Numerical solution of the coupled Haïssinski equations for the equilibrium state of an arbitrary bunch train in an electron storage ring

• DOI: 10.1016/j.nima.2021.165434
• Publication Date: 2021-05-11T02:31:55Z
• Authors: Tianlong He; Weiwei Li; Zhenghe Bai; Lin Wang
• Keywords: Harmonic

Abstract We study the effects of the beam loadings in the main and harmonic cavities and short-range wakefields on the bunch lengthening performance, in an electron storage ring. The compensation of the main cavity beam loading is modeled by adjusting the RF generator voltage so that the total voltage from the main cavity for each bunch can get as close as possible to the desired effective accelerating voltage under the ideal main cavity assumption. A system of coupled Haissinski equations, which determine the bunch positions and profiles in the equilibrium state for arbitrary beam-fill patterns, are derived and solved numerically by a relaxation iteration. The proposed method has advantages of being a simple algorithm, displaying effectiveness as well as good convergence. The parameters of the planned Advanced Light Source upgrade (ALS-U) storage ring are used to test the method and good agreement is obtained comparing with particle tracking simulations.