MAGNETRON AS GENERATOR OF CENTIMETER WAVES 203 



Since \B, (\/raYV, and (\^/ra~h)I must remain invariant, 



\'B' = XB or B' = B/a, 



(\'/r',y- V = {X/raY VovV = V, 



and (X'V'-'a' h') I' = (X'/ra- h) 7 or /' = 7. 



Thus the magnetic field changes by 1/a and the operating voltage and 

 current remain unchanged. 



The idea of scaling has been extended to magnetrons of varying rdra 

 and N by the introduction of sets of reduced variables for F, B and 7 in- 

 volving rc/ra and N, in terms of which the performance may be expressed 

 independently of the exact nature of the magnetron, 



4.5 Effect oj Other Components in the Interaction Field: In the discussion 

 of the traveling wave magnetron oscillator, it has been considered that the 

 electrons interact with a single traveling RF field component, generally a 

 component of the fundamental of the tt mode. The justification for this, 

 as has been stated, is that from the point of view of the electron the fields 

 of all other Hartree harmonics of the -k mode vary so rapidly that their 

 effects average out over an appreciable number of RF cycles. This is gen- 

 erally true, as well, for the harmonics of other modes which may be excited. 

 The fact has been mentioned that it is possible for the values of V and B 

 for oscillation in the tt mode very nearly to satisfy equation (16) for oscilla- 



2Trf' 

 tions in a harmonic of another mode. Then the angular velocity, .-77- , of 



\k I 



lirf 

 the harmonic very nearly equals that of the tt mode, -irry- , and the Hartree 



line of the harmonic lies very close to that of the it mode (see Fig. 16). The 

 effect of this situation on magnetron operation will be discussed in connection 

 with the problem of "moding" in Section 10.6 Oscillation Buildup — Starting. 

 Of particular interest is the presence in the interaction space, in addition 

 to the TT mode field, of an RF field component which is independent of angle . 

 Such a component appears, for example, as an inherent contamination in 

 the interaction field of the so-called "rising sun" type resonator system to be 

 described later. Generally, this component is of no concern because the 

 electrons interact with the x mode component throughout a time interval 

 covering several cycles, during which the effect of the contamination aver- 

 ages out. The exception to this occurs when the frequency of the rotational 

 component of the electron motion, approximately the cyclotron frequency, 

 resonates with the RF frequency as in a Type II magnetron. From equa- 

 tion (2) this occurs for the plane case when/ = c/X = eB/lvm, from which 

 XJB = l-Kcm/e = 10,700 gauss-cm. For a typical cylindrical case the con- 

 stant is somewhat greater, being about 12,500 gauss-cm. When XB has this 



