Probabilistic approach to Monte Carlo operators

A general method for constructing Monte Carlo collision operators is formulated based on the introduction of a stochastic Liouville equation. The approach is applied to the investigation of a suitable discretized gyrokinetic equation describing the dynamics of a strongly rotating multispecies plasma, in a toroidally axisymmetric configuration. Improved expressions are obtained for the Monte Carlo collision operators for general non‐normal (in v space) coordinate systems. As an application, the important case of the bounce‐averaged gyrokinetic equation is discussed, in various cases of interest. Finally, using an approximate collision operator, the friction coefficients are evaluated and expressed in terms of energy and momentum restoring coefficients, thus yielding for the Monte Carlo operators a representation convenient for their numerical implementation.