The resistive evolution of magnetic flux in toroidal devices is studied. The formulation is applicable to general nonaxisymmetric (three-dimensional) toroidal configurations. In particular, it can treat highly shaped, high β, three-dimensional stellarator configurations, as well as two-dimensional (axisymmetric) tokamak plasmas. The time evolution of the poloidal magnetic flux is posed in terms of the rotational transform, ι̸, and allows for a transparent inclusion of stellarator specific current-free contributions to ι̸. Strong diamagnetic and paramagnetic contributions to toroidal magnetic flux, as evident in spherical tokamaks and similar concepts, are calculated by direct iteration with an equilibrium solver. The nonlinear evolution equation is derived using a susceptance matrix formulation originally introduced by Grad and co-workers [Bateman, Nucl. Fusion 13, 227 (1973)]. Here, it is extended to general, nonstraight field line coordinate systems. The basic equations are described, explicit expressions for the susceptance matrix are given, and example applications using the stand-alone code, THRIFT (THRee-dimensional Inductive Flux evolution in Toroidal devices), are discussed.
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Strand et al. (2001) studied this question.
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