MOTION OF GASEOUS IONS IN STRONG ELECTRIC FIELDS 



175 



molecules become such that momentum is lost quickly, but energy is 

 accumulated in the form of random motion. As a result of this we end up 

 with a distribution function which is very nearly spherically symmetrical 

 in velocity space. Such a situation permits obvious procedures through 

 which the entire calculation is simplified. These procedures will not longer 

 be available when assumption (a) is dropped. 



Knowledge concerning the structure of the velocity distribution func- 

 tion for gaseous ions is practically nonexistent at this time. Hershey, 

 who deals with the motion of ions in the high field case, simply substi- 

 tutes for it a Maxwellian distribution with an unknown offset of the 

 origin and unknown temperature parameter, shown in Fig. 1(a). He 

 then computes these two parameters by applying the laws of conserva- 

 tion of momentum and kinetic energy. It is to be expected that this 

 procedure should give reasonable values for the mobility and the mean 

 energy of the ion; indeed, if we consider the polarization force only, we 

 get exactly the right values ; the reason for this is that one may evaluate 

 velocity averages for inverse fifth powder forces ignoring the distribution 

 function^ and that he did this in effect for the drift velocity and the 



(a) (b) 



Fig. 1 — Simplified pictures for the high field velocity distribution of gaseous 

 ions, (a) Hershey 's assumption, (b) Modification with correct second moments. 



« Hershey, A. V., Phys. Rev., 56, p. 916, 1939. 

 ^ This will be shown in Section IIB. 



