The problem of calculating MHD equilibria consistent with experimental plasma discharges generally involves an iterative procedure of adjusting input parameters to an equilibrium code until a best fit between relevant experimental and calculated data is reached. These so-called interpretive methods for equilibrium determination are widely used in tokamak analysis [64]. They are generally impractical for stellarators since each iteration involves at least one full solution of a 3-D MHD equilibrium, a task which, even using the relatively fast NEMEC code, requires roughly an hour of CPU time on a single processor of a Cray J-90 vector supercomputer for standard W7-AS calculations at IPP. Newer supercomputers are now capable of outperforming the J-90, nevertheless an equilibrium calculation in 3-D is still a costly operation.
In this chapter, we present a method for fast interpretive equilibrium identification on W7-AS. We adopt the following strategy to overcome the fundamental difficulty of the prohibitively long time taken for equilibrium calculations: we apply FP methodology to a database of simulated W7-AS equilibria, not in terms of external measurements, but in terms of intrinsic parameters which are not normally measurable. This allows rapid, predictive 3-D equilibrium flux surface reconstruction in terms of a modest number of experimentally known input parameters consisting of measured coil currents and a (variable) limiter position, together with parameters which are not measurable directly describing, in this instance, the equilibrium pressure profile.
Based on this FP reconstruction technique, we develop an interpretive procedure for equilibrium identification which uses measurements of full profiles from the 20-channel Thomson scattering diagnostic on W7-AS via an iterative non-linear least squares minimization algorithm. Here, the equilibrium pressure profile parameters used in the FP reconstructions are varied until the resulting equilibrium flux surfaces are consistent with the topology of the Thomson data. Due to the speed of the FP stage, the interpretation can be performed in times many orders of magnitude faster than conventional methods. We compare results obtained with our method with standard W7-AS equilibrium calculations for some experimental cases.