An analytical approach for beam loading compensation and excitation of maximum cavity field gradient in a coupled cavity-waveguide system

The critical process of beam loading compensation in high intensity accelerators brings under control the undesired effect of the beam induced fields to the accelerating structures. A new analytical approach for optimizing standing wave accelerating structures is found which is hugely fast and agrees very well with simulations. A perturbative analysis of cavity and waveguide excitation based on the Bethe theorem and normal mode expansion is developed to compensate the beam loading effect and excite the maximum field gradient in the cavity. The method provides the optimum values for the coupling factor and the cavity detuning. While the approach is very accurate and agrees well with simulation software, it massively shortens the calculation time compared with the simulation software.