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Existence and control of plasma equilibrium in a Tokamak. (English) Zbl 0614.35082

The purpose of this paper was to study a simplified model for the equilibrium of a fusion plasma confined within a toroidal vessel by the magnetic field. The plasma current is produced by magnetic induction from a primary circuit made of poloidal field coils. The free boundary of plasma is a flux surface in contact with a ”limiter”. The configuration was assumed to be axisymmetric, so that the problem can be reduced to a two-dimensional one in the meridian section of the torus. The main text of this paper is organized as follows. The mathematical model is presented in Section 1. Section 2 deals with an annex mathematical problem. The existence of a solution for the equilibrium is studied in Section 3. The control of the plasma shape by the external currents is treated in Section 4. The first-order necessary optimality conditions are obtained by introducing a suitable adjoint state.
Reviewer: L.Shih

MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B37 PDE in connection with control problems (MSC2000)
76W05 Magnetohydrodynamics and electrohydrodynamics
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