Resistive wall wakefields in the extreme anomalous skin effect regime

Abstract

Usual treatments of resistive wall effects in accelerators are limited to the normal skin effect regime of electrical conductivity in metals. Therefore they do not generally apply to the situations when beamexposed metallic surfaces of the vacuum chamber are held at cryogenic temperatures, where simple metals exhibit anomalous skin effect behavior. These situations occasionally occur in accelerators with cold-bore devices, such as small-gap superconducting undulators. The amount of anomalous resistivity material can be substantial to significantly influence beam dynamics. To accurately estimate these effects, we expand the conventional treatment of resistive wall in accelerators into the extreme anomalous skin effect region. Starting with the surface impedance expressions, we derive resistive wall related quantities commonly used in accelerator physics, such as wake functions, wake potentials, loss factor, etc. in the extreme anomalous skin effect region. We follow with examples for resistive wall generated heat and transverse mode-coupling instability.

Resistive wall wakefields of short bunches at cryogenic temperatures

“…In order to calculate the wakefields analytically, that work was restricted to the so-called "extreme" range of the ASE regime, where the surface impedance expressions can be significantly simplified. As a tradeoff, the results of [3] are not directly applicable to bunches shorter than approximately 0.1 ps rms, which is more than adequate for storage ring applications, such as those described in [3].…”

“…The energy loss of the beam due to the resistive wall wakefield in the undulator interferes with the lasing process, and its knowledge and control is important for optimization of the FEL performance. The results of [3] cannot be directly used for very short bunches in x-ray FELs, where the typical bunch length could be as low as a few femtoseconds, and, in addition, the bunch shape is non-Gaussian, extending the bunch shape spectrum further in frequency. It is the goal of this paper to present numerical calculations of wakefields for such extremely short bunches in the ASE regime.…”

“…In the latter case, metals enter the anomalous skin effect regime (ASE) where the conductivity is substantially different from NSE. A detailed study [3] of wakefields in the ASE regime was conducted earlier by one of the co-authors of this paper (BP). In order to calculate the wakefields analytically, that work was restricted to the so-called "extreme" range of the ASE regime, where the surface impedance expressions can be significantly simplified.…”

Design and system integration of the superconducting wiggler magnets for the Compact Linear Collider damping rings

“…Therefore, the average power deposition per unit length due to the wakefield of the beam in the extreme anomalous skin effect regime of a cold beam pipe for aluminum or copper (coating) is given by [26] P=L ¼ Àð 5 6 ÞcZ 0 4b 2…”

“…The angles of observation in horizontal and vertical directions are and c . The emitted light, which will not be absorbed by upstream absorbers (yz plane), shown in cones, will (11) and (12); parameter values from [8,26]. partly irradiate the beam pipe.…”