DSMC: Add impact ionization

[roelof-groenewald]

This PR extends the work already done by @RemiLehe and @oshapoval in #5524.

Some changes were made to how the ionization process is initialized, for example, the user must now specify the target_species (i.e., the species which undergoes ionization) as well as the product_species. The product species can include the colliding species (for example electron + neutral -> 2 x electron + ion), but does not have to (for example H$^+$ + D -> H$^+$ + D$^+$ + electron).

The test created by @archermarx is now passing (at least early on):

Todo:

• test implementation
• fix scattering process to conserve momentum
• clean up code

[roelof-groenewald]

At this point the existing DSMC test (as part of the capactive discharge test) succeeds, indicating that the existing DSMC functionality is not broken.

[roelof-groenewald]

At present running the capacitive discharge problem while using DSMC for electron-impact ionization, results in a slightly higher average plasma density than the Turner result:

[archermarx]

The results on the comparison to the global model look about as good as we were able to get with MCC, so that's good. I'm still curious why we're off from the theory. I can't think of any missing physics that we're not accounting for. Also, it's a bit strange that we get higher densities in DSMC vs MCC, as MCC doesn't permit neutrals to be depleted and should have an overall higher ionization rate.

[archermarx]

Could we extract the max process count into a compile-time constant that the user could specify (i.e. -DWARPX_MAX_SCATTERING_PROCS=10 or the like?) Or set the number much larger than five? While we're doing this PR it would also be good to actually address this in the constructor like the comment says we should.

[roelof-groenewald]

It looks like a change to template the max number of processes was partly overwritten in this PR. I fixed that now.

[archermarx]

Thanks for getting this close to the finish line! I think this looks pretty good. In the spirit of cleanliness I think it would be good to go ahead and move the process count check to the constructor. I also think it would be worth exploring increasing the max process count (see prev comment), but I don't have a good enough understanding of what the performance implications would be to say. That could perhaps wait for a second PR, however.

[roelof-groenewald]

The results on the comparison to the global model look about as good as we were able to get with MCC, so that's good. I'm still curious why we're off from the theory. I can't think of any missing physics that we're not accounting for. Also, it's a bit strange that we get higher densities in DSMC vs MCC, as MCC doesn't permit neutrals to be depleted and should have an overall higher ionization rate.

I'm guessing the reason must be that the electron energy distribution function starts to deviate substantially from a Maxwellian. The theory and simulation seem to match up pretty nicely until the plasma density has increased by ~20%, at that point a sizeable fraction of electrons have been involved in a collision, and therefore likely do not follow a Maxwellian disrtibution anymore. I guess we could check this since we output the electron velocities in during the test. An alternative approach could be to use the electron distribution function at every output to predict the ionization rate over the next diagnostic interval.
In terms of why the DSMC density is higher than the MCC density, I'm not sure either. One possibility is that the binary ion-elastic scattering is causing the neutral gas to heat up a bit leading to a higher ionization rate. I can check this by switching the ion collisions back to MCC.

Update: It does seem like the ion-neutral collisions causes a drift in the ionization rate. Here is what I get if I only use DSMC for the ionization collisions:

[archermarx]

The results on the comparison to the global model look about as good as we were able to get with MCC, so that's good. I'm still curious why we're off from the theory. I can't think of any missing physics that we're not accounting for. Also, it's a bit strange that we get higher densities in DSMC vs MCC, as MCC doesn't permit neutrals to be depleted and should have an overall higher ionization rate.

I'm guessing the reason must be that the electron energy distribution function starts to deviate substantially from a Maxwellian. The theory and simulation seem to match up pretty nicely until the plasma density has increased by ~20%, at that point a sizeable fraction of electrons have been involved in a collision, and therefore likely do not follow a Maxwellian disrtibution anymore. I guess we could check this since we output the electron velocities in during the test. An alternative approach could be to use the electron distribution function at every output to predict the ionization rate over the next diagnostic interval.

That's a nice idea. In that approach, we'd run the simulation to completion, saving electron information at each output step. In the analysis, we'd then compute the empirical ionization rate coefficient (instead of pre-computing it for a Maxwellian over a range of temperatures).

Alternatively, we could add binary e-e collisions to try and thermalize the electrons a bit more (though at ne = 1e14 they'd be pretty infrequent)

In terms of why the DSMC density is higher than the MCC density, I'm not sure either. One possibility is that the binary ion-elastic scattering is causing the neutral gas to heat up a bit leading to a higher ionization rate. I can check this by switching the ion collisions back to MCC.

Update: It does seem like the ion-neutral collisions causes a drift in the ionization rate. Here is what I get if I only use DSMC for the ionization collisions:

That's interesting, and I'm surprised that the result is so noticeable, but good to see that we can match MCC well if we neglect them.

[archermarx]

I think this looks good for now. We agree with the model in early times before any potential deviations from Maxwellian occur. A better test which accounts for that deviation could be added in a followup PR