230 BELL SYSTEM TECHNICAL JOURNAL 



resonators are in phase and tt radians out of phase with all the small reso- 

 nators. Similarly the n' = 1 modes of the two component sets of reso- 

 nators added in phase give the « = 1 mode, added tt radians out of phase 

 give the w = 8 mode. The n' = 2 modes yield the n = 2 and « = 7 modes 

 of the total resonator, and so on. Modes of the component resonator systems 

 of different periodicities do not add as they are uncoupled in the same sense 

 as two modes of a resonator system with resonators all of the same size. 

 The curve showing the distribution in mode frequency from n = to n = 4 

 thus has the usual shape for increasing periodicity of the field pattern. 

 The distribution in mode frequency for the remaining modes, however, is 

 reversed in form and, as n goes from 9 down to 5, appears as a distribution 

 should for which the mode periodicity increases. The two branches of the 

 mode frequency distribution curve thus appear as approximate mirror 

 images which are shifted relative to one another along the frequency scale 

 by virtue of the difference in phase of the mutual coupling between the two 

 sets of resonators. As far as frequency is concerned, the x mode of the 

 total system has the characteristics of a mode whose field pattern is inde- 

 pendent of angle, and its frequency is well separated from those of other 

 modes. 



As in the case of both unstrapped and strapped symmetrical resonator 

 systems, equivalent circuits have also been devised and studied for the 

 "rising sun" structure. Sufl&ce it to say here concerning them that in each 

 case it has been possible to explain and predict the mode frequency behavior 

 to a surprising degree of accuracy. 



As a magnetron resonator the "rising sun" system has both advantages and 

 disadvantages. Its most obvious advantages are its lack of strapping with 

 consequent ease of construction for short wavelengths and the abihty to 

 make an anode structure of any length with no penalty in mode frequency 

 separation. Although the frequency separation of the x mode from other 

 modes is not as great as is possible in strapped magnetrons, its independence 

 of anode length and the fact that it can be realized at higher values of .V are 

 both important for high power magnetrons. Furthermore, the "rising sun" 

 structure, having no strap losses, possesses an inherently higher unloaded Q 

 than strapped resonator systems. This results in an improvement in circuit 

 efficiency by a factor which may be as high as 1.2 at 1.25 cm. wavelength. 



The major disadvantage of the "rising sun" resonator system is the 

 presence in its tt mode interaction field of a strong admixture of a com- 

 ponent independent of angle. How this comes about may be seen from the 

 following considerations: The x mode frequency of the composite resonator 

 system lies somewhere between the free oscillation frequencies of the large 

 and small resonators. When oscillating in the x mode, therefore, the large 

 resonators are longer and the small resonators shorter than an equivalent 



