Magnetohydrodynamics and Magnetic Confinement Geometries

Abstract

A universal model that plays a key role in plasma physics is the MHD model. From the perspective of Chapter 2 that gives the kinetic theory and Chapter 4 that develops the two-component (ion and electron) fluid equations, the MHD model is a further step down in the accuracy and detailed description of the plasma dynamics. In fact, it is not possible to derive precisely the conditions under which the MHD model is valid. It is not unusual in science, and physics in particular, that the simpler less detailed description, is more useful. In physics two famous examples of this rule come to mind: Ohm's law and the Bohr atom. From the perspective of the more complex models introduced in Chapters 2 and 4, one can say that the ideal MHD model is to plasma physics as the Bohr atom model is to quantum atomic physics. One concludes that the MHD model is rarely precisely correct, but is always useful just as with the Bohr model of the atom. There are phenomena, of course, that are well-described by the idealized Bohr atomic and MHD plasma models. For plasma MHD the key properties that make the model so useful, and often adequate, are the conservation laws the model embodies. The MHD model is a set of seven partial differential equations advancing in time a single perfectly conducting fluid of mass density ρ, flow velocity u, and isotropic pressure p that obeys the adiabatic gas law with a user-specified adiabatic gas constant Γ. The MHD model is needed for various purposes. Essentially all laboratory plasma confinement experiments are designed to have large parameter regions that are MHD stable. The drift wave and Kelvin-Helmholtz instabilities are of interest in MHD stable plasmas.First and foremost, the study of drift waves and anomalous transport assumes that there already exists a stable MHD equilibrium. The point is that, even if the details of the MHD stability description are not precisely known, it is unlikely that drift waves and microinstabilities are of interest, or even well-posed mathematically, if the plasma is already unstable in the MHD description. There are some exceptions to this rule at marginal stability, and we discuss such a case below. But, the exceptions are rare. The very formulation of the equilibrium, or even the evolving ambient plasma state, requires the MHD equations be satisfied locally on the time 128 Turbulent Transport in Magnetized Plasmas Downloaded from www.worldscientific.com by NANYANG TECHNOLOGICAL UNIVERSITY on 08/23/15. For personal use only.