Plasma equilibrium in tokamaks

This lecture treats the magnetohydrodynamic (MHD) equilibrium of axisymmetric plasmas, as given by the Grad-Shafranov equation. In a brief introduction, equilibrium parameters such as the q-profile, the internal inductance, and the poloidal beta are introduced. The properties of these quantities will be illustrated in the case of the tokamak, by applying the large aspect ratio tokamak approximation. The properties of a non-circular plasma cross-section and the role of the vertical field will also be discussed in this approximation. Some attention is given to the (numerical) problem of solving the equilibrium equation and of reconstructing a plasma equilibrium from external measurements. The numerical methods themselves are presented in [1].