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

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.