MAGNETRON AS GENERATOR OF CENTIMETER WAVES 187 



The mean angular velocity which the electrons must possess is then given by 



dd 2tj^ lirf 



dt^kT^ k ' ^^^^ 



in which 6 is the azimuthal angle. 



For the tt mode (« = -) it is seen that the negative integers, p, give the 



same series of values for | ^ [ as do the positive integers including zero. 

 The sequence is | ^ | = 4, 12, 20, 28, • • • . Reference to Fig. 9 indicates 

 that electrons may travel in either direction around the interaction space 

 and interact favorably with the RF field, provided their mean angular 

 velocity is given by equation (11) with values of k specified by equation 

 (10). That this should be so is clear from the fact that the anode potential 

 wave is a standing wave with respect to which direction has no meaning. 

 Fig. 9 also makes clear how an electron moving with velocity different from 

 that corresponding to the lines shown, will fall out of step with the field, 

 and on the average be accelerated as much as it is retarded, thus eilecting 

 no net energy transfer. 



In Figs. 10 and 11, diagrams for the n = 2 mode similar to that of Fig. 9 

 for the TT mode are shown. Fig. 10 is for electronic interaction with a stand- 

 ing wave of periodicit}- n = 2 and Fig. 1 1 for a traveling wave of the same 

 periodicity. Again, as in the case of the t mode, the values of k for favorable 

 electronic interaction are given by equation (10). 



The sequence of positive integral values of p (including zero) and the 

 sequence of negative integral values of p do not each give the same sequence 

 of values for | ^ | as was the case for the 7r mode. For ^ ^ 0, ] ^ | = 2, 

 10, 18, • • •, and for ^ < 0, | ^ | = 6, 14, 22, • • • . For the standing po- 

 tential wave (Fig. 10) each of these values of | ^ | does specify the velocity 

 of possible electron motion in either direction for favorable interaction with 

 the field. For the traveling potential wave (Fig. 11), on the other hand, 

 only the positive values oi k (p ^ 0) correspond to electron motion in the 

 same direction as the traveling wave, the negative values oi k (p < 0) cor- 

 responding to electron motion in the direction opposite to the traveling 

 wave. The sign of k has significance. If the electrons are moving with 

 v^elocities specified by equation (11) with the negative values of k from equa- 

 tion (10), and are thus moving counter to the traveling RF field wave, the 

 electrons are said to be driving a "reverse" mode. 



The actual electron orbits do not correspond to simple translation but, 

 as has been discussed, to rotation superposed on translation. The epi- 

 cycloid-like scallops in the orbit are of no significance to the fundamental 

 electronic mechanism. It is the mean velocity of the electron motion 

 around the interaction space, specified by the relative values of V and B, 

 that is of importance. The magnetron may operate, for example, at such 



