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

A nonlinear theory has been developed for the generation of perfect azimuthal bunching on a beam with axial initial electron velocity by slow radiation fields generated by the interaction itself, under conditions of the anomalous Doppler shift. The dynamics of the beam is formulated in the framework of a Hamiltonian analysis and the helical equations 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 utilized for calculating the properties of an electron beam buncher. The latter is also optimized to maximize the generated transverse momentum.