ABSTRACT
In this chapter we consider the time evolution of magnetically confined plasmas over time scales that are very long compared to the Alfve´n transit time, and are thus characterized by resistive diffusion and particle and heat transport. This will lead into and provide motivation for a discussion of finite difference methods for parabolic equations in Chapter 7. Because the electron and ion heat fluxes qe and qi are extremely anisotropic in a highly magnetized plasma, it becomes essential to work in a coordinate system that is aligned with the magnetic field. The derivation of an appropriate set of transport equations to deal with this is presented in Section 6.2 and its subsections. These transport equations need to be supplemented by an equilibrium constraint obtained by solving a particular form of the equilibrium equation as described in Section 6.3. Together, this system of equations provides an accurate description of the long time scale evolution of a MHD stable plasma.
