The Influence of Longitudinal Space Charge Fields on the Modulation Process of Coherent Electron Cooling

TL;DR

This paper develops an analytical model to study how long-range longitudinal space charge fields affect the ion shielding and modulation process in coherent electron cooling, which is crucial for understanding and optimizing the technique.

Contribution

It introduces a new analytical approach to evaluate the impact of space charge fields on ion shielding in electron beams used for coherent electron cooling.

Findings

Long-range space charge fields can significantly influence ion shielding.

The model estimates the effects of uniform electric fields on modulation dynamics.

Results are relevant for experimental setups like RHIC.

Abstract

The initial modulation in the scheme for Coherent electron Cooling (CeC) rests on the screening of the ion charge by electrons. However, in a CeC system with a bunched electron beam, inevitably, a long-range longitudinal space charge force is introduced. For a relatively dense electron beam, its force can be comparable to, or even greater than the attractive force from the ions. Hence, the influence of the space charge field on the modulation process could be important. If the 3-D Debye lengths are much smaller than the extension of the electron bunch, the modulation induced by the ion happens locally. Then, in that case, we can approximate the long-range longitudinal space charge field as a uniform electric field across the region. As detailed in this paper, we developed an analytical model to study the dynamics of ion shielding in the presence of a uniform electric field. We solved the coupled Vlasov-Poisson equation system for an infinite anisotropic electron plasma, and estimated the influences of the longitudinal space charge field to the modulation process for the experimental proof of the CeC principle at RHIC.