Abstract
Simple magnetohydrodynamic models provide the framework for much of our understanding of the macroscopic behavior of magnetically confined laboratory plasmas. In even the simplest of models, however, the many different time and spatial scales, the multidimensionality, and the nonlinearity of the equations make finding solutions difficult. In realistic geometries obtaining quantitative results to aid our understanding, to interpret experiment, and to design new devices, involves the development of large scale numerical codes. During the past decade considerable effort has been extended in the fusion community to develop equilibrium, linear stability, and nonlinear time evolution codes in two and three dimensions, some of which have had a considerable impact on the fusion program. An overview of the various types of codes and numerical methods is given. Emphasis is on the spectrum of linear perturbations and ideal MHD stability, boundary layer methods and resistive MHD stability, and modeling of nonlinear, time evolution resistive MHD phenomena in tokamak configurations.
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