Coherent error study in a retarding field energy analyzer

A novel cylindrical retarding electrostatic field energy analyzer for low-energy beams has been designed, simulated, and tested with electron beams of several keV, in which space charge effects play an important role. A cylindrical focusing electrode is used to overcome the beam expansion inside the device due to space-charge forces, beam emittance, etc. In this paper, we present the coherent error analysis for this energy analyzer with beam envelope equation including space charge and emittance effects. The study shows that this energy analyzer can achieve very high resolution (with relative error of around 10−5) if taking away the coherent errors by using proper focusing voltages. The theoretical analysis is compared with experimental results.