Finding plasma equilibria with magnetic islands
The traditional method of solving the helically symmetric plasma equilibrium equation, of the form \(L[G]=F(G,r)\), where L is an elliptic linear operator, has been the simple iteration \(L[G^{n+1}]=F(G^ n,r)\). A model of a Tokomak equilibrium is constructed and used to illustrate the divergence of the simple iteration for plasma equilibria with magnetic islands. Although the problem of equilibria with magnetic islands is two dimensional, for small islands the numerical stability of the simple iteration may be analyzed using a one-dimensional equation similar to the linearized equilibrium equation used to analyze physical (resistive) instability. This analysis is used to prove that any equilibria of the Tokamak type with small islands cannot be obtained by the simple iteration and to illustrate the superlinear convergence of Newton's method on these problems. The implementation of Newton's method is discussed and examples are given.
helically symmetric plasma equilibrium equation
scientific article; zbMATH DE number 4093113
scientific article