fieldIonization

Works with VSimPA license.

Kind of MonteCarlo interaction that models the tunneling ionization of a kinetically modeled background pre-ionized gas. This process is similar to the nullFieldIonization, except that the background gas is described by a Species block, i.e. the background medium can be ionized.

Built-in models for field ionization of H, He, Li, Na, Rb and Cs exist, using Tech-X’s proprietary txphysics library. This uses the analytical expressions derived by [K+65].

An OAFunc can be used to get the rate of this interaction. It must provide the effective ionization rate from the initial state to the final state as a function of electric field E (V/m). This OAFunc can either be an analytical expression or import from a two column data file. See OAFunc Block for details.

The modified ADK [ADK86] (Ammosov, Delone, and Krainov) formula, updated in [DK91] and first adapted to PIC by Penetrante and Bardsley [PB91] and later corrected by Ilkov et al. [IDC92], which gives the ionization rate for any type of atom, can also be used. The user must specify the ionization potential of each atom by using the energy keyword. Both time averaged and time resolved formula are implemented. The time averaged formula (ionizationKind = averagedADK) should be used when modeling a linearly polarized electric field and the time step is larger than the oscillation period (i.e., dt is much larger than the period of the field in question). This might occur, for example, when using an envelope model for the laser pulse. The time resolved formula (ionizationKind = DCADK) is the correct choice in most cases, i.e., any time the total electric field is fully time resolved.

The ionization rate for a time resolved field is given by:

\[R_i = 4.13 \times 10^{16} \frac{Z^2}{2 n_{\rm eff}^2} \left( \frac{2e}{n_{\rm eff}} \right)^{2 n_{\rm eff}} \frac{1}{2\pi n_{\rm eff}} \left( 2 \frac{E_h}{E_L} \frac{Z^3}{n_{\rm eff}^3}\right)^{2n_{\rm eff} -1 } \exp \left[ -\frac{2}{3}\frac{E_h}{E_L} \frac{Z^3}{n_{\rm eff}^3} \right] {\rm \left(s^{-1}\right)}\]

where \(Z\) is the charge state of the ionized particle, \(n_{\rm eff}=Z/\sqrt{U_{\rm ion}/13.6[{\rm eV}]}\), \(U_{\rm ion}\) is the ionization potential in eV, \(E_h = 5.13 \times 10^{11} {\rm V/m}\), and \(E_L\) is the electric field strength at the particle position.

The time averaged modified ADK formula is given by:

\[R_i = 6.6\times10^{16} \frac{e}{\pi} \frac{Z^2}{n_{\rm eff}^{4.5}} \left( 10.87 \times \frac{E_h}{E_L} \frac{Z^3}{n_{\rm eff}^4}\right)^{2n_{\rm eff}-1.5} \exp \left[ -\frac{2}{3}\frac{E_h}{E_L} \frac{Z^3}{n_{\rm eff}^3} \right] {\rm \left(s^{-1}\right)}\]

Subsequent validation work on the tunneling ionization models in VSim was conducted and is demonstrated in [CSMZ06], [CES+12] and [CCMG+13]. The model is valid up to approximately energy densities of \(10^{23}-10^{24}\) above which Barrier Suppression Ionization is likely to be the dominant effect, and one way also want to consider vacuum pair-production in the ionization cross-section.

The model assumes the background is a gas, that is to say that atoms are well separated with respect to their size. At very high number density, the model may break down. See references to the Mott Transition for further information.

<Interaction FieldIonizationCs1>
  kind = fieldIonization
  input = Cs1
  charge = 1
  atomicName = Cs
  electrons = electrons
  ions = Cs2
  polarizationFlag = 1
  frequency = 1.e15
</Interaction>