点电荷电动力学问题
Problems in point charge electrodynamics
摘要：
（因字数限制而缩短）本文由两部分组成。在第一部分中，我们考虑了点电荷的电磁自作用力的推导中的一个矛盾。在点电荷框架中，自作用力可以定义为在适当定义的世界管上的Lienard-Wiechert应力3-形式的积分。我们表明，肖特长期可以得到使用零位移矢量定义的worldtube提供一定的条件实现。第二部分包括对加速器物理问题的调查。在高能加速器中，束管的横截面是不连续的，存在准直器和空腔等几何不连续性。当相对论性粒子束通过这样的不连续性时，由领先电荷产生的场可以与壁相互作用，从而影响尾随电荷的运动。作用在尾随电荷上的场称为（几何）尾场。我们模拟一束粒子作为一个一维连续的点电荷，并通过计算累积的Lienard-Wiechert场，我们解决的可能性，减少尾场在准直器接口通过改变光束的路径之前准直。轻子加速器在高度相对论性的状态下运行，其中从Lienard-Wiechert势给出的库仑场在运动方向上高度准直，这有助于这种方法。可以看出，潜在的减少取决于束团长度与准直器孔径宽度的比率以及相对论因子和束的路径。假设准直器的孔径通常为毫米量级，我们将看到，对于非常短的聚束，在百分之一皮秒的量级上，实现了显著的减小。
英文摘要：
(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.
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