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BELL SYSTEM TECHNICAL JOURNAL 



resonator constant, so as to keep the field constant, but vary /. The capaci- 

 tance will be proportional to (L — t)~^ and, as the stored energy is the 

 voltage squared times the capacitance, we see that {E?/0^P) ^'^ will be re- 

 duced by a factor /, 



/ = (1 - //L)i/3 

 The factor/ is plotted vs. t/L in Fig. 5.9. 



(5.27) 



1.0 

 0.9 

 0.8 

 0.7 

 0.6 

 0.5 

 0.4 

 0.3 

 0.2 

 0.1 



2 4 6 8 10 12 14 16 18 20 22 



TRANSIT ANGLE IN RADIANS 



Fig. 5.10— The lower curve shows the factor by which E?/^P is reduced by gap length, 

 d in radians. If the gap spacing is greater than 2.33 radians, it is best to make the gap 2.33 

 radians long. Then the upper curve applies. 



5.4b Transit Time 



As it is impractical to make the resonators infinitely thin, there will be 

 some transit angle dg across the resonator, where 



dg = ^t (5.28) 



Here (, is the space between resonator walls, or, the length of the gap. 

 If we assume a uniform electric field between walls, the gap factor M, 

 that is, the ratio of peak energy gained in electron volts to peak resonator 

 voltage, or the ratio of the magnitude of the sinusoidal field component 

 produced to that which would be produced by the same number of infinitely 

 thin gaps with the same voltages, will be (from (4.69) with r = a) 



sin {dg/2) 



M = 



dg/2 



(5.29) 



