254 BELL SYSTEM TECHNICAL JOURNAL 



dW 

 This corresponds to a conductance term, G, obtained by equating -j- and 



GFL : ^' 



G = 2C ^ -L . (46) 



dt Vrf 



The necessary condition for oscillation during buildup is thus: 



GeiVHF) + G. + G = 0, (47) 



from which one obtains 



Ge (F«.) + G, + 2 -^ ^ = 0. (48) 



V RF at 



Since oscillation in the magnetron does in fact build up, | GeiVRp) \ must 

 be greater than G^ when oscillation starts. When equilibrium is reached, 

 GeiVRp) + Gs = 0. Thus I GeiVRp) 1 must be a decreasing function of 

 Vrf crossing the value Gs at the operating point. By equation (48), Vrf 

 thus builds up rapidly at first and then more slowly as | Ge(FRf) | ap- 

 proaches Gs . 



Increase in load, resulting in an increase of Gs , decreases the rate of 

 oscillation buildup.- The dependence on the total resonator capacitance 

 indicates that for magnetrons of dififerent sizes related by a simple scale 

 factor, Ge and Gs under such scaling presumably remaining invariant, the 

 rate of buildup decreases with increasing wavelength. Unknown in rela- 

 tion (48) is, to be sure, the exact transient dependence ofGe on RF and DC 

 voltages, magnetic field, and interaction space geometry. It is known , 

 however, that an increase of cathode diameter, although it is accompanied 

 by a decrease in electronic efficiency, does reduce the difficulty with ''mod- 

 ing" resulting from failure to start in the ir mode. 



Associated with the rate of buildup of RF oscillation in determining mag- 

 netron starting behavior is the rate at which the DC voltage is applied. 

 From the discussion of the electronics of the magnetron it is clear that 

 oscillation is not possible at all values of V but only for a limited range near 

 that which provides synchronism between the electron motion and the ro- 

 tating field pattern. If the pulser can apply a voltage which rises to a 

 value in this region and which can remain at substantially this value regard- 

 less of the current drawn, no difficulty is encountered. However, should 

 the pulser regulation be such that to secure operation at a given voltage 



^^ This is directly the opposite of the behavior with respect to load variations of a 

 circuit being driven in such a way that a constant amount of energy is fed in per cycle, in 

 which case the rate of buildup is inversely proportional to Q. 



