Beam transfer functions for relativistic proton bunches with beam-beam interaction

We present a method for the recovery of the transverse tune spread directly from the beam transfer function (BTF). The model is applicable for coasting beams and bunched beams at high energy with a tune spread from transverse nonlinearities induced by the beam-beam effect or by an electron lens. Other sources of tune spread can be added. A method for the recovery of the incoherent tune spread without prior knowledge of the nonlinearity is presented. The approach is based on the analytic model for BTFs of coasting beams, which agrees very well with simulations results for bunched beams at relativistic energies with typically low synchrotron tune. A priori the presented tune spread recovery method is usable only in the absence of coherent modes, but additional simulation data shows its applicability even in the presence of coherent beam-beam modes. Finally agreement of both the analytic and simulation models with measurement data obtained at RHIC is presented. The proposed method successfully recovers the tune spread from analytic, simulated and measured BTF.