THERMIONIC ELECTRON EMISSION 



441 



field out to infinity or a distance large compared to R is just sufficient 

 to reduce the potential to zero again. Hence when the applied field 

 is zero so that z,- is very large, the work function over the condenser or 

 patch is not reduced at all. Calculations show that if a small accelerat- 

 ing field is applied, the work function is reduced more than it would 

 have been if there had been no condenser. For a sufficiently large 

 applied accelerating field, Zc moves so close to the surface that Zc <C R. 

 At this distance the potential at Zo due to the sheets of charge will not 



APi, 



A Pi 



100 



9.9 



9.8 



9.7 



9.6 



Q- 



-0.1 



-0.2 



-0.3 



4 6 8 10 12 14 16 



Z — DISTANCE FROM CATHODE IN CENTIMETERS 



18X10" 



Fig. 8 — Potential energy vs. distance from cathode surface for electrons moving 

 agamst nnage field plus field due to a uniform circular patch for applied fields of 

 zero or 6000 volts/cm. 



differ greatly from the potential just outside the condenser. The 

 work function will now be 300 X 47ra/ less than it would have been 

 without the patch. Hence the extra reduction of the work function 

 due to the patch is zero at zero accelerating field and increases with 

 this field up to its limiting value 300 X 4x0-/. 



To treat this case in more detail consider the curves in Fig. 8. 

 Curve 1 is a plot of P i\e in volts vs. z in cm. Pi is the potential 

 energy due to the image force and is given by 



Pile = PJe - 300g/4s, 



(62) 



