Negative-energy waves in an inhomogeneous force-free Vlasov plasma with sheared magnetic field

Considering arbitrary perturbations of general Vlasov-Maxwell equilibria, Morrison and Pfirsch derived expressions for the second variation of the free energy and concluded that negative-energy perturbations (which are potentially dangerous because they may become nonlinearly unstable and cause anomalous transport) exist in any Vlasov-Maxwell equilibrium whenever the unperturbed distribution function fν(0) of any particle species ν deviates from monotonicity and/or isotropy in the vicinity of a single point, i.e. whenever the condition (v·k)(k·∂fν(0)/ ∂v)>0 holds for any particle species ν for some position vector x and velocity v and for some vector k. The proof of this result is based on infinitely strongly localized perturbations. This raises the question of the degree of localization actually required for negative-energy modes to exist in a certain equilibrium. Studying a homogeneous Vlasov-Maxwell plasma with constant magnetic field, Correa-Restrepo and Pfirsch showed that negative-energy waves exist for any deviation of the equilibrium distribution function of any of the species from monotonicity and/or isotropy, without having to impose any restricting conditions on the perpendicular wave number k, i.e. without requiring large k. These investigations are extended in the present paper to the more interesting case of an inhomogeneous, force-free equilibrium with a sheared, y-dependent magnetic field. (author) 6 refs