Azimuthally periodic electrostatically focused electron ribbon beams

Methods of enhancing transmission of ribbon-shaped electron beams undergoing circular motion in azimuthally periodic cylindrical electrostatic lenses are treated. Lens forces add to the naturally occurring curvature focusing to achieve this increase in beam transmission. Three basic configurations, differing only in the method of applying lens voltages, are treated: symmetrical focusing, deflection focusing, and asymmetric focusing (including inner and outer electrode segmentation). Expressions for beam perveance and rippling are derived from the paraxial-ray equation for thin electron ribbons advancing along a two-dimensional curved optical axis. The stiffness of azimuthally periodic electrostatically focused electron ribbons (i.e., the immunity of the beam to transverse disturbing forces) also receives attention. Mathematical extensions of the analysis to ribbon beams undergoing helical motion are discussed, and numerical results applicable to selected values of lens parameters are presented. Experimental results for an azimuthally periodic lens, constructed to test the analysis, are discussed in light of the theory developed.