192 BELL SYSTEM TECHNICAL JOURNAL 



action field. Both points of view are of value. That involving the motion 

 of electrons past the anode gaps is more fundamental physically. That in 

 terms of a traveling wave component, on the other hand, is more convenient 

 in calculations of electron orbits including space charge effects, where by 

 transformation to a coordinate system rotating with the field it is possible 

 to treat of motions in static fields. 



3.4 Phase Focusing: It has been seen from two points of view how groups 

 of electrons which move around the interaction space of the magnetron 

 oscillator are formed by a process of selection and rejection of electrons by 

 the tangential component of the RF field. However, space charge de- 

 bunching and the discrepancy at all but one radius between the mean veloc- 

 ity of translation of the electrons and the velocity of the interaction field 

 would tend to disperse these groups and prevent efficient interaction, were 

 it not for the phase focusing provided by the radial component of the RF 

 field. 



The mechanism of the phase focusing may be discussed either in terms 

 of the interaction of electrons with the actual fields existing at the anode gaps 

 or in terms of the traveling wave picture of the electronic mechanism. The 

 fundamental mechanism involved depends upon the effect of the radial 

 component of the RF field in aiding or opposing the radial DC field in de- 

 termining the mean drift velocity of the electron around the interaction 

 space. If the radial RF field increases the net radial field in which the 

 electron finds itself at any instant, the mean velocity of the electron in- 

 creases as can be seen from equation (5) for the plane case. Similarly, a 

 decrease in the net radial electric field, caused by the RF radial component, 

 results in decreased electron translation velocity. These changes in the 

 electron's velocity operate so as to keep the electron near the position in 

 which it can interact most favorably with the tangential component of the 

 RF field. 



Consider an electron which crosses an anode gap at the instant the RF 

 field there is maximum retarding, that is, an electron which is to be found 

 on the plane marked M in Fig. 14 at this instant. It experiences about as 

 great an increase of velocity by virtue of the radial component aiding the 

 DC radial field before crossing the gap as decrease by virtue of the radial 

 component opposing the DC radial field after crossing the gap. Another 

 electron which is lagging behind the electron just considered is to be found 

 opposite a positively charged anode segment, as at P in Fig. 14, when the 

 RF field passes through its maximum value. Since the RF field component 

 decreases with time after this instant, the effect of the radial component of 

 the field on the electron's velocity after crossing the gap will be less than its 

 effect before crossing the gap, the net effect being one of increasing the mean 

 velocity of translation, bringing the electron more nearly into the proper 

 phase. An electron which leads the electron first considered, on the other 



