# Cylindrical Cavity Resonator

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An electromagnetic wave can be confined inside a space surrounded by conducting walls, which is called a cavity. Consider a cylindrical cavity with inner radius and height . There are two possible wave modes: transverse electric (TE) and transverse magnetic (TM). For appropriate field variables for those modes, separation of variables leads to harmonic solutions to the wave equation (from Maxwell's equations) of the form , where is a Bessel function of the first kind. The constant is an integer . Noting that is an eigenvalue of the Helmholtz equation and taking into account the boundary condition for the trigonometric function , introduce the additional integer indices: , (TE), and (TM).

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Contributed by: Y. Shibuya (August 2015)

Open content licensed under CC BY-NC-SA

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References

[1] J. D. Jackson, *Classical Electrodynamics*, 3rd ed., New York: John Wiley and Sons, 1999.

[2] W. K. H. Panofsky and M. Phillips, *Classical Electricity and Magnetism*, 2nd ed., New York: Dover Publications, 2005.

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