The ideal MHD model

Abstract

Introduction The goal of Chapter 2 is to provide a physical understanding of the ideal MHD model. Included in the discussion are (1) a basic description of the model, (2) a derivation starting from a more fundamental kinetic model, and, most importantly, (3) an examination of its range of validity. In particular, it is shown that ideal MHD is the simplest fluid model that describes the macroscopic equilibrium and stability properties of a plasma. The claim of “simplest” is justified by a discussion of the large number of important plasma phenomena not covered by the model. However, in spite of its simplicity it is still a difficult model to solve analytically or even computationally because of the geometrical complexities associated with the two and three dimensionality of the configurations of fusion interest. The derivation of the MHD model follows from the standard procedure of starting with a more fundamental and inclusive kinetic description of the plasma which describes the behavior of the electron and ion distribution functions. The mass, momentum, and energy moments of the kinetic equations are then evaluated. By introducing the characteristic length and time scales of ideal MHD, and making several corresponding ordering approximations, one is then able to close the system. The end result is the set of ideal MHD fluid equations.