Algorithms developed to obtain particular numerical solutions to the ideal MHD equilibrium problem
✍ Scribed by T.S. Wang; F.J. Helton
- Publisher
- Elsevier Science
- Year
- 1981
- Tongue
- English
- Weight
- 532 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0010-4655
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✦ Synopsis
The determination of axially symmetric MHD equilibria with free plasma-vacuum interface requires the solution of a two-dimensional, elliptic, nonlinear partial differential equation. The shape of the boundary is not specified but is determined as the nonlinear response of the plasma to external boundary conditions. Neither existence nor uniqueness of solution is guaranteed for this nonlinear elliptic free-boundary problem. That is, for the same input to the numerical algorithm, two or more different solutions may result from internal changes to the algorithm. Thus, in addition to obtaining a solution, it is necessary to distinguish the various branches of the solution and to develop numerical methods which ensure that the solution on a particular branch can be obtained when required. Often, the solution of interest is the solution which is least stable numerically. In this paper we discuss algorithms which we have developed to obtain particular numerical solutions to the MHD equilibrium problem. These algorithms have been divided into two categories, those involving current initialization and those involving feedback stabilization.