Newton-ADE FDTD Method for Time-Varying Plasma

A novel finite-difference time-domain (FDTD) method is proposed in this article for electromagnetic (EM) wave propagation in time-varying plasma. It is formulated based on the fundamental Newton's equation of motion, which governs the relationships among the time-varying electron density, current density and electric field. Utilizing the auxiliary differential equation (ADE) FDTD scheme, the method is aptly referred to as the Newton-ADE FDTD method for time-varying plasma. Traditionally, the previous ADE FDTD methods directly apply the time-varying electron density for the plasma frequency in the update equations of current density and electric field. This is inadequate and incorrect in general time-varying plasma conditions. The formulation of the Newton-ADE FDTD method is provided and compared to that of the traditional ADE FDTD method. It is found that the key difference lies in the new compact term being the time-derivative of logarithm of electron density. Two discretization schemes for this term are provided. The Newton-ADE FDTD method is validated based on the matrix exponential method. Novel stability and convergence analyses are provided for the proposed method in time-varying dispersive media. These analyses show that our proposed method is stable and achieves second-order temporal accuracy. Numerical results are presented for various time-varying plasma conditions. It is demonstrated that when the absolute value for time-derivative of logarithm of electron density is large, e.g., greater than the collision frequency, the Newton-ADE FDTD method can provide correct results, while the traditional ADE FDTD method yields significant differences.