Diffusion regime in plasma SOL

[The Alchemist]

Homework Statement

Find out whether particle or heat diffusion determines the width of the SOL, and whether the ions or electrons are the determining factor. (just compare all of those).
Give an expression to estimate the thickness of the SOL and evaluate the expression for Te = 10 and 100 eV.

Homework Equations

The diffusion coefficient is estimated as [itex]D= \lambda^2/\tau[/itex]. [[itex]\lambda[/itex]= mean free path; [itex]\tau[/itex] = collision time].
Parallel to the B-field the [itex]\lambda_\parallel = v \tau[/itex].
Perpendicular to the B‐field, [itex]\lambda_\perp = \frac{m v_\perp}{|q| B}[/itex], the gyro radius.

conductivities: [itex]\chi_{\parallel,e} = v_{th,e}^2 \tau_e[/itex]
[itex]\chi_{\perp,e} = \frac{v_{th,e}^2}{\omega_{ce}^2 \tau_e}[/itex]

The Attempt at a Solution

I tried to fill in the mean free paths (lambdas) in the formulas of [itex]D[/itex] and compare them with [itex]\chi[/itex], but I get exactly the same expression.
So I'm not really sure if I use the right approach, I can't really think straight on this one.

 

[NateD]

For the thickness of the SOL, I think we can use this expression: \Delta_SOL = \sqrt{2 D \tau}.Evaluating for Te = 10 eV, we have D = 5.45*10^4 m^2/s and \tau = 1.14*10^-7 s. So \Delta_SOL = 0.26 m.For Te = 100 eV, we have D = 7.67*10^5 m^2/s and \tau = 9.05*10^-7 s. So \Delta_SOL = 0.91 m.