Stability Theory of a Confined Toroidal Plasma. Part I. Existence and Uniqueness.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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The linear MHD stability of a confined plasma is generally studied by means of energy principles. Up to date, these energy principles have never been justified rigorously, and the existence of a solution to the linearized equations is also tacitly assumed. In this report, based upon a variational approach, we shall first establish the existence and uniqueness of a generalized solution to the linearized Lundquist equations for a toroidal plasma confined in a conducting shell. In a subsequent report, the so-called modified energy principle, which includes linear energy principle as a special case, will be justified rigorously and a solid foundation will then be application of these energy principles to the linear MHD stability of a confined plasma.
- Numerical Mathematics
- Plasma Physics and Magnetohydrodynamics