Progress In Electromagnetics Research M
ISSN: 1937-8726
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By B. Makkinejad

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The problem of the shift and broadening of the normal modes of electromagnetic oscillations in a cylindrical cavity resonator with axisymmetric interior and ideally conducting walls with a circular hole at the base is solved. It is shown that the existence of the hole perturbs the normal frequencies, and this perturbation is calculated. The method of solution is based on the Rayleigh-Schrodinger perturbation theory. It is found that the frequency shift depends on the value of the perturbed electric field at the hole. This field is calculated using the quasistatic approximation, which involves the solution of a mixed boundary value problem for the potential. An expression for the frequency shift and broadening is obtained.

B. Makkinejad, "An Axisymmetric Cylindrical Resonating Cavity with Hole," Progress In Electromagnetics Research M, Vol. 51, 83-91, 2016.

1. Strayer, D. M., G. J. Dick, and J. E. Mercereau, "Performance of a superconductor cavity stabilized ruby maser oscillator," IEEE Trans. Magnetics, Vol. 23, No. 2, 1624, March 1987.

2. Dick, G. J. and D. M. Strayer, "Development of the superconducting cavity maser as a stable frequency source," Proceedings of 38th Annual Frequency Control Symposium, Cat. No. 84CH2062-8, 435-436, IEEE, 1984.

3. Strayer, D. M., G. J. Dick, and E. Tward, "Superconductor-sapphire cavity for an all-cryogenic SCSO," IEEE Trans. Magnetics, Vol. 19, 512, 1983.

4. Iny, O. and M. B. Barmatz, JPL New Technology Report, NPO-19356, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, December 1995.

5. Barmatz, M. B. and O. Iny, JPL New Technology Report, NPO-19101, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, December 1995.

6. Dick, G. J., D. G. Santiago, and A. Prata, "Mode orientation control for sapphire dielectric ring resonator," JPL New Technology Report, NPO-18933, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, January 1996.

7. Dick, G. J. and D. G. Santiago, "Temperature compensated sapphire microwave resonator," JPL New Technology Report, NPO-19414, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, March 1996.

8. Estin, A. J. and H. E. Bussey, "Error in dielectric measurements due to a sample insertion hole in cavity," IRE Trans. Microwave Theory and Techniques, Vol. 8, 650-653, 1960.

9. Meyer, W., "Dielectric Measurements on polymeric materials by using superconducting microwave resonators," IEEE Trans. on Microwave Theory and Techniques, Vol. 25, 1092-1099, January 1977.

10. Thomassen, K. I., "Microwave plasma density measurements," J. Appl. Phys., Vol. 36, 3642-2286, 1965.

11. Li, S. H. and R. G. Boisiso, "Composite hole conditions on complex permittivity measurements using microwave cavity perturbation technique," IEEE Trans. on Microwave Theory and Techniques, Vol. 30, No. 1, 100-103, January 1982.

12. Gauthier, S., L. Marchildon, and C. Akyel, "Shift of the complex resonance frequency of a dielectric-loaded cavity produced by small sample insertion holes," IEEE Trans. on Microwave Theory and Techniques, Vol. 37, No. 4, 801-804, April 1989.

13. Jackson, J. D., Classical Electrodynamics, 2nd Ed., 353-356, Wiley, New York, 1975.

14. Abromovitz, M. and I. A. Stegun, Handbook of Mathematical Functions, Chap. 9, Dover Publications, New York, 1965.

15. Watson, G. N., Theory of Bessel Functions, 2nd Ed., Cambridge University Press, Cambridge, (I obtained the formula for the normalization constant by noting the equality of normalization integrals for electric and magnetic fields.), 1952.

16. Makkinejad, B. and G. W. Ford, "An axisymmetric spherical cavity resonator II. Effect of the hole," Physical Review B II, Vol. 44, No. 16, 8547, October 15, 1991.

17. Goubau, G., Electromagnetic Waveguides and Cavities, 124, Pergamon Press, London, 1961.

18. Stokes, G. G., "On the dynamical theory of diffraction," Trans. Cambridge. Phil. Soc., Vol. 9, 1-62, 1849.

19. Lorenz, L., "Ueber die refexion des Lichs an der Gr¨anzfl¨ache zweier isotropen durchsichtigen Mittel," Pogg. Ann.,, Vol. 111, 460, 1860.

20. Strutt, J. W., "On the incidence of aerial and electric waves upon small obstacles in the form of ellipsoids or elliptic cylinders, and on the passage of electric waves through a circular aperture in a conducting screen," Phil. Mag., Vol. 44, 28-52, 1897.

21. Bethe, H. A., "Theory of diffraction by small holes," Phys. Rev., Vol. 66, No. 7, 163, 1944.

22. Bouwkamp, C. J., "Diffraction theory, a critique of some recent developments," Research Report, No. EM-50, Mathematics Research Group, New York University, 1953.

23. Landau, D. and E. M. Lifshitz, Electrodynamics of Continuous Media, Pergamon Press, Oxford, 1960.

24. Ford, G. W. and W. H. Weber, "Electromagnetic interactions of molecules with metal surfaces," Physics Reports, Vol. 113, No. 4, 205, 1984.

25. Forsythe, W. E., The Smithsonian Physical Tables, 9th Ed., 430, The Smithsonian Institution, Washington D.C., 1954.

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