Ionisation rates#
The rate at which an intense, linearly polarised field ionises a noble-gas atom:
optmat.gas.ionisation_rates. It is built from published theory and published
constants, and validated against all-electron calculations, time-dependent Schrödinger
calculations and measured yields (optmat.gas.ionisation_validation). The
parameters it rests on are those of Ionisation.
import numpy as np
from optmat.gas.ionisation_rates import ionisation_rate_model
field = 2.74e10 * np.cos(np.linspace(0.0, 2 * np.pi, 101)) # one cycle, V/m
argon = ionisation_rate_model("Ar", 800e-9)
argon.cycle_averaged_rate(2.74e10) # 1/s, at the amplitude of 1e14 W/cm^2
argon.instantaneous_rate(field) # 1/s, along a carrier-resolved field in V/m
argon.keldysh(2.74e10), argon.barrier_suppression_field, argon.maximum_field
argon.electrons, argon.channels, argon.static_constants # what it is made of
argon.citation, argon.sources, argon.reasons # and where each part comes from
The gases are He, Ne, Ar, Kr and Xe. The field is in V/m and the rate in s⁻¹; the amplitude of an intensity \(I\) is \(F = (2I/\varepsilon_0 c)^{1/2}\).
Read the Quick start for the shorter first calculation. Continue with Noble-gas ionisation: rate theory for the physical definitions, or Noble-gas ionisation: accuracy and limitations for the supported range and uncertainty.
The models#
Model |
Coulomb factor |
Static correction |
Coefficient |
Fine structure |
N_eff |
|---|---|---|---|---|---|
|
frequency |
tong-lin |
tong_2002 |
yes |
1, 1.35, 1.47, 1.5 |
|
static |
none |
hartree |
no |
1 |
|
ilkov |
none |
hartree |
no |
1 |
|
popruzhenko |
none |
tong_2002 |
no |
1 |
|
frequency |
tong-lin |
tong_2002 |
no |
1 |
|
static |
tong-lin |
tong_2002 |
yes |
1, 1.47 |
|
static |
tong-lin |
tong_2002 |
no |
1 |
default is the model above. one_electron is the default without \(N_\text{eff}\)
and the fine structure, which is what a one-electron calculation in Tong & Lin’s
potentials computes. default_static and one_electron_static are the same two with
the static Coulomb factor, the default until TC-848; the comparisons of the register
before then were made with them. The ppt_* models are the rates of one electron
as their sources give them, for comparison.
Validation#
The validation separates static normalisation, frequency dependence, and the atom’s effective electron count. Some references set parameters: helium’s electron count uses Parker et al., the frequency-dependent Coulomb correction is fitted to one-electron argon calculations, and Kr and Xe electron counts use Wallace et al. The chapters identify those choices alongside independent tests.
Tables are generated from optmat.gas.ionisation_validation and checked against
the stored results. default and one_electron use the frequency-dependent Coulomb
factor adopted in TC-848; default_static and one_electron_static preserve the
older static-factor calculation. Historical comparisons are identified explicitly.
See Noble-gas ionisation: rate theory.
See Noble-gas ionisation: static references.
See Noble-gas ionisation: all-electron laser calculations.
See Noble-gas ionisation: one-electron calculations.
See Noble-gas ionisation: measured yields.