ABSTRACT
In choosing an accelerating structure producing a required beam of charged particles, one has to solve equations describing the electromagnetic fields and the motion of charged particles in these fields. This problem is usually split into equations of electrodynamics and equations of particle motion. Two types of operation charged particle accelerators are common, namely, the traveling wave (TW) and standing wave (SW) operations. In the TW case, the electrodynamic structure is an accelerating waveguide; in the SW case, an accelerating resonator in the form of a single cavity or a chain of coupled cavities. For linear electron accelerators, a widely accepted accelerating system is the disk-loaded waveguide (DLW). Standing wave accelerators use biperiodic structures. For standing wave linacs, the DLW is no longer an effective accelerating structure. In SW structures, the shunt impedance is equal to the product of the shunt impedance of a cell to the number of cells at 0 and p phase shifts only.
