Negative energy waves in a magnetically confined guiding center plasma

The conditions for the existence of negative-energy waves for electrostatic initial perturbations (which could be nonlinearly unstable and cause anomalous transport) are investigated for an equilibrium with space dependent, sheared magnetic field. The method of investigation consists in evaluating the general expression for the second-order wave energy derived by Pfirsch and Morrison for the case of the Maxwell-drift kinetic theory, based on the Lagrangian formulation of the guiding center theory given by Littlejohn and later regularized by Correa-Restrepo and Wimmel. In Cartesian coordinates, the equilibrium magnetic field is given by B(0) = Bx(0)(y)ex + Bz(0)(y)ez, and the mean Lorentz force, acting along the y-axis, balances the force due to the pressure gradient; thus, the equilibrium condition P(0) + (B(0))2/8π = constant is satisfied. The guiding center drift velocity vgν(0) of any species ν possesses, in addition to the component vgν|| = g4/g'ν parallel to the magnetic field, a perpendicular component due to the grad-B drift (q4 is a velocity variable and the function gν(z) regularizes the theory). The equilibrium guiding center distribution function fgν(0) is a function of y, y being a conserved quantity because the guiding centers move on a plane perpendicular to the y-axis, q4 and the adiabatic invariant magnetic moment μ[fgν(0)(y,q4,μ)]. (author) 7 refs., 1 tab