Abstract
A modified precise-integration time-domain (PITD) formulation is presented to model the wave propagation in magnetized plasma based on the auxiliary differential equation (ADE). The most prominent advantage of this algorithm is using a time-step size which is larger than the maximum value of the Courant–Friedrich–Levy (CFL) condition to achieve the simulation with a satisfying accuracy. In this formulation, Maxwell’s equations in magnetized plasma are obtained by using the auxiliary variables and equations. Then, the spatial derivative is approximated by the second-order finite-difference method only, and the precise integration (PI) scheme is used to solve the resulting ordinary differential equations (ODEs). The numerical stability and dispersion error of this modified method are discussed in detail in magnetized plasma. The stability analysis validates that the simulated time-step size of this method can be chosen much larger than that of the CFL condition in the finite-difference time-domain (FDTD) simulations. According to the numerical dispersion analysis, the range of the relative error in this method is 10−6 to 5×10−4 when the electromagnetic wave frequency is from 1 GHz to 100 GHz. More particularly, it should be emphasized that the numerical dispersion error is almost invariant under different time-step sizes which is similar to the conventional PITD method in the free space. This means that with the increase of the time-step size, the presented method still has a lower computational error in the simulations. Numerical experiments verify that the presented method is reliable and efficient for the magnetized plasma problems. Compared with the formulations based on the FDTD method, e.g., the ADE-FDTD method and the JE convolution FDTD (JEC-FDTD) method, the modified algorithm in this paper can employ a larger time step and has simpler iterative formulas so as to reduce the execution time. Moreover, it is found that the presented method is more accurate than the methods based on the FDTD scheme, especially in the high frequency range, according to the results of the magnetized plasma slab. In conclusion, the presented method is efficient and accurate for simulating the wave propagation in magnetized plasma.
Highlights
The simulations of the electromagnetic (EM) wave propagation in the magnetized plasma are attractive and have a wide range of applications, e.g., high frequency components, PCB design, microstrip antenna, and so on [1,2,3,4,5,6]
The typical algorithms based on the finite-difference time-domain (FDTD) method for modeling the dispersive material include the recursive convolution (RC) FDTD method [7,8], the auxiliary differential equation (ADE) FDTD method [9,10,11], and the Z-transform (ZT) FDTD
Based on both the auxiliary differential equation and the precise integration (PI) technique, a modified precise-integration time-domain (PITD) method has been proposed for modeling the EM wave propagation through magnetized plasma in this paper
Summary
The simulations of the electromagnetic (EM) wave propagation in the magnetized plasma are attractive and have a wide range of applications, e.g., high frequency components, PCB design, microstrip antenna, and so on [1,2,3,4,5,6]. We use the PI scheme to solve the ODEs. After establishing the modified PITD method in magnetized plasma, the stability condition and the dispersion error are analyzed numerically. The stability analysis verifies that the numerical stability criterion of the presented method in magnetized plasma is much looser than the CFL stability condition of the FDTD methods so as to increase the maximum allowable time step, and the numerical dispersion errors are almost invariant when the time-step size is increased. This method has the potential to balance both the efficiency and the accuracy. Theinstability analysis verifies stability condition and the dispersion error are analyzed numerically
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