The Lattice with Imaginary $\gamma$-Transition for the CERN Proton Synchrotron PS2

At present the new proton synchrotron PS2 with the energy range 4-50 GeV is discussed to upgrade LHC injector’s complex . Two lattices with and without the transition energy crossing are considered. In second option the momentum compaction factor must be kept low enough or negative. On the basis of the theory of “resonant” lattices for synchrotrons with complex transition energy developed in , the lattice with imaginary gamma-transition γtr for construction of PS2 lattice is proposed. Additionally the lattice should meet a number of important requirements, e.g., dispersion-free straight sections, a flexible scheme of chromaticity correction, a large enough dynamic aperture, etceteras.