3T physics with PTE

[acreyes]

Is there any recommendations on using the pressure-temperature equilibrium with 3T eos? I see that in the tests that there is a use case with only IdealElectrons for the eos indexer, which would suggest to me to do separate PTE solves for ions and electrons.

Naively my first thought was to do the PTE with two equations for the total ion & electron internal energies and equate P = Pion + Pele. This seems manageable to build from what is already in singularity, but am curious if anyone has thought about this already.

Thanks in advance!

[Yurlungur]

Yes. This is a messy issue. I believe the proper thing to do is to thread the solve for the mean ionization state and the electron temperature through PTE. So one would have an additional temperature to solve for in the multidimensional root find.

What we're currently doing in riot is not that. Instead we lag the mean ionization state. I.e., we compute it from the electron temperature and freeze it during PTE, allowing us to solve for just the ion pressure and temperature as in the 1T mode. Then after PTE, an electron temperature is computed assuming per-species ion microphysical densities and electron thermal (but not pressure) equilibrium. That is, the sum of electron internal energies evaluated over each material at a given material density but a single electron temperature Te must be equal to the total electron internal energy. Note these internal energies are by volume, not specific. So in singularity's convention, they must be multiplied by the volume averaged material density per material. The total electron pressure is then a sum of the electron partial pressures, as per a Dalton closure.

We have this worked out and I can probably add a description to the singularity docs. Also some of this machinery can probably be ported into singularity-eos out of riot if you're interested.

[acreyes]

Thanks @Yurlungur! This is really helpful.

That is, the sum of electron internal energies evaluated over each material at a given material density but a single electron temperature Te must be equal to the total electron internal energy. Note these internal energies are by volume, not specific. So in singularity's convention, they must be multiplied by the volume averaged material density per material. The total electron pressure is then a sum of the electron partial pressures, as per a Dalton closure.

In this model the electrons are evaluated at the ion species densities but then share the entire cell volume?

We have this worked out and I can probably add a description to the singularity docs. Also some of this machinery can probably be ported into singularity-eos out of riot if you're interested.

We already have a partial pressure mix for our electron eos using singularity, so I think with the above description I can put this together without too much effort with what is already there.

I believe the proper thing to do is to thread the solve for the mean ionization state and the electron temperature through PTE. So one would have an additional temperature to solve for in the multidimensional root find.

Is the idea here to equate the electron number density with the ions in pressure equilibrium?

[Yurlungur]

In this model the electrons are evaluated at the ion species densities but then share the entire cell volume?

See my answer below. Basically we assume electron number density is related to ion material density in a simple way to enforce charge neutrality at least in a cell averaged sense.

Is the idea here to equate the electron number density with the ions in pressure equilibrium?

Since we don't support charged plasmas, we enforce a quasi charge neutrality where we assume electrons are tied to materials. Then each material m has a separate electron number density

n_e,m = (Z/A) rho_m

Where Z is mean ionization state (possibly lagged), A is mean atomic mass and rho_m is microphysical material density.

And the total electron number density is the sum of the contribution for each material.

In the PTE case, the ions would equilibrate with each other but not the electrons. But the electron number density is partially set by the ion material density. And similarly, electron temperature depends on this number density. The real chicken and egg is that mean ionization state depends on electron temperature. But in Z-splitting, the e.,g., ion pressure depends on mean ionization state. That's why in principle it needs to be a solve of the rep subsystems.

[acreyes]

But in Z-splitting, the e.,g., ion pressure depends on mean ionization state. That's why in principle it needs to be a solve of the rep subsystems.

I see, so the method you're describing in RIOT is working around This Pion(Tion, Tele) dependence that is implicit in the model, but isn't captured because the Z-splitting assumes a fixed ionization state.

[Yurlungur]

Well we could implement a free-floating mean ionization state. But we wanted the same codepath between 3T and 1T so it's really working around not modifying the PTE solver.

And also working around a future where the mean ionization state requires a solve itself (eg Saha) which would be painful inside the inner loop of the PTE solver.

But I'd like to implement a 3T aware PTE solver at some point.