Single-invariant nonlinear optics for a small electron recirculator

This paper describes the design and simulation of a proof-of-concept octupole lattice at the University of Maryland Electron Ring (UMER). This experiment tests the feasibility of nonlinear integrable optics, a novel technique that is expected to mitigate resonant beam loss and enable low-loss high-intensity beam transport in rings. Integrable lattices with large amplitude-dependent tune spreads, created by nonlinear focusing elements, are proposed to damp beam response to resonant driving perturbations while maintaining large dynamic aperture. At UMER, a lattice with a single octupole insert is designed to test the predictions of this theory. The planned experiment employs a low-current high-emittance beam with low space charge tune shift ($\ensuremath{\sim}0.005$) to probe the dynamics of a lattice with large externally-induced tune spread. Design studies show that a lattice composed of a 25-cm octupole insert and existing UMER optics can induce a tune spread of $\ensuremath{\sim}0.13$. Stable transport is observed in PIC simulation for many turns at space charge tune spread 0.008. A maximum spread of $\mathrm{\ensuremath{\Delta}}\ensuremath{\nu}=0.11$ (rms 0.015) is observed for modest octupole strength (peak $50\text{ }\text{ }\mathrm{T}/{\mathrm{m}}^{3}$). A simplified model of the system explores beam sensitivity to steering and focusing errors. Results suggest that control of orbit distortion to $l0.2\text{ }\text{ }\mathrm{mm}$ within the insert region is essential. However, we see only weak dependence on deviations of lattice phase advance ($\ensuremath{\le}0.1\text{ }\text{ }\mathrm{rad}$.) from the invariant-conserving condition.