A charged particle traveling along the axis of a circular waveguide

Abstract

The aim of this chapter is to demonstrate that a satisfactory choice of the reference system and the use of Lorentz transformations can help determine the solution of electromagnetic problems, if moving sources are present in the system. This is a typical situation that occurs in particle accelerators, in particular, in linear accelerators, a functional scheme is shown in Figure 9.1. A linear particle accelerator, often shortened to linac, is a type of particle accelerator that accelerates charged subatomic particles or ions to a high speed by subjecting them to a series of oscillating electric potentials along a linear beamline. The design of a linac depends on the type of particle that is being accelerated: electrons, protons, or ions [1]. However, the length of the machine must be quite large in order to give sufficient thrust to accelerated particles, while in a circular machine, the packets can pass many times before being collided. The most powerful linear accelerator is located in Stanford, California at the Stanford linear accelerator centre (SLAC) laboratory and is about 3 km long. Electrons and positrons can be accelerated simultaneously and then separated and brought to collide. The maximum energy of each beam reached almost 50 GeV when, in the 1990s of the last century, the machine was used to study collisions e+e− at the Z 0 resonance, in competition with the LEP, circular accelerator, which in those years, was operating at CERN in Geneva. For the future, there are plans to build even longer and more powerful linear accelerators for fundamental research, such as International Linear Collider (ILC) for collisions e+e− at about 500-1,000 GeV in the center of mass or even Compact LInear Collider (CLIC) for energies up to 2,000-4,000 GeV, achieving such energies with circular machines would be practically impossible.