Rca1948FrequencyModu.. - The New Jersey Antique Radio Club

A:MODULATION BY ELECTRON BEAMS 491determined from the unperturbed vector potential, so that it is notnecessary to calculate the field as modified by the electrons in orderto determine the change in frequency caused by the electron stream,provided the change is small.The quantity u> / computed from (74) will, in general, be complex,so that the frequency change is actually the real part of (74), theimaginary terms giving rise to a net energy transfer from field to electrons.If the electrons gain energy and the wall losses in the cavityare small, this losscavity, so that (74)of energy to the electrons determines the Q of thefurnishes the basis for the following two formulasAm = — Rp-2eo) 0n /| A 0n|2dr(75)°>0n2Q— Im-/•fl» (1) («>oJ • A2eo) „/ |0n|0n *dr2dr(76)An£nfJnOPTIMUM FREQUENCYDECREASE01 OPTIMUM FREQUENCYINCREASE(a) (b) (c)Fig. 10— -Phase diagrams for A, E, and J.where A« is the change in frequency, Q 0n is the Q of the cavity withinjected electrons, and the cavity is oscillating in the wth mode.Before calculating the electron currents in some special cases, it willbe of interest to discuss the implications of (75) and (76) with regardto the nature of the currents necessary to produce optimum frequencyshifts, etc, If the unperturbed electric field in the cavity is representedbyE n (r)e*""**,then from the relation (55) the vector potential may be written asiE n (r)^•on (r ) e' uo"' = E n (r) e ,M0"' = e in/2 e°"">*.°>0n"On(77)Consequently the vector potential leads the electric field intensity intime phase by 90 degrees. The vector diagram in Figure 10 (a) showsthe time-phase relationship of E 0n, A 0)t , and A * 0n taking the phaseangle of E n as zero,