[WIP] Add support for electron impact ionization in binary collisions (DSMC module)

[RemiLehe]

Note: could we do binary charge exchange in the same way?

TODO:

• Use the proper energy cost: store the energy cost in the SplitAndScatter functor
• Add a dedicated test for DSMC ionization
• Add support for excitation in DSMC (right now, it prevents us from running the capacitive discharge)
• Test on GPU
• Check physics, esp. assumptions on the velocity of the indident electron after scattering.

[RemiLehe]

I attempted to fit impact ionization within the DSMC framework, but I now realize that this is making the book keeping complicated:

The amount of memory to be allocated (in SplitAndScatter) after the first pass (Executor, that checks which type of reaction is occurring for each pair) will depend on the type of reaction for each pair. (Because, if a pair does impact ionization, we need to allocate space for the scattered electron, the produced electron and the ionized species, whereas if a pair does one of the other reactions, we allocate space only for the scattered electron and the scattered target.) As a consequence, the offset (in SplitAndScatter will depend on the type of reaction.)

To simplify things, here I will always allocate space for the ionized species and the new electron, but if the reaction is not impact ionization, I will set the ID of the ionized species and the new electron to invalid.

[RemiLehe]

Need to do the transform back to labframe for e_u

[archermarx]

I've written a test script for this feature (attached)
picmi.py.txt

It should work with both MCC and DSMC, once everything is implemented

In brief, this script sets up a simulation of electrons, ions, and neutrals in a periodic box. Ionization is then allowed to happen for a short time, and the resulting electron density and temperature curves are compared to the output of very simple global model, the equations of which are given below:

Here, $\epsilon_{iz}$ is the ionization energy and $k_{iz}$ is the ionization rate coefficient, which the script computes by integrating over the provided cross sections (i.e. those from https://github.com/ECP-WarpX/warpx-data/tree/master/MCC_cross_sections/Xe)

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At present, this segfaults when using DSMC after O(10-20) iterations, but completes when using MCC. When MCC is enabled, the global model neglects the depletion of neutrals. Some results obtained when using Xenon at a few electron temperatures, are given below

$T_e$ = 10 eV

$T_e$ = 30 eV

$T_e$ = 50 eV

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Overall, the results are close, but seem to be off from the global model in a consistent manner -- namely that WarpX ionizes less than the global model predicts that it should. The relative discrepancy gets smaller as the temperature increases but the absolute value of the temperature difference between the model and WarpX is roughtly constant. I'd appreciate some extra eyes on this to make sure both my physics or my WarpX set up are correct. The script runs fast (~11 seconds on my machine), so hopefully it will be useful for debugging the DSMC implementation. Once energy loss and excitation are added, I can update the script to incorporate those as well.

[jwestern]

Could this functionality be extended to do recombination? Even resulting in the deletion of the recombination product (i.e. back into the neutral "background" gas).