GENERALIZED REDUCED MAGNETOHYDRODYNAMIC EQUATIONS

A new derivation of reduced magnetohydrodynamic (MHD) equations is pre sented. A multiple-time-scale expansion is employed. It has the advant age of clearly separating the three time scales of the problem associa ted with (1) MHD equilibrium, (2) fluctuations whose wave vector is al igned perpendicular to the magnetic field, and (3) those aligned paral lel to the magnetic field. The derivation is carried out without relyi ng on a large aspect ratio assumption; therefore this model can be app lied to any general toroidal configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-Alfven wave tim e scale!, which is the time scale of interest for MHD instability stud ies. Careful attention is given in the derivation to satisfy energy co nservation and to have manifestly divergence-free magnetic fields to a ll orders in the expansion parameter. Additionally, neoclassical closu res and equilibrium shear flow effects are easily accounted for in thi s model. Equations for the inner resistive layer are derived which rep roduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson [Phys. Fluids 18, 875 (1975)]. (C) 1998 American I nstitute of Physics. [S1070-664X(98)02012-6].