Spatio-temporal parameter estimation using data assimilation for plasma dynamics

Dynamical models for many plasma phenomena are governed by partial differential equations (PDEs) with physical parameters that undergo variations over a range of spatial and temporal scales. In this work, we develop a data assimilation (DA) framework that utilizes sparse spatially distributed measurements for estimating the unobserved state variables and parameters in such plasma dynamical systems. Our DA approach utilizes spatially correlated noises within a continuous-discrete extended Kalman filter (EKF) to account for the spatio-temporal propagation of numerical errors associated with the numerical solution of hyperbolic and parabolic PDEs with source terms. We first evaluate performance of the proposed approach in a one-dimensional (1D) stochastic PDE example by determining spatially distributed diffusion coefficient in the presence of stochastic reaction-diffusion dynamics. Then, we estimate the spatio-temporal variations of electron temperature within a 1D nonlinear reaction-advection model of low-frequency plasma oscillation driven by ionization using the EKF with spatially correlated noises and sparse measurement data.