Magnetofluid and Plasma Behavior with Non-Ideal Boundary Conditions #

David Montgomery, Dartmouth College, Hanover, New Hampshire

Magnetohydrodynamic (MHD) confinement theory has to a large extent revolved around the stability of ideal MHD equilibria without flow, as described by the Grad-Shafranov equation. Such ideal equilibria are very numerous: as numerous as the solutions of the Euler equations for inviscid pipe flow, for example. Investigating the stability of such ideal equilibria is a task that could literally go on forever. However, if small but non-zero resistivity and viscosity and appropriate boundary conditions are introduced, the class of MHD steady states collapses to a very small one. In a periodic, straight cylinder, zero-flow, current-carrying steady states exist, and their stability boundaries and slightly non-linear behavior can be investigated. However, for toroidal geometry, the situation appears very different, and there seem to be no current-carrying, steady-state, MHD configurations without flow, or at least none with physically realizable resistivity profiles. The necessity of including flow in stability analyses, together with the loss of self-adjointness in the dissipative, linearized MHD equations, appears as a setback for MHD theory; but it may also open the door to the kind of realism that is taken for granted in Navier-Stokes fluid theory.

Reference: J.W. Bates and D. Montgomery, Phys. Plasmas 5, 2649 (1998).