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#1
May1110, 07:05 AM

P: 9

Any help on the following theoretical plasma problem would be greatly appreciated!
The diffusion eqn for a onedimensional plasma, varying in the x direction only is D d^{2}n/dx^{2} =Q Letting Q=nv_{i} we can show the diffusion eqn has a solution of the form n=Asin[sqrt(v_{i}/D)x] + Bcos[sqrt(v_{i}/D)x] Supposing boundary conditions of plasma are set at x= +/ L/2 where n=0 and x=0 where n=n_{0} one can show n=n_{0}cos(x pi/L) The bit I am finding trouble with is what the implications of sqrt(v_{i}/D)=pi/L are with respect to the electron temperature T_{e}, I have recalled that v_{i} has an exponential dependence on T_{e} but cannot reason what this means. Many thanks in advance for any help. 


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