Finite Element Approximation and Input Parameterization for the Optimal Control of Current Profiles in Tokamak Plasmas

Abstract In this paper, we consider a simplified dynamic model describing the evolution of the poloidal flux during the ramp-up phase of the tokamak discharge. We first use the Galerkin method to obtain a finite-dimensional model based on the original PDE system. Then, we apply the control parameterization method to obtain an approximate optimal parameter selection problem governed by a lumped parameter system. Computational optimization techniques are subsequently deployed to solve this approximate problem. To validate our approach, we perform numerical simulations using experimental data from the DIII-D tokamak in San Diego, California. The results show that our numerical optimization procedure can generate optimal controls that drive the current profile to within close proximity of the desired profile at the terminal time, thus demonstrating that the Galerkin and control parameterization methods are effective tools for current profile control in tokamak plasmas.