On a nonlocal stationary free-boundary problem arising in the confinement of a plasma in a stellarator geometry
type: Item
instance of: scholarly article
title: On a nonlocal stationary free-boundary problem arising in the confinement of a plasma in a stellarator geometry
zbMATH Open document ID: 0863.76092
DOI: 10.1007/BF00376255
published in: Archive for Rational Mechanics and Analysis
publication date: 1996-07-24T00:00:00Z
review text: An existence theorem is proved and some qualitative features of the solution of a two-dimensional free-boundary problem are discussed for a model of the magnetic confinement of plasma in a stellarator configuration. Though the original problem is a three-dimensional one, the averaging arguments (Hender and Carreras) and suitable coordinates (Boozer) are used leading to a nonlinear elliptic partial differential equation in two dimensions. The free boundary separates the plasma and vacuum, and the model -- with some unknown nonlinear terms -- can be classified as an inverse-type problem. Using the zero net current conditions applied to stellarator configurations, the problem is reformulated employing the relative arrangements (a mathematical procedure), which leads to non-local terms in the new equation. The latter is solved by iterations, the validity and convergence of which are discussed.
Mathematics Subject Classification ID: 76X05
Mathematics Subject Classification ID: 35R35
zbMATH DE Number: 909630
zbMATH Keywords: iterative procedure
zbMATH Keywords: existence theorem
zbMATH Keywords: averaging
zbMATH Keywords: nonlinear elliptic partial differential equation
zbMATH Keywords: inverse-type problem
zbMATH Keywords: zero net current conditions
zbMATH Keywords: relative arrangements
zbMATH Keywords: non-local terms
zbMATH Keywords: convergence
author: J. I. Díaz
author: J.-M. Rakotoson
reviewed by: Iván Abonyi
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 909630