Beam response to rf-generator noise in the presence of higher-harmonic passive cavities

We examine the effect of higher-harmonic passive cavities (HHCs) on the beam response to rf noise. Upon invoking certain assumptions to make the problem tractable, we employ Vlasov methods to show that when the dipole approximation applies the HHCs have a generally limited impact. Beam loading in the main cavity is included in the analysis. We illustrate our results and the limitations of our model in application to the Lawrence Berkeley National Laboratory ALS (Advanced Light Source) and the future ALS Upgrade (ALS-U) offering validation against macroparticle simulations