Variational Principle for a Guiding-Center Plasma

Abstract

A new variational formulation is presented for the equilibrium and stability of a guiding-center plasma with emphasis on open-ended systems confined by mirrors. In contrast to all earlier formulations, this is a classical one in which equilibria arise as stationary states of a certain potential and stable equilibria minimize the same potential. The formulation is more general than earlier ones in that it includes nonlinear perturbations, a variety of boundary conditions (lines tied or not), multiple turning points, and a correct treatment of electric fields along the lines. In addition, a number of ambiguous procedures and incorrect statements which are found in earlier stability analyses are corrected.