326 BELL SYSTEM TECHNICAL JOURXAL 



rect? Well, they both are. It is not correct to speak of an electrostatic 

 potential within a resonant cavity; nevertheless, we may and do talk about 

 the voltage between the top and bottom of a resonant cavity. What do 

 we mean? Simply the maximum instantaneous line integral of the electric 

 held taken along some speciiied path. In any practical device utilizing 

 electron beams we are naturally interested in the path taken by the elec- 

 trons. The fact that the line integral is different for different paths is of no 

 great concern. We are interested in but one of these paths. We shall 

 therefore have occasion to talk about voltages in cavities but we must always 

 remember what is meant, and we must never for one instant forget that this 

 voltage is not unique but that it depends upon some assumed path. 



The second peculiarity of this voltage must also be emphasized. The line 

 integral must be taken at a specified instant in time. In effect one takes a 

 photograph of the field at some instant in time and then at one's leisure 

 performs the integration. 



Now, of course, an electron when projected through such a cavity will 

 perform yet another type of integration. The change in squared velocity 

 of the electron as expressed in volts will be given by the line integral of the 

 field encountered by the electron; that is, integrated not instantaneously 

 but with the electron velocity. This is not a simple process, because the 

 electron velocity is continuously being changed by the field interaction and 

 therefore the velocity with which the integration is performed depends 

 upon the integrated value of the field up to the point in question. This 

 has nothing to do with the concept of voltage in a resonant cavity. The 

 cavity voltage can, however, be considered as the maximum change in 

 squared velocity expressed in volts which an electron could receive if its 

 entrance velocity was very large so that the transit time was small compared 

 with the period of the cavity field. 



The four basic concepts which I have chosen to recall to your mind are, 

 by way of summary: (l)*the total current is the same in all parts of a circuit, 

 that is div. / = 0; (2) the only way we can act on an electron is to change its 

 velocity; (3) the changes in the velocity component of an electron along 

 any one rectangular coordinate have no effect on the velocity components 

 along any other coordinate; and (4) for convenience, a voltage can be defined 

 in a resonant circuit as the line integral of the electric field taken along some 

 prescribed path. 



Transit Angle 



Since we are to deal with the interaction of electrons and high-frequency 

 fields, we frequently find it convenient to measure electron velocity not 

 directly but in terms of the equivalent potential difference through which an 

 electron must fall to obtain the velocity in question, and the unit of measure 



