Plasma Physics

maverik

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=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=n₀ one can show

n=n₀cos(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.