- nullFieldIonization
nullFieldIonization¶
Works with VSimPD and VSimPA licenses.
Kind of MonteCarlo interaction that models tunneling ionization
of a background neutral gas, the quantum mechanical phenomena
where by applying an electric field, an electron can escape the
potential barrier of an atom represented by a background neutral
gas. The background gas is described by a Fluid
block in
the input file. If you require a background gas represented by a
Species
block see
fieldIonization.
During the interaction, an ion and an electron are created; these
must be defined by two Species block in the input file. Vorpal
uses the field associated with the ion species to determine if
the background gas is ionized. When ions are created due to
tunneling ionization, the density of the background gas is
reduced accordingly at the position of the ionization event.
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].
Alternatively an OAFunc can be used to provide 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 (Ammosov, Delone, and Krainov)
[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. 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:
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, \(E_h = m_e^2q_e^5/(4\pi\epsilon_0 \hbar^4)=5.13 \times 10^{11} {\rm V/m}\), and \(E_L\) is the electric field strength at the particle position.
The time averaged modified ADK formula is given by:
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, \(10^{26}/m^{3}\) the model may break down. See references to the Mott Transition for further information.
nullFieldIonization Parameters¶
- ionizationKind (optional, default = builtIn)
The ionization rate to be used in the interaction. Possible values are
builtIn
,averagedADK
,DCADK
anduserDefinedFunc
. See below for required parameters for each choice.
- input (string)
This specifies the name of the Fluid block used to described the neutral gas. For more information on the kinds of allowed neutral Gases, please see Working with neutralGas Fluids and the gasKind Parameter.
- electrons (string)
This specifies the name of the Species block representing the electron product of the ionization.
- ions (string)
This specifies the name of the Species block representing the ion product of the ionization.
- 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. Use0
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)
This parameter is 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 (required)
Effective field ionization rate as a function of electric field E (V/m). If not provided, built in rates are used.
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.
Example nullFieldIonization Block¶
<NullInteraction FluidIonizationCs>
kind = nullFieldIonization
input = CsNeutralGas
electrons = electrons
ions = Cs1
polarizationFlag = 1
frequency = 1.e15
</NullInteraction>