The anomalous skin effect and copper cavity operation at cryogenic conditions

TL;DR

This paper presents a geometric model for calculating surface resistance in copper cavities at cryogenic temperatures, compares it with traditional models, and validates findings through experiments on a 340 MHz cavity, relevant for ion linac applications.

Contribution

It introduces an exact solution for skin-layer conduction electrons in copper cavities and compares it with classical models, providing improved understanding for cryogenic RF cavity design.

Findings

Geometric model yields up to 15% higher resistance at GHz frequencies.

Experimental measurements on a copper cavity align closely with model predictions.

Cryogenic operation at 40°C enhances cavity quality factor and heat conduction performance.

Abstract

A geometric model based on a spherical Fermi - surface and using the equivalent skin-layer model allows to calculate the surface resistance, which is relevant for the RF power losses in the cavity walls. An exact solution for this conduction electron model in skin layers was derived. It is compared with measurements and with predictions from the traditional diffusion model as formulated by Reuter, Sondheimer and Chambers. A focus is put on frequencies with relevance in ion linac acceleration. At frequencies up to the GHz - range the geometric model gives up to 15% higher resistance values - when the electron free path length is about five times longer then the classical skin depth. Though both model assumptions differ a lot, the results are close to each other. A 340 MHz test cavity was built from bulk copper. The quality - factor measurements were performed in a liquid helium cryostat during the warming up phase of the cavity.The cavity was at first measured after just polishing the bulk copper surface. In the next step this surface was copper-plated. After annealing for one hour at 400 deg Celsius, a corresponding RRR - value around 120 was reached. An ion linac with copper cavities operated at cryogenic temperatures around 40 deg Celsius is expected to allow attractive, compact future linac designs. Simulations on heat conduction in pulsed operation give promising results.