Electron conduction kappa is wrong

[mikekryjak]

@bendudson our electron conduction is incorrect.

In the code we have the equivalent of:

$$\tau_{ee} = \frac{12 \pi^{3/2} \varepsilon_0^2 m_e^{1/2} T^{3/2}}{ln \Lambda e^4 n_e}$$

Now, this agrees with Fitzpatrick (3.187):

But it is not consistent with the Braginskii form which has an additional sqrt(2) in the denominator:
$$\tau_{ee} = \frac{12 \pi^{3/2} \varepsilon_0^2 m_e^{1/2} T^{3/2}}{\sqrt(2) ln \Lambda e^4 n_e}$$

In Hermes-3, we used the Braginskii prefactor of 3.16:

hermes-3/src/evolve_pressure.cxx

Lines 75 to 77 in 8c45022

	kappa_coefficient = options["kappa_coefficient"]
	.doc("Numerical coefficient in parallel heat conduction. Default is 3.16 for electrons, 3.9 otherwise")
	.withDefault((name == "e") ? 3.16 : 3.9);

But this is not consistent with tau_ee which uses the Fitzpatrick formulation!

The 3.16 should be divided by sqrt(2) - our electron conduction should be sqrt(2) lower. This is anecdotally in line with what I've been seeing in my 2D runs once I switch on my Braginskii branch.

[mikekryjak]

Big thanks to Stefan Mijin for working through this with me!

[bendudson]

Good find, @mikekryjak ! We should document this carefully so as not to get caught by different definitions of tau_ee

[mikekryjak]

This is being resolved in #195