The figure shows initial conditions of particles in phase space which are stable (red) and unstable (yellow). Three different methods are used to calculate the stable region with a variational method (green curve) doing best. The curves form an oblong shape. There is a black cloud of particles at the center that is the equilibrium distribution which we calculate along with the escape rate of particles (not shown).

Raju, A., Choudhury, S., Rubin, D. L., Wilkinson, A. & Sethna, J. P.

Storage rings have particles that go around in trajectories that are bent by magnets, some of which are nonlinear. The resulting trajectories have regions of chaos but also have noise from various sources. The paper used and compared analytic methods to capture the stable region in phase space (dynamic aperture). Moreover, the paper calculated the equilibrium distribution (emittance) and escape rate of particles from the dynamic aperture.

Particles in storage rings escape due to chaos and nice. We calculate the stable region and the rate at which they escape. This was one of goals of the Beam Dynamics group of CBB for the better construction of storage rings.

Link to full publication:

https://arxiv.org/abs/1707.09336