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A new self-consistent semi-analytical method for calculating the stationarybeam-induced voltage in the presence of arbitrary filling patterns andimpedance sources in storage rings is presented. The theory was developed inspace-domain with resonator wake-functions and in frequency-domain witharbitrary impedance functions. The SIRIUS storage ring parameters were used tobenchmark the results, demonstrating good agreement between the two approachesand with macroparticle tracking simulations. Additionally, a different approachto simulate the beam-loading compensation of active rf cavities wasinvestigated in frequency-domain, proving to be a more generic description thanthe methods generally used. The impact of broadband impedance on thelongitudinal equilibrium was straightforwardly evaluated with thefrequency-domain framework, without intermediate steps such as fittingbroadband resonators or convolving short-range wakes with bunch distributions.Finally, a simple study of Touschek lifetime improvement with a passive higherharmonic cavity is presented.

Equilibrium of longitudinal bunch distributions in storage rings with arbitrary impedance sources and generic filling patterns