MAGNETIC EFFECTS ON NOISE IN A GERMANIUM FILAMENT 661 



To find Nh = (^oD/i^gl^) we need the limit of /!« r^ as $ ^ 0. 

 After some tedious algebra, we find this limit to be 



2 ^a 



Th=o — 



15Z)2 



so that 



/ 



(A^7/)^1.^2=* ~ ~ 



/'• 



30 



$2 



1^ ..* *''^°*'^l^8- 

 _ + eoth--— ^+- 



(15) 



In the general case we can again take the limit of (14) as $ — > in 

 order to determine A^^ , but this would be too tedious. Instead, we 

 solve the diffusion equation directly when <i> = 0. The equation is then 

 simply 





= 



and the solution subject to the correct boundary conditions and allowing 

 for a steady unit injection at Xq is 



Wi = Ai(x — Xq) -\- B 

 W2 = A2{x — Xq) + B 



X > Xq 



X < Xq 



where 



Ai = -^ lAi [l + "^2 ('l + ^) / ih + 4^2 + 2M2), 

 A2 = ^Ml + h (l - ^° j / (tAi + h + 2iAi</'2), 



B = 



1 + 



D 



We now have 



h (1 - ^')] [1 + ^2 (1 + f )]/ (^1 + ^2 + 2M2). 



Th= 



/+a /•Xq /•O 



w dx = j W2dx -\- I widx 

 a J— a Jxn 



^[ 



2axo{Ai + A2) + 



D J 



+ 2aB. 



From this we can compute 



a 



Tff=o(^o) dxQ 



