Analytical model of the magnetic field enhancement at pits on the surface of superconducting accelerating cavity

TL;DR

This paper presents an analytical model for calculating magnetic field enhancement at surface pits of superconducting cavities, aiding in predicting vortex penetration based on pit geometry.

Contribution

It introduces a simple, analytical formula linking pit geometry to magnetic field enhancement, validated against numerical calculations.

Findings

Analytical formula accurately predicts field enhancement factors.

The model helps evaluate vortex penetration thresholds.

Agreement with numerical results confirms model validity.

Abstract

A simple model of the magnetic field enhancement at pits on the surface of superconducting accelerating cavity is proposed. The model consists of a two-dimensional pit with a slope angle, depth, width, and radius of round edge. An analytical formula that describes the magnetic field enhancement factor of the model is derived. The formula is given as a function of a slope angle and a ratio of half a width to a round-edge radius. Agreements between the formula and numerical calculations are also demonstrated. Using the formula, the field vortices start to penetrate can be evaluated for a given geometry of pit.