Electronic Admittances of Parallel-Plane Electron Tubes at 4000 Megacycles

HE high-frequency admittances of electron streams flowing between parallel-plane electrodes have stimulated considerable theoretical interest. Llewellyn 1,2,3,5 has given an analysis of the particular case in which all electrons in any plane perpendicular to the direction of flow are assumed to have identical velocities. In practice, this approximation gives a reasonably accurate expression for electron stream admittances if the electrode spacing is relatively large, and if the frequency is not so high that the actual spread in electron velocities represents an appreciable fraction of the transit time. Others have treated various aspects of the general problem-i,5,o.7,8,9,io Theoretical consideration has also been given to the problem of electron flow in which the electrons possess a Maxwellian velocity distribution 11,12,13,14 . There has been, however, no complete analysis of the microwave-frequency case which takes account of the Maxwellian velocities. In order to orient the present work properly with previous work let us consider briefly the parallel plane diode shown in Fig. 1, which shows three representative potential distribution curves. If only a relatively few electrons are available at the cathode, the potential distribution between electrodes will be approximately equal to the space-charge-free distribution indicated by curve a. If an ample supply of electrons is provided by the cathode and if all electrons leave the cathode with zero velocity, then the space charge is complete in accordance with Child's law, and the potential distribution follows curve b.