Description of the effective rates
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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