Ponderomotive Force and Rotational Effects on the Stability of Plasmas in a Tandem Mirror

Analytical and numerical analyses are presented to study the effects of electromagnetic waves and an equilibrium radial electric field on the stability of plasmas in a tandem mirror. A kinetic approach derived from the Vlasov equation is used to include the microscopic effects arising from the finite Larmor radius and plasma temperature effects. Electromagnetic waves give rise to a time independent force in a plasma known as the ponderomotive force. This force can affect the stability of plasmas as has been demonstrated experimentally in the Phaedrus tandem mirror. The results from our analyses are consistent with the experimental results that the plasma was stable for (omega)(,rf) > (OMEGA)(,ci) and unstable for (omega)(,rf) <(, )(OMEGA)(,ci).(' 34 ). The ponderomotive force component from the left hand circularly polarized (E(,L)) wave is not singular at (omega)(,rf) = (OMEGA)(,ci), which is contrary to the prediction of the fluid approach. Here, (omega)(,rf) is the frequency of the electromagnetic wave and W(,ci) is the ion cyclotron frequency. The model predicts that for Phaedrus tandem mirror parameters, the force from the E(,L) wave component gives a dominant contribution to stability and has a clear transition from destabilizing to stabilizing plasmas near (omega)(,rf) (TURN) (OMEGA)(,ci). The ponderomotive force from the parallel component of the wave can be stabilizing or destabilizing depending on the electron temperature T(,e) and parallel wave number k(,(PARLL)). This result is also different from the prediction of fluid analysis in which the force is independent of both T(,e) and k(,(PARLL)). This parallel wave component force stabilizes a plasma of relatively cold electrons. Finally, the ponderomotive force component from the right hand polarized wave depends slightly on the plasma temperature and thus the cold plasma approximation (fluid or single particle analysis) is valid in this case. Our analysis indicates that the ponderomotive force can stabilize even the m = 1 mode, the most difficult mode to stabilize. The analysis of the rotational effects and the finite Larmor radius (FLR) effects confirms the well known theory that the m = 1 rigid flute mode is not affected by the plasma rotation and FLR effects, but that the m (GREATERTHEQ) 2 modes can be stabilized by the FLR effects. It is found that the rotational effects on stability for the m (GREATERTHEQ) 2 modes depend on the direction of the radial electric field and its magnitude. Specific analytical and numerical estimations of the stabilization effects of the ponderomotive force, FLR, and plasma rotation using the geometry of the Phaedrus tandem mirror are provided.