Analytical study of fringe fields and nonlinear transport in a sector-based energy analysis system

Energy Analysis (EA) systems based on sector magnets are widely applied in accelerators. Nevertheless, for low-energy electron beams below 15 MeV, extra measurement errors introduced by fringe fields of the sector magnet cannot be neglected. Moreover, initial beams with large momentum spread will encounter system errors arising from nonlinear transport. Such fringe-field-induced aberrations and their impact on momentum spectrum are studied analytically and a compensation scheme considering high-order momentum spread terms is proposed. Further, the theoretical derivation is validated with simulations, and correction of second-order aberration errors is explored via data processing. These methods and conclusions improve the accuracy of built/operational EA systems without extra costs.