190 BELL SYSTEM TECHNICAL JOURNAL 



generally possible, however, to restrict oscillation to only one mode, usually 

 the T mode. Further, the fact that the electronic motion in crossed DC 

 electric and magnetic fields results in a meaji drift of electrons around the 

 interaction space, enables one to restrict his attention to a single traveling 

 wave corresponding to the fundamental or a single Hartree harmonic of the 

 field of this mode; for it is possible, in principle at least, by proper adjust- 

 ment of V and B to equate the mean angular velocity of the electrons to 



the angular velocity, ^, of any one of the traveling field components. 



When this is true, only the field of this component has an appreciable effect 

 upon the electron's motion. With respect to the fields of the oppositely 

 traveling component of the same harmonic (same k), and the components 

 of all other harmonics (different k), the electron finds itself drifting rapidly 

 through regions of accelerating and decelerating field with no net energy 

 transfer. From the point of view of the electron, the fields of the other 

 components vary so rapidly as to average out over any appreciable interval 

 of time. The only exception to these statements occurs when a harmonic 

 of periodicity k' of another mode of frequency/' has the same angular veloc- 



ity as the harmonic of periodicity k, that is, when —y- = -v— ^ The effect 



' ' ' ' 

 on magnetron operation of this coincidence of angular velocities will be 



discussed further in a later section. In the calculation of electron motions, 

 the restriction to the field of a single traveling wave component has been 

 called the rotating field approximation. 



The consideration of the electronic mechanism has thus been reduced to 

 that of the motion of electrons under the combined influence of the radial DC 

 electric field, the axial DC magnetic field, and a sinusoidal field wave travel- 

 ing around the interaction space. From what has been said thus far it is 

 clear that for energy to be transferred to the RF field it is necessary that the 

 mean electron velocity very nearly equal that of the traveling wave. Then 

 an electron leaving the cathode in such phase as to find itself moving in a 

 region of decelerating tangential component of the RF field, may continue 

 to move with this region and lose energy to the field. In contrast to the 

 Type II magnetron oscillator, the energy transferred to the RF field in this 

 case is the potential energy of the electron in the radial DC electric field. 

 The energy in the rotational component of the motion remains practically 

 unaffected and the electron orbit from cathode to anode looks something 

 like that plotted in Fig. 12 for the case with plane electrodes. On the other 

 hand, an electron which leaves the cathode in such phase as to gain energy 

 in a region of accelerating tangential RF field, is removed at the cathode after 

 only one cycle of the epicycloid-like motion. If this did not occur, the elec- 

 tron would continue to move with the field and absorb energy. An approxi- 



