Magnetohydrodynamics (MHD) in Fusion Plasmas

Abstract

Magnetohydrodynamics (MHD) has been greatly advanced throughout the whole fusion programs, exhibiting the elegance of theory against seemingly daunting experimental results. Despite a set of vastly simplified assumptions (e.g. single fluid description rather than electron and ion fluids), both ideal and resistive MHDs have proven valid in a majority of fusion plasmas, providing an excellent infrastructure for equilibrium and stability. Assuming the plasma resistivity (K = 0) goes to zero, ideal MHD model describes a single-fluid, low-frequency, long-wavelength, macroscopic plasma behavior. One of the strongest merits of ideal MHD description enables us to figure out the magnetic field topology which affects the macroscopic equilibrium and stability. Indeed, the knowledge and accuracy of the magnetic field configurations at equilibrium play a key role in clarifying a variety of global and local MHD instabilities. In that regard, the understanding of the validity and limitation of ideal MHD could be more important than what needs to be further elaborated. Given the enormously rich literatures of MHD (more than thousands, if not ten-thousands, e.g. [1]), it may not be fair to list up only a few selective materials. Nonetheless, for the sake of speedy understanding for beginners in a limited time of class, a few examples in equilibrium and stability will be discussed, including Grad-Shafranov equation, tearing mode, Mercier mode and resistive wall mode (RWM).