Uncertainties on atomic data

Transcription

1 Uncertainties on atomic data Connor Ballance (Auburn University) Stuart Loch (Auburn University) Mike Witthoeft & Tim Kallman (NASA-Goddard) Adam Foster & Randall Smith (CfA,Harvard) Joint ITAMP-IAEA Technical Meeting on Uncertainty Assessment for Theoretical Atomic and Molecular Scattering Data 7-9th July, Cambridge, MA 2014

2 Although, the momentum to include uncertainties in modeling increases.

3 Background The modeling community has been asking for some time to have meaningful uncertainty on atomic data. We categorize the problem into 2 groups: Baseline uncertainty data to give an indication of the parameter space. Method sensitivity uncertainty data with tighter and more realistic error bars. Our primary goal is not cross sections in isolation but rather how they interact to provide uncertainty in an magnetic fusion /astrophysical plasma diagnostic.

4 eg. Effective total ionisation of Lithium at DIII-D (General Atomic) (not dependent on the state-of-the-art groundstate ionisation)

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6 For more details : Fusion and Technology Vol 63, May 2013

7 He like line ratio diagnostics For O6+ The (G)ratio of the (X+Y+Z)/W is Te dependent for Ne < 1x107 cm 3. The (R)ratio of the Z/(X+Y) is density dependent.

8 Plasma density regimes Coronal Collisional radiative LTE

9 Baseline uncertainties The aim for the baseline uncertainty data is to generate a range of values that should encompass most of the currently available data in the databases. So we are looking for generous error bars. We also want uncertainties that have the correct temperature and n shell behavior.

10 Uncertainties on electron impact excitation data O6+ There are two previous R matrix calculations. Plus one DW calculation, we also did our own DW calculation. They all agree very well for the background cross section.

11 Effective collision strengths forbidden transition Our baseline uncertainty data for excitation is the difference between the RM and DW upsilons. Shown is our baseline uncertainty data for the 1 2 transition in O6+

12 Effective collision strengths allowed transition Note that the errors are very small for the resonance line. The difference at the highest temperatures is due to different last energy points in the RM and DW calculations.

13 Uncertainties on ionization cross sections Shown is the ground state ionization of O6+. We took the difference between a Post and Prior scattering potential calculations. We calculated level resolved data for the first 4 n shells.

14 Uncertainties in recombination The uncertainty in the RR data is the difference between a Gaunt factor calculation of ADAS and a DW calculation from AUTOSTRUCTURE. ~2% error in RR. The uncertainty in the DR is the difference between two DW AUTOSTRUCTURE calculations. One with and one without shifts to NIST core excited energies. ~8% error at low Te which decreases to close to zero for the highest temperatures.

15 4+ O example EXPT THEORY EXPT THEORY From Fogle et al. A&A ( 2s + e > 2s2p nl ) Theory does well for high energy resonances Theory does poorly for the low energy resonances.

16 The low energy resonances can dominate the low temperature rate coefficients. The uncertainty in the low temperature DR rates is high (order of magnitude) This mostly affects modeling of photo ionized plasmas From Fogle et al. A&A 2005

17 Impact of shifting target thresholds

18 Method Sensitivity (variation within a chosen method ) With the advent of supercomputers we can adopt a Monte Carlo approach to R matrix calculations, and and build up meaningful statistics from hundreds of calculations. This has been implemented within an perl script. To build up a distribution : atomic structure calculation to effective collision strengths without user intervention 100s/1000s of times.

19 Method Sensitivity (variation within a chosen method ) This requires a rigorous and well defined output to manage perhaps a thousand calculations In the case of excitation, we have Maxwellian averaged collision strengths for every transition for a range of temperatures and now the associated error file and eventually the 'correlation file'.

20 ADAS adf04 : helike_cb12#o6.dat

21 We shall start with simpler systems, though the approach can be applied to the near neutral stages of Tungsten Total electron impact groundstate ionisation of W^{3+} (5d^3), including large indirect 5p^55d^4 contributions. Blue = distorted wave Red = R matrix

22 Propagation of uncertainties (Baseline) So we have a recommended dataset, plus an uncertainty dataset. We initially used a Gaussian distribution about the recommended data, with the uncertainty providing the standard deviation for the Gaussian. We then do a Monte Carlo set of collisional radiative calculations (typically about 1,000,000) and produce excited populations and emissivities. These are post processed to give line ratios, with error bars

23 Results R ratio

24 Distribution functions We initially used Gaussian distributions with the standard deviation provided by the uncertainty value. We changed this to a log normal distribution to ensure that there were no negative values.

25 Log normal distribution The log normal represents a random distribution of numbers that are also bounded by zero. However, it means that we almost never sample the very small values on the left hand side of the peak our error bar on the plus side is too large.

26 Conclusions We think that our method of generating baseline uncertainty data is reasonable. We need to explore the effect of different distribution functions for the input atomic data. The next major step will be generation of the method sensitivity data. These will naturally have the appropriate distribution functions.