volume | PIER Journals

Abstract

Degree of the electric field (EF) amplification at the tips of thin and long conductive rods array has been calculated. It is shown that such amplification depends on the rods height (H) and radius (R), as well as on distance between separate rods in the array. For simulation, an approach to numerical calculation of the EF near conductive rods with a large ratio of height to radius: H/R>10²-10⁴ has been proposed. Rods with such parameters may represent carbon nanotubes, channels of breakdowns in insulation, lightning leader channels, lightning rods, etc. The proposed approach is based on the finite integration technique. It uses also the analytical law of decrease of the EF strength and potential of a conductive ellipsoid under potential in the directions perpendicular to the ellipsoid axis and above its tip. As a result, numerical calculations of the EF distribution in systems with such rods were carried out applying calculation grids with steps proportional to the rods length, not their diameters. It permits substantial decrease of the required computational resources such as memory and time.

1. Cooray, V., "Lightning Protection," The Institution of Engineering and Technology, London, 2010.

2. Bazelyan, E. M. and Yu. P. Raizer, "Lightning Physics and Lightning Protection," IOP Publishing, Bristol, 2000.

3. Cole, M. T., K. B. K. Teo, O. Groening, L. Gangloff, P. Legagneux, and W. I. Milne, "Deterministic cold cathode electron emission from carbon nanofibre arrays," Scientific Reports, Vol. 4, 1-5, 2014.

4. Park, S., A. P. Gupta, S. J. Yeo, J. Jung, S. H. Paik, M. Mativenga, S. H. Kim, J. H. Shin, J. S. Ahn, and J. Ryu, "Carbon nanotube field emitters synthesized on metal alloy substrate by PECVD for customized compact field emission devices to be used in X-ray source applications," Nanomaterials, Vol. 8, 378-1-378-9, 2018.

5. Bocharov, G. S., A. V. Eletskii, and S. Grigory, "Theory of carbon nanotube (CNT)-based electron field emitters," Nanomaterials, Vol. 3, 393-442, 2013.
doi:10.3390/nano3030393

6. Collins, C. M., R. J. Parmee, W. I. Milne, and M. T. Cole, "High performance field emitters," Advanced Science, Vol. 3, 8, 2016.

7. Singer, H., H. Steinbigler, and P. Weiss, "A charge simulation method for the calculation of high voltage fields," IEEE Transactions on Power Apparatus and Systems, Vol. 93, No. 5, 1660-1668, 1974.
doi:10.1109/TPAS.1974.293898

8. Delves, L. M. and J. L. Mohamed, Computational Methods for Integral Equations, Cambridge University Press, Cambridge, 1985.
doi:10.1017/CBO9780511569609

9. Gibson, W. C., The Method of Moments in Electromagnetics, Chapman and Hall/CRC, Boca Raton, FL, 2008.

10. Volakis, J. L., A. Chatterjee, and L. C. Kempel, Finite Element Method for Electromagnetics: Antennas, Microwave Circuits, and Scattering Applications, IEEE Press, New York, 1998.

11. Taflove, A. and S. Hagness, Computational Electromagnetics: The Finite Difference Time Domain Method, Artech House, Boston, London, 2000.

12. Rezinkina, M. M., "Growth of dendrite branches in polyethylene insulation under a high voltage versus the branch conductivity," Technical Physics, Vol. 50, No. 6, 758-765, 2005.
doi:10.1134/1.1947354

13. Rezinkina, M., O. Rezinkin, F. D’Alessandro, et al. "Experimental and modelling study of the dependence of corona discharge on electrode geometry and ambient electric field," Journal of Electrostatics, Vol. 87, 79-85, 2017.
doi:10.1016/j.elstat.2017.03.008

14. Clemens, M. and T. Weiland, "Discrete electromagnetism with the finite integration technique," Progress In Electromagnetics Research, Vol. 32, 65-87, 2001.
doi:10.2528/PIER00080103

15. Clemens, M. and T. Weiland, "Regularization of eddy current formulations using discrete grad-div operators," IEEE Transactions on Magnetics, Vol. 38, No. 2, 569-572, 2002.
doi:10.1109/20.996149

16. Stratton, J. A., Electromagnetic Theory, IEEE Press, NJ, 2007.

17. Berenger, J. P., "Perfectly matched layer for the FDTD solution of wave-structure interaction problems," IEEE Trans. Antennas and Propag., Vol. 44, 110-117, 1996.
doi:10.1109/8.477535

18. Rezinkina, M. M., "The calculation of the penetration of a low-frequency three-dimensional electric field into heterogeneous weakly conducting objects," Elektrichestvo, No. 8, 50-55, 2003.

19. Rezinkina, M. M. and O. L. Rezinkin, "Modeling of the electromagnetic wavefront sharpening in a nonlinear dielectric," Technical Physics, Vol. 56, No. 3, 406-412, 2011.
doi:10.1134/S1063784211030169

20. Bocharov, G. S. and A. V. Eletskii, "Effect of screening on the emissivity of field electron emitters based on carbon nanotubes," Technical Physics, Vol. 50, No. 7, 944-947, 2005.
doi:10.1134/1.1994978

21. Bocharov, G. S., A. V. Eletskii, and T. J. Sommerer, "Optimization of the parameters of a carbon nanotube-based field-emission cathode," Technical Physics, Vol. 56, No. 4, 540-545, 2011.
doi:10.1134/S1063784211040086

Professor Marina Rezinkina