A 3-D Global FDTD Courant-limit Model of the Earth for Long-time-span and High-altitude Applications
DOI:
https://doi.org/10.13052/2024.ACES.J.390205Keywords:
ELF, electromagnetic wave propagation, FDTD, global propagation, long-time and high-altitude simulations, scatteringAbstract
A new global 3-D finite-difference time-domain (FDTD) model is introduced to simulate electromagnetic wave propagation around the Earth, including the lithosphere, oceans, atmosphere, and ionosphere regions. This model has several advantages over existing global models, which include grids that follow lines of latitude and longitude and geodesic grids comprised of hexagons and pentagons. The advantages of the new model include: (1) it may be run at the Courant-Friedrichs-Lewy (CFL) time step (as a result, it is termed the Courant-limit model); (2) subgrids may be added to specific regions of the model as needed in a straight-forward manner; and (3) the grid cells do not become infinitely larger as the grid is extended higher in altitude. As a result, this model is a better candidate than the others for investigating electromagnetic phenomena over long time spans of interest and for investigating atmosphere-ionosphere-magnetosphere coupling. The new model is first described and then validated by comparing results for extremely low frequency (ELF) propagation attenuation with corresponding analytical and measurement results reported in the literature.
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References
K. G. Budden, The Wave-Guide Mode Theory of Wave Propagation, London: Logos Press,1961.
P. B. Morris, R. R. Gupta, R. S. Warren, and P. M. Creamer, Omega Navigation System Course Book Vols. 1 and 2. Reading, MA: Analytical Sciences Corp.
M. A. Tyler, “Round-the-world high frequency propagation: A synoptic study, DSTO-RR-0059,” 1995.
R. W. Moses, “The high-latitude ionosphere and its effects on radio propagation,” Eos, Transactions American Geophysical Union, vol. 85, no. 19, p. 192, 2004.
M. B. Cohen, U. S. Inan, R. K. Said, and T. Gjestland, “Geolocation of terrestrial gamma-ray flash source lightning,” Geophysical Research Letters, vol. 37, no. 2, 2010.
L. Liebermann, “Extremely low-frequency electromagnetic waves. I. Reception from lightning,” Journal of Applied Physics, vol. 27, no. 12, pp. 1473-1476, 2004.
S. A. Cummer, U. S. Inan, T. F. Bell, and C. P. Barrington-Leigh, “ELF radiation produced by electrical currents in sprites,” Geophysical Research Letters, vol. 25, no. 8, pp. 1281-1284, 1998.
S. A. Cummer, U. S. Inan, and T. F. Bell, “Ionospheric D region remote sensing using VLF radio atmospherics,” Radio Science, vol. 33, no. 6, pp. 1781-1792, 1998.
A. Taflove and S. C. Hagness, “Computational Electromagnetics: The Finite-Difference Time-Domain Method,” 3rd ed. Norwood, MA: Artech House, Inc., p. 1038, 2005.
M. Hayakawa and T. Otsuyama, “FDTD analysis of ELF wave propagation in inhomogeneous subionospheric waveguide models,” Applied Computational Electromagnetics Society (ACES) Journal, vol. 17, no. 3, pp. 239-244, 2002.
J. J. Simpson and A. Taflove, “Three-dimensional FDTD modeling of impulsive ELF propagation about the Earth-sphere,” IEEE Transactions on Antennas and Propagation, vol. 52, no. 2, pp. 443-451, 2004.
J. J. Simpson, R. P. Heikes, and A. Taflove, “FDTD modeling of a novel ELF radar for major oil deposits using a three-dimensional geodesic grid of the Earth-ionosphere waveguide,” IEEE Transactions on Antennas and Propagation, vol. 54, no. 6, pp. 1734-1741, 2006.
J. J. Simpson, “Current and future applications of 3-D global Earth-ionosphere models based on the full-vector Maxwell’s equations FDTD method,” Surveys in Geophysics, vol. 30, no. 2, pp. 105-130, 2009.
C. Yue and Q. Zong, “Solar wind parameters and geomagnetic indices for four different interplanetary shock/ICME structures,” Journal of Geophysical Research: Space Physics, vol. 116, no. A12, 2011.
J. T. Gosling, “The solar flare myth,” Journal of Geophysical Research: Space Physics, vol. 98, no. A11, pp. 18937-18949, 1993.
F. Zheng, Z. Chen, and J. Zhang, “A finite-difference time-domain method without the Courant stability conditions,” IEEE Microwave and Guided Wave Letters, vol. 9, no. 11, pp. 441-443, 1999.
C. C.-P. Chen, T.-W. Lee, N. Murugesan, and S. C. Hagness, “Generalized FDTD-ADI: An unconditionally stable full-wave Maxwell’s equations solver for VLSI interconnect modeling,” in IEEE/ACM International Conference on Computer Aided Design. ICCAD - 2000. IEEE/ACM Digest of Technical Papers (Cat. No.00CH37140) IEEE [Online]. Available: https://ieeexplore.ieee.org/document/896466/.
Y. Yang, R. S. Chen, Z. B. Ye, and Z. B. Wang, “Analysis of planar antennas using unconditionally stable three-dimensional ADI-FDTD method,” in 2005 IEEE Antennas and Propagation Society International Symposium, 2005: IEEE [Online]. Available: https://ieeexplore.ieee.org/document/1551512/.
D. L. Paul and C. J. Railton, “Spherical ADI FDTD method with application to propagation in the Earth ionosphere cavity,” IEEE Transactions on Antennas and Propagation, vol. 60, no. 1, pp. 310-317, 2012.
M. A. Clilverd, C. J. Rodger, R. Gamble, N. P. Meredith, M. Parrot, J.-J. Berthelier, and N. R. Thomson, “Ground-based transmitter signals observed from space: Ducted or nonducted?,” Journal of Geophysical Research: Space Physics, vol. 113, no. A4, 2008.
G. V. Khazanov, M. W. Chen, C. L. Lemon, and D. G. Sibeck, “The magnetosphere-ionosphere electron precipitation dynamics and their geospace consequences during the 17 March 2013 storm,”Journal of Geophysical Research: Space Physics, vol. 124, no. 8, pp. 6504-6523, 2019.
T. Xiao and Q. H. Liu, “A Staggered Upwind Embedded Boundary (SUEB) method to eliminate the FDTD staircasing error,” IEEE Transactions on Antennas and Propagation, vol. 52, no. 3, pp. 730-741, 2004.
K. H. Dridi, J. S. Hesthaven, and A. Ditkowski, “Staircase-free finite-difference time-domain formulation for general materials in complex geometries,” IEEE Transactions on Antennas and Propagation, vol. 49, no. 5, pp. 749-756, 2001.
P. R. Bannister, “ELF propagation update,” IEEE Journal of Oceanic Engineering, vol. 9, 1984.
J. J. Simpson and A. Taflove, “Efficient modeling of impulsive ELF antipodal propagation about the Earth sphere using an optimized two-dimensional geodesic FDTD grid,” IEEE Antennas and Wireless Propagation Letters, vol. 3, no. 1, pp. 215-218, 2004.
P. R. Bannister, “The determination of representative ionospheric conductivity parameters for ELF propagation in the Earth-ionosphere waveguide,” Radio Science, vol. 20, no. 4, pp. 977-984, 1985.
D. Shepard, “A two-dimensional interpolation function for irregularly-spaced data,” in Proceedings of the 1968 23rd ACM National Conference, New York: ACM Press, 1968.
G. Tóth, D. L. De Zeeuw, T. I. Gombosi, W. B. Manchester, A. J. Ridley, I. V. Sokolov, and I. I. Roussev, “Sun-to-thermosphere simulation of the 28-30 October 2003 storm with the Space Weather Modeling Framework,” Space Weather, vol. 5, no. 6, 2007.
K. G. Powell, P. L. Roe, T. J. Linde, T. I. Gombosi, and D. L. De Zeeuw, “A solution-adaptive upwind scheme for ideal magnetohydrodynamics,” Journal of Computational Physics, vol. 154, no. 2, pp. 284-309, 1999.
T. I. Gombosi, G. Tóth, D. L. De Zeeuw, K. C. Hansen, K. Kabin, and K. G. Powell, “Semirelativistic magnetohydrodynamics and physics-based convergence acceleration,” Journal of Computational Physics, vol. 177, no. 1, pp. 176-205, 2002.
T. I. Gombosi, K. G. Powell, D. L. De Zeeuw, C. R. Clauer, K. C. Hansen, W. B. Manchester, A. J. Ridley, I. I. Roussev, I. V. Sokolov, Q. F. Stout, and G. Toth, “Solution-adaptive magnetohydrodynamics for space plasmas: Sun-to-Earth simulations,” Computing in Science & Engineering, vol. 6, no. 2, pp. 14-35, 2004.
M. W. Liemohn, D. T. Welling, J. J. Simpson, R. Ilie, B. J. Anderson, S. Zou, N. Y. Ganushkina, A. J. Ridley, J. W. Gjerloev, A. Kelbert, M. Burleigh, A. Mukhopadhyay, and H. Xu, “CHARGED: Understanding the Physics of Extreme Geomagnetically Induced Currents,” presented at the American Geophysical Union Fall Meeting December 01, 2018 [Online]. Available: https://ui.adsabs.harvard.edu/abs/2018AGUFMNH31C0993L