MAGNETRON AS GENERATOR OF CENTIMETER WAVES 189 



which shows that the complete lield jmttern may be considered to consist of 

 a rotating wave superposed on a standing wave, each having a fundamental 

 component of periodicity n. 



The fact that the periodicities, k, of the harmonics in the expressions 

 (12) or (13) are those for which k has the values given by (10) may be de- 

 termined from a Fourier analysis of the complete anode potential waves like 

 those of Figs. 9, 10, and 11. Only those harmonics which specify the same 

 pattern of potentials at the centers of the anode segments as the fundamental 

 are admitted in the analysis. 



As has been mentioned before, the complete field patterns for » = 



N . . . 



and « = ^ are standing waves. Thus for these modes of oscillation Ak = Bk 



in the expressions (12) and (13). For the other modes, n — 1, 2, 3, • • •, 



N 



— — 1, the electrons may interact with the traveling field component of 



expression (13) or with the standing field components which, in case Ak = 

 Bk, is the only component present (see Figs. 10 and 11 for the case n = 2, 

 .¥ = 8). 



The terms in expressions (12) and (13) for which \ k\ = n are the funda- 

 mental components; those for which | ^ | 9^ 7i are called the Hartree har- 

 monics. The components of field strength corresponding to these harmonics 

 in the interaction field pattern fall ofif in intensity from anode to cathode 

 more rapidly the higher the value of k. The variation with radius is of the 



(--) 



form I ~ I . Thus the farther from the anode one samples the field, the 



more like the fundamental sinusoidal pattern it appears. 



For each value of k in expression (12), whether or not Ak = Bk, there 

 are two oppositely traveling sinusoidal wave components of periodicity k. 

 Since each requires k cycles of the RF oscillation to complete one trip around 



the interaction space, the linear velocity at the anode surface is —4—" cor- 



k 



2irf 

 responding to an angular velocity of -^ . Thus, as seen in Fig. 11 for the 



k 



instant t + r/8, the change of shape of the total traveling wave indicates 



that the components of which it is composed travel with different velocities. 



In Fig. 23 are shown instantaneous RF interaction field patterns for the 



fundamental components {p = 0) of the n = 1, 2, 3, and 4 modes of an anode 



block having eight resonators. 



Z.i The Traveling Wave Picture: It is instructive to discuss the operation 



of the Type III magnetron oscillator in terms of electron interaction with 



the traveling wave components present in the interaction field. This might 



at first appear to be difficult in view of the many components of several 



possible modes. By mode frequency separation, as discussed later, it is 



