Analysis of radio-frequency absorption and electric and magnetic field enhancements due to surface roughness

The radio-frequency (rf) power absorption due to a small hemispherical protrusion on a resonant cavity’s surface is computed analytically. This protrusion may assume arbitrary values of permittivity, permeability, and conductivity so that it may represent a foreign object. Under the assumption that the protrusion radius, $a$⁠, is small compared with the rf wavelength, the power dissipated in the protrusion by the rf electric field and by the rf magnetic field are calculated explicitly. It is found that, in general, the heating by the rf magnetic field is dominant when $δ/a<1$⁠, even for nonmagnetic materials, where $δ$ is the skin depth associated with the protrusion material. The field enhancement factors for both the rf electric field and the rf magnetic field on the protrusion are also calculated analytically. They are found to decrease as $δ/a$ increases. They are spot checked against the MAXWELL 3D code. These field enhancement factors are also consistent with the published results in the $δ=0$ limit, in which case the protrusion may represent a small local bump on the surface of a superconducting cavity.