Electron Ballistics in High-Frequency Fields* 



By A. L. SAMUEL 



THIS, the final lecture of a series on Electron Ballistics, is not a summary 

 of the material which has been previously presented but rather it is an 

 attempt to show how the ballistic approach can be extended to the analysis 

 of high-frequency devices. Much that might otherwise be said about ultra- 

 high frequencies cannot be said because of secrecy requirements. However, 

 there is considerable material which can be presented, within the limits of 

 the necessary security regulations, which may be of interest to those who are 

 not already well acquainted with the subject. I will, perforce, not be able 

 to say anything specific about actual devices utilizing the principles to be 

 discussed. 



Many of the ultra-high-frequency devices which have come into use 

 during the last few years have employed electron beams of one sort or 

 another. These devices can be analysed in any one of a number of ways. 

 For example, we can write the equation of space-charge flow. This ap- 

 proach considers the electric charge as a continuous fluid subject to Poisson's 

 equation. The small-signal theory of Peterson and Llewellyn is an example 

 of this type of analysis. Or if we wish we can consider the various types of 

 wave motion which can exist in a space-charge region. The space-charge- 

 wave analysis of Hahn and Ramo as applied to velocity- variation tubes is an 

 example of this. In addition there is an elect ron-baUistic approach to the 

 problem and it is with this method that we will be concerned in the present 

 lecture. 



Before we become involved in the details of the analysis, we should perhaps 

 spend a few moments considering the relationship between these various 

 methods. If we have an interaction taking place between electric fields 

 and moving charges, we know at once from Newton's second law that the 

 forces acting on the electrons must of necessity be equal and opposite to 

 those acting on the fields. It is therefore a matter of small concern whether 

 we consider the forces acting on the electrons and the effects of these forces 

 on the electron motion or whether we consider the alteration in fields which 

 the electron motion produces. We can, if we wish, compute the energy 

 transfer to an electric field by the motion of an electric charge or we can 

 compute the change in energy of the electron which accompanies this trans- 



* Originally presented on April 11, 1945 as the concluding lecture of a symposium on 

 Electron Ballistics sponsored by the Basic Science Group of the American Institute of 

 Electrical Engineers. 



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