fieldIonization

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.

fieldIonization Parameters

ionizationKind (optional, default = builtIn)

The ionization rate to be used in the interaction. Possible values are builtIn, averagedADK, DCADK and userDefinedFunc. See below for required parameters for each choice.

input (string)

The species that undergoes the tunneling ionization process.

charge (integer)

Charge of the input species (in unit of \({\rm |e|}\)).

atomicName (string)

Atomic name of the gas corresponding to the ionized species. Possible names are the fluid names listed in the nullFieldIonization interaction.

electrons (string)

Name of the species representing the electrons product of the ionization process.

ions (string)

Name of the species representing the ionized particles after the ionization process has occurred.

polarizationFlag (integer)

When the electric field magnitude is approximately constant in a Vorpal time step, 1 is the correct choice; i.e. any time the total electric field is fully time-resolved. 0 is used for the case where you are modeling a linearly polarized electric field, but the time step is larger than the oscillation period. This might occur, for example, when using an envelope model for the laser pulse. This should be applied when the dt of Vorpal is much larger than the period of the field in question.

frequency (real)

Used in the initialization process; the frequency of a laser pulse if there is such a pulse (the default scenario when using field ionization). If a static field is used, this parameter should be set to 0.

builtIn Parameters

Please see Types of collisions for the available builtIn gases.

userDefinedFunc Parameters

If the userDefinedFunc ionizationKind type is used, the following parameters must be set:

OAFunc (block,required)

Effective field ionization rate as a function of electric field E (V/m). If not provided, built in rates are used. The kinds of OAFunc available for this interaction are interpolatedFromFile, or expression.

Please see OAFunc Block for more information on the OAFunc block.

averagedADK or DCADK Parameters

If the averagedADK or DCADK ionizationKind type is used, the following parameters must be set:

energy (real, required)

The ionization potential in eV.

fieldIonization Block

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