fieldIonizationDCADK

Field Ionization DCADK

This cross-section models the tunneling ionization of a kinetically modeled species or background gas induced by an electric field. The “DCADK” should be used when the time step taken in the simulation resolves the oscillations of the fields.

The following formula for the ionization rate is used:

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

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 modified ADK [ADK86] 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.

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.

Note

Must be paired with a Field Ionization ProductGenerator in a RxnProcess Block

fieldIonizationDCADK Attributes

kind (string, required)

Use the string fieldIonizationDCADK

ionizationEnergy (float, optional)

The ionization energy of the species to be ionized. The species that will be ionized by this process is determined by the Reactants parameter in the RxnProcess Block. By default, vorpal will take the ionization energy from the block defining the ionized species or fluid. The value provided in this block will overwrite the default value.

charge (float, optional)

The charge of the species to be ionized. The species that will be ionized by this process is determined by the Reactants parameter in the RxnProcess Block. By default, vorpal will take the charge from the block defining the ionized species or fluid. A value provided in this block will overwrite the default value.

Example fieldIonizationDCADK Block

<RxnRate rxnRate>
  kind = fieldIonizationDCADK
  #ionizationEnergy = 4.0
  #charge = 2.0
</RxnRate>