Potential-well bunch lengthening in electron storage rings

TL;DR

This paper critically examines Zotter's cubic equation for electron storage ring bunch lengthening, proposes a more accurate alternative, and discusses its implications for predicting bunch lengthening and determining effective impedance.

Contribution

It introduces a self-consistent equation for potential-well bunch lengthening, challenging the validity of Zotter's widely used cubic equation.

Findings

The new equation provides more accurate predictions of bunch lengthening.

It improves the calculation of effective impedance from bunch length measurements.

The study clarifies the limitations of Zotter's equation in practical applications.

Abstract

The cubic equation derived by B. Zotter has been popularly used for electron storage rings to describe the scaling law of potential-well bunch lengthening. This equation has also often been used to calculate the effective impedance when the bunch lengthening is measured or simulated. This paper discusses the validity of Zotter's equation and presents an alternative but self-consistent equation for potential-well bunch lengthening. Its applications to predicting bunch lengthening and extracting effective impedance from bunch length measurements are also addressed.