Blum, J.; Gallouet, T.; Simon, J. Existence and control of plasma equilibrium in a Tokamak. (English) Zbl 0614.35082 SIAM J. Math. Anal. 17, 1158-1177 (1986). 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 Cited in 7 Documents 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 Keywords:magnetic confinement; uniqueness; equilibrium; fusion plasma; free boundary; mathematical model; existence; necessary optimality conditions PDFBibTeX XMLCite \textit{J. Blum} et al., SIAM J. Math. Anal. 17, 1158--1177 (1986; Zbl 0614.35082) Full Text: DOI