634 



BELL SYSTEM TECHNICAL JOURNAL 



I I (very narrow gap) 



y OR r 



Fig. 120. — A gap consisting of pairs of semi-infinite i)lanes or semi-infinite tubes. 



0.9 

 0.8 



<Q 



yo.6 



O0.3 



1.0 1,5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 

 HALF DISTANCE BETWEEN PLANES, Ty, IN RADIANS 



7.0 



Fig. 121. — Modulation coefiicient for two semi-infinite pairs of parallel planes with the 

 edges very very close together, plotted vs the half distance between planes in radians. 

 /3n is the modulation coefficient for electrons travelling along the axis, i^a is the average 

 modulation coefficient and /J^ is the r.m.s. modulation coefiicient. The separation of the 

 l)lanes is 2v, % = 1/ cosh yy, 



13,. = tanh yy/yy. 



a. 



-r^ 



sinh 27y + 2yy 



j 27y(cosh 2yy -\- 1) 



]' 



assume a linear variation of potential with distance in the space between 

 them. In this case, (b9) gives 



^y or I3r = I'\(yd) = sin (yd/2)/iyd/2) 



(h25) 



This is the same function shown in I'"ig. 119. 



If the tube wall or plates are very thin, one may, following Petrie, Strachey 

 and W'allis"^' assume a |)ot('ntial N'arialion between the edges of the gap of 



