HESR lattice with non-similar arcs for stochastic cooling

Abstract

The advanced HESR lattice with two arcs having the identical layout and the different slip factors are developed. The conception of arcs with three families of quadrupole allows easy adjusting the imaginary transition energy in one arc and the real transition energy in another arc with the absolute value close to the beam energy in whole required region from 3.0 GeV to 14 GeV. The arcs have the special feature, when the high order non-linearities are fully compensated inside of each arc, and therefore the dynamic aperture of the whole machine is conserved. We consider and compare two lattices with the same absolute value of transition energy: the current lattice with the negative momentum compaction factor in both arcs and the lattice having the negative and positive momentum compaction factors in different arcs correspondingly. Simultaneously we analyzed the 4 and 6 fold symmetry arcs machine. It allows making the conclusion that the 4 fold symmetry lattice is more suitable to get the required slip factors. At the lowest energy 3 GeV, it is eta <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">imag</sub> /eta <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">reaI</sub> ap 4divide5 in the imaginary and the real arc correspondingly. For the higher beam energy this ratio is much bigger.