Ionization

Ionization is an optional operator in GUERNICA that removes neutrals from the distribution function. It acts as a linear loss term of the form

\[ \left.\frac{\partial f_n}{\partial t}\right|_{\mathrm{iz}} = -\nu_{\mathrm{iz}}(\mathbf{x})\, f_n, \]

where \(f_n\) is the neutral distribution function and \(\nu_{\mathrm{iz}}\) is the ionization frequency. The frequency depends on position only, not on velocity. It is evaluated once from the electron background, projected onto the DG space, and applied pointwise at each spatial node and velocity.

Ionization is enabled through [components]. To use it, operators must include ionization, and species must include both n and e. The neutral species n is the distribution that evolves; the electron species e is a prescribed background whose density and temperature come from [e:init] and its profiles.

Two models are available, selected by model in [ionization].

`model = constant`

A spatially uniform frequency set directly by nu0, in normalized units:

[components]
species = n, e
operators = ionization

[ionization]
model = constant
nu0 = 10.0

`model = Voronov`

The frequency is built from the local electron density and temperature,

\[ \nu_{\mathrm{iz}}(\mathbf{x}) = n_e(\mathbf{x})\,\langle\sigma v\rangle_{\mathrm{iz}}\big(T_e(\mathbf{x})\big), \]

using the Voronov (1997) fit for hydrogen,

\[ \langle\sigma v\rangle_{\mathrm{iz}} = A\,\frac{(1+P\sqrt{U})\,U^{K}e^{-U}}{X+U}, \qquad U = \frac{13.6\ \mathrm{eV}}{T_e}, \]

with \(A = 2.91\times10^{-14}\ \mathrm{m^3/s}\), \(P = 0\), \(X = 0.232\), \(K = 0.39\). The result is converted to code units with the reference density \(n_0 = 10^{18}\ \mathrm{m^{-3}}\) and the time unit \(t_0\) (which depends on [units] mass_amu). Points where \(n_e = 0\) or \(T_e \le 0\) have no ionization. Electron temperature is in eV and electron density is in units of \(n_0\).

[components]
species = n, e
operators = ionization

[ionization]
model = Voronov

[e:init]
density = electron_density
temperature = electron_temperature

[profile:electron_density]
type = constant
value = 1.0

[profile:electron_temperature]
type = constant
value = 10.0

nu0 is ignored by the Voronov model. The nodal frequency is written to diag/nu_iz.gf at the end of a run (see Post Processing).