Control of momentum-compaction factor in synchrotron with "resonant" lattice

In the construction of different types of synchrotrons we are often restricted in our choice of the momentum compaction factor, which must be kept low enough or negative to satisfy many conditions of beam stability. Some accelerators must have the dispersion-free straight sections desired for RF stations, Siberian Snakes, etc. The dynamic aperture in the presence of chromaticity-correcting sextupoles should be sufficiently large. The theory of momentum compaction factor control is discussed in this article.

1 Introduction

The momentum-compaction factor is one of the most important characteristics of an accelerator, which defines its transition energy. In proton accelerators the losses of particles are extremely restricted and this parameter plays a significant role, since the transition-energy crossing causes a longitudinal instability of the beam. In connection with this problem, many methods have been developed for crossing the transition energy with a minimum of particle loss [1]. Even in the case, when the crossing of this point is avoided, the Lattice design appears to be significantly connected to the RF system. For instance, in electron machines of the electron- positron collider type a small momentum-compaction factor is needed to reduce the synchrotron tune, while keeping the bunch length and momentum spread constant [2]. In synchrotron-light sources the minimum momentum-compaction factor and the minimum modulation of the dispersion function are both required simultaneously to have a small horizontal emittance[3]. Finally, in a high-intensity proton accelerator of the kaon- and neutron-factory type, the transition-energy crossing must be completely avoided because of the requirement of extremely low losses at the 10⁻¹ −10⁻¹ level [4]–[6]. Moreover, the slip factor, , should be as high as possible in order to increase the stability threshold.