Centripetal Transverse Wakefield in Relativistic Beam

TL;DR

This paper revises previous analysis of the transverse self-force in relativistic beams, showing that its impact on emittance growth in long bends is negligible compared to longitudinal CSR effects.

Contribution

It corrects earlier miscalculations and clarifies that transverse self-force effects are less significant than longitudinal CSR in beam emittance growth.

Findings

Transverse self-force impact is smaller than longitudinal CSR.

Previous estimates of emittance growth were overestimated.

Corrected analysis shows minimal transverse self-force effect.

Abstract

The effect of the transverse self-force in a relativistic beam has been studied in the earlier paper of the author [1]. However, the analysis of [1] missed an important observation and has lead to an incorrect estimate of the emittance growth of the beam when it passes through a long bending magnet. Here we correct that analysis. In particular, we conclude that the emittance growth due to the transverse self-force in a long bend is always much smaller than the emittance growth due to the longitudinal coherent synchrotron radiation (CSR) wake.