BTF measurements with beam-beam interactions

We present considerations about the transverse beam transfer function (BTF) of beams under the influence of two effects: The strong-strong beam-beam effect and the influence of a Gaussian electron lens. The BTF are investigated using two methods: BTF excitation is simulated in a particle-in-cell (PIC) code. The BTF model is verified using a known analytic expectation. Analytic expectations for BTF of beams under a stationary electron lens are derived by extending BTF from the formalism of Berg and Ruggiero. Finally we compare the analytic BTF results for a stationary Gaussian lens to both the PIC simulation for split tune conditions and to PIC simulations for a beam influenced by an electron lens. We conclude that the formalism represents the electron lens well and can be applied to a limited extend to the beam-beam effect under split tune conditions. The analytic formalism allows us to recover the strength of an electron lens by means of fitting and can give clues regarding the strength of the beam-beam effect under split tune conditions.Comment: 5 pages, contribution to the ICFA Mini-Workshop on Beam-Beam Effects in Hadron Colliders, CERN, Geneva, Switzerland, 18-22 Mar 201

Analysis of resonancesinduced by the SIS-18 electron cooler

Besides beam cooling, an electron cooler also acts as a non-linear optical element. This may lead to the excitation of resonances possibly resulting in an increase of the beam emittance. The aim of this work is the calculation of resonances driven by the electron space charge field in the cooler installed in the SIS heavy ion synchrotron at GSI Darmstadt. For our calculations, we used a numerical model consisting of a rotation matrix representing the ideal lattice together with a non-linear transverse kick element representing the electron cooler. Within this model, we studied the dominant resonance lines resulting from the interaction with the cooler