Investigations in the Field of the Ultra-short Electromagnetic Waves III. Electronic Oscillations in Vacuum Tubes and the Causes of the Generation of the Dwarf Waves

The purpose of this paper is the elucidation of the causes of the generation of the dwarf waves i.e., of waves with frequencies exceeding many times the frequency of the oscillations of the electrons about the grid of the tube. The existing theories of the generation of ultra-short waves cannot give a satisfactory explanation of the origin of dwarf waves of different orders. This is due to the simplifying assumptions made by the theories in the conditions of the problem. The phenomena of generation of ultra-short waves are closely connected with the motion of electrons. Therefore, in order to obtain the explanation in question an investigation was made of the motion of the electrons in tubes generating ultra-short waves. The motion of the electrons was investigated graphically by means of special diagrams which simultaneously represented the trajectories of the electrons and the alternating potentials at the electrodes of the tube. In this manner it was shown that the reason a vacuum tube can generate dwarf waves is because the tube can transmit energy into the oscillating circuit coupled with it and transmit it periodically with a period equal to the natural period of the circuit not only when this period $T$ is equal to the period of the electronic oscillations $\tau$ (normal waves), but also when $T=\frac{\tau }{2}, T=\frac{\tau }{3}, T=\frac{\tau }{4}, \cdots$ (dwarf waves). This property of the tube depends on the fact that in all the cases described a periodic division of the electrons into two groups is possible. According to the theory of E. Gill and J. Morrell this division determines the transmission of energy into the oscillating circuit. The above property of the tube means also that the dynamic resistance of the tube is negative under these conditions. The diagrams of the trajectories and the velocities of the electrons, constructed on the basis of the computations of G. Kreutzer, confirmed the above deductions.