Problems in point charge electrodynamics

TL;DR

This paper addresses discrepancies in deriving the electromagnetic self-force for point charges and explores methods to reduce wakefields in high-energy accelerators by beam path adjustments, with implications for accelerator design.

Contribution

It clarifies the derivation of the Schott term in self-force calculations and proposes a novel approach to mitigate wakefields through beam path modifications in relativistic regimes.

Findings

The Schott term can be derived using a null displacement vector under certain conditions.

Beam path adjustments can significantly reduce wakefields for very short bunches.

Potential reduction of wakefields depends on bunch length, collimator width, and relativistic factors.

Abstract

(Shortened due to character limit) This thesis consists of two parts. In part I we consider a discrepancy in the derivation of the electromagnetic self force for a point charge. In the point charge framework the self force can be defined as an integral of the Lienard-Wiechert stress 3-forms over a suitably defined worldtube. We show the Schott term may be obtained using a null displacement vector to define the worldtube providing certain conditions are realized. Part II comprises an investigation into a problem in accelerator physics. In a high energy accelerator the cross-section of the beampipe is not continuous and there exist geometric discontinuities such as collimators and cavities. When a relativistic bunch of particles passes such a discontinuity the field generated by a leading charge can interact with the wall and consequently affect the motion of trailing charges. The fields acting on the trailing charges are known as (geometric) wakefields. We model a bunch of particles as a one dimensional continuum of point charges and by calculating the accumulated Lienard-Wiechert fields we address the possibility of reducing wakefields at a collimator interface by altering the path of the beam prior to collimation. This approach is facilitated by the highly relativistic regime in which lepton accelerators operate, where the Coulomb field given from the Lienard-Wiechert potential is highly collimated in the direction of motion. It will be seen that the potential reduction depends upon the ratio of the bunch length to the width of the collimator aperture as well as the relativistic factor and path of the beam. Given that the aperture of the collimator is generally on the order of millimetres we will see that for very short bunches, on the order of hundredths of a picosecond, a significant reduction is achieved.