Nonlinear effects at the Fermilab Recycler e-cloud instability

TL;DR

This paper presents a theoretical analysis of the nonlinear effects in the e-cloud instability at Fermilab Recycler, showing how nonlinearity limits amplitude growth and aligns well with experimental data.

Contribution

It introduces a model considering nonlinear effects in e-cloud instability, highlighting their role in amplitude growth restriction and comparing results with experiments.

Findings

Nonlinear effects are the main factor restricting bunch amplitude growth.

Injection errors lead to instability amplification over time.

Model results show good correlation with experimental data.

Abstract

Theoretical analysis of e-cloud instability in the Fermilab Recycler is represented in the paper. The e-cloud in strong magnetic field is treated as a set of immovable snakes each being initiated by some proton bunch. It is shown that the instability arises because of injection errors of the bunches which increase in time and from bunch to bunch along the batch being amplified by the e-cloud electric field. The particular attention is given to nonlinear additions to the cloud field. It is shown that the nonlinearity is the main factor which restricts growth of the bunch amplitude. Possible role of the field free parts of the Recycler id discussed as well. Results of calculations are compared with experimental data demonstrating good correlation.