Monte Carlo approach to collisional transport

A linearized discretization approach is proposed for the numerical investigation of the gyrokinetic equation describing the dynamics of a strongly rotating plasma in a toroidally axisymmetric configuration. The discretization scheme allows the numerical evaluation of the neoclassical transport matrix in terms of a suitably discretized distribution function. A basic feature of the discretization scheme here developed is that it permits the introduction of Monte Carlo collision operators to advance in time the gyrokinetic state of a suitable set of test particles. Such operators, which apply to general non‐normal gyrokinetic coordinates, are constructed in such a way as to conserve exactly the collisional invariants. A fundamental consequence is that the neoclassical transport coefficients determined in this way fulfill exactly both Onsager’s symmetry relations and the condition of strict ambipolarity for the particle‐flux transport coefficients. Such properties are proven to be satisfied independently of the number of test particles used in the discretization scheme.