Monte Carlo approach to collisional transport

Abstract

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.