ELECTRON BALLISTICS IN HIGH-FREQUENCY FIELDS 325 



to our thinking. My only point in all this discussion is to emphasize that 

 the basic method of acting on the electron stream has not really been changed 

 at all. The entire matter is summarized in the original statement that the 

 only thing which we can do to an electron is to change its velocity. 



Before going on to the next aspect of the problem there is a closely related 

 concept which should be mentioned. This concept is that a change in the 

 component of the velocity of an electron along one space coordinate does not 

 introduce components of velocity in directions orthogonal to the first. For 

 example, if an electron beam is deflected by a transverse electric field, there 

 will be no accompanying change in the longitudinal velocity. The difficulty 

 in the way of doing this in a practical case has nothing to do with the concept 

 but only with the problem of producing unidirectional fields. Analyses of 

 deflecting field problems which ignore the longitudinal components of the 

 fringing fields are apt to be wrong. The problem of high-frequency deflect- 

 ing fields has been treated in great detail in the literature and frequently 

 with more acrimony than accuracy. 



One further note should be added at this point. In an earlier lecture it 

 was pointed out that the magnetic effects of an electromagnetic field are in 

 general very much smaller than the electric effects. We will not stop to 

 prove that this is still true at the frequencies which now interest us but will 

 accept it without further discussion. 



For our next concept we leave electron flow for a moment and consider the 

 fields within a resonant cavity. You may very properly object that this 

 has nothing to do with electron ballistics, and indeed it does not. However, 

 we will find it necessary to discuss problems involving cavity resonators, and 

 a failure to understand some of the properties of these circuit elements can 

 cause a great deal of trouble. There are two conflicting approaches to this 

 problem which I will attempt to reconcile. 



The physicist when first presented with the problem of a resonant cavity 

 is inclined to say: This is a boundary value problem. The solution consists in 

 writing Maxwell's equations subject to the conditions that the tangential com- 

 ponent of E must be zero along the conducting walls. While a scalar and a mag- 

 netic vector potential can be defined, the field is not related to the former in the 

 simple manner used in electrostatic problems. 



The engineer, on the other hand, is inclined to say: This looks like an 

 extension of the usual resonant circuit. A capacitance exists between the top 

 and bottom walls of the cavity; charging currents will flow through the single 

 turn toroidal inductance formed by the side walls. I would like to know 

 what voltage difference exists between the top and bottom walls, and what 

 currents exists in the side walls. 



Now, actually, I am maligning both the physicist and the engineer by my 

 statements; nevertheless, there are these two approaches. Which is cor- 



