Motion of Gaseous Ions in Strong 

 Electric Fields 



By GREGORY H. WANNIER 



(Manuscript received August 20, 1952) 



This paper applies the Boltzmann method of gaseous kinetics to the prob- 

 lem of charged particles moving through a gas under the influence of a static, 

 uniform electric field. The particle density is assumed to be vanishing low, 

 and the ion-atom collisions are assumed elastic, but the field is taken to be 

 strong; that is the energy which it imparts to the charges is not assumed 

 negligible in comparison to thermal energy. In Part I, the formal framework 

 of such a theory is built up; the motion in the field is describable by the drift 

 velocity concept, and the smoothing out of density variations as an aniso- 

 tropic diffusion process. In Part II, the "highfield^' case is treated in detail; 

 this is the case, for which thermal motion of the gas molecules is negligible; 

 the equation is solved completely for the case that the mean free time between 

 collisions may be treated as independent of speed; complete solutions are 

 also presented for extreme mass ratios of the ions and the molecules; special 

 attention is given to the case of equal masses, which has to be handled by 

 numerical methods. In Part III, information about the ''intermediate 

 fiM^^ case is collected; with the help of a convolution theorem the case of 

 constant mean free time is solved; beyond this, only the case of small ion 

 mass {electrons) is available. In Part IV, the diffusion process, whose 

 existence was proved in Part I, is pushed through to numerical results. 

 Part V discusses the scope of the results achieved and demonstrates the possi- 

 bility of extending them semiquantitatively beyond their original range. 



Part I — General Theory of Strong Field Motion 



lA. qualitative discussion 



It is well known that if we consider a mixture of gases under no ex- 

 ternal forces the steady velocity distribution which establishes itself 

 in the mixture does not depend on the interactions between the gas 

 molecules; we have always a Maxwellian distribution for each species 



170 



