Unable to include both field ionization and impact ionization

[Wang-Zhongwei]

Hi warpx team,

I tried to include both field ionization and impact ionization into the simulation but I realized with the current input structure I wasn't able to. My understanding is that field-ionized hydrogen will still be tracked by h_neutral container but with a different charge state. This would create a problem because DSMC mechanism will treat the electron having the same impact ionization cross section with both H+ and neutral hydrogen atoms (e_h_ion.species = electron h_neutral). It might be solved if the field ionized species besides electrons can be customized (h_neutral.ionization_product_species = electrons H) but currently only the ionized electrons are allowed.

# Species
particles.species_names = electron h_neutral hydrogen

# Field ionization on the neutral reservoir
h_neutral.charge = 0
h_neutral.physical_element = H
h_neutral.do_field_ionization = 1
h_neutral.ionization_product_species = electron  # only electrons are rerouted

# Ion container (separate species)
hydrogen.charge = q_e
hydrogen.physical_element = H
hydrogen.injection_style = none

# DSMC electron–neutral impact ionization
collisions.collision_names = e_h_ion
e_h_ion.type = dsmc
e_h_ion.species = electron h_neutral
e_h_ion.product_species = electron hydrogen
e_h_ion.scattering_processes = ionization
e_h_ion.ionization_cross_section = ../warpx-data/MCC_cross_sections/H/electron_impact_ionization.dat
e_h_ion.ionization_energy = 13.6

[RemiLehe]

Hi @Wang-Zhongwei, thanks for the detailed report. Your diagnosis is correct, and this is a real limitation of the current implementation rather than something wrong with your input file.

The main reason

As you correctly identified, field ionization and DSMC collisional ionization track ionization state in two fundamentally different, and currently incompatible, ways:

• Field ionization keeps every macroparticle in the same species container for its whole life. The charge state is just a per-particle runtime attribute (ionizationLevel). A particle is never moved out of h_neutral, no matter its ionization level.

• By contrast, in DSMC (and MCC), macroparticles at different ionization levels are stored in different species. And nothing in the DSMC/MCC code path looks at ionizationLevel.

So when some h_neutral macroparticles have been field-ionized to $H^+$, the DSMC code indeed has no way to know that. It will keep applying the electron-impact-ionization cross section to them exactly as if they were still neutral atoms, spuriously creating extra electrons/ions from particles that no longer have anything left to strip.

Possible ways to fix this

Your proposed fix (letting ionization_product_species also reroute the ionized macroparticles to a distinct species) would solve it, but it isn't supported today and it would be a significant change. In addition, it would need some thoughts to define a syntax that would work well for species that (unlike Hydrogen) can go through several ionization levels.

For instance, for Helium, which can field-ionize to $He^+$ and then to $He^{2+}$, should the syntax be:

he_neutral.charge = 0
he_neutral.ionization_product_species = electron he_1plus

he_1plus.charge = 1
he_1plus.ionization_product_species = electron he_2plus

but then this might get tedious for e.g. Argon which has many levels of ionization.

Alternatively, a reasonably contained improvement would be to make the DMSC code aware of the target species' ionizationLevel attribute (the same one already threaded through the push/gather kernels) and skip the ionization scattering process for a pair once that particle's level has reached the physical maximum for its element (1, for hydrogen). That would stop the spurious re-ionization, though the field-ionized and DSMC-ionized populations would still end up as two separate species pools rather than one unified one. It is not perfectly elegant for diagnostics, but physically correct.

[RemiLehe]

The alternative mentioned at the end is implemented in this branch: #7014 ; feel free to give it a try.

[Yu-Hung-Yeh]

Hello, I also encountered this issue recently. Thank you for the replies in this discussion; they have been very helpful! However, after reviewing PR-7014, I found a fundamental incompatibility issue when using the new DSMC collisional ionization alongside the existing Field Ionization (FI) model on the same species.

For example, consider a case where we simulate Helium (He) and enable both FI and CI:

particles.species_names = electron He He_plus

#------------ HELIUM ------------#
He.charge          = 0    # Neutral initially
He.mass            = 4.002602 * m_u

He.do_field_ionization = 1
He.ionization_initial_level = 0
He.physical_element = He
He.ionization_product_species = electron

#------------ HELIUM_PLUS ------------#
He_plus.charge          = q_e 
He_plus.mass            = 4.002602 * m_u - m_e
He_plus.injection_style = none

#------------ Enable Collisional Ionization ------------#
collisions.collision_names = helium_impact_ioniz

helium_impact_ioniz.type = dsmc
helium_impact_ioniz.scattering_processes = ionization
helium_impact_ioniz.species = electron He
helium_impact_ioniz.ionization_target_species = He
helium_impact_ioniz.product_species = electron He_plus

helium_impact_ioniz.ionization_cross_section = ./He_ioniz_cross_section.txt
helium_impact_ioniz.ionization_energy = 24.5 # eV

Under this architecture, two severe hidden issues arise:

1. Inconsistent State Tracking & Wrong Cross-Sections
   When a neutral He macroparticle is exposed to a strong laser field, FI correctly increments its ionizationLevel to 1 (it becomes $He^+$) but keeps it in the original He species container. However, the DSMC model only identifies targets by their species container name (He) and completely ignores the ionizationLevel attribute. As a result, when an electron collides with this macroparticle, DSMC mistakenly treats this already-ionized $He^+$ as a neutral $He$ atom. It applies the wrong (neutral) ionization cross-section and incorrectly undergoes another neutral impact ionization.

2. Fatal Violation of Charge Conservation
   Because DSMC misidentifies the target's ionization state, the weight-splitting mechanism breaks global charge conservation. Let's trace a collision event where DSMC splits a weight of $\Delta W$ from the target:

The target particle (which is actually $He^+$ due to FI) has a charge contribution of $+1e$ per weight. When DSMC subtracts $\Delta W$ from its weight, the grid loses $+1e \times \Delta W$ of positive charge.
DSMC then spawns a new He_plus macroparticle (Charge: $+1e \times \Delta W$).
DSMC also spawns a new electron macroparticle (Charge: $-1e \times \Delta W$).
Net Charge Change on the Grid: $-1e (\text{lost from target}) + 1e (\text{new ion}) - 1e (\text{new electron}) = \mathbf{-1e}$
The system essentially destroys existing positive charge and spawns a neutral pair, creating net negative charge out of thin air. This violation of charge conservation will lead to spurious electric fields and cause the Maxwell/Poisson solvers to produce unphysical results.

This implies that the current DSMC implementation (which spawns new species) is fundamentally incompatible with the FI implementation (which increments ionizationLevel in-place) if they are to be used on the same element.