Generalised collisional-radiative modelling for Silicon and beyond

1. ADAS workshop, Auburn University Generalised collisional-radiative modellingfor Silicon and beyond Alessandra Giunta

2. ADAS workshop, Auburn University Introduction and motivation In both the astrophysics and fusion domains, various studies confirm that the use of zero-density population model and truncation of the population structure at a set of low levels (even if accurate data are available for them) can lead to mis-interpretation in comparing measurements and theory. The application to all densities and the distinguishing of metastable states, oriented to dynamic conditions, place the issue in the environment of Generalised Collisional-Radiative (GCR) model (Summers et al. 2006). ADAS population modelling, at its highest precision, has been applied to the ions of the elements from Hydrogen up to Neon. New analysis in the lower temperature solar chromosphere and transition region (e.g. need of Si1+) and developments in the fusion context (e.g. ITER) require the extension of the range of species up to Argon and possibly beyond.

3. ADAS workshop, Auburn University GCR ionisation and recombination coefficients The GCR ionisation and recombination coefficients are supplied within ADAS by the adf11 data files and are needed to provide the fractional abundances. Black: in the database Red: new done Blue: new in progress

4. ADAS workshop, Auburn University Silicon GCR work scheme adf07 STEP 1 Ionisation rates adf04 STEP 2 Specific ion files adf04 + S & R lines Supplemented specific ion files STEP 3 STEP4 Projection data adf17 STEP 5 Fractional abundances adf11

5. ADAS workshop, Auburn University STEP 1 – Ionisation rates specific driver from promotion rules adf56 adf32 promotion rules dataset CADW ionisation cross-section calculations ADAS8#2 adf07 adf23 total ground state ionisation coefficients (ground to ground and metastable resolved) direct + excitation/ autoionisation cross-section dataset

6. ADAS workshop, Auburn University STEP 1 – Ionisation rates Metastable resolved adf07 CADW calculations provide ground to ground ionisation rates. The need of ionisation resolved into ground and metastable initial and final parents has been addressed using the semi-empirical formula of Burgess & Chidichimo (1983), which has been adjusted to the CADW calculations. Automation is important

7. ADAS workshop, Auburn University STEP 2 – Specific ion files Revised adf04 for light elements Details for Silicon Si0+ Si1+ Si2+ Si3+ Si4+ Si5+ Si6+ Si7+ Si8+ Si9+ Si10+ Si11+ Si12+ Si13+ Cowan calculations Dufton & Kingston (1991) Griffin et al. (1990) Liang et al. (2009) Liang et al. (2009) Witthoeft et al. (2007) Bhatia & Landi (2003) Bhatia & Landi (2003) Bhatia & Doschek (1993) Liang et al. (2009) Bhatia & Landi (2007) Zhang et al. (1990) Whiteford et al. (2005) Sampson et al. (1983)

8. ADAS workshop, Auburn University STEP 3 – Supplemented specific ion files state selective recombination dataset (for archiving) adf04 with S lines specific ion dataset adf08 adf04 S lines radiative recombination mapping dataset ionisation rate coefficient dataset adf07 ADAS807 adf08_adas807 ADAS211 integrated mapping generator adf09 RR lines state selective dielectronic dataset adf18_a09_a04 dielectronic recombination mapping dataset adf04 with RR lines ADAS212 RR+DR lines full GCR adf04

9. ADAS workshop, Auburn University STEP 4 – Projection data specific ion dataset adf04 ADAS407 resolved ionisation rate coefficient dataset adf07 driver file for bundle-n calculation adf25 adf18/a09_p204 cross-reference driver file for DR data and ls-breakdown auto-ionisation rate ADAS204 adf17 projection matrix bundle-n population calculation

10. ADAS workshop, Auburn University STEP 4 – Projection data Cross-reference driver files adf18/a09_p204 driver file containing the configurations adf27 DR data AUTO- STRUCTURE ADAS701 oic Supplementary Auger break-up post- processor ADAS704

11. ADAS workshop, Auburn University STEP 5 – Fractional abundances full GCR adf04 low-level resolved population model ADAS208 adf18/a09_p204 adf17 initial tabulation of GCR coefficients at z-scaled electron temperature and density projection matrix cross-reference driver file adf10 fragment ADAS403 iso-electronic master file containing GCR metastable resolved coefficients adf10 iso-electronic final stage to stage and metastable resolved GCR coefficients fractional abundances ADAS404 ADAS405 adf11

12. ADAS workshop, Auburn University Results for Silicon – ionisation rates Comparison with Dere (2007) – This is a zero density direct coefficient comparison from the ground state, using the underlying CADW adf07. CADW Dere

13. ADAS workshop, Auburn University Results for Silicon – recombination rates Comparison with RR+DR of Badnell (2006) - The GCR recombination coefficients are compared with the zero density RR+DR rates of Badnell (2006). The lowest densities used in the ratios are 103 cm-3 for Si+2→Si+1 and 107 cm-3 for Si+7→Si+6. GCR Badnell

14. ADAS workshop, Auburn University Results for Silicon – fractional abundances Comparison with Bryans et al. (2009) - The finite density effects are more evident for low ionisation stages where the peaks move to lower electron temperatures. GCR (at Ne=108 cm-3) Bryans

15. ADAS workshop, Auburn University Beyond Silicon Needs: ▪ Reconstructing the emission and interpreting the behaviour of elements heavier than Ne and even Si is essential in both astrophysics (e.g. Mg, S, Fe) and fusion (e.g. Ar). Issues: ▪ Which resolution is appropriate. ▪ Continued update of data sources in response to improved calculations (excitation, ionisation, RR, DR). ▪ Automation and precision are both essential at this stage.

16. ADAS workshop, Auburn University Issues ▪ Resolution GCR model is implemented in ADAS as ls resolution but: - moving to medium and heavy species and more highly ionised ions ic resolution becomes appropriate - in finite plasma, going to higher quantum shells, terms of the same nl-shells move into relative statistical proportions, so ca resolution is adequate - finally l-subshells of the same n-shell move into relative statistical populations and bn resolution becomes suitable. * the model exists ◊ the model almost exists

17. ADAS workshop, Auburn University Issues ▪ Increasing the baseline An ADAS requirement is that a baseline collisional-radiative capability is available for any elements: - raising the quality of the baseline is systematically in progress - currently a new AUTOSTRUCTURE based distorted wave excitation upgrade is in progress, with undergoing and validation checks. This will strengthen particularly excitation data from the ground and metastable levels of ions. A later upgrade will extend the distorted wave data to all transitions in the adf04 data set with R-matrix used for transitions in the ground complex. These are general baseline lifting developments and are distinct from very detailed individual ion studies. ▪ Automation - In the GCR computation procedure a number of steps were performed as ad hoc hand manipulation (e.g. metastable fractionation). - An objective is to set up a basis for implementing all of the steps automatically without losing the underlying precision (in progress).