Hybrid Monte Carlo simulation of ripple transport in stellarators

Abstract A rapid “hybrid” Monte Carlo simulation has been developed to investigate helical ripple transport at low collision frequencies in stellarators. The simulation is a hybrid in the sense that the majority of ripple trapped particles are followed through the iterative conservation of their longitudinal adiabatic invariant, J , while those particles in a narrow region of phase space on either side of the ripple trap/detrap boundary are followed using guiding center equations of motion. This formulation is much faster than a purely guiding center treatment, making all collision frequency regimes of interest accessible at reasonable costs in computer time. It is shown that local toroidal variation of the magnetic field yields considerably more complicated trapping/detrapping orbits than allowed in analytic theory and that the form of J used in this work correctly describes this behavior. The methods employed allow the examination of stellarator configurations for which the magnitude of the toroidal well, e t , is larger than that of the helical well, e h , as well as configurations more often treated in which e h > e t . Results are obtained for the usual analytic model of the helical ripple, e h = e h ( r ), as well as a more realistic model for which e h = e h ( r , θ ). It is shown that even a rather weak dependence of e h on poloidal angle can alter the magnitude of the diffusion coefficient as well as its scaling with collision frequency.