ELECTRON BALLISTICS IX IIIGII-TREQL'ENCV FIELDS 337 



This result is obtained by neglecting all of the higher order terms and is 

 therefore only a small signal theory of a very restricted sort. 



Now let us consider what we have done. Well, we have followed a small 

 interval of time through the drift tube. At the input this time <//o had a 

 current /o associated with it; at the output the size of this unit of time is 

 different- — it is now dti and the current associated with it is /i . The physi- 

 cal picture corresponding to this phenomenon is that of a uniform distribu- 

 tion of electric charge becoming bunched with time as it traverses the drift 

 space. 



The next step in the analysis is to carry our approximation a step further 

 and consider higher-order terms. Expanding the expression for j'l and using 

 our nomenclature the desired expression is 



ii = io [1+2 (j, (y )cos CO/ + /o (2^Jcos loot + Jn (u ^Jcos nc^tj . 



This equation is not exact since it neglects space charge effects but it does 

 indicate the presence of harmonics in the beam current and it reveals cer- 

 tain non-linear effects which can also be illustrated by the so-called phase- 

 focusing diagrams of Bruche and Rechnagel. 



Phase-Focusing Diagrams 



Bruche and Recknagel pointed out that an analogy exists between the 

 focusing in space of a parallel light beam and the focusing in phase of the 

 electrons in a uniform electron beam. In fact a small-signal theory can be 

 developed entirely in terms of optical equations. We will not go into 

 this aspect in detail but we will use their diagram (Fig. 4) to illustrate the 

 bunching effect graphically. A uniform beam of electrons is represented by 

 a series of parallel lines in distance and time coordinates, focus being indi- 

 cated by a crossing of these lines after they have been deflected by the veloc- 

 ity modulation. 



This general type of diagram has been popularized in this country by the 

 \'arians, and their associates under the name Applegate diagram, the only 

 difference being an interchange of axis. Figure 5, taken from a recent paper 

 by Dr. A. E. Harrison, illustrates this version of the Bruche and Recknagel 

 diagram. 



Now if instead of judging the current density by the density of the lines 

 on the diagram, we make a plot of the current density as a function of time 

 for different fixed distances from the input gap, the pictures are somewhat as 

 shown on Fig. 6. Figure 7 represents a plot presented by Kompfner and 

 combines in one illustration the type of presentation used by Tombs. 



