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First Results

Here are plots of the neutral density near the target for the first run. Both codes used 5000 flights; the relative standard deviation near the target is around or slightly less than 10%. The same maximum value is used in both plots so that the colors can be compared directly. At least on a qualitative basis, the results agree within the error bars:

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Once we're happy with the density comparison, we can proceed to look at the plasma source terms. Again, because of the treatment of CX in EIRENE, this may be problematic.

In a second run (not shown here), I replaced the reaction rates for CX and ionization in DEGAS 2 with the values used in EIRENE. The dominant (presumably) molecular processes have the same rates and dissociation energies, so I didn't bother making any changes there. I ran both codes for about 80,000 flights to get the errors down to about 2%. Over all of the high D density region, the DEGAS 2 values were larger, by 20% immediately in front of the target. Finding this unacceptable given my efforts to ensure that the two codes had the same physics.

Start By Turning Everything Off

In these steps, I'll attempt to determine what it is that I'm missing. I began by turning off as much physics as possible. In both codes I launch a 3 eV (monoenergetic) D atom with an initial cosine distribution. From there it bounces off of mirrors everywhere until it finds the exit.

This proved to be an interesting exercise. For reasons I do not understand, EIRENE gave truly bizarre results at around 6000 flights. At about 200,000 flights, the codes agree to within the error bars. The puzzling thing is that those error bars remain quite large, about 10-20%. Believe it or not, these runs are not quick (perhaps because of the occasional "stuck" flight; this may also be the cause of EIRENE's problems and the poor statistics). So, I'll be content with what I have for now:

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As you can see, these runs made for beautiful plots. Maybe we should rename DEGAS 2 as "Rothko"?

In two subsequent runs, I added ionization of D and then charge exchange; using the EIRENE rates in both codes. In both cases, the results agree to within the error bars. E.g., for the first three rows in front of the targets, the relative standard deviations for the two codes are about 5%; giving a combined error of about 7%. About 2/3 of the fractional differences in the D densities (again, will come back to the other densities and plasma transfers later) in those three rows are less than 7%; 1/3 are more. This is what I call "statistical agreement".

Two things to note which will likely be true throughout these comparisons:

  1. The two codes invariably interpolate reaction rates, etc. differently. Deviations of a few percent should be expected in those rates, and should be reflected in the overall results. So, I do not anticipate pushing the codes to agree to better than about 5%.
  2. EIRENE does not do suppressed absorption during the ionization of D (as DEGAS 2 does). An immediate consequence is that the EIRENE results are considerably noisier than those of DEGAS 2 more than one ionization mfp from the plate. Hence, I plan to confine comparisons to that region.


For the next comparison, I replaced the simple source model above with the original one in which we have D+ ions with a specified (flux surface dependent) energy reflecting off of Molybdenum; only the private flux cut and the symmetry boundary (ix = 0) remain as mirrors. To keep the molecules from impacting the results at this point, I pared down their reactions to include just: e + H2 -> e + H2+ + e and e + H2+ -> e + 2H+ + e.

At this point significant differences of 20% or more were present. To further focus on the surface physics, I did a subsequent run without charge exchange and found differences of nearly a factor of two. A large part of the error was caused by a bug inserted when the EIRENE surface physics data were being adapted for use in DEGAS 2.

Most of the remaining differences in this second run were due to differences in the low energy part of the reflected atom distribution. As discussed on the first page, I chose to extrapolate the data differently here than does EIRENE. However, the atom densities, the score for which is proportional to 1/velocity, are most sensitive to the lowest energy neutrals. In order to prevent this difference from confusing further comparisons, I chose to modify the DEGAS 2 version of the data to mimic the EIRENE extrapolation:

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Repeating the DEGAS 2 run without charge exchange led to an improved agreement, but the differences were still outside the error bars. My guess is that the remaining discrepancy has the same origin, but is now related to the fact that EIRENE does a linear interpolation of the reflected energy; DEGAS 2 uses a log interpolation (this cannot easily be altered).

Rather than continuing to beat on this small problem, I replaced CX and repeated that DEGAS 2 run. Recall that the only physics missing is that of molecular dissociation. We now get again get statistical agreement of the two codes:

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Since it is difficult to discern the differences from these graphics, here are the fractional differences. Note that again the relative standard deviations immediately in front of the target are about 5%:

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For the next run, we'll be back to the full physics...

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