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

Abstract

The radio-frequency ͑rf͒ 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 ␦ / a Ͻ 1, even for nonmagnetic materials, where ␦ 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 ␦ / a increases. They are spot checked against the MAXWELL 3D code. These field enhancement factors are also consistent with the published results in the ␦ = 0 limit, in which case the protrusion may represent a small local bump on the surface of a superconducting cavity.

Electromagnetic power absorption due to bumps and trenches on flat surfaces

“…30,31 Accurate analytical scaling has been obtained for the power absorption due to a single hemispherical protrusion, of arbitrary permittivity e, conductivity r, and permeability l, located on a resonant cavity's surface. 5 In this paper, we provide an accurate assessment of the enhanced electromagnetic power absorption caused by small local surface defects consisting of cylindrical bumps or trenches, where we assume the radius a of the defect is much smaller than the free space wavelength k (a ( k) and the radius of curvature of the surface at the location of the defect (in the absence of the defect) is much larger than k, so that the surface can be considered as locally flat in the absence of the defect. The 2D surface defect is assumed to be in the form of either a single semi-cylindrical bump or trench located on an otherwise flat surface (Figs.…”

“…II B we consider problems whereby a semi-cylindrical bump lies on a perfectly conducting surface (PEC) under various electromagnetic incident fields ( Figs. 1 and 2; Zhang et al, 5 Perez-Arancibia and Bruno 32 ). Thus validated, the HIEM approach is used to treat important structures which defy analytical treatment, namely, cylindrical bumps and trenches on finitely conducting flat surfaces (Fig.…”

“…Despite extensive usage, the frequency regime of validity for this scaling relation is not fully determined as yet. 5 Recently, both periodic 28,29 and random 16 roughness profiles have been studied using various methods. Holloway and Kuester 28 calculated the power loss associated with periodic conducting and superconducting rough interfaces using a generalized impedance boundary condition.…”

“…14, 15 The enhanced power loss due to surface and interface roughness exerts significant effects on signal integrity of microelectronic circuits. [16][17][18][19][20] Other effects due to surface roughness, such as local electric and magnetic field enhancements, may trigger RF-breakdown 5,8,11,[19][20][21][22][23] and abrupt quenching 2,7,9 (i.e., rapid loss of superconductivity) of a superconducting cavity.…”

“…Interaction of electromagnetic waves with rough surfaces is an important topic in science and engineering: surface roughness is known to cause excessive electromagnetic power absorption, [1][2][3][4][5][6] and it is one of the major limiting factors to the performance of radio-frequency (RF) cavities and slow wave structures 3,[7][8][9][10][11][12] with an impact on communication systems, 1,8,11 particle accelerators, 1,9,13 and material characterization at microwave frequencies. 14, 15 The enhanced power loss due to surface and interface roughness exerts significant effects on signal integrity of microelectronic circuits.…”