Electron Optics of Cylindrical Electric and Magnetic Fields

Some preliminary experiments on electron-image formation led to the arrangement of a photocathode and fluorescent target in the same plane and immersed in the magnetic field of a large horseshoe magnet to form an electron image of an optical picture projected on the photocathode. In this arrangement, an opaque photocathode may be used; the fluorescent image may be viewed from the bombarded side; and light from the photocathode is prevented from falling directly on the fluorescent screen. An analysis of the motion of electrons in coaxial, cylindrical electric and magnetic fields shows that electrons originating in a plane passing through the axis of the fields may be brought to a focus at another plane passing through the axis for all values of r (distance from the axis) for which the fields are cylindrical. Two limiting cases are considered: case I, for which electrons start with small random emission velocities and are accelerated by the cylindrical electric field to the anode target; and case II, for which the electrons start with a large initial φ velocity in addition to their small random emission velocities and move in an electric-field-free space to the anode target. In both cases a cylindrical magnetic field is used to focus the electrons. The properties of the images formed (cases I and II) are expressed in terms of the order of focus. The most prominent distortion is a shearing of the image in the direction of the axis of the fields.