196 BELL SYSTEM TECHNICAL JOURNAL 



this DC current is directly proportional to anode length, h. If the magne- 

 tron is driven at greater DC current, the space charge in the interaction 

 space increases but the phase of its structure with respect to the traveling 

 anode wave does not change to a first approximation. Thus both the 

 in-phase and quadrature components of Irf increase with no change in 

 electronic admittance. The second order effects which do arise from small 

 shifts in the phase of the rotating space charge structure are discussed in 

 Section 10.4 Electronic Effects on Frequency. 



4. Conditions Relating Measurable Parameters 



4.1 Necessary Conditions for Oscillation: After having discussed the elec- 

 tron motions in the interaction space of the Type III magnetron oscillator, 

 the viewpoint will now be changed to that looking from the outside in, so to 

 speak, and it will be asked what conditions relating measurable parameters 

 are imposed by the nature of the electronic mechanism. Beyond the geo- 

 metrical parameters of cathode and anode radii, re and ra, one can determine 

 the DC voltage, V, applied between cathode and anode; the magnetic field 

 B, in which the magnetron is placed; the DC current, /, drawn by the anode; 

 the frequency of oscillation,/; and, from impedance measurements, the RF 

 load, Ys = Gs -\- jBs , presented to the electrons by the resonator, output, 

 and load. 



Perhaps the most fundamental condition for oscillation of the traveling 



wave magnetron is that imposed by the requirement of synchronism between 



the electron drift and the RF field. As has been indicated, the angular 



velocity of a rotating component of a Hartree harmonic of the interaction 



lirf 

 field, of order y^, is jyy . An approximate expression for the mean angular 



'I . . ■ . . 



velocity of the electrons may be determined b}' neglecting the variation of 



electric field with radius and calculating the angular velocity midway be- 

 tween cathode and anode, thus: 



V E/B V/(ra - rc)B 2V 



(ra + ^c)/2 (r„ + rc)/2 (r„ + rc)/2 (K - ri)B- 



2irf 

 Equating this to the angular velocity -Tf| , one obtains the relation: 



27r/ 

 In this derivation it should be recognized that the angular velocity ttt 



may be considered either to be that of a traveling component of the RF 

 field with which the electron interacts or the mean angular velocity which the 



