The Large Hadron Collider (LHC) upgrade, which aims at reaching significantly higher luminosities at the experiment sites, requires the existing injector chain to provide proton beams with unprecedented beam intensity and brightness. The required beam parameters are out of reach for the CERN accelerator complex in its present state. Therefore, upgrade possibilities of the existing injectors for mitigating their performance limitations or their partial replacement by new machines have been studied. The transition energy plays a central role for the performance of synchrotrons. Designing a lattice with negative momentum compaction (NMC), i.e. imaginary transition energy, allows avoiding transition crossing and thus the associated performance limitations. In the first part of this thesis, the properties of an NMC cell are studied. The limits of betatron stability are evaluated by a combination of analytical and numerical calculations. The NMC cell is then used for the design study of a new synchrotron called PS2, which has been proposed to replace the existing CERN Proton Synchrotron (PS) in the LHC injector chain. Two lattice options are presented, the baseline racetrack lattice and the alternative option based on a threefold symmetry. They are compared with respect to their tuning flexibility as well as their linear and nonlinear properties. The effect of machine imperfections on the dynamic aperture is studied in detailed tracking simulations. The direct impact of the transition energy and the phase slip factor on the performance of an operating synchrotron is described in the second part of this thesis. The intensity thresholds for the instabilities, that are presently limiting the performance of the LHC-type proton beams in the Super Proton Synchrotron (SPS), scale linearly with the slip factor. A new optics for the SPS is presented, which provides lower transition energy and thereby a three times higher slip factor at injection energy. The resulting increase of the intensity threshold for the transverse mode coupling instability at injection is demonstrated in experimental and simulation studies. Furthermore, numerical simulations show that the electron cloud density at which bunches become unstable is twice higher in the new optics. In addition to that, the expected improvement of longitudinal beam stability at higher energies is confirmed by a series of measurements. Finally, a reduction of the incoherent space charge tune shift by about 15% is achieved due to the larger dispersion function in the arcs, which helps minimizing incoherent emittance growth at the injection plateau for high brightness beams. Since fall 2012, the new optics is being successfully used for LHC filling in routine operation providing improved beam characteristics compared to the nominal SPS optics.