## Free-Boundary Axisymmetric MHD Equilibrium

##### Abstract

The calculation of equilibrium conditions is a common task in the study and modeling of magnetic-confinement experiments for con- trolled nuclear fusion, in which a high-temperature plasma is confined in a finite region of space by magnetic fields. Given the plasma shape, for toroidal devices with axial symmetry, such as tokamaks, the equilibrium calculation reduces to the solution of an elliptic PDE. In several circumstances, the plasma shape may not be known a priori, or one may desire to also compute the magnetic fields in the volume surrounding the plasma through the calculation of a free-boundary equilibrium. This requires either the coil currents or the magnetic poloidal flux on a curve in the vacuum region to be known ab initio. It is well known how to calculate both, but surprisingly until the introduction of the FREE- FIX code no general tools were available in the fusion community for this task. FREE-FIX is a general tool for calculating coil currents to be used as the input for a free-boundary equilibrium. A new formulation is presented, which considerably reduces the computational cost of the calculation. FREE-FIX performs well for different geometries and experiments. Some possible future applications are also suggested.