A Precise-Integration Time-Domain Formulation Based on Auxiliary Differential Equation for Transient Propagation in Plasma

Zhen Kang,Yufeng Wang,Weilin Li,Fang Yang,Ming Huang

doi:10.1109/access.2020.2982999

Abstract

The electromagnetic wave propagation through plasma medium is one of the most important research fields in computational electromagnetics. A numerical formulation based on both the auxiliary differential equation (ADE) and the precise-integration time-domain (PITD) method for solving the plasma problems is proposed to break through the Courant-Friedrich-Levy (CFL) limit on the time-step size in a finite-difference time-domain (FDTD) simulation. In this new method, the current density J is introduced as the auxiliary variable to deal with the complex permittivity of the plasma which is dependent on the frequency, and the precise integration (PI) technique makes the selectable maximum time-step size become much larger and removes the impact of the time-step size to the numerical dispersion error. Numerical experimentations of the typical plasma problems verify and validate the reliability of the proposed formulation. Through the numerical results, it can be found that the maximum allowable time-step size of the new method is much larger than that of the CFL limit of the FDTD method, and the calculation error of the new method is nearly independent of the time-step size. As a consequence, the execution time is significantly reduced by using a larger time-step size.

Highlights

Calculation of the electromagnetic wave propagation through dispersive materials, e.g., plasma, is a complex problem and has attracted much attention in recent years [1]–[3]
NUMERICAL RESULTS In order to verify the performance of the proposed method, four typical plasma examples are simulated in the following subsection
The numerical results are compared with the analytical solution and the results of the JEC-finite-difference timedomain (FDTD), auxiliary differential equation (ADE)-FDTD, RC-FDTD and PLRC-FDTD methods

Summary

INTRODUCTION

Calculation of the electromagnetic wave propagation through dispersive materials, e.g., plasma, is a complex problem and has attracted much attention in recent years [1]–[3]. Convolution (RC) method [12]–[14], the auxiliary differential equation (ADE) method [15]–[17], and the Z-transform (ZT) method [18]–[21] These algorithms based on the FDTD method have two significant problems, the limit of the Courant-Friedrich-Levy (CFL) condition and the increasing numerical dispersion error, which have limited the intense utilization of the FDTD method as the problem size expands. A new 3-D time-domain method, called precise-integration time-domain (PITD) method, has attracted much attention for solving Maxwell’s equations in free space and lossy space [33]–[38], since the PITD method breaks through the limit of the CFL condition on the time-step size in a FDTD simulation. The numerical experimentations validate that the PITD method in plasma still keep its characteristics in free space and lossy space, i.e. using a larger time-step size and invariable numerical dispersion errors in any time-step size

FORMULATIONS

INFINITE PLASMA SPACE

STABILITY ANALYSIS

CONCLUSION