MAGNETRON AS GENERATOR OF CENTIMETER WAVES 219 



electric field lines of the fundamental component (p = 0) of each mode are 

 shown in the interaction space. Only the magnetic field lines are shown in 

 the resonators. Below these is plotted the distribution in potential for 

 each of the fundamentals, sin ii9 and cos ii6, n = 0, \, 2, 3, and 4. For the 

 w = mode the magnetic flux threads through all the resonators in the 

 same direction and returns through the interaction space. That all the 

 segments are in phase and the interaction space field is independent of angle 

 may be seen. That there is but one tt mode is also seen from the fact that 

 the cos 46 term corresponds to zero potential on all the anode segments. 

 The first Hartree harmonic for the w = 1 mode, namely that for which 

 p = 1, having seven repeats (k = 7) or a total phase shift of l-iir radians 

 around the anode, is also plotted in Fig. 23 in addition to the fundamental. 

 The fact that it yields the same variation of anode segment potential around 

 the anode as the fundamental is apparent. 



If the system of N resonators were shock excited it would oscillate in all 

 of its modes simultaneously, producing beats in a manner analogous to but 

 considerably more complicated than that for the system of two resonators 

 already discussed. Furthermore, if the system were forced to oscillate by 

 an external drive whose frequency can be varied, the admittance of the 

 system would go through a minimum at each of the mode frequencies. With 

 each such resonance there are associated values of the Qs, characteristic 

 admittances, energy storage capacities, and the like. 



The loading of the two modes of the same value of n by the output circuit 

 of the magnetron depends on the position of the output loop relative to 

 the respective standing wave patterns. If the output coupling loop forms 



right. The interaction field plots represent only the fundamental components in each 

 case. The higher harmonics would affect the fields as i)lotted most radically near the slots 

 in the anode surface. The arrow shown in one of the slots in each case indicates the res- 

 onator which is coupled to the output circuit. The field fines in each plot are spaced 

 correctly relative to one another but not relative to those in any other plot. In the plot 

 of magnetic field fines in the resonator system (shown as dashed fines), the anode is de- 

 veloped from the cylindrical case, the anode segments being represented by the shaded 

 rectangles. At the center is a representation of the output loop. The magnetic fines for 

 the M = mode thread through each resonator in the same direction and back through the 

 interaction space in the opposite direction as indicated by the open circles at the ends of 

 the lines. For each mode the magnetic fines are shown for the instant when RF current 

 flow is maximum and all anode segments are at zero potential. In the plots of anode 

 potential, the full lines represent the potential variations with azimuthal angle d of the 

 fundamental components sin kd, k = >i. 6 is measured from the position of the output 

 coupling loop. The full circles on these curves indicate the potentials of the anode seg- 

 ments. The dashed lines represent the cos kO, k = n, modes. It should be noted that 

 the cos 40 configuration is trivial as it yields zero potential on each anode segment at all 

 times. The cosine curves may also be taken to represent the azimuthal variation of mag- 

 netic field intensity which is in time rjuadrature with respect to the corresponding sine curves 

 of potential. Similarly, the sine curves may represent magnetic field intensity correspond- 

 ing to the cosine curves of potential. For the « = 1 mode the potential variation for the 

 second Hartree harmonic {n = \, p = —1) is also plotted (actually sin Id is plotted in- 

 stead of sin —Id for comparison with sin 6). It is to be noted that it corresponds to the 

 same anode segment potentials as its fundamental. 



