NEGATIVE-ENERGY WAVES IN A MAGNETIZED HOMOGENEOUS PLASMA

The general expression for the second-order wave energy of a Vlasov-Maxwell system derived by Morrison and Pfirsch [Phys. Rev. A 40, 3898 (1989); Phys. Fluids B 2, 1105 (1990)] is evaluated here for the case of electrostatic perturbations in a magnetized, homogeneous plasma. It is again shown that negative-energy waves (which could become nonlinearly unstable and cause anomalous transport) exist for any deviation from monotonicity and/or any (however small) anisotropy in the equilibrium distribution function of any of the particle species. The partly unexpected and particularly interesting feature of the results is that, contrary to the proof of Morrison and Pfirsch, no restricting condition has to be imposed on the perpendicular wave number k perpendicular-to of the perturbation (i.e., large k perpendicular-to is not required). Finite-gyroradius effects are therefore not expected to improve the situation. Anisotropy alone would, however, impose a restriction on k(z), the parallel wave number, relating it to the gyroradius. As far as distribution functions with upsilon(z)(partial derivative f(nu)(o) /partial derivative upsilon(z)) > 0 in some region of v space are concerned, however, this result agrees with a result found by Pfirsch and Morrison within the framework of drift-kinetic theory.