Variational formulation for a multifluid flowing plasma with application to the internal tilt mode of a field-reversed configuration

Standard magnetohydrodynamic (MHD) equations are extended to include arbitrary equilibrium flows and multiple fluids and an equivalent variational form is developed. This system is appropriate for the study of stability in any multifluid flowing plasma, e.g., allowing for arbitrary poloidal and toroidal equilibrium flows and accounting for the Hall terms. The variational formalism is applied to the particular case of the internal tilting instability in a field-reversed configuration (FRC). A solution by means of the Rayleigh–Ritz technique leads to the dispersion relation, from which the growth rate and marginal stability conditions are determined. A new stability regime is found for sufficiently elongated FRC’s, arising as a consequence of the Hall effect. These results are compared with experiment and related theory.