volume | PIER Journals

Abstract

An efficient and stability-improved finite-difference time-domain (FDTD) method with auxiliary difference equations (ADE) for cold magnetized plasma is developed in this paper. The two equations of Ampere's law and the auxiliary equation for plasma are unified as a single equation at first. Then the leapfrog difference scheme is applied to it and Faraday's law, respectively. By introducing a mid-term computation into the unified equation, the iterative equations of the ADE-FDTD for plasma are derived. Its stability condition remains the same as that of a vacuum which is analyzed and numerically verified. Numerical experiments show that our proposed method is more efficient than those provided by others but with the same accuracy. Finally, the transmission properties of a magnetized plasmonic slab are investigated. The reflection and transmission coefficients of the right-circularly-polarized (RCP) and left-circularly-polarized (LCP) waves are calculated. The results show that our proposed method can be applied to study these plasma-based structures accurately and efficiently.

1. Taflove, A. and S. C. Hagness, Computational Electromagnetics: Finite-Difference Time-Domain Method, 3rd Ed., Artech House, Norwood, MA, 2005.

2. Teixeira, F. L., "Time-domain nite-difference and finite-element methods for Maxwell equations in complex media," IEEE Trans. Antennas Propag., Vol. 56, No. 8, 2150-2166, 2008.
doi:10.1109/TAP.2008.926767

3. Luebbers, R. J., F. Hunsberger, and K. S. Kunz, "A frequency-dependent finite-difference time-domain formulation for transient propagation in plasma," IEEE Trans. Antennas Propag., Vol. 39, No. 1, 29-34, 1991.
doi:10.1109/8.64431

4. Xu, L. and N. Yuan, "FDTD formulations for scattering from 3-D anisotropic magnetized plasma objects," IEEE Antennas Wireless Propag. Lett., Vol. 5, 335-338, 2006.
doi:10.1109/LAWP.2006.878901

5. Zhang, J., H. Fu, and W. Scales, "FDTD analysis of propagation and absorption in nonuniform anisotropic magnetized plasma slab," IEEE Trans. Plasma Sci., Vol. 46, No. 6, 2146-2153, 2018.
doi:10.1109/TPS.2018.2830416

6. Young, J. L., A. Kittichartphayak, Y. M. Kwok, and D. Sullivan, "On the dispersion errors related to (FD)²TD type schemes," IEEE Trans. Microw. Theory Tech., Vol. 43, No. 8, 1902-1909, 1995.
doi:10.1109/22.402280

7. Surkova, M., W. Tierens, I. Pavlenko, D. Van Eester, G. Van Oost, and D. De Zutter, "3-D discrete dispersion relation, numerical stability, and accuracy of the hybrid FDTD model for cold magnetized toroidal plasma," IEEE Trans. Antennas Propag., Vol. 62, No. 12, 6307-6316, 2014.
doi:10.1109/TAP.2014.2361902

8. Liu, S. B., J. J. Mo, and N. C. Yuan, "An auxiliary differential equation FDTD method for anisotropic magnetized plasma," Acta Physica Sinica, Vol. 53, No. 7, 2233-2236, 2004.
doi:10.7498/aps.53.2233

9. Samimi, A. and J. J. Simpson, "An efficient 3-D FDTD model of electromagnetic wave propagation in magnetized plasma," IEEE Trans. Antennas Propag., Vol. 63, No. 1, 269-279, 2015.
doi:10.1109/TAP.2014.2366203

10. Pokhrel, S., V. Shankar, and J. J. Simpson, "3-D FDTD modeling of electromagnetic wave propagation in magnetized plasma requiring singular updates to the current density equation," IEEE Trans. Antennas Propag., Vol. 66, No. 9, 4772-4781, 2018.
doi:10.1109/TAP.2018.2847601

11. Yu, Y. and J. J. Simpson, "An E-J collocated 3-D FDTD model of electromagnetic wave propagation in magnetized cold plasma," IEEE Trans. Antennas Propag., Vol. 58, No. 2, 469-478, 2010.
doi:10.1109/TAP.2009.2037770

12. Smith, G. D., Numerical Solution of Partial Differential Equations, Oxford Univ. Press, Oxford, U.K., 1978.

13. Roden, J. A. and S. D. Gedney, "Convolutional PML (CPML): An efficient FDTD implementation of the CFS PML for arbitrary media," Microw. Opt. Tech. Lett., Vol. 50, 334-339, 2000.
doi:10.1002/1098-2760(20001205)27:5<334::AID-MOP14>3.0.CO;2-A

14. Hu, W. and S. A. Cummer, "An FDTD model for low and high altitude lightning-generated EM fields," IEEE Trans. Antennas Propag., Vol. 54, No. 5, 1513-1522, 2006.
doi:10.1109/TAP.2006.874336

15. Hunsberger, F., R. Luebbers, and K. Kunz, "Finite-difference time-domain analysis of gyrotropic media. I. Magnetized plasma," IEEE Trans. Antennas Propag., Vol. 40, No. 12, 1489-1495, 1992.
doi:10.1109/8.204739

16. Balanis, C., Advanced Engineering Electromagnetics, Wiley, New York, 1989.

Dr. Jian-Yun Gao

Prof. Xiang-Hua Wang