Coupling impedance and wake functions for laminated structures with an application to the Fermilab Booster

Abstract

We calculate the impedance and wake functions for laminated structures with parallel-plane and circular geometries in the ultrarelativistic limit. We critically examine the approximations used in the literature for the coupling impedance in laminated chambers and find that most of them are not justified because the wall surface impedance is large. A comparison between flat and circular geometry impedances is presented. We apply our calculation in a state-of-the-art beam dynamics simulation of the Fermilab Booster which includes nonlinear optics, laminated wakefields, and space charge impedance. The latter can have a significant effect away from the ultrarelativistic limit. Even though the simulations and the comparison with the experiment are done at the Booster injection energy, where the relativistic factor γ=1.42, we find good agreement between our calculation of the coherent tune shift and recent experimental measurements. © 2011 American Physical Society.