504 BELL SYSTEM TECHNICAL JOURNAL 



conditions in the cathode region are very complex, and an exact analysis 

 would entail an unwarranted amount of effort. However, from an approxi- 

 mate analysis one can obtain a very simple and adequate understanding of 

 the processes involved. 



Let us examine the conditions existing after the electrons have returned 

 through the gap of the idealized reflex oscillator. In the absence of oscilla- 

 tion, with an ideal rectilinear stream and ideally fine grids all the electrons 

 which leave the cathode will return to it. When oscillation exists all elec- 

 trons which experience a net gain of energy on the two transits will be cap- 

 tured by the cathode, while those experiencing a net loss will not reach it, 

 but instead will return through the gap for a third transit, etc. In a prac- 

 tical oscillator even in the absence of oscillation only a fraction of the elec- 

 trons which leave the cathode will be able to return to the cathode, because 

 of losses in axial velocity produced by deflections by the grid wires and vari- 

 ous other causes. As a result, it will not be until an appreciable amplitude 

 of oscillation has been reached that a major proportion of the electrons 

 which have gained energy will be captured by the cathode. On the other 

 hand, there will be an amplitude of oscillation above which no appreciable 

 change in the number captured will occur. 



The sorting action which occurs on the cathode will produce a source of 

 electronic admittance. Another contribution may arise from space charge 

 interaction of the returning bunched beam with the outgoing stream. A 

 third component arises from the continued hunching , ^suiting from the iirst 

 transit of the gap. From the standpoint of this third component the reflex 

 oscillator with multiple transits suggests the action of a cascade amplifier. 

 The situation is greatly complicated by the nature of the drift field in the 

 cathode space. All three mechanisms suggested above may combine to 

 give a resultant second source. Here we will consider only the third com- 

 ponent. Consider qualitatively what happens in the bunching action of a 

 reflex oscillator. Over one cycle of the r.f. field, the electrons tend to bunch 

 about the electron which on its first transit crosses the gap when the field 

 is changing from an accelerating to a decelerating value. The group re- 

 crosses the gap in such a phase that the field extracts at least as much energy 

 from every electron as it gave up to any electron in the group. When we 

 consider in addition various radial deflections, we see that very few of the 

 electrons constituting this bunch can be lost on the cathode. 



Although it is an oversimplification, let us assume that we have a linear 

 retarding field in the cathode region and also that none of the electrons are 

 intercepted on the cathode. To this order of ai)pr()ximation a modified 

 cascade bunching theory would hardly be warranted and we will consider 

 only that the initial bunching action is continued. Under these conditions, 



