402 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956 



5. NUMERICAL DATA FOR ELECTRON GUN AND BEAM DESIGN 



A. Choice of Variables 



Except for a scaling parameter, the electrical characteristics of an 

 ideal Pierce electron gun are completely determined when three param- 

 eters are specified, e.g., fc/fa , perveance, and Va/T. Also, for the simp- 

 lest case r is equal to 1 so that (since K depends only on gun perveance) 

 in this case no additional parameter is needed. This implies that nor- 

 malized values of ?-/, a, a', and K at the drift side of the anode lens are 

 not independent. If, however, the value of F at the anode lens is taken 

 as an additional variable, four parameters plus simple scaling are re- 

 quired before complete predictions of beam characteristics can be made. 

 In assembling analog computer data which would adequately cover 

 values of fc/fa , perveance, and Va/T which are likely to be of interest 

 to us in designing future guns, we chose to present the major part of 

 our data with T fixed at 1.1. This has seemed to be a rather typical value 

 for r, and by choosing a specific value we decrease the total number of 

 significant variables from 4 to 3. (The effect of variations in T on the 

 minimum radius which contains 95 per cent of the beam is, however, 

 included in Fig. 16 for particular values of Va/T and perveance.) Al- 

 though the boundary conditions for our mathematical description of the 

 beam in a drift space are simplest when expressed in terms of Vg , r/, a 

 and ct', we have attempted to make the results more usable by express- 

 ing all derived parameters in terms of fc/fa , s/Va/T, and the perveance, 

 P. 



B. Tabular Data 



The rather extensive data obtained from the analog computer for the 

 r = 1.1 case and for practical ranges in perveance, Ve/T, and fc/fa 

 are summarized in Tables IIA to E where the parameters r^ and a which 

 specify the beam cross section are given as functions of axial distance 

 from the anode plane. Some feeling for the decrease in accuracy to be 

 expected as the distance from the anode plane increases can be obtained 

 by reference to Section 6B where experiment and theory are compared 

 over a range of this axial distance parameter. 



C. Graphical Data, Including Design Charts and Beam Profdes 



In typical cases, the designer of Pierce electron guns is much more 

 concerned with the beam radius at the axial position where it is smallest 

 (and in the axial position of this minimum) than he is in the general 



