On nonlinear axisymmetric equilibria in the magnetohydrodynamic approximation
Abstract
The second order elliptic differential equation which describes the static equilibrium of an axisymmetric ideally conducting plasma toroid, in the magnetohydrodynamic approximation, may be transformed into an equivalent equation which admits at least one class of exact analytic solutions for which the original equation is essentially nonlinear. Necessary and sufficient conditions are given for the existence of systems in this category having closed toroidal flux surfaces and a result is proved which gives some insight into the mathematics by which the spatial variation of the hydrodynamic pressure can be represented by families of nested closed curves.
 Publication:

Journal of Plasma Physics
 Pub Date:
 December 1977
 DOI:
 10.1017/S0022377800023564
 Bibcode:
 1977JPlPh..18..537W
 Keywords:

 Elliptic Differential Equations;
 Equilibrium Equations;
 Magnetohydrodynamic Flow;
 Nonlinear Equations;
 Toroidal Plasmas;
 Approximation;
 Boundary Value Problems;
 Existence Theorems;
 Plasma Conductivity;
 Symmetry;
 Transformations (Mathematics);
 Plasma Physics