Oscillation center theory and ponderomotive stabilization of low‐frequency plasma modes

Nonlinear, nondissipative ponderomotive theory is developed in relation to recent experimental results showing that externally imposed rf fields can stabilize an axisymmetric mirror plasma. First, the ponderomotive force problem is reexamined, with emphasis on self‐consistency of the interaction between the plasma and high‐frequency field. The averaged action principle for the antenna–plasma system yields self‐consistent plasma and electromagnetic field dynamics on the oscillation‐center time scale. The plasma equilibrium condition is expressed as a balance among plasma and magnetic pressure forces, including interchange, ponderomotive, and magnetization forces. Next, the spectral stability of such static equilibria is studied in the low‐frequency magnetohydrodynamic (MHD) approximation, with a ΔW principle that incorporates the various ponderomotive contributions: particle effects, magnetization effects, and self‐consistent adjustment of the rf field resulting from displacements of the plasma away from equilibrium. The ponderomotive potential energy functional is related to the antenna inductance and antenna current amplitude. Finally, the noncanonical Hamiltonian formulation for the system’s dynamics is given, in terms of Eulerian fields. It allows the construction of nonlinearly conserved functionals, which yield criteria for linearized Lyapunov stability, for both multifluid and MHD models. The Lyapunov stability conditions are related to the modified ΔW variational principle.