Geometrical (Lienard-Wichert) approach in accelerator physics

A geometrical (Lienard-Wichert) approach is used to define the field of a relativistic beam (both in vacuum approximation and taking into account reflections from vacuum chamber walls). The approach allows to take into account the curvature of the trajectory and discreteness of the beam current. Such an approach to the problems of accelerator physics was first used by I.Tamm in 1947-1948. Recently the importance of the curvature effects is admitted in accelerator physics. However, these works are based on the continuous approximation of the current and in reality the whole component of the field related to the radiation is fallen out. This component essentially distorts the Coulomb term at distances as small as interparticle distances within the beam. Adequate to the physical condition is the conception of representing the field as a sum of microscopic fields of individual particles averaged over the specific physical effect. The continuity of the current over the total field is not satisfied in modern electron accelerators. In this report the results of the previous works based on the remarkable spatial pattern of the Lienard-Wichert field of a particle are presented (the influence of these fields on dynamics is estimated). The reflections of the beam self-field from conducting surfaces of the accelerator are also considered. The incidence of the hard part of synchrotron radiation on the exterior wall of the vacuum chamber results in a localized spot of induced charge, which moves along that wall faster-than-light. The field and the force lines resulting from motion of this spot are determined