A SLOW-WAVE AUTONOMOUS CYCLOTRON BUNCHER - EXACT HAMILTONIAN ANALYSISAND SIMPLIFIED HELICAL MODEL

A nonlinear theory has been developed for the generation of perfect az imuthal bunching on a beam with axial initial electron velocity by slo w radiation fields generated by the interaction itself, under conditio ns of the anomalous Doppler shift. The dynamics of the beam is formula ted in the framework of a Hamiltonian analysis and the helical equatio ns of motion are derived along with the two exact invariant quantities of the system in hand. Utilizing time separation a simplified set of equations is derived which compares favourably with the exact model at least for small initial pitch ratios. The simplified model is then ut ilized for calculating the properties of an electron beam buncher. The latter is also optimized to maximize the generated transverse momentu m.