Zero Flux Eigenvalues of Relaxed Axisymmetric Compact Tokamaks (CT’s)

Abstract

Compact toroidal configuration is of simpler construction than the conventional tokamak and has important advantages due to the novel physics properties of low aspect ratio. In this paper we are developing a numerical program to study the magnetic dynamo or relaxation of CT’s characterized by arbitrary tight aspect ratio. It is shown that the numerical method (Collocation Method), used here, works quite well to calculate numerically the lowest zero flux eigenvalues μ of Taylor’s relaxed plasma state equation \( \vec{\nabla } \times \vec{B} = \mu \vec{B} \) for an axisymmetric tokamaks of circular cross section. An excellent fulfillment of the toroidal flux vanishing boundary condition \( \iint {B_{\emptyset } {\text{d}}r{\text{d}}z = 0} \) along the whole boundary for such tokamaks are achieved. Dependence of μ on the aspect ratio is also obtained. Several runs of the program for various wave numbers k showed that μ is very insensitive to the choice of k. Besides, the poloidal magnetic field topologies inside the tokamak are well represented.