MOTION OF GASEOUS IONS IN STRONG ELECTRIC FIELDS 171 



with a temperature common to all. This result arises from statistical 

 mechanics; the derivation of it is simple and requires few assumptions, 

 yet it enjoys a wide degree of generality. As soon, however, as a non- 

 equilibrium feature is imposed upon the system this simplicity vanishes, 

 and the subject acquires ramifications. Results must now be derived by 

 kinetic theory. The amount of labor required increases, while, at the 

 same time, the result achieved becomes less general. 



A mixture of charged particles (ions or electrons ; in the following often 

 simply referred to as ions) and gas molecules can in principle never be 

 in equilibrium since the presence of the former in itself represents an 

 instability. However, one might expect, that equilibrium exists in a 

 restricted sense, for instance, as regards motion. Even this is rarely the 

 case under actual conditions of observation. The non-equilibrium fea- 

 tures of greatest importance for analyzing ion motion are a constant 

 force (electric field) acting upon one species but not the other (mobility 

 theory), and a concentration gradient for one particular species (diffusion 

 theory). It is the purpose of this paper to apply kinetic theory to these 

 problems, and to compute with its help the most important properties 

 which such a gas of charged particles possesses. The work will be dis- 

 tinguished from similar ones in that the electric field will not be sup- 

 posed weak; velocity distributions which have no resemblance to the 

 Maxwellian distribution will thus make their appearance. Furthermore, 

 the mass of the charged particles will not be assumed small, which 

 means the possibility of getting results for gaseous ions as well as elec- 

 trons. Magnetic fields, plasma and A.C. phenomena will, however, be 

 excluded. The quantities of interest under those conditions are the drift 

 velocity of the ions, their energy, energy partition and diffusion con- 

 stants. These quantities will be calculated by assuming plausible mechan- 

 ical models. The work just outlined has been published in part in 

 abbreviated form in the Physical Review;^ the exposition to follow will, 

 however, proceed independently from these articles. 



Much of the work which concerns itself with transport processes in 

 gases makes use of perturbation theory. This method permits us to 

 predict the behavior of a gaseous assembly under an electric field or a 

 concentration gradient in the limit when the field or the gradient are 

 vanishingly small. The result of so perturbing a Maxwellian distribution 

 can be expressed through certain constants, such as the mobility or the 

 diffusion coefficient, which involve the Maxwellian distribution and 

 the internal interactions, but not the perturbation itself. 



1 Wannier, G. H., Phys. Rev., 83, p. 281, 1951 and Phys. Rev., 87, p. 795, 1952, 



