Energy gain in a two-gap RF cavity

TL;DR

This paper develops correction formulae for energy gain in a two-gap RF cavity accounting for velocity changes in non-relativistic particles, validated against particle tracking, extending analytical accuracy.

Contribution

It introduces new correction formulae for energy gain in two-gap RF cavities considering velocity variations, improving analytical predictions for non-relativistic particles.

Findings

Correction formulae improve accuracy of energy gain calculations.

Analytical results closely match particle tracking simulations.

Applicability extends to cavity phasing analysis.

Abstract

Velocity of a deeply non-relativistic particle can change during its acceleration inside an RF cavity significantly enough to cause a deviation of the energy gain from a linear model. This paper derives formulae for corrections to the energy gain in a two-gap RF cavity calculated by taking into account this velocity change in the next approximation. Then, the results are compared with direct particle tracking of an HWR cavity used at the PIP2IT test accelerator. The formulae significantly extend the range of parameters where analytical calculations work with a good accuracy. The approach is applied to two aspects of cavity phasing.