  (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.
