A Data-Assimilation Based Method for Equilibrium Reconstruction of Magnetic Fusion Plasma: Solution by Adjoint Method

Abstract

Accurately determining the magnetohydrodynamic (MHD) equilibrium is fundamentally important in controlling and stabilizing fusion plasmas. Development of reliable methods for equilibrium reconstruction is therefore crucial to advancing the fusion plasma research. However, since the dynamics of plasma phenomena are highly nonlinear and highly complicated dynamics, it is difficult to develop their rigorous mathematical model. We already proposed a method of equilibrium reconstruction for fusion plasmas based on data assimilation. In the method the problem is formulated as a parameter optimization and a solution by the sensitivity equation method is proposed. In this paper, we propose a solution of equilibrium reconstruction for fusion plasmas by the adjoint method for the purpose of reducing computation time. In order to ensure the applicability of the adjoint method to a wide class of fusion plasmas, the problem formulation and derivation of the reconstruction algorithm based on the adjoint method are performed in generic form. Furthermore, we implement the proposed method as equilibrium reconstruction algorithms applicable to axisymmetric toroidal plasmas, typical examples of which are tokamaks and reversed field pinches (RFPs). Finally, the proposed method is applied to a real RFP experiment, and it is shown that the proposed method has the capability of reconstructing the equilibrium with sufficient accuracy and dramatic reduction of computation time compared with the existing methods.