On the possibility of footprint compression with one lens in nonlinear accelerator lattice

Electromagnetic interaction of colliding beams along with other nonlinear fields often limits the beams' lifetimes and luminosities. Nonlinearities result in the spread of betatron frequencies (footprint) and, thus, may enhance dynamic diffusion of particles due to high order resonances. One of the possible ways to eliminate nonlinearities and overcome the corresponding difficulties is compensation of nonlinear forces, but, in practice, it is hardly possible to obtain exact linearity of the system. The compensation with a single nonlinear lens cannot cope with distributed nonlinearities, nonlinearities due to parasitic crossings, etc. In the article, we present a method to compute parameters of nonlinear element (lens) that eliminates both the footprint and resonance strength without achieving full compensation.

Automated summary

The electromagnetic interaction of colliding beams and other nonlinear fields can limit beam lifetimes and luminosities. Nonlinearities can lead to the spread of betatron frequencies and enhance dynamic diffusion of particles due to high order resonances. Compensating nonlinear forces is one possible way to address these issues, although achieving exact linearity in the system is challenging. Existing methods can eliminate footprint and resonance strength without full compensation of nonlinearities.