions Statistical kinetic treatment of relativistic binary collisions

2009-02-10

arxiv.org/abs/0902.1762v1

Physics

Plasma Physics

Accepted for publication as a Rapid Communication in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.79.025701

In particle-based algorithms, the effect of binary collisions is commonly described in a statistical way, using Monte Carlo techniques. It is shown that, in the relativistic regime, stringent constraints should be considered on the sampling of particle pairs for collision, which are critical to ensure physically meaningful results, and that nonrelativistic sampling criteria (e.g., uniform random pairing) yield qualitatively wrong results, including equilibrium distributions that differ from the theoretical J\"uttner distribution. A general procedure for relativistically consistent algorithms is provided, and verified with three-dimensional Monte Carlo simulations, thus opening the way to the numerical exploration of the statistical properties of collisional relativistic systems.

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