PHYSICAL LIMITATIOXS IX ELECT ROX BALLISTICS 



319 



ending in collapse. However, even if, as in lib, there is no sidewise loading 

 and no bending during loading, we know from Euler's formula that beyond a 

 certain loading the column will still collapse. This behavior is analogous to 

 that of an electron beam in which the electronic space charge is neutralized 

 by positive ions and there is no depression of potential in the beam. 



This space charge limitation either in the presence or absence of ions 

 allows the passage of quite a large current through a tube, as the table 

 below will show: 



We might therefore feel that the space charge is disposed of in a practical 

 sense, and so it is in many cases.* 



f^ F 



I 



i 



.kf 



1 



A 



T=29.3y\0~\^^^ 



1 = 190x10"^^^^ 



Fig. 11 — Comparison of limiting stable beam currents with and without positive ions. 



Power Dissipation Limitations 



Having talked about various limitations imposed by wave effects, aber- 

 rations, thermal velocities and space charge on the electron flow in the 

 beam itself, I want to close by discussing briefly a topic which seems hardly 

 included in electron ballistics but yet is vital to any application in that 

 field. I refer to the problems associated with power dissipation when 

 electrons strike something and stop. This is a good deal like the problem 

 imposed by suddenly coming down to earth while studying the sensations 

 of a free fall. It is inevitable and may be fatal unless satisfactory provision 

 is made for the dissipation of kinetic energy. 



What I want chiefly to bring out are the consequences of scaling a given 

 electronic device down in size. If we change the size of each part of an 



* It appears that in many gas discharges, including those in which plasma oscillations 

 are observed, the current is too high to allow persistence of the homogeneous flow upon 

 which the plasma oscillation equations are based. 



