Multi-element cylindrical electrostatic lens systems for focusing and   controlling charged particles
  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 3rd 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. 
Omer Sise, Melike Ulu and Mevlut Dogan