Kinetics Model Setup

The Kinetics Model setup widget is used to set parameters that affect how the atomic level populations of DCA materials are computed.

There are two population models in SPECT3D:

• LTE (Local Thermodynamic Equilibrium)
• Collisional-Radiative

For LTE modeling, populations are computed assuming the plasma is in local thermodynamic equilibrium. The Saha equation and Boltzmann statistics are utilized. The populations in any volume element depend only on the properties of that volume element, and are not affected by the properties of any other volume elements.

• Collisional ionization, recombination, excitation, deexcitation
• Spontaneous emission
• Radiative recombination
• Dielectronic recombination, autoionization, electron capture
• Photoionization, photoexcitation, stimulated emission, stimulated recombination

Photon-induced transitions (photoionization, photoexcitation, stimulated emission, stimulated recombination) are non-local in nature; that is, the rates in a given volume element depend not only the properties of that element, but also on the radiation emitted from other volume elements. Because of this, the atomic level populations in one volume element can depend on the atomic level populations in other volume elements. For simulations with many volume elements and complex atomic models, the calculation of photon-induced transition rates dominates the CPU and memory requirements of a simulation.

• None
• Escape Probability - Local Approximation
• Multi-angle long characteristics (supported for all geometries)
• Multi-angle short characteristics (supported for 2-D and 3-D geometries)

The Multi-Angle Long Characteristics model is the most accurate. It computes photon-induced rates by performing radiative transfer along multiple rays that extend through the entire plasma grid (a "long characteristics" approach). It is also the most CPU and memory intensive model.

In the Multi-Angle Short Characteristics model, radiative transfer is computed similar to the long characteristics model along rays, but the transfer equation is solved exactly only for a limited number of adjacent volume elements (the number of cells to be used is specified by the user). At the beginning of each ray (i.e., at the boundary of the last adjacent cell), a boundary condition for the specific intensity is applied that is based on an average of the specific intensities near that point. In many cases, the CPU time can be considerably reduced with a modest sacrifice in accuracy. For details, see the Appendix Short-N Characteristics method. Additionally, Prism has developed a correction technique for improving the accuracy of short characteristics based on summed path lengths of N-cell steps through the plasma. For details, see the Appendix Short C Boundary Condition Scaling. If desired, this can be turned off in Preferences (in the Edit menu).

The Escape Probability Model computes photoexcitation rates for a given volume element based on the probability that photons can escape that volume element. This is considered a "local approximation" because, using this, the atomic level populations in a volume element depend only on the properties of that volume element.

For Collisional-Radiative modeling (i.e., non-LTE plasmas), additional options are available on the Advanced settings:

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On the Rate Multipliers tab (see above), users have the option of applying multipliers to the rates computed for each class of atomic process. This is sometimes useful when investigating the role of individual processes in affecting atomic level populations and the resulting spectral emission.

Rate multipliers affect the calculation of atomic level populations, and, because of this, they can indirectly affect the calculation of emissivities, opacities and resulting spectra. Note, however, that the multipliers are not used directly in the calculation of emissivities and opacities. The emissivities and opacities are only affected through the change in the atomic level populations.

When both the photoexcitation and photoionization multipliers are set to zero, a calculation may require significantly less CPU time because the calculation of these radiation field-induced rates is bypassed.

On the Photoabsorption Grid tab, parameters used for generating the photon energy (frequency) grid and the angle grid that are used to calculate photon-induced rates can be adjusted.

• Frequency grid parameters:
  • Number of Continuum Points: These points are evenly-spaced (logarithmically) points across the frequency grid.
  • Number of Extra Points Per Line Transition: These are extra points added for each line transition. Only lines with oscillator strengths above Minimum Oscillator Strength for Adding Points have extra frequency points added.
• Angle grid parameters:
  • For all 1-D plasma geometries, the number of polar angles can be adjusted. For 1-D cylindrical geometry, the number of azimuthal angles can also be adjusted. Required CPU time will increase with the number of angles chosen.
  • For 2-D cylindrical R-Z geometry, two types of models are available:
    • discrete ordinates (S_N) radiative transfer model. In this case, the S_N angle model can be adjusted. The higher the S_N model number, the more angles are used in computing photoabsorption rates. Conceptually, all directions are treated equally. Thus, if the plasma volume contains a localized intense "hotspot" source of photons that can influence the atomic kinetics in other volume elements, this model may not adequately simulate this radiation transport for all volume elements. Many cells may miss the hotspot radiation completely. In such a case, the hotspot radiative transfer model is recommended.
    • hotspot radiative transfer model. In this case, ray angles are set up such that all plasma cells resolve a central, spherical hotspot. For detailed description of this model and its benchmarks, see the Appendix Hotspot Angle Grids. The user defines:
      • the hotspot radius vs. time in a table. If only a single radius value is entered, it will be used a constant value for all simulation times. If more than one value is entered, linear interpolation will be done if the simulation time lies between two times in the hotspot radius table. If the simulation time is out of the bounds of the times in the hotspot radius table, the closest table value will be used (i.e., no extrapolation is done).
      • the number of angle grid points for (a) the azimuthal (phi, measured around the vector pointing to the hotspot center) direction, which is used by both the hotspot and non-hotspot solid angle regions, (b) the polar (theta, measured from the vector pointing to the hotspot center) direction for the hotspot solid angle region, and (c) the polar (theta, measured from the vector pointing to the hotspot center, beginning at the edge of the hotspot solid angle) direction for the non-hotspot solid angle region. See image below. Recommendation: setting all three to use 3 angle grid points is a good place to start if you aren't sure. It results in the same total number of angles as the SN-6 model (48 angles). Increasing the angles may result in higher accuracy, but will cost more computation time. The total number of angles will be: 2a ( 2b + c ).

Zoom into a hotspot portion of an angle grid, as seen from the cell's perspective (with more angles than a user would likely use). Only the upper half of the grid is shown in this image:

These cartoons help illustrate the two model types (real models are in 3D):

On the Transitions tab, parameters which affect the modeling of atomic transitions can be adjusted.

• Set Stark Broadening Modifiers: The calculated Stark widths for selected transitions can be modified. For details see Modifying the Stark Widths.
• Set Transition Modifiers: See Modifying Transition Energies and Strengths for details on how to adjust transition energies, oscillator strengths, and photoionization cross-sections for selected transitions.
• Include dense plasma shifts. An option to apply density-dependent shifts to the energies of bound-bound transitions (Stark shift). This option is in beta stage and may not be available to all users.
• The Doppler width calculation can include a user-specified turbulent velocity. To enable this option, click on the Include turbulent velocity in Doppler width check box and enter the velocity.
• Kα and Kβ transitions can be added for ions with a large number of bound electrons where the atomic model may not include these transitions. These Kα and Kβ models have extensively benchmarked for Cu (see Appendix Modeling Kα, Kβ Line Emission From Targets). The models should also be accurate for other elements; however, thorough benchmarking has not been performed. An example of application for Ge is described in the Appendix Modeling of Kα and Kβ Line Emission From Ge Dopants in Capsule Implosion Experiments.
• The Continuum Lowering modeling can be adjusted. This option is useful for testing the sensitivity of results to continuum lowering effects. Models include:
  • None
  • Hummer-Mihalas (occupation probabilities model)
  • Stewart-Pyatt
  • Ecker-Kroll
  Prior to SPECT3D version 14.0.0, the Hummer-Mihalas model was used in all simulations.
  For all models, a scaling factor for the ionization potential lowering can be adjusted. For the Stewart-Pyatt and Ecker-Kroll models, this multiplier is used in both computing the atomic level populations and the spectra. For the Hummer-Mihalas model, only the spectra are affected.
• Treat implicit multiply excited state transitions in detail. SPECT3D models highly-excited (doubly-excited, triply-excited,...) states of complex ions using a technique in which levels and transitions are bundled together. This is done because of the extremely large number of multiply-excited states that can exist for an ion. By default, transitions involving these states are modeled as Unresolved Transition Arrays. By checking this option, the user can enable models that treat these transitions in detail, thereby providing more detailed spectral structure. If the detailed calculations are included, the calculation may take considerably longer.

On the Populations Solution Method tab, the options are:

• Use an accelerated convergence method when calculating atomic level populations. This option can be applied if problems occur with the atomic level populations solver.
• For time-dependent calculations, as well as for steady-state with non-local radiation transport (Multi-angle long [or short] characteristics), there is a choice of using the Standard solver or the LSODE (Livermore Solver for Ordinary Differential Equations) solver when computing the populations. The Standard solver splits the time interval between simulation timesteps into equally spaced sub timesteps. The number of sub-timesteps is chosen by the user. The minimum is 1, the maximum is 10,000 and the default value is 1000. The LSODE solver computes the sub-timesteps based on the convergence of the solution. Sometimes this can result in very small sub timesteps being used and consequently a long CPU time. The LSODE solver remains as the default method.

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