Description of the effective rates

The calculations carried out here are derived from a compilation of effective ionization and recombination rate coefficients calculated with atomic physics and plasma modeling codes from Los Alamos National Laboratory (published in APID Vol. 11).

Complete sets of atomic data including energy levels, electron impact excitation and ionization, radiative transition probabilities, and photoionization cross sections were calculated for large sets of configurations for all stages of ionization for the elements neon, silicon, argon, titanium, and iron. Recently results have been added for tungsten. The resulting data were used in a collisional radiative modeling code. The complete model was solved for a range of temperatures for several electron densities. From the final model, an effective ionization and effective recombination rate coefficient for each ion stage was calculated. The total radiation per ion stage was also calculated. These data were then stored and are used in the present calculations.

In the steady state case it can be shown that solving for the populations of all ion stages can be accomplished by simply interpolating on the stored ion stage populations. Then the total radiated power can be calculated by multiplying the interpolated radiation from an ion stage by its population. The results are displayed in tabular form and graphs are available. Possible output includes the total radiated power, average charge per ion, and the relative populations of all ion stages, all as functions of electron temperature.

In the time dependent case the effective rate coefficients are interpolated to the current temperature and density. This gives one ionization and one recombination rate coefficient for each ion stage. The resulting rate equations are easily solved. As in the steady state case, the resulting ion stage populations are multiplied by the interpolated radiation per ion resulting in the total radiated power. The output is the same as in the steady state case.

For the time dependent case there are currently two possible methods to specify initial conditions. One method is to use the steady state solution at the initial temperature and density. The model then follows the populations through any changes in temperature and density. The other method is to start with all the population in one specified ion stage. In this case the population can evolve even with no change in temperature and density. As an example, it is possible to initiate a problem with only the fully ionized iron ion populated at a low temperature, say 10 eV, and follow the evolution of the populations of all ion stages as a function of time at the same 10 eV temperature.

The basic atomic physics data were calculated in the configuration average mode. For light elements this can have significant effect on the calculated radiation due to collisional disruption of metastable levels. However, for heavier element there is significant spin orbit coupling mixing of the metastable levels. This allows the metastable levels to mix with allowed levels so that they do radiate with minimal collisional disruption. Therefore, for the heavier elements the configuration average calculation results are not in serious error. It is estimated that the accuracy of the total radiated power from these calculations should be on the order of 20-30%.

Click here to proceed with the steady state calculations

Click here to proceed with the time dependent calculations

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