First Advisor

Gertrude F. Rempfer

Date of Publication


Document Type


Degree Name

Master of Science (M.S.) in Physics






Electrostatic lenses



Physical Description

1 online resource (50 p.)


A theoretical and experimental study of the three-ring electrostatic lens is presented. The lens consists of three isolated ring-shaped conductors, equally spaced along a common axis of symmetry. When appropriate potentials are applied to the conductors an electric field is produced near the axis which is capable of focusing a collimated beam of electrons. In the theoretical study the charge density method is used to find a closed-form solution for the field. This method approximates the field by replacing each ring with an infinitely thin hoop of uniform charge. The radial and axial equations of motion are then solved numerically, and the paraxial values of focal length, focal distance and their second order aberrations are found. In the experimental study these focal quantities are determined by a ray tracing method that uses two grids placed in the beam path outside the field of the lens. One grid is placed in front of the lens while the other is placed behind it. The shadow pattern cast by the grids is then analyzed to find the focal properties. This method, which is independent of the type of lens being investigated, is also used on a plano-convex glass lens. Comparison of the experimental and theoretical results shows satisfactory agreement in both cases.


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