Electrostatic analyzers with different geometries have been used extensively in space plasma investigations. When the energy resolution requirements are such that ΔE/E≊10% the instrument is rather simple to design and to manufacture. However, when an energy resolution of ≊1% is required, the manufacturing costs increase rapidly. For analyzers with an energy resolution of ≊10% the calibration can also be used to correct for manufacturing errors when they appear. In this paper, it has been shown that to reach an energy resolution ΔE/E=(1.6±0.2)% using a hemispherical electrostatic analyzer with outer and inner radii 101.25 and 98.75 mm respectively and plate thickness 0.4 mm, an accuracy of 25 μm in the alignment of one hemisphere with respect to the other is sufficient. It is also shown that the effect on the energy resolution of an indentation of the surface of one of the conductors can be neglected as long as its depth is less than ≊100 μm. Larger indentations can easily be detected in the manufacturing process. For each case considered, the maximum permitted loss of transmitted particles with respect to the transmission of an ideal instrument has been defined as 10%. Similarly, it has been specified that the deviations in the distributions of entrance angles of transmitted particles shall be less than 0.1°.
Vilppola, J., Keisala, J., Tanskanen, P., & Huomo, H. (1993). Optimization of hemispherical electrostatic analyzer manufacturing with respect to resolution requirements. Review of Scientific Instruments, 64(8), 2190 - 2194. https://doi.org/10.1063/1.1143958