MAGNETRON AS GENERATOR OF CENTIMETER WAVES 



213 



the coupled circuit system, as for the simple single frequency resonator, Q 

 parameters and a characteristic admittance may be delined which specify 

 sharpness of resonance and energy storage capacity, respectively. 



6.2 The MullicavUy Anode Structure: As an introduction to the dis- 

 cussion of the multicavity resonator system of the magnetron oscillator 

 having cylindrical symmetry, consider the system of a series of resonators 

 machined side by side in a linear block as shown in Fig. 22. One may con- 

 sider such a linear array either to be infinite in extent or to be terminated 

 in some manner at the ends of a string of N identical resonators. 



Fig. 22. — A linear array of resonators terminated at both ends by generalized termina- 

 tions represented by planes. The figure is meant also to indicate the nature of the infinite 

 array of resonators referred to in the text. 



The oscillation in each resonator of the array of coupled resonators is 

 specified by a differential equation in terms of a variable, such as current 

 or voltage, the constants of the circuit itself, and the mutual interaction 

 between the circuit and its neighbors. Each solution of the set of simul- 

 taneous differential equations for all the resonators involved corresponds 

 to a definite phase shift between adjacent resonators. The allowed values 

 of this phase shift depend upon the boundary conditions imposed on the 

 string of resonators. If the block is infinitely long, all values of phase shift 

 are allowed. In terms of the electromagnetic field pattern formed on the 

 front surface of the block by the fringing fields of the individual resonators, 

 this means that traveling wave solutions representing waves of any velocity, 

 traveling over the surface of the block in directions normal to the slots, are 

 possible. If the block is terminated, on the other hand, the boundary 



