Transition crossing of proton beams in SIS100

The proton cycle in the SIS100 synchrotron is designed to deliver single bunches with $2\times10^{13}$ particles at 29 GeV. During the cycle beam dynamics near transition energy have to be analyzed to avoid a significant emittance blow-up. In the past two scenarios were discussed, a shift of the transition energy above the extraction energy and a transition crossing with a so called $\gamma_\mathrm{t}$ jump. To estimate the possible emittance blow-up in both scenarios, longitudinal simulations are presented including the Johnsen effect based on the second order phase slip factor and the effect of longitudinal space charge. Furthermore, different parameters in the design of the $\gamma_\mathrm{t}$ jump are varied and a set of parameters is proposed that shows minimal longitudinal emittance growth in the simulations.