Differential algebraic methods for single particle dynamics studies of the University of Maryland electron ring

The University of Maryland electron ring is a small low energy machine for the study of space-charge dominated beams. Differential algebraic methods as implemented in COSY INFINITY offer an accurate method to study and analyze single particle nonlinear dynamics. As a starting point for space-charge related studies, we undertook a comprehensive examination of the single particle nonlinear dynamics based on differential algebra methods. Quantities such as tunes, chromaticities, dispersion, amplitude dependent tune shifts, and resonance strengths were calculated, and robustness of the solutions with respect to errors tested. The model demonstrated that the earth's magnetic field has a significant impact on the beam, and adds rich dynamics even in the absence of space charge. Initially we determined the tunes for which an injection-free idealization of the ring had the largest dynamic aperture. Our study then showed that the actual ring also had the largest dynamic aperture at these same tunes, and at these tunes was also least sensitive to errors. Comparison of predicted beam trajectories with measured data showed that the model was accurate for the examined area.