Status of the PIES 3D Equilibrium Code

PIES is a 3D, free-boundary, equilibrium code that can handle islands and stochastic regions. We discuss the present status of the code, focusing particularly on improvements that have been made over the last few years. The code has been modified to provide two additional options for convergence algorithms: 1) a Jacobian-Free Newton-Krylov (JFNK) algorithm, with an adaptive preconditioner, globalized by a subspace restricted backtracking scheme [1]; 2) a full Newton algorithm, appropriate for massively parallel computation. An adaptive grid for calculating the current has also been implemented in recent years, providing a more accurate treatment of the physically important currents near the island separatrices, and of neoclassical effects on tearing modes. In addition, a theory of equilibria in stochastic regions has been developed, and a version of the corresponding algorithm has been implemented in the PIES code [2]. This has been motivated by indications in contemporary stellarator experiments that there are large stochastic regions with significant nonzero pressure gradients.\\[4pt] [1] D. Raburn, Ph.D. Thesis, Princeton University, 2011.\\[0pt] [2] A. Reiman, M. Zarnstorff, D. Monticello, et al, Nucl. Fusion 47, 572-578 (2007); J. A. Krommes and A. H. Reiman, Phys. Plasmas, 16, 072308(2009).