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Plasma Physics

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May11-10, 07:05 AM
P: 9
Any help on the following theoretical plasma problem would be greatly appreciated!

The diffusion eqn for a one-dimensional plasma, varying in the x direction only is

D d2n/dx2 =-Q

Letting Q=nvi we can show the diffusion eqn has a solution of the form

n=Asin[sqrt(vi/D)x] + Bcos[sqrt(vi/D)x]

Supposing boundary conditions of plasma are set at x= +/- L/2 where n=0 and x=0 where n=n0 one can show

n=n0cos(x pi/L)

The bit I am finding trouble with is what the implications of sqrt(vi/D)=pi/L are with respect to the electron temperature Te, I have recalled that vi has an exponential dependence on Te but cannot reason what this means.

Many thanks in advance for any help.
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