Analytical Wake Potentials in a Closed Pillbox Cavity

TL;DR

This paper derives analytical expressions for wake potentials in a closed pillbox cavity, applicable to various beam positions, and validates them through numerical evaluation and simulation comparison.

Contribution

It provides a new analytical method to calculate wake potentials in closed pillbox cavities, extending previous models to off-axis and on-axis cases.

Findings

Analytical wake potentials match simulation results for Gaussian drive bunch.

The derived expressions are valid for both on- and off-axis particles.

Numerical evaluation confirms the accuracy of the analytical approach.

Abstract

Wake potentials are derived for a closed (cylindrical) pillbox cavity as a sum over cavity modes. The resulting expression applies to on- and off-axis beams and test particles. The sum is evaluated numerically for a Gaussian drive bunch and compared to the wake potential derived from simulation.