On the MHD analogue of the Brunt-Vaisala frequency in a magnetized plasma

The MHD analogue of the Brunt-Vaisala frequency N-B, in a magnetized, ideal ly conducting plasma is obtained, with the vertical component of the magnet ic field, B-r, taken into account. The magnetic field vector (B-r, B-theta, B-phi) is assumed to satisfy the condition B(.)delB approximate to B-r dB/ dr, which holds in many cases of interest. The frequency N-B happens to dep end, generally speaking, on the magnetic field orientation relative to the direction of gravity However, for an isentropic gas, the convective instabi lity criterion is governed by the magnetic field strength (rather than by t he orientation of B). In general, the magnetic field has a stabilizing (des tabilizing) effect if B/rho grows (decreases) along the vertical axis r. Th is conclusion seems not to depend on the specific magnetic field configurat ion.