ADAS workshop, Auburn University1 Generalised collisional-radiative modelling for Silicon and beyond Alessandra Giunta

ADAS workshop, Auburn University 2 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 Si 1+ ) and developments in the fusion context (e.g. ITER) require the extension of the range of species up to Argon and possibly beyond.

ADAS workshop, Auburn University 3 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. Main date mnemonic within ADAS ElementsSourcesComments 85 He,C,N,O,Ne,Na,Mg, Al,Si,S,Ar,Ca,Fe,Ni Arnaud & Rothenflug (1985) scaled in N e -No full GCR -No metastables -Finite density effects 89 from H to Ne, Al,Si,S,Cl,Ar,Cr,Fe,Ni, Cu,Ge,Kr,Mo,Xe Empirical Van Maanen (1985) -No full GCR -No metastables -Less accurate density correction 96 H,He,C,N,O,Ne Si Na,Mg,Al,P,S,Cl,Ar Full GCR Summers et al. (2006) -Full GCR -Metastables -Finite density effects Black: in the database Red: new done Blue: new in progress

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

ADAS workshop, Auburn University 5 STEP 1 – Ionisation rates adf32 adf23adf07 ADAS8#2 adf56 promotion rules dataset specific driver from promotion rules CADW ionisation cross-section calculations direct + excitation/ autoionisation cross-section dataset total ground state ionisation coefficients (ground to ground and metastable resolved)

ADAS workshop, Auburn University 6 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

ADAS workshop, Auburn University 7 STEP 2 – Specific ion files Revised adf04 for light elements Si 0+ Si 1+ Si 2+ Si 3+ Si 4+ Si 5+ Si 6+ Si 7+ Si 8+ Si 9+ Si 10+ Si 11+ Si 12+ Si 13+ Cowan calculations Dufton & Kingston (1991) Griffin et al. (1990) Liang et al. (2009) Witthoeft et al. (2007) 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) Details for Silicon

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

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

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

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

ADAS workshop, Auburn University 12 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

ADAS workshop, Auburn University 13 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 10 3 cm -3 for Si +2 →Si +1 and 10 7 cm -3 for Si +7 →Si +6. GCR Badnell

ADAS workshop, Auburn University 14 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 N e =10 8 cm -3 ) Bryans

ADAS workshop, Auburn University 15 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.

ADAS workshop, Auburn University 16 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

ADAS workshop, Auburn University 17 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).