Ferris, Michael and Gratus, Jonathan
(2012)
*Problems in point charge electrodynamics.*
PhD thesis, Lancaster University.

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## Abstract

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. The self force is given by the Abraham-von Laue vector, which consists of the radiation reaction term proportional to the 4-acceleration, and the Schott term proportional to the 4-jerk. 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. In order to define such a worldtube it is necessary to identify a map which associates a unique point along the worldline of the source with every field point of the worldline. One choice of map is the Dirac time, which gives rise to a spacelike displacement vector field and a Dirac tube with spacelike caps. Another choice is the retarded time, which gives rise to a null displacement vector field and a Bhabha tube with null caps. In previous calculations which use the Dirac time the integration yields the complete self force, however in previous calculations which use the retarded time the integration produces only the radiation reaction term and the Schott term is absent. We show in this thesis that the Schott term may be obtained using a null displacement vector 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.