Beam perturbations in confined flow electron beams with planar symmetry

An analysis of the perturbations in a confined flow beam from a two-anode gun as a result of lens effects at the gun apertures is presented for the case of parallel flow with planar symmetry. The results are presented in the form of plots of the amplitude of the perturbation as a function of the ratio of the final beam voltage at the second anode to the voltage of the first anode. The parameters are the magnetic field and the ratio of spacings between cathode and the first and second anodes. For magnetic fields greater than about twice the Brillouin field corresponding to the first anode voltage, the result is a very broad minimum of perturbation extending over a voltage ratio of the order of thirty to one up to a maximum voltage determined by the spacing ratio. The conditions for exact cancellation of the perturbation introduced at the first anode by the lens action of the second anode are considered, and a convenient chart for determination of these conditions is presented. The lens effect perturbation amplitude is shown to be much greater than that resulting from space charge in the absence of lens effects, except at or very near the voltage and spacing ratio that is correct for cancellation and at relatively low voltages and magnetic fields. It is also shown how these results can be applied to hollow cylindrical beams with and without center conductors.