Booster racetrack lattices

In this paper for the small rings (Accumulator and Booster) of the proposed TRIUMF KAON Factory, the possibility of using racetrack lattices rather than lattices of the current circular design is investigated. The design goal is to design a lattice with dispersion-free straight sections for injection/extraction and rf, as well as a moderately high γt of about 10 in order to avoid transition and maintain stability against microwave instability with the natural negative chromaticity of the machine. In addition, one of the straight sections in the Accumulator ring has to be dispersive for the phase-space-painting injection process. Due to the high γt, no special dispersion suppressors are foreseen in the lattices; rather, the dispersion will be matched to zero in the straight sections by tuning the arcs to an integer multiple of 2φ phase advance. In the regular arcs we can then introduce a periodic modulation of the horizontal β function which in turn will modulate the dispersion function η, thus decreasing the average value of η and raising γt. Alternatively, the arcs can be tuned to a sufficiently large phase advance (4 x 2φ per arc) that γt of the full machine reaches 10 or higher. The same lattice structure can be used for the Accumulator by retuning the machine to create dispersion in one straight section, while maintaining the second straight section dispersion-free. Finally, a regular structure of the arcs helps in reducing the number of depolarizing resonances