When a uniform finite magnetic field passing through the cathode is used for focusing a beam of electrons, random emission at the cathode results in the electrons traveling down the beam in a helical manner. Such a rotational motion severely limits the amount of current that can be made to travel through a small tube or between closely spaced parallel plates. The amount of current transmitted through such structures is calculated in this paper and presented in the form of normalized curves. It is assumed that the current initially fills the tube or the region between the parallel plates.
If an alternating electric field having a frequency comparable to the rotational frequency of the electrons is applied normal to the beam, the average electron radius of motion is increased. Should the electron beam be made to flow through a tube after the application of such an alternating electric field, the current transmission through the tube will be reduced over that when no electric field exists. The first‐order correction term for this case is calculated and presented in the form of normalized curves. The fact that the average electron radius is increased when an electric field is present implies added energy and leads to the formulation of a conductance expression relating the power in the rotational motion of the beam to the electric field normal to the beam.
The current interception and the equivalent beam conductance are important in many electronic devices such as traveling‐wave tubes. The beam conductance may be quite large in some cases—on the order of that present off the axis of a helix.