This paper describes theoretical modelling of electrostatic lenses based on 3, 4 and 5 closely spaced cylindrical electrodes, respectively. In each case, modelling is carried out numerically using commercial packages SIMION and LENSYS, and a variety of performance parameters are obtained. These include the magnification, the 3 rd order spherical and chromatic aberration coefficients. Special cases such as zoom lens (i.e., lenses whose magnification may be changed without losing focus) are considered. Results are obtained as a function of the ratios of the electrode lengths and gaps, and as a function of ratios of the controlling voltages.As a result, it is shown that how a multi-element lens system can be operated with the whole focal properties in a useful mode for using in experimental studies.
The energy resolution of a hemispherical deflector analyser (HDA) can be substantially improved by using its entry fringing fields advantageously, rather than trying to eliminate them—the traditional approach. The intrinsic lensing properties of these fringing fields, as shown in simulations, are able to not only restore, but even improve first-order focusing at the 180° deflection plane in a controlled way, without the use of any additional field correction electrodes. This is accomplished by changing the entry radius R0 and bias from their conventional values of , the mean radius and to new values with or with . An HDA with , ΔR = R2 − R1 = 58.4 mm and maximum entry angle αmax = 2° demonstrates the impressive resolution gains that can be attained, 34 for a point entry (Δr0 = 0) and 4.2 for an aperture diameter of Δr0 = 1 mm, over corresponding conventional entry conditions.
Strong fringing fields at the entry and exit of a real hemispherical deflector analyser (HDA) significantly degrade the 180° first-order focusing conditions, one of the central advantages of the ideal-field HDA. Over the past 50 years, traditional approaches to cure this problem have primarily sought to suppress these fields by improving field termination conditions typically requiring the unwieldy use of additional electrodes. Recently, Zouros et al (2006 Meas. Sci. Technol. 17 N81–N86) have shown in simulation that a simple repositioning of the HDA entry when appropriately biased results in the effective utilization of the intrinsic lensing properties of these fields to restore and even improve first-order focusing. Here, we investigate in simulation the efficacy of the new controlled lensing approach and compare it to the traditional Herzog and Jost field corrector approach. HDA focusing properties and energy resolution are reported as a function of entry angle, source extent and hemispherical interelectrode separation. For all cases considered, HDAs using controlled lensing always came out ahead demonstrating superior focusing along the 180° deflection plane and improved energy resolution.
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