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Due to the requirements concerning the quality of the particle beams in the FAIR project, i.e. a small momentum uncertainty together with high currents and, in the case of the storage rings, particle target interaction, there will be a strong need of electron cooling. On the other hand, an electron cooler acts as a non-linear optical element besides electron cooling. This may lead to the excitation of resonances possibly resulting in an increase of the emittance. The aim of this work is the calculation of resonances driven by the electron cooler in the Schwerionensynchrotron (SIS) 18 being a present device at GSI Darmstadt having an electron cooler. So, we get the opportunity to prove our results experimentally. For our calculations, we used a model system consisting of a rotation matrix representing the lattice and giving the according phase advance, and a non-linear transverse momentum kick representing the electron cooler in thin lens approximation. Proceeding in this way, we got only the resonances driven by the cooler. Furthermore, we used the MAD-X code to perform our calculations.
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