Spatiotemporal state and parameter estimation of plasma dynamics using data assimilation

In this paper, we introduce a data assimilation (DA) framework for estimating the spatiotemporal profiles of state and parameters in dynamical plasma systems. We develop a DA framework based on an extended Kalman filter that is applicable to dynamical problems governed by partial differential equations (PDEs). To achieve robust state and parameter estimation, we utilize spatially correlated uncertainties and propose a regularization based on the uncertainty covariance associated with the parameter estimates. As a test case of the PDE-based DA for plasma dynamics, the present framework is applied to a simplified one-dimensional plasma model that consists of ion and neutral continuity equations, incorporating advection and ionization. To demonstrate its capabilities, we assimilate spatially sparse and noisy measurement data of low-frequency discharge oscillations in a Hall effect thruster, including time-varying discharge current and spatiotemporally varying ion bulk velocities obtained using laser-induced fluorescence. The numerical results illustrate a robust estimation of the spatiotemporal profile of the ion density, neutral atom density, and electron temperature without any prior knowledge of these quantities, showcasing the efficacy of the proposed approach. We demonstrate that the proposed uncertainty covariance regularization enables physically realizable bounded estimation of state variables and parameters of the PDEs.