. The Bell System technical journal . ¢> \ \ \, N V ^ ^ \ p^ ^ \ \ P>0^ \ â ^ 1,5 DISTANCE BETWEEN PLANES, Ty, IN RADIANS Fig. 121.âModulation coefiicient for two semi-infinite pairs of parallel planes with theedges very very close together, plotted vs the half distance between planes in is the modulation coefficient for electrons travelling along the axis, i^a is the averagemodulation coefficient and /J^ is the modulation coefiicient. The separation of thel)lanes is 2v, % = 1/ cosh yy, 13,. = tanh yy/yy. a. -r^ sinh 27y + 2y
. The Bell System technical journal . ¢> \ \ \, N V ^ ^ \ p^ ^ \ \ P>0^ \ â ^ 1,5 DISTANCE BETWEEN PLANES, Ty, IN RADIANS Fig. 121.âModulation coefiicient for two semi-infinite pairs of parallel planes with theedges very very close together, plotted vs the half distance between planes in is the modulation coefficient for electrons travelling along the axis, i^a is the averagemodulation coefficient and /J^ is the modulation coefiicient. The separation of thel)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 betweenthem. In this case, (b9) gives ^y or I3r = I\(yd) = sin (yd/2)/iyd/2) (h25) This is the same function shown in Iig. 119. If the tube wall or plates are very thin, one may, following Petrie, Stracheyand Wallis^ assume a |)ot(ntial Narialion between the edges of the gap of REFLEX OSCILLATORS 635 , V VZZZZZZZZ^TZZ. \ ~. OF TUBE, Tr, IN RADIANS Fig. 122.âModulation coefficient for two semi-infinite tubes separated by a very smalldistance, plotted vs the radius of the tube in radians. j3n is the modulation coefficient onthe axis, (3o is the average modulation coefficient and /3s is the root mean square modulationcoefficient, r is the radius of the cylinders. So = \IU{yr), /3â = 2/i(7r)/Tr/c(7-),ft = [1 - 7?(7-)//o(7-)]^ the form In this case, (b9) gives ,r 1 . -1 2xV â - sin â-IT a 0y or Br = F,(yd) = .h(yd/2) (b26) (b27) Both Fi{yd) and Fiiyd) are plotted vs. yd in Fig. 123. Figures 121, 122 and 123 cover fairly completely the case of slits andholes. The same methods may be used to advantage in making an ap-proximate calculation taking into account the effect of grid pitch and wiresize on modulation coefficient. Assume we have a pair of lined up grids, as shown in Fig. 124. Approxi-mately, the potential near the left one is give
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