Three-Dimensional MHD Equilibria*

The numerical calculation of three-dimensional MHD equilibria is an essential step in designing and analyzing toroidal magnetic confinement devices. The type of equilibrium is determined by the assumptions used in designing the code that calculates the equilibrium. The VMEC code is an Ideal MHD code that assumes nested toroidal flux surfaces [S. P. Hirshman and H. K. Meier, Phys. Fluids 28, 1387 (1985)] and it has been widely used in stellarator and tokamak physics. The SIESTA code relaxes the assumption of nested toroidal flux surfaces and switches between Ideal and Resistive MHD in the process of searching for an equilibrium [S. P. Hirshman, R. Sanchez and C.R. Cook, Phys. Plasmas 18, 062504 (2011)]. The SPEC code is designed with the concept of multi-region, relaxed MHD [S. R. Hudson, et al., Phys. Plasmas 19, 112502 (2012)]. In this work, these three codes are used to calculate tokamak and stellarator equilibria, with a comparison of the differences and similarities of the results. The challenges and limitations of the codes will be discussed.