Neoclassical Viscosities in NCSX and QPS with Few Toroidal Periods and Low Aspect Ratios

Previously reported benchmarking examples of the analytical formulae of neoclassical viscosities were presented implicitly assuming applications in a future integrated simulation system of the Large Helical Device (LHD). Therefore, the assumed toroidal period numbers were mainly N = 10. However, in this type of calculation, an implicit (or sometimes explicit) assumption of ι/N « 1 is sometimes included. This assumption is included not only in simplified bounce-averaged drift kinetic equations for ripple diffusions, but also in the equation before the averaging for non-bounce-averaged effects determining neoclassical parallel viscosity and banana-plateau diffusions. For clarifying the applicability of the analytical methods for configurations with extremely low toroidal period numbers (required for low aspect ratios), we show recent benchmarking examples in the National Compact Stellarator Experiment (NCSX) with N = 3 and the Quasi-Poloidal Stellarator (QPS) with N = 2.