Theoretical and Experimental Investigations of Electron Motions in Alternating Fields with the Aid of Ballistic Models

The motion of electrons and the exchange of energy in ultra-high-frequency transverse and longitudinal fields is investigated theoretically and experimentally by means of ballistic models in which single balls or a beam of balls roll over potential slopes whose gradients change with time. In this way there are represented by models, first a cathode-ray tube, then the Heil two-field generator, and finally the Klystron. As is well known, the motion of electrons in electric fields may be imitated in gravitation models in which the potential fields are represented by surfaces whose heights everywhere correspond to the potential lines. The electrons are replaced by balls which roll over the surfaces. In the case of complicated potential fields, for example, the fields in multiple-grid tubes, a sheet of rubber may be stretched out horizontally. By means of supports located below the rubber sheet, its surface, at places corresponding to the electrodes, may be provided with height adjustments corresponding to the electrode potentials at those places. When the surface tension of the membrane is constant, each point obeys the Laplace differential equation, provided that the surfaces do not have too steep slopes in order that the three-dimensional model can, without great error, be regarded as the equivalent of the two-dimensional electric field. There is a further slight difference because of the fact that the balls cannot be regarded as frictionless sliding mass points, but, through the rolling friction, transform part of their energy of motion into rotation energy.