The Role of Ordinary Bessel Function and Hankel Function in Simulation of Plasma Valve Mechanism in a Loss-Free Metallic Cylindrical Waveguide

Document Type : Original Scientific Paper


Department of Laser and Photonics, Faculty of Physics, University of Kashan, Kashan, I. R. Iran



In this paper, a finite cylindrical plasma waveguide is investigated as a plasma valve in the path of a non-dissipative cylindrical waveguide with metal walls. Theoretical simulation to investigate the effect of the main parameters of this plasma valve on the transmission coefficients and reflection coefficients of the symmetric modes is the main part of this paper. The transmittance coefficients of electromagnetic waves in each symmetric mode are introduced in terms of Henkel functions and ordinary Bessel functions, and the role of these functions in the purification of some modes is investigated. Taking into account the boundary conditions, the transmission coefficient of the output wave modes from the plasma valve are obtained. The diagrams of the mentioned coefficient versus the incident wave frequency, geometry dimensions and the type of the used plasma in the valve are studied.


Main Subjects

[1] A. F. Alexandrov, L. S. Bogdankevich and A. A. Rukhadze, Principles of Plasma Electrodynamics, (Vysshaya Shkola, Moscow, 1978) in Russian, and (Springer-Verlag, Berlin, 1984).
[2] G. B. Arfken, H. J. Weber and E. Frank, Mathematical Methods for Physicists, 7th ed., Academic Press, Elsevier, India, 2012.
[3] R. E. Collin, Foundations for Microwave Engineering, 2nd ed., Wiley-IEEE Press, New York, 2001.
[4] G. Conciauro, M. Guglielmi and R. Sorrentino, Advanced Modal Analysis: CAD Techniques for Waveguide Components and Filters, John Wiley and Sons Inc., New York, 2000.
[5] M. Françon, Optical Interferometry, Academic Press, New York, 1966.
[6] J. R. Gaudier, L. Castellanos, K. Encarnación, N. Zavala, R. Rivera, N. Fara hat and E.Leal, Impedance mismatch study between the microwave generator and the PUPR plasma machine, AIP Conf. Proc. 875 (1) (2006) 192 − 194.
[7] A. A. Grigoreva, A. V. Tyukhtin, V. V. Vorobev, T. Y. Alekhinan, S. Antipov, Mode transformation in a circular waveguide with a transverse boundary between a vacuum and a partially dielectric area, IEEE Trans. Microw. Theory Tech. 64 (2016) 3441 − 3448.
[8] N. Hodgson and H. Weber, Optical Resonators, 1st ed., Springer-Verlag, London, 1997.
[9] K. Iizuka, Engineering Optics, 3rd ed., Springer, New York, 2008.
[10] J. D. Jackson, Classical Electrodynamics, 3rd ed., John Wiley Sons, New York, 1999.
[11] M. Mbonye, R. Mendis and D. M. Mittleman, Study of the impedance mismatch at the output end of a THz parallel-plate waveguide, Appl. Phys. Lett. 100 (11) (2012) 111120.
[12] S. Najari and B. Jazi, The description of mode matching method, in electromagnetic wave transmission from a loss free semi-bounded waveguide to the plasma waveguide, Eur. Phys. J. Plus 135 (10) (2020) 835.
[13] S. Najari and B. Jazi, The role of adiabatic and non-adiabatic phenomena in passing waves from a semi-bounded loss-free waveguide to semi-bounded plasma waveguide, Indian J. Phys. 96 (5) (2021) 1559 − 1567.
[14] S. Najari and B. Jazi, The heating phenomenon of a plasma column by electromagnetic wave injection from a semi-bounded waveguide, Optik 224 (2020) 165643.
[15] S. Najari, B. Jazi and S. Jahanbakht, The mode generation due to the wave transmission phenomena from a loss free isotropic cylindrical metallic waveguide to the semi-bounded plasma waveguide, Waves Rand. Complex Med. 31 (6) (2019) 1287 − 1302.
[16] J. S. Orfanidis, Electromagnetic Waves and Antennas, ECE Department, Rutgers University Press, NJ, 2002.
[17] U. Papziner and F. Arndt, Field theoretical computer-aided design of rectangular and circular iris coupled rectangular or circular waveguide cavity filters, IEEE Trans. Microw. Theory Tech. 41 (1993) 462471.
[18] D. M. Pozar, Microwave Engineering, 4th ed., Hoboken, John Wiley and Sons, NJ, 2011.
[19] J. Reitz and F. Milford, Foundations of Electromagnetic Theory, Addison-Wesley Publishing Company Inc., Boston, 1960.
[20] C. Saavedra, D. Pandey, W . Alt, H. Pfeifer and D. Meschede, Tunable fiber Fabry-Perot cavities with high passive stability, Opt. Express 29 (2021) 974−982.
[21] A. E. Siegman, Lasers, University Science Books, Mill Valley, CA, 1986.
[22] Y. G. Smirnov and D. V. Valovik, Guided electromagnetic waves propagating in a plane dielectric waveguide with nonlinear permittivity, Phys. Rev. A. 91 (2015) 013840.
[23] M. Suter and P. Dietiker, Calculation of the finesse of an ideal Fabry–Perot resonator, Appl. Opt. 53 (2014) 7004 − 7010.
[24] J. M. Vaughan, The Fabry-Pérot Interferometer: History, Theory, Practice and Applications, Adam Hilger, Bristol, UK, 1989