Plasma Descriptions II: MHD

The preceding chapter discussed the microscopic, kinetic and two-fluid decsriptions of a plasma. But we would actually like a simpler model — one that would include most of the macroscopic properties of a plasma in a “one-fluid” model. The simplest such model is magnetohydrodynamics (MHD), which is a combination of a one-fluid (hydrodynamic-type plus Lorentz force effects) model for the plasma and the Maxwell equations for the electromagnetic fields. The main equations, properties and applications of the MHD model are developed in this chapter. In the first section, we further approximate and combine the two-fluid description in Section 5.5 to obtain a “one-fluid” magnetohydrodynamics (MHD) description of a magnetized plasma. Section 6.2 presents the MHD equations in various forms and discusses their physical content. Subsequent sections discuss general properies of the MHD model – (force-balance) equilibria (Section 6.3), boundary and shock conditions (Section 6.4), dynamical responses (Section 6.5), and the Alfvèn waves (Section 6.6) that result from them. Then, Section 6.7 discusses magnetic field diffusion in the presence of a nonvanishing plasma electrical resistivity. Finally, Section 6.8 discusses the relevant time and length scales on which the kinetic, two-fluid and MHD models of magnetized plasmas are applicable, and hence usable for describing various magnetized plasma phenomena. This chapter thus presents the final steps in the procedures and approximations used to progress from the two-fluid plasma model to a macroscopic description, and discusses the key properties of the resultant MHD plasma model.