On a nonlocal stationary free-boundary problem arising in the confinement of a plasma in a stellarator geometry
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.
nonlinear elliptic partial differential equation
scientific article; zbMATH DE number 909630
scientific article