NEGATIVE-ENERGY PERTURBATIONS IN GENERAL AXISYMMETRICAL AND HELICAL MAXWELL-VLASOV EQUILIBRIA

The expression for the free energy of arbitrary perturbations of gener al Vlasov-Maxwell equilibria derived by Morrison and Pfirsch is transf ormed and put in a concise form, which is subsequently evaluated for a rbitrary equilibria which have one ignorable coordinate, e.g., axisymm etric and helical equilibria, in the case of internal perturbations, i .e., perturbations which vanish outside the plasma, and on its boundar y. In order to generate the electric currents necessary for equilibriu m in the presence of pressure gradients, the equilibrium distribution function of at least one particle species must be anisotropic. As a co nsequence, these equilibria always allow negative-energy perturbations , without requiring a large spatial variation of the perturbation acro ss the equilibrium magnetic field.