Magnetohydrodynamic Equilibrium Configurations

This lecture covers the general introduction to magnetohydrodynamic (MHD) equilibrium configurations, including the MHD model for plasma description, equilibrium, configurations for magnetic confinement, and stability limits. It discusses the tokamak and stellarator concepts, deriving static MHD equilibrium equations, multi-dimensional equilibria, and the toroidal axisymmetric equilibrium. The lecture explains the example of a 2D toroidal device, the tokamak, its geometry, symmetry, and force balance equations. It also delves into the Grad-Shafranov equation, force balance, and solutions, emphasizing the importance of flux functions and safety factors. The lecture concludes with a comparison between stellarators and tokamaks in terms of magnetic field generation, plasma shaping, and confinement properties.