Chaos in a Gravo-Magneto Neutron Trap

Performance of a neutron trap for cleaning quasi-trapped neutrons depends on what fraction of the neutron orbits are chaotic. In this paper we argue that the Lyapunov characteristic exponent is a good measure the chaos because regular orbits have Lyapunov exponent zero and chaotic orbits of a given energy have a common non-zero Lyapunov exponent. The Lyapunov exponent describes the rate of exponential divergence for infinitesimally perturbed initial conditions [1,2]. We show how to calculate the fraction of chaotic trajectories using Benettin's algorithm [1]. We evaluate the fraction of non-chaotic orbits for a trap that consists of a vertical multipole, gravity, and a current loop at the bottom of the trap.