Non-Axisymmetric Tokamak Plasma Equilibrium by 3-D Multi-Layers Method

A three-dimensional (3-D) Multi-Layers Method (MLM) of an extension of the axisymmetric version has been developed to compute non-axisymmetric tokamak plasma equilibria with a separatrix. Conventional axisymmetric tokamak control codes cannot simulate non-axisymmetric effects, while stellarator equilibrium solvers such as VMEC do not include the effects of conducting structures. Moreover, VMEC cannot obtain equilibria with separatrices since it uses magnetic coordinates. The 3-D MLM removes these limitations by using a deformable circuit model of a magnetic confinement system. Plasma is modeled by multiple current layers coinciding with magnetic surfaces, and equilibria are obtained as solutions of a variational problem of a free energy functional with current sources. Validations of equilibrium solutions against a stellarator vacuum field and a VMEC solution for a small non-axisymmetric tokamak show good agreement in magnetic configurations, pressure profile, and plasma current. By incorporating conducting structures and extension to dynamic simulations, the 3-D MLM establishes a method for simulating tokamak plasma control under non-axisymmetric magnetic fields.