Any help on the following theoretical plasma problem would be greatly appreciated!(adsbygoogle = window.adsbygoogle || []).push({});

The diffusion eqn for a one-dimensional 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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# Plasma Physics

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