BEAM FORMATION WITH ELECTRON GUNS 



391 



2.0 

 1.8 

 1.6 



> 1.4 

 t 1.2 



\%y 



1.0 



0.8 



0.6 



0.4 





1.0 



1.2 



1.4 



1.6 



1.8 2.0 2.2 2.4 



2.6 



2.8 3.0 3.2 3.4 3.6 3.8 4.0 



Fig. 5 — Curves useful in finding the transverse displacement of electron tra- 

 i jectories at the anode of Pierce-type guns. 



i 



tlie same as the forces involved in the equations above. Thus if o- <3C J'e , 



(18) may be taken as the distribution, in a transverse plane, of those 

 electrons which were simultaneously emitted at the cathode center. 

 I Furthermore, the nature of the Pierce gun region is such that electrons 

 emitted from any other point on the cathode will be similarly distributed 

 \\ ith respect to the path of an electron emitted from this other point 

 w ith zero transverse velocity (so long as they stay within the confines 

 , of the ideal beam). Hines and Cutler have integrated (15) with n^ = 

 ' and {dn/dt)c = 1 to give g/ {fc\/kT/'2eV^ at the anode as a function of 

 ; /", /fo . This relationship is included here in graphical form as Fig. 5. 

 , For a large class of magnetically shielded Pierce-type electron guns, 

 including all that are now used in our traveling wave tubes, Ve/a at the 

 anode is indeed found to be greater than 5 (in most cases, greater than 

 10) so that evaluation of a at the anode of such guns can be made with 

 considerable accuracy by the methods outlined above. One source of 

 error lies in the assumption that electrons which are emitted from a 

 point at the cathode edge become normally distributed about the cor- 

 responding non-thermal (no transverse velocity of emission) electron's 

 path, and with the same standard deviation as calculated for electrons 

 from the cathode center. In the gun region where Ve/a tends to be large 

 this difference between representative a- values for the peripheral and 

 central parts of the beam is unimportant, but it must be re-examined in 

 tlie drift region following the anode. 



