Finding plasma equilibria with magnetic islands
type: Item
instance of: scholarly article
title: Finding plasma equilibria with magnetic islands
zbMATH Open document ID: 0667.76160
DOI: 10.1016/0021-9991(88)90023-X
author: S. H. Smith
published in: Journal of Computational Physics
publication date: 1988-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 76X05
zbMATH DE Number: 4093113
zbMATH Keywords: helically symmetric plasma equilibrium equation
zbMATH Keywords: elliptic linear operator
zbMATH Keywords: Tokomak equilibrium
zbMATH Keywords: plasma equilibria with magnetic islands
zbMATH Keywords: linearized equilibrium equation
MaRDI profile type: Publication
cites work: Some Stable Hydromagnetic Equilibria
cites work: Equilibrium and stability code for a diffuse plasma
cites work: Q4196165
cites work: A Characterization of Superlinear Convergence and Its Application to Quasi-Newton Methods
cites work: Error magnetic fields in a cylindrical plasma: Stability with zero pressure
cites work: Q3703206
cites work: Solution Fields of Nonlinear Equations and Continuation Methods
cites work: Q3809173
cites work: Q3909906
description: scientific article; zbMATH DE number 4093113