A Dielectric Parameters Reconstruction Algorithm for 2-D Plasma Media

In this article, a parameter reconstruction algorithm for 2-D plasma is proposed based on the time-domain Maxwell’s equations. The main contributions of this article are as follows: based on the Lagrange multiplier method (LMM), the partial derivatives of the resonance frequency and collision frequency are derived so that the plasma parameters can be easily reconstructed by gradient-based optimization algorithm. Unlike previous plasma parameter reconstruction algorithms that mainly focus on collisionless plasma, our algorithm also considers the impact of collision frequency and can reconstruct the distribution of collision frequencies. To further verify the stability and effectiveness of the proposed algorithm, the effects of noise and regularization terms are also analyzed. The LMM is used to obtain the augment cost function and adjoint equations. The Ploak–Ribiere conjugate gradient method (PRCGM) is used to update the parameters, such as resonance frequency, of the unknown plasma region. What is more, the finite-difference time-domain (FDTD) method is used to calculate the electromagnetic field and Lagrange multipliers value. Besides, the Thiknov regularization term is employed to improve the ill-posedness. Three numerical examples are given to indicate the accuracy and effectiveness of the proposed 2-D plasma dielectric parameters reconstruction algorithm. This method can provide a useful reference for the reconstruction of plasma distribution on the ionosphere and the surface of high-speed aircraft.