A periodic field formed with three or five lens elements can be used as an image-forming lens in ion-optics. Generally, it possesses much stronger focusing ability than a single lens element under the same voltage ratio. Periodic field lenses have been used as initial focusing systems of ion sources in some electrostatic accelerators, yet its image-forming characteristics have not been fully studied.This paper proposes a method to investigate the image-forming characteristics of periodic field lenses. Treating periodic field lens as a lens-element-combination, the expressions of its cardinal points can be obtained by using Ferrarias characteristic determinant. For a general case, with immersion lens as lens element, the expressions of cardinal points of periodic field lenses of three and five lens elements have been given. In these expressions only cardinal parameters of lens element and geometrical parameters of electrode system are involved. These derived expressions are quite simple in form, easy for calculation with sufficient accuracy. Thus there is no difficulty in studying the general characteristics of these lenses.Using these expressions, the image-forming characteristics of some periodic field lenses with symmetrical two-tube lens of small gap-spacing as lens element have been calculated and analysed.
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