Energy of linear quasi-neutral electrostatic drift waves

An exact energy expression for linear quasi-neutral electrostatic perturbations is derived within the framework of dissipationless multi-fluid theory, valid for any geometry. Taking the mass as a tensor with, in general, different masses parallel and perpendicular to an ambient magnetic field allows one to treat the full dynamics and also to restrict consideration to parallel dynamics or to the completely adiabatic case. Application to slab configurations yields the result that in plane geometry the adiabatic approximation does not allow negative-energy perturbations, whereas inclusion of the parallel dynamics does. This is in agreement with a numerical study of drift-wave turbulence within the framework of collisional two-fluid theory by B. Scott. Unlike Scott, we consider a dissipationless theory. Whereas the nonlinear energy is just kinetic plus potential plus thermal energy, the energy of perturbations depends on constraints. In a multi-fluid quasi-neutral electrostatic theory, from which we start, such constraints are mass conservation and entropy conservation. The latter is violated if heat conduction, heat sources (e.g. Joule heating) and heat sinks play a role. Hence, the energy expressions obtained are, valid only when situations where this is not the case or where these phenomena do not influence the entropy constraint. The latter is the case if the heat conduction is infinitely large such that the equilibrium temperature profiles Tν(x) of the various particle species ν are independent of x and δTν=0. A vanishing temperature perturbation results in an entropy-conserving theory if one takes the adiabatic coefficients γν=1. This is possible, however, only for the perturbations; the equilibrium energy would diverge. When we consider this case, we do it in the way that the γs are put equal to 1 only after having obtained the perturbed energy for general γs. (author) 7 refs