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

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. INDEX TERMS Auxiliary differential equation, computational electromagnetics, numerical solution, plasma, precise-integration time-domain (PITD) method.

Precise-Integration Time-Domain Formulation for Optical Periodic Media

“…T is a one-column vector containing both all of the electromagnetic field components. The matrix M contains the information related to the spatial-step and the medium parameters, and f(t) is a column vector with the excitations [3,10]. Here, harmonic plane waves are considered for illuminating the PITD grid.…”

“…where I is the identity matrix and T a is computed by the iterative process fully defined in Equations ( 5)- (7) in [14]. The interested reader in PI technique can find more specific information about the implementation in [7,10]. It is convenient to introduce here the Courant-Friedrichs-Lewy (CFL) condition for standard FDTD formulations to link it with the time step previously defined.…”

“…In recent years, researchers have focused their efforts on taking advantage of this paradigm in different areas using the precise-integration time-domain (PITD) for solving Maxwell's equations in free and lossy space [3][4][5][6][7][8]. There have been different contributions focused on improving PITD method: e.g., the extension of an unconditionally stable PITD for the numerical solutions of Maxwell's equations to the circular cylindrical coordinate system was reported by Zhao et al [9], and the works of Kang et al related to the application of the PITD method to model the wave propagation in magnetised plasma based on the auxiliary differential equation (ADE) [10,11]. In the last years, some problems related to memory requirements on PITD have been addressed from different perspectives.…”

An Efficient Numerical Formulation for Wave Propagation in Magnetized Plasma Using PITD Method

“…The PITD method, which is presented by Ma, et al, has been used to solve Maxwell's equations in free space, lossy space, and unmagnetized plasma [19,22,23]. Although the PITD method is not unconditionally stable, it can still employ a time step which is much larger than the maximum value allowed by the CFL stability condition in the FDTD method [24].…”