194 BELL SYSTEM TECHNICAL JOURNAL 



space charge. The calculations have been carried out by the so-called self 

 consistent field method using the rotating field approximation mentioned 

 earlier. In this method, orbits of electrons are calculated in an assumed 

 field, and the space charge due to these electrons determined. The field 

 calculated on the basis of this space charge distribution may then be com- 

 pared with that assumed. This cycle of calculations is repeated, each 

 time using the calculated field of the previous cycle as that in which the 

 electrons move, until a field is obtained which is consistent with that used in 

 calculating the electron orbits. This method will be recognized as that used 

 in the calculation of electron orbits about the nucleus in atoms. 



The result of one such calculation is shown in Fig. 15. The orbits of 

 four electrons which were emitted from the cathode in different phases are 

 plotted in a set of coordinates rotating with the RF field component. One 

 electron is returned to the cathode, and the other three reach the anode. 

 The boundaries of the space charge cloud are shown as dashed lines. The 

 spoke-shaped structure is clear, and its position with respect to the rotating 

 anode potential wave is as expected. The number of spokes of the cloud is 

 equal to the periodicity of the component of the mode with which the elec- 

 trons are interacting. In the case of Fig. 15 there are four spokes, since 

 the magnetron is operating in the fundamental of the n = 4 mode {k = 

 4, ^ = 0). 



3.6 Induction by the Space Charge Cloud: Another view of the mechanism 

 by which the electrons drive the resonator S3'stem may be obtained by 

 considering the effect of the space charge spokes in inducing current flow 

 in the anode segments themselves. For example, the oscillation of the 

 resonator block in its it mode corresponds to the periodic interchange of 

 electric charge from each anode segment, around a resonating cavit}' to the 

 next anode segment. This oscillation is maintained, much in the manner of 

 a pendulum escapement drive, by the space charge spoke appearing in front 

 of an anode segment at that instant in the oscillation cycle when it can aid 

 in building up the net positive charge on the segment. At the same instant, 

 the adjacent segments, being opposite a "gap" in the space charge wheel, 

 may build up a negative charge. 



The RF current, Irf, induced in the anode structure, thus results from 

 the motion of the spoke-shaped space charge cloud in the interaction space. 

 It is not to be confused with the total circulating RF current in the resonator 

 system. Whereas Irf must be in a phase with the space charge cloud it 

 need not be in phase with the RF voltage, Vrf, between the anode segments. 

 In terms of the electron motions, this means that the spokes of the space 

 charge cloud may lead or lag the maxima in the tangential field. In general, 

 the electronic admittance defined by the ratio of Irf to Vrf may thus in- 

 clude a susceptance as well as a conductance. Tlie product of Vrf and 

 the in-phase component of Irf, integrated over a period of one cycle of_RF 



