REFLEX OSCILLATORS 657 



\iously referred to as Fo is 



Vo=V{() (f8) 



In the notation as it has been modified, the transit time is 



-=(^/^2~,)jf^. (f9) 



For a constant retarding field in the drift space of magnitude Eq , we can 

 write 



vEo(ti/2) = V = a/2VF (flO) 



Here F is the total energy with which electrons are shot into the drift 

 space. From (flO) 



fe)= 



27 



(fll) 

 (fl2) 



Now we will compare r' from (f7) with ri, the rate of change of transit time 

 for a linear field, taking ri for the same resonator voltage F(/) and the same 

 transit time, given by (fl), as the nonlinear field. The factor F relating 

 t' and Tl will then be 



F-r/ 



Tl 



^^^^'^l\v'mV{C)\' (fl4) 



r Hv'{z)/v'(o) - i]dz \ [^ dz y 



"^io 2[V(z)]i jJo [F(2)]0 • 



If an electron is shot into the drift space with more than average energy, 

 its greater penetration causes it to take longer to return, but it covers any 

 element of distance in less time. Consider a case in which the gradient of 

 the potential is small near the zero potential (much change in penetration 

 for a given change in energy) and larger near the gap. The first term in 

 the brackets of (fl4) will be large, and the second is in this case positive. 

 This means that in this type of field the increased penetration per unit energy 

 and the effect of covering a given distance in less time with increased energy 

 work together to give more drift action than in a constant field. However, 



