Possibilities for reduction of transverse projected emittances by partial removal of transverse to longitudinal beam correlations

TL;DR

This paper demonstrates that transverse projected emittances can be reduced by passing the beam through a magnetostatic system with carefully chosen lattice dispersions to remove linear correlations, with maximum reduction achieved when all dispersions are zeroed.

Contribution

It introduces a method to reduce transverse emittances by adjusting lattice dispersions based on beam correlations, providing explicit conditions for maximum reduction.

Findings

Maximum emittance reduction occurs when all beam dispersions are zeroed.

Lattice dispersions can remove linear correlations between longitudinal and transverse coordinates.

The solution for lattice dispersions is unique when removing beam dispersions, but not for beam tilts.

Abstract

We show that if in the particle beam there are linear correlations between energy of particles and their transverse positions and momenta (linear beam dispersions), then the transverse projected emittances always can be reduced by letting the beam to pass through magnetostatic system with specially chosen nonzero lattice dispersions. The maximum possible reduction of the transverse projected emittances occurs when all beam dispersions are zeroed, and the values of the lattice dispersions required for that are completely defined by the values of the beam dispersions and the beam rms energy spread and are independent from any other second-order central beam moments. Besides that, we prove that, alternatively, one can also use the lattice dispersions to remove linear correlations between longitudinal positions of particles and their transverse coordinates (linear beam tilts), but in this situation solution for the lattice dispersions is nonunique and the reduction of the transverse projected emittances is not guaranteed.