  A fast method for dynamic aperture (DA) optimization of storage rings has
been developed through the use of reversal integration. While chaotic dynamical
systems have exact time-reversal symmetry, numerical forward integration
differs from its reversal due to scaled cumulative round-off errors. The
difference, intrinsically associated with the Lyapunov exponent, is a generic
indicator of chaos because it represents the sensitivity of chaotic motion to
an initial condition. A chaos indicator of the charged particle motion is then
obtained by comparing the forward integrations of particle trajectories with
corresponding reversals, a.k.a. "backward integrations." The indicator was
confirmed to be observable through short-term particle tracking simulations.
Therefore, adopting it as an objective function could speed up optimization.
The DA of the National Synchrotron Light Source II storage ring, and another
test diffraction-limited light source ring, were optimized using this method
for the purpose of demonstration.
