484 BELL SYSTEM TECHNICAL JOURNAL 



never becomes very negative and may remain positive and the gap loading 

 conductance due to longitudinal fields be always positive. In such gaps, 

 however, transverse fields can have important effects, and (6.3) no longer 

 gives the total gaj) conductance. Transverse fields act to throw electrons 

 approaching the gap outward or inward, into stronger or weaker longitudinal 

 tields, and in this manner the transverse felds can either cause the electrons 

 to give up part of their forward velocity, transferring energy to the reso- 

 nator, or to pick up forward velocity, taking energy from the resonator. 

 An analysis of the effect of transverse fields is given in Appendix VIII, and 

 this is applied in calculating the total conductance, due both to longitudinal 

 and to transverse fields, of a short gap between cylinders with a uniform cur- 

 rent density over the aperture. It is found that the transverse fields con- 

 tribute a minor part of the total conductance, and that this contribution 

 may be either positive or negative, but that the total gap conductance is 

 always positive (see Appendix \TII, Fig. 140). 



The electron flow across the gap produces a susceptive component of 

 admittance. This susceptive component is in general more difficult to cal- 

 culate than the conductive component. It is not very important; it serves 

 to affect the frequency of oscillation sHghtly but not nearly so much as a 

 small change in repeller voltage. 



Besides such direct gap loading, the velocity modulation and drift action 

 within a gap of fine grids actually produce a small bunching of the electron 

 stream. In other words, the electron stream leaving such a gap is not only 

 velocity modulated but it has a small density modulation as well. This 

 convection current will persist (if space-charge debunching is not serious) 

 and, as the electrons return across the gap, it will constitute a source of elec- 

 tronic admittance. We find however, that in typical cases (see Appendix 

 VIII, (h59)-(h63)), this effect is small and is almost entirely absent in gaps 

 with coarse grids or large apertures. 



Secondary electrons produced when beam electrons strike grid wires and 

 grid frames or gap edges constitute another source of gap loading. It has 

 been alleged that if the frames supporting the grids or the tubes forming a 

 gap have opposed parallel surfaces of width comparable to or larger than the 

 gap spacing, large electron currents can be produced through secondary 

 emission, the r-/ field driving electrons back and forth between the opposed 

 surfaces. It would seem that this phenomenon could take place only at 

 quite high r-f levels, for an electron would probably require of the order of 

 100 volts energy to produce more than one secondary in striking materials 

 of which gaps are usually constructed. 



VH. Electronic Tuning — Arbitrary Drift Angle 



So far, the "on tune" oscillation of reflex oscillators has been considered 

 except for a brief discussion in Section II, and we have had to deal only with 



