MHD stability comparison theorems

Introduction Three models have been introduced to investigate the MHD equilibrium and stability properties of a general multidimensional magnetic fusion configuration: ideal MHD, kinetic MHD, and double adiabatic MHD. Ideal MHD is by far the most widely used model although there is concern since the collision dominated assumption used in the derivation is not satisfied in fusion-grade plasmas. The collisionless kinetic MHD model provides the most reliable description of the physics but is difficult to solve in realistic geometries because of the complex kinetic behavior parallel to the magnetic field. Double adiabatic MHD is a collisionless fluid model that is much easier to solve than kinetic MHD but the closure assumptions cannot be justified by any rigorous mathematical or physical arguments. Based on this assessment one sees that the situation is not very satisfactory from a theoretical point of view. In practice, ideal MHD, because of its mathematical simplicity, is the model that is most widely used to design, predict, and interpret fusion experiments. Many years of experience have shown, perhaps surprisingly, that the model is far more accurate and reliable than one might have anticipated.