202 



BELL SYSTEM TECHNICAL JOURNAL 



good example of how intimately the electronics and circuit of the magnetron 

 oscillator are associated. 



4.4 Scaling: Once an efficient design has been achieved for a given wave- 

 length, voltage, current, and magnetic field, one is interested in reproducing 

 it at other values of these parameters. In doing this, use is made of the 

 theory of scaling. For cases where the interaction space remains geo- 

 metrically similar and the magnetron operates in the same mode, the same 

 efficiency is presumably achieved when it is arranged that the electron 

 orbits remain similar. Directly from dimensional arguments apphed to 

 Maxwell's equations for the electromagnetic field and to the equations of 



60 



g/Yq in output line 



Fig. 19.^ — A plot of electronic efficiency as a function of load conductance. The con- 

 ductance G/Vo in the output line is related to that presented by the circuit to the electrons, 

 G„ directly through the magnetron resonator and output circuits. The magnetron with 

 which these data were obtained is a 3.2 cm. magnetron having sixteen resonators. 



motion of the electrons, it can be shown that the orbits and operation will 

 be equivalent for all conditions for which the loacUng and the quantities 



\B, i\/ra)-V, and (\'/ra-h)I 



remain invariant. 



It would perhaps be of interest to consider, as a simple example, the case 

 for which all the linear dimensions of a given magnetron are changed by a 

 factor a. The new resonant wavelength, X', is equal to a\ since the new 

 resonator is a times the size of the original, while the new frequency is /' = 

 f/a. The new anode radius, cathode radius, and anode length scale directly 

 so that 



r'a = (xra,r'c = arc and // = ah 



