A Comparison of Ideal MHD Stellarator Equilibria with and without Islands

The numerical calculation of three-dimensional MHD equilibria depends crucially on 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 Ideal MHD equilibrium [S. P. Hirshman, R. Sanchez and C.R. Cook, Phys. Plasmas 18, 062504 (2011)], thus allowing for magnetic islands to develop in the equilinrium. The SPEC code is designed with the concept of multi-region, relaxed MHD [S. R. Hudson, et al., Phys. Plasmas 19, 112502 (2012)], where regions of zero pressure gradient (force-free regions) are separated by interfaces with pressure jumps. In this work, these three codes are used to calculate stellarator equilibria for various configurations. A rotating ellipse equilibrium is used as a test case for comparison. Comparison of rotational transform and magnetic surfaces are presented for both vacuum and finite-pressure equilibria. Additional configurations will be examined.