Title: Integral equation methods for computing equilibria in magnetically confined plasmas

Magnetic confinement of plasma in devices such as stellarators is used to create fusion conditions for energy generation. In this talk we will present a numerical scheme for computing ideal magnetohydrodynamic (MHD) stepped-pressure equilibrium in such devices. In the stepped-pressure equilibrium problem the plasma volume is partitioned into regions separated by ideal MHD interfaces. Each region has constant pressure and the magnetic field in each region can be represented efficiently using a boundary integral equation (BIE) formulation. In the equilibrium configuration, the force-balance condition must be satisfied at each point on the interfaces.

We will present a fast, high-order accurate BIE solver for computing the magnetic field in each constant pressure region. Since BIE formulations only discretize the boundary of the domain, our method requires significantly fewer unknowns compared to volume discretizing schemes. In addition, the representation leads to a well-conditioned (away from physical interior resonances) second-kind integral equation which can be numerically inverted to high-precision. We use a gradient descent algorithm to determine the position of the ideal MHD interfaces in the equilibrium configuration. Each iteration of this scheme requires computing shape derivatives of an objective function and we will give an efficient algorithm for computing such shape derivatives for BIE formulations.

Dhairya Malhotra is a postdoc at the Courant Institute of Mathematical Sciences, New York University. He received his PhD in Computational and Applied Mathematics from The University of Texas at Austin in 2017. His research interests are in developing fast scalable high-order integral equation methods for elliptic boundary value problems in complex fluids, incompressible flows, and magnetohydrodynamics. He was a co-recipient of the ACM Gordon Bell Prize in supercomputing in 2010. He also received a bronze medal in ACM Student Research Competition in 2013, the ACM/IEEE George Michael Memorial HPC Fellowship in 2015, and the ACM SIGHPC Outstanding Dissertation Award in 2018.