E-cloud Map Formalism: an Analytical Expression for Quadratic Coefficient

TL;DR

This paper derives an analytical expression for the quadratic coefficient in the electron cloud map formalism, improving the theoretical understanding of electron density evolution in particle accelerators.

Contribution

It provides the first analytical formula for the quadratic map coefficient, validated against simulation results across various bunch populations.

Findings

Analytical expression matches simulation data well

Validates the quadratic coefficient's theoretical estimate

Enhances predictive modeling of electron cloud dynamics

Abstract

The evolution of the electron density during electron cloud formation can be reproduced using a bunch-to-bunch iterative map formalism. The reliability of this formalism has been proved for RHIC [1] and LHC [2]. The linear coefficient has a good theoretical framework, while quadratic coefficient has been proved only by fitting the results of compute-intensive electron cloud simulations. In this communication we derive an analytic expression for the quadratic map coefficient. The comparison of the theoretical estimate with the simulations results shows a good agreement for a wide range of bunch population.