Stochastic Mapping Technique and Neoclassical Transport

The evaluation of neoclassical transport coefficients is an essential element in stellarator studies. It is needed for the optimization of magnetic configurations, and for the analysis and planning of experiments. It is also of relevance for stellarator specific issues of fusion reactors. In an arbitrary 3-dimensional magnetic field configuration of a stellarator this problem has to be solved numerically. At the present time methods which provide the most general solution are the conventional MC (Monte Carlo) method, which has been realized in numerous codes and DKES (Drift Kinetic Equation Solver). These two methods do not have principal limitation from the geometry of the device or from the confinement regime, however, as an adverse consequence of problem generality, these methods have low computational efficiency in certain collisionality regimes. This low efficiency becomes a substantial obstacle for optimization procedures where new, more effective methods are necessary, e.g., for the creation of neoclassical databases for a certain magnetic field configuration, which are used for the analysis and the planning of experiments and are planned at the IPP Greifswald. Within the current proposal, the stochastic mapping technique (SMT), which provides a very efficient solution for the drift kinetic equation in the long mean free path regime, should be applied to compute transport coefficients, the bootstrap current, supra-thermal particle fluxes, and alpha particle losses. Up to now SMT works for magnetic fields given in real space coordinates and therefore a version of the code working directly with magnetic fields represented in Boozer coordinates has to be developed, as well as a version of the SMT code applicable to stellarator equilibria of general topology provided by the PIES code. The procedure to calculate the bootstrap current, developed for the conventional MC method, has to be implemented in SMT. This includes the implementation of the proper orbit-integrated Coulomb collision operator into the code. Convective transport of supra-thermal electrons can play a significant role in the energy balance of stellarators in the presence of high power electron cyclotron heating. Here, together with neoclassical thermal particle fluxes, also the supra- thermal electron flux should be taken into account in the flux ambipolarity condition, which defines the self- consistent radial electric field. In this approach, SMT which is more effective than the conventional MC method, will be used. Furthermore, the confinement characteristics of alpha-particles, which is another important issue relevant to reactor scale stellarator optimization, will be computed. Another aim of the project is the evaluation of symmetric neoclassical losses.