''Advanced''- δf simulations of the NBI heating in Wendelstein 7-X

The δf Monte Carlo technique is a powerful tool for kinetic calculations in tokamak and stellarator plasmas. The idea of the commonly used δf approach depends on the determination of the deviation δf from a Maxwellian. Starting from the drift kinetic equation, linearization yields a marker equation for the weights of the test particles. In the case of NBI heating, one wants to simulate the slowing down behavior of suprathermal particles, which are far away from a Maxwellian. The application of the commonly used δf Monte Carlo technique is such a case offers no advantage over the ''full-f'' method. The ''full-f'' method in this case is a very time consuming task, because one has to calculate several slowing down times of fast particles. In contrast to tokamaks, the radial drift of ripple-trapped particles results in a significantly enhanced radial transport in classical stellarators. In the quasi-isodynamic W7-X configurations, fast particles remain near their ''birth'' flux surface for a long time. With the assumption pf slowing-down on the flux surfaces, a Fokker-Planck solver delivers a rather good estimate being very fast and accurate. A new approach for the NBI heating starts with the ansatz for the distribution function f=fM+f1+δf, where fM represents the Maxwellian. The second part, f1, describes the flux-surface-averaged part of the deviation from f. These two parts, fM and f1, are used in the marker equation with the appropriate sources and sinks. A δf scheme formulated in this way solves the problem in 2nd order to determine a δf which contains the desired information on drift effects. Therefore the ''advanced'' δf Monte Carlo method offers improved statistical behavior compared with full-f and usual δf methods. (orig.)