Microwave Cavities and Detectors for Axion Research by Gianpaolo Carosi & Gray Rybka & Karl van Bibber

Author:Gianpaolo Carosi & Gray Rybka & Karl van Bibber
Language: eng
Format: epub
ISBN: 9783319927268
Publisher: Springer International Publishing

(9.7)

This equation is called the Hagen-Rubens reflectance. The absorbance is

(9.8)

because the transmittance is zero. Now, the skin depth in the classical limit is

(9.9)

After more algebra, we arrive at the neat equation:

(9.10)

We can now use Eq. (9.10) to recast Qs in terms of the absorbance of the sidewall, something that we can calculate even if there are multilayer coatings on the wall:

(9.11)

We will use Eq. (9.11) not only for the copper cavity but for the coated cavity. From the point of view of the loss of the stored energy, there is no difference between a homogeneous sidewall and a layered sidewall. We can calculate the reflectance (and absorbance) of a multilayer film on a thick substrate using the ABCD matrix method described in Heavens [5].1 Then we convert this to Q using Eq. (9.11).

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