720 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1953 



with a velocity corresponding to Fo volts. During their traversal of 

 the interaction gap, i.e., the space bounded by the two grids, this 

 velocity is changed by an amount depending on the instantaneous direc- 

 tion and intensity of the electric field and on the fraction of a cycle spent 

 in traversing the gap. They then enter the retarding dc field of the re- 

 peller drift space. Here, they are slowed down, brought to a standstill 

 and returned to the interaction gap for a second transit. During this 

 process, the velocity modulation acquired during the first transit is 

 converted to intensity modulation such that the convection current 

 returning through the gap does so in the form of sharp and well defined 

 pulses mth a repetition rate equal to the frequency of the applied RF 

 voltage. This pulsed current may now be harmonically analyzed and 

 its fundamental component evaluated. The ratio of this fundamental 

 component of current to the applied RF voltage is termed electronic 

 admittance, Ye . Providing the amplitude, F, of the applied RF voltage 

 is small compared to the dc accelerating voltage, Fo , the value of Ye 

 is given by: 



y _ hff e \2Fo/ ,-((»/2)-»J fr, , ^ 



\2Vo) 



where Iq = dc beam current. 



(3 = beam coupling coefficient.* 



d = round trip transit time in repeller drift space, in radians. 

 Fo = dc beam voltage. 

 F = amplitude of RF gap voltage. 

 Ji = Bessel function operator. 

 Of all these parameters affecting Yg we shall focus our attention on 

 two, namely F and 6. The other parameters depend on such factors as 

 tube geometry, electron gun perveance etc. and, within the scope of this 

 investigation, will be considered constant. 



Referring to equation (2.1), it is seen that the phase angle associated 

 with Ye is a function of 6 only, whereas the amplitude of Ye depends on 

 both e and the RF gap voltage, F. Suppose now 6 is held constant while 

 * /S, also referred to as modulation coefficient, is given by 



/3- 



smj- 



?£ 

 2 



where 6,, the transit angle in the interaction gap, is expressed in radians. 



