Collision processes

A CollisionProcess names its kind, the background it collides with and its cross_section. All kinematics are evaluated with a neutral partner drawn from the background’s Maxwellian, in the centre-of-mass frame where that matters. $m$ is the incident mass, $M$ the neutral mass, $\mu = mM/(m+M)$ the reduced mass, $\mathbf V$ the centre-of-mass velocity, $\mathbf w$ the neutral’s velocity and $\mathbf g$ the relative velocity. “Scattered” means isotropically, or with the process’s scattering model.

Kind	Reaction	What happens	Product roles
`elastic`	$A + B \to A + B$	$\mathbf g$ scattered, $\lvert\mathbf g\rvert$ kept	none
`backscatter`	$A^+ + A \to A + A^+$	$\mathbf g$ reversed: for equal masses the ion leaves with the neutral’s velocity	optional `neutral`
`excitation`	$A + B \to A + B^*$	scattered, $\tfrac12\mu g^2$ reduced by the energy loss	none
`dissociation`	$e + AB \to e + A + B$	as excitation	optional `fragment`
`ionization`	$e + B \to 2e + B^+$	$E - E_{iz}$ shared by the two electrons, both scattered in the neutral frame; ion at $\mathbf w$	`electron`, `ion`
`dissociative_ionization`	$e + AB \to 2e + A^+ + B$	as ionization	`electron`, `ion`, optional `fragment`
`attachment`	$e + B \to B^-$	electron removed, negative ion created at $\mathbf w$	`negative_ion`
`dissociative_attachment`	$e + AB \to A^- + B$	as attachment	`negative_ion`, optional `fragment`
`detachment`	$A^- + B \to A + B + e$	negative ion removed, electron emitted isotropically about $\mathbf V$ with $\tfrac12\mu g^2 - E_{th}$	`electron`
`charge_transfer`	$A^+ + B \to A + B^+$	incident removed; with an `ion` product, $B^+$ created at $\mathbf w$	optional `ion`, `neutral`

products maps each role to a species name, for example {"electron": "e", "ion": "Ar+"}. Every species involved needs a mass in species_masses. Products take the position and the weight of the incident marker, which conserves charge and particle number marker by marker, so markers may carry any weight. A code with one fixed weight per species must give species that exchange particles the same weight. To keep the number of markers in check, see marker weights.

Tracking neutrals

Neutrals are a prescribed background, not markers, but the fast neutrals of charge exchange and the fragments of dissociation can be kept as a species of their own:

neutral (backscatter, charge_transfer): the fast neutral, with the incident ion’s velocity before the collision.
fragment (the dissociative kinds): one neutral fragment at the neutral’s velocity.

Without a species for these roles they are dropped. Those species usually have no processes of their own and only receive products.

Excitation, dissociation, ionization and detachment lose energy_loss (eV), which defaults to the threshold of the cross section. Ionization shares the residual energy $E - E_{iz}$ between the primary and the secondary electron:

energy_sharing="equal" (default): half each.
"uniform": a uniformly distributed fraction.
"opal": the secondary energy $E_s \in [0, (E-E_{iz})/2]$ drawn from the Opal–Peterson–Beaty distribution $\propto 1 / (1 + (E_s/w)^2)$ , with sharing_energy=w in eV (about 10 eV for argon, 8.3 eV for H₂). This is the usual choice for electron swarms and discharges: most secondaries are slow.

If the incident species is not the product electron (ion impact, $A^+ + B \to A^+ + B^+ + e$ ), the electron takes its share of the centre-of-mass energy $\tfrac12\mu g^2 - E_{iz}$ and is emitted isotropically from $\mathbf V$ , and incident and target ion separate along the incident direction with the rest.

Scattering models

scattering sets the angular distribution of elastic, excitation, dissociation and ionization collisions about the incident direction:

"isotropic" (default).
"vahedi_surendra": $\cos\chi = (2 + E - 2(1+E)^R)/E$ with $E$ in eV and $R$ uniform (Vahedi and Surendra, Comput. Phys. Commun. 87, 179 (1995)).
"okhrimovskyy": $\cos\chi = 1 - 2R(1-\xi)/(1 + \xi(1-2R))$ with $\xi = 4\varepsilon/(1+4\varepsilon)$ and $\varepsilon$ the energy in Hartree (Okhrimovskyy et al., Phys. Rev. E 65, 037402 (2002)).

Both are screened-Coulomb forms for electrons: isotropic at low energy and forward-peaked above a few eV. They change which cross section belongs in the elastic process. With isotropic scattering it must be the momentum-transfer cross section, so that momentum relaxes at the right rate; with an anisotropic model it must be the integral elastic cross section. Ionized electrons are scattered with their own energies after the collision.

plasmacoll.scattering_cosine(model, energy, uniform) evaluates the models directly.

Energy frames

energy_frame selects the energy the cross section is looked up at:

"center_of_mass" (default): $E = \tfrac12\mu g^2$ . Use it for ion-neutral data given in the centre-of-mass frame.
"lab": $E = \tfrac12 m g^2$ , the incident particle’s energy in the rest frame of the target. This is the convention of electron cross-section compilations such as LXCat, and of most ion-beam data.

For electrons the two agree to $O(m_e/M)$ . For ions on a gas of similar mass they differ by a factor $(m+M)/M$ , so pick the one the data was tabulated in.

Marker weights

Every ionization doubles a marker, and attachment and charge transfer remove them, so the number of markers drifts away from what a run can afford. plasmacoll.population controls it on any marker container:

merge_markers(markers, target, cell_size=None) groups markers in the same spatial cell and velocity octant by speed and replaces every group of three or more by two markers that keep the group’s weight, momentum and kinetic energy exactly (Vranic et al., Comput. Phys. Commun. 191, 65 (2015)).
split_markers(markers, max_weight) divides markers heavier than max_weight into equal copies.

ZeroDReactor(..., max_markers=N) merges a species down to $N/2$ markers whenever it exceeds $N$ .

Process sets for hydrogen

plasmacoll.proton_hydrogen_processes returns the six processes of a test-particle model for protons in negative-ion sources: momentum transfer with H and H₂, charge exchange with H (backscatter) and H₂ (charge transfer), and rotational and vibrational excitation of H₂. It takes the cross-section tables as input. See negative-ion sources.

Out of scope

The targets are always neutral gases. Collisions between charged particles (Coulomb collisions such as electron–electron or electron–ion, recombination, mutual neutralization) need a different operator (e.g. Takizuka–Abe or Nanbu) and are not part of plasmacoll.