FZJ, Jülich
A possible solution to avoid the transition energy crossing is the lattice with a negative momentum compaction factor. The developed lattice is based on the resonantly correlated curvature and gradient modulations in arcs with integer tunes in horizontal or both planes, and it called the “resonant” lattice*. This method was adopted for the TRIUMF and Moscow Kaon Factories. It was then applied in the SSC Low Energy Booster, the CERN Neutrino Factory, and in the Main Ring of the Japan Proton Accelerator Research Complex facility. For the superconducting option of High Energy Storage Ring lattice of the FAIR project, the same idea was also accepted, and at last it is one of the candidates for PS2 in CERN as well. Due to special features the idea of “resonant” lattice can be applied for the lattice with the stochastic cooling where the different arcs have the different mixing factors with conservation of the dynamic aperture for whole machine. The “resonant” lattice is appeared to be useful for electron machines where the minimum momentum-compaction factor and the minimum modulation of the dispersion function are both required simultaneously to have a small horizontal emittance.
*Yu. Senichev and A. Chechenin, Journal of Experimental and Theoretical Physics, 2007, v. {10}5, No. 6, p. 1141
