MOTION OF GASEOUS IONS IN STRONG ELECTRIC FIELDS 185 



find, after simplification with (13) 



^,dg(^_^N rr |^(c)j,(c) _ M(,C')g{c')h^iy)U{x) d%. dC 



dC 4:7r J J Qg\ 



= -k.(c-<c)){/(c) + !7(c)l 



This is an equation in velocity space only, r and t having disappeared 

 completely; this justifies the assumptions. In solving the equation we 

 observe that our interest is only in diffusion, that is, the current resulting 

 from a concentration gradient when treated in first order perturbation. 

 In this case both k and g{c) are to be treated as small and their product 

 in (19) is to be neglected. The equation then becomes 



a- ^ + ? ff i^(C)!7(c) - M(.C')gic')}y^(.y)n{x) d^' dC _ ^ 

 dc 4x J J (20) 



= -k.(c - <c»/(c) 



The homogeneous prototype of this inhomogeneous equation is (13) ; an 

 arbitrary amount of /(c) could thus be added to a particular solution 

 of (20) were it not for the orthogonality condition (18) which makes the 

 solution definite. 



The existence of the diffusion phenomenon follows easily from equation 

 (20). The total current j< is given by 



hit, t) = j die r, t)c dc (21) 



Upon substitution of (17) into this expression two terms result 



j,(r, t) = n{T, 0(c) + j(r, t) (22) 



with 



j(r, t) = n(r, t) j g(c)c dc (23) 



The first term in (22) is seen from (15) to just equal the product of the 

 density and the drift velocity; this is the expected drift current. The 

 new current j(r, t) induced by the density gradient is thus given by (23). 

 From (20) it follows that g(c) is a linear function of the three com- 

 ponents K,ky, kz with coefficients which do not depend on the density 

 or its gradient, but only on the unperturbed velocity distribution /(c) ; 

 furthermore, the first two of these coefficients are equal. Hence, from 

 (23) j comes out as a linear function of the three quantities n(r, t)'K, 

 n(r, t)'ky, n(r, t)'kz) these are the components of the density gradient 



