Bayesian modelling of a diagnostic helium beam ADAS workshop, Armagh Observatory, October 4th, 2010 Maciej Krychowiak M. Brix, D. Dodt, R. König, O. Schmitz, J. Svensson, R. Wolf

2 Helium beam diagnostic  Radial profiles of n e and T e at the plasma edge n e : m -3 T e : eV   r  1 mm,  t  1 ms plasma line of sight helium beam nozzle  Measure three spectral lines of atomic helium (typically 667, 706, 728 nm)  Compare two line ratios with CR model  T e : triplet/singlet  n e : singlet/singlet singlettriplet

3 direction of the gas flow beam relaxation (steady-state solution) no beam relaxation (time dependent solution) nozzle =0 (stationary beam) electron (de)excitationradiationtransport ionisation charge exchange  Beam atoms penetrate the plasma, radiate, get ionised, leave the observation volume  Movement in one direction → 1-dim transport equation: CR modelling of helium beams  ~ 200 uncertain rate coefficients for electron collisions, known only from calculations  Collisions with protons, neutrals

4 Comparisons to other diagnostics  Comparisons to TS and lithium beam (Schmitz et al. 2008):   n e 10%,  T e 30%  Observed beam penetration smaller than model by 30% Comparative measurements on TEXTOR (Schmitz, et al., Plasma Phys. Control. Fusion 50 (2008) )

5  CR model of the helium beam is a complex system with many uncertain parameters  Quantitative errors in n e /T e  Probabilistic approach provides: Diagnostic design study: application of helium beam in the high density divertor plasma of the stellarator W7-X Statements on atomic data (correction factors, uncertainties) by analysis of (uncertain) experimental data. Why probabilistic CR model for helium beam

prior knowledge likelihood Bayesian CR modelling of (relaxed) helium beam posterior marginalised posterior  Take n e /T e, simulate line ratios, D 2-dim posterior (parameters of interest) further marginalise 1-dim posteriors 6

7 Model assumptions  Steady state solution (transport neglected, n e > 2×10 12 cm -3 )  Collisional processes included: electronic (de)excitation and ionization, no charge exchange  n = 1-5 included (29 levels)  n = 1-4: „helike_hps02he_t3.adf”, n = 5: compilation by Brix (phd)  High density, low temperature W7-X divertor plasma: n e = cm -3, T e = 5 eV

9%9% 4.7% 3.2% 15% 21% 31% 25% n=3-4 30% 45% 8 ADAS dataset „helike_hps02he_t3.adf”: uncertainties 5%5% 20% n=3-4 50%

Measure 2 line ratios  Relatively large n e /T e errors  Diagnostic design study 9  n e =128%  T e =45%

Measure 3 absolute line intensities beam density (attenuation) uncertain: +/- 50%  Strongly reduced n e /T e errors 10  n e =66% Te=8%Te=8%

Fit 3 line intensities Measurement error: 5%  n e = 66%  T e = 8% Enlarge signal noise Increase number of spectral lines Measurement errors 5 → 10%  T e : 8.7% 11 Fit one additional line (501.6 nm)  T e : 8.5% Fit two more lines (492.2, nm)  T e : 7.8% n e [cm -3 ]  n e = 122%  n e = 103%  n e = 107%

12  n e =50%  T e =26%  Use comparisons to other diagnostics at TEXTOR:  n e = 10%,  T e = 30%  T e = 32 eV, n e = 4×10 12 cm -3  Run Bayesian analysis using RCs and their uncertainties from „helike_hps02he_t3.adf” Refining the beam excitation model  Some RC uncertainties in „helike_hps02he_t3.adf” are overestimated !

13 Refining the beam excitation model  Priors: RCs from „helike_hps02he_t3.adf” as before New: n e, T e : Gauss profile, width of 10% and 30% respectively (observation)  Marginalise over n e, T e and all rate coefficients except for the ones of interest prior knowledge likelihood posterior marginalised posterior  Result:  RC (1 1 S-3 1 S) 9.9% (11% in ADAS)  RC (3 1 S-3 1 P) 18.2% (30% in ADAS)  But: The model is not complete  Principle suitability of Bayesian analysis for judging atomic data

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