1. Member of the Helmholtz Association C. Salmagne 1, D. Reiter 1, P. Börner 1, M. Baelmans 2, W. Dekeyser 1,2 M. Reinhart 1, S. Möller 1, M. Hubeny 1, B. Unterberg 1, O. Marchuk 1 Special thanks to C. Brandt 1,3 and the PISCES-A team Tokamak edge transport studies using linear plasma devices 21 st International Conference on Plasma Surface Interactions in Controlled Fusion Devices Kanazawa, Japan, May 26-30 2014 1 – Forschungszentrum Jülich GmbH, IEF-4, Association EURATOM – Jülich, 52428 Jülich, Germany 2 - Department of Mechanical Engineering, Katholieke Universiteit Leuven, Celestijnenlaan 300A, 3001 Leuven, Belgium 3 - Center for Energy Research, University of California at San Diego, La Jolla, CA, USA

2. 2 Outline Why use a tokamak divertor “edge code” for linear plasma devices ? SONIC, B2-EIRENE (=SOLPS), UEDGE, EDGE2D-EIRENE, SOLEDGE-EIRENE, etc… How to use tokamak divertor codes for linear devices ? What do we find from simulation of PSI-2 conditions ? Summary & Outlook

3. 3 div(nv ║ )+div(nv ┴ )= ionization/recombination/charge exchange I: midplain II: target Relative importance of plasma flow forces over chemistry and PWI: I edge region  II divertor parallel vs. (turbulent) cross field flow parallel vs. chemistry and PWI driven flow div(nv ║ )+div(nv ┴ )= ionization/recombination/charge exchange Dominant friction: p + H 2, detachment

4. 4 div(nv ║ )+div(nv ┴ )= ionization/recombination/charge exchange I: midplain II: target Relative importance of plasma flow forces over chemistry and PWI: I edge region  II divertor parallel vs. (turbulent) cross field flow parallel vs. chemistry and PWI driven flow div(nv ║ )+div(nv ┴ )= ionization/recombination/charge exchange Dominant friction: p + H 2, detachment In tokamak edge, all three phenomena are active everywhere In Computational Science: “Diffusion-advection-reaction” problem We use edge code to do the “bookkeeping” between these three processes. Linear plasma devices often operate in the advection-reaction dominated regime

5. 5 Edge codes: 2D Divertor conditions (detachment transition) are controlled by gas-plasma interaction (hydrogen plasma chemistry) Relevant species in divertor (tokamak edge) and linear plasma devices Electrons Hyd. Ions: H + Neutral atoms (H, H*) Neutral molecules (H 2, H 2 (v), H 2 *) Molecular Ions (H 2 +, H 3 +, H - ) + Impurities: He, C, W, Be, ….,+ their ions and hydride-molecules 2D fluid flow (Navier Stokes Eqs. for magnetized plasmas: “Braginskii”) r, Θ, ignore toroidal Φ dependence 3D3V multi species kinetic transport, Typically formulated as Boltzmann eq., Often solved by Monte Carlo Integration Minority species, treated in quasi steady state (QSS) with other species

6. 6 specialized models --- tokamak edge codes Specialized “linear device” codes for plasmas with rich hydrogen chemistry: D. Tskhakaya, TU Wien, Austria, “BIT1” (PIC + MC) K. Sawada et al, Shinshu Univ., Nagano, JP (0D-CR+3D MC neutrals) A. Pigarov et al, USCD, US “CRAMD” (0D-CR) D. Wünderlich et al, IPP Garching, G, “YACORA” (0D-CR) and many more…… Supported by: extensive IAEA atomic and molecular data network (codes, data centers, databases…..) But: TRANSFORMATION of results to fusion devices ?  Try to apply fusion edge/divertor codes directly: Assess “similarity” of linear divertor simulators to “real” tokamak divertors, by applying same simulation code to both.  Present talk: proprietary version of B2-EIRENE, but with EIRENE from SOLPS-ITER * * S. Wiesen et al, P1-069

7. Plasma temperature in K Courtesy: S. Lisgo Step 1: consider an up down symmetric double null tokamak. Example: MAST (UK)

8. 8 Midplane Target Plasma source Aspect ratio: R/a=0 Pitch: B pol /B tor = ∞ topol. equiv. A quite counterintuitive interpretation of coordinates, but avoids duplicating programming work polar (toroidal) coordinates are neglected (symmetry is assumed) Tokamak lineartokamak radial polartoroidal axialpoloidal PSI-2 For 2D edge codes: a linear device is a “0 aspect ratio -- infinite pitch torus”. Capitalize on general curvilinear metric formulation, already in place in edge codes

9. 9 Upstream: Plasma generation by arc: Indirectly prescribed (e.g. as boundary condition) Arc power coupled to plasma? Ionization fraction? Dissociation fraction? (additional model parameters) Downstream: PMI, sheath, plasma chemistry vs. parallel flow 2D parallel-radial plasma flow, plus 3D kinetic gas-plasma reactions Gas inflow Pump plasma energy source (arc)

10. 10 The PSI-2 device (initially: operated by IPP in Berlin  FZ Jülich, since 2012)  Six coils create a magnetic field B < 0.1 T.  Plasma column of approx. 2.5 m length and 5 cm radius  Densities and temperatures: 10 17 m -3 < n < 10 20 m -3, T e < 30 eV  MFP of electrons indicate that fluid approximation is likely to be marginally valid (  test bed for parallel electron kinetics)

11. 11 [1] Kastelewicz, H., Fussmann, G. (2004). Contributions to Plasma Physics, 44(4), 352-360 [2] Salmagne C. et al., Report JUEL-4340, April 2012 (ISSN 0944-2952)  B2-EIRENE model details: see [1], [2]  Full recovery of previous results [1], with the current code versions of EIRENE, as part of SOLPS-ITER (S. Wiesen, et al P1-067)  results are particularly sensitive to kinetic corrections in parallel electron heat flux

12. 12 Outline Motivation: Why use a tokamak divertor “edge code” for linear plasmas ? SONIC, B2-EIRENE (=SOLPS), UEDGE, etc… How to use tokamak divertor codes for linear devices ? What do we find from simulation of PSI-2 conditions ? Summary & Outlook

13. 13 B2-EIRENE for PSI-2, low power, partially recombining plasma (2500 W, 0.03Pa) Electron Temperatur input parameters: H.Kastelewicz et al.... CPP (2004) New runs: New pumping configuration, Gas inlet, 70sccm Low arc power (2500 W) T e, radial-axial Colours: 0 – 15 eV

14. 14 Probe data Spectroscopic data Not PSI-2 is upright, but the code’s X-Y coordinates are...

15. 15 B2-EIRENE, for PSI-2, low power, partially recombining plasma: T e (eV) Electron Temperatur Probe data Spectroscopic data

16. 16 Pospieszczyk, A. et al., J. Nucl. Mat, 438 (2013) Paper P3-097 PSI-conf. 2012, Aachen and: M.Reinhart et al, Trans. Fus. Sci. Techn. 63 (May 2013) PSI-2, 2500 W, 0.03 Pa, 70 sccm, T e (eV) Langmuir Probe, T e B2-EIRENE, PSI-2 Te at probe position Te at spectr. position Minor radius, cm T i, (D + ) temperature (not measured) B2-EIRENE electron and ion temperatures (eV), radial profiles at probe and spectrometer axial positions, case: 0.03 Pa

17. 17 0.02 Pa Pump 2: 1320 l/s D 2 Pump 1: 600 l/s D 2 Experiment: 0.033 Pa B2-EIRENE, PSI-2, neutral gas pressure [Pa]

18. 18 Axial variation of gas pressure [Pa], w/o plasma Axial positions of pumps EIRENE, nominal pump speeds measured

19. 19 PISCES-A, UCSD, US Jan 2014: similar study using PISCES A configuration & data (C Brandt), same code B2-EIRENE Scan power to plasma  best match to probe data: 25% Scan ionization efficiency of arc  best match to probe data: 10% 200W, 10% ioniz. B2-EIRENE, 400W, 10% ionz.

20. 20 PISCES-A, identical plasma input conditions, gas inlet, @ three efficiencies of pump nominal, specification of pump 558 l/s Plasma density, lin. colour code Further lowered pumping speed 165 l/s Effective pumping speed from exp. w/o plasma 330 l/s

21. 21 Plasma conditions: n e, T e, v i, Q e,i, … Gas Pressure P H 2  In the linear devices, and in the parameter range considered here, the gas pressure sets the plasma conditions, not vice versa.  modelling: need to get vacuum system right first (within few %) before turn to plasma modelling Distinct from tokamaks :

22. 22 PSI-2, necessary step before modelling: plasma off: Gas pressure – Gas inlet –  pumping speed (each pump individually) Then: Experiment vs. pure gas simulation, Linear Monte Carlo: match within 15% Non-lin. Monte Carlo: match within 5% plasma on: does (almost) not modify gas pressure. changes in gas pressure strongly affect PSI-2 plasma (nominal pumping speed of PSI-2 pumps quite too high, compared to actual values P_H 2, EIRENE, [Pa]

23. 23 Axial variation of gas pressure [Pa], w/o plasma Axial positions of pumps EIRENE, nominal pump speeds measured EIRENE, exp. pumping speeds

24. 24 Gas pressure at given gas inflow rate: A very sensitive input model parameter, can be exactly measured, and calculated (don’t trust pump-specifications) very sensitive, but “in hand” Scan fraction of electrical arc power that goes into plasma (typically for PISCES A and PSI-2: 10-30 % efficiency) very sensitive, model parameter scan Scan: ionization (and dissociation) efficiency of plasma source: Fortunately: only amount of gas injected into system matters, not its ionization/dissociation,vibrational excitation state quite insensitive model parameter Adjust parallel electron heat flux kinetic correction parameter needs axial plasma information Adjust cross field transport parameters needs radial plasma information Redefine “calculation“ to mean: “postdiction of a complicated model with lots of parameters, to fit the data”.

25. 25 Plasma density, Log scale B2-EIRENE, PSI-2, electron density Plasma (electron) density Log scale in colours ~5e18 m -3 Probe Spectrometer “plausible“ from other considerations Colour code 1e11 – 1e13 cm -3

26. 26 Less clear experimental plasma density information: 1) Probe data 2) Balmer line ratio B2-EIRENE electron densities (cm -3 ), radial profiles at probe and spectrometer axial positions, case: 0.03 Pa n e at probe position n e at spectr. position B2-EIRENE plasma can be made roughly consistent with Balmer line ratio fitting (see below). Distinct from quite similar PISCES-A case and earlier PSI-2 (Berlin) studies with same code: probe data (n e, T e ) sometimes way out of code results, even if probe plasma flux (J sat ) is matched. Exp. Data: [4],[5] [4] Pospieszczyk et al, J. Nucl. Mat, 438 (2013) [5] Reinhart et al, Trans. Fus. Sci. Techn 63 (2013) B2-EIRENE, PSI-2, electr. density  bring on Thomson scattering !  For the time being: P H2 (exp.=calculated), scan arc power fraction to plasma, to match J sat, rely on spectroscopy to sort out T e, n e

27. 27 For experimentally given gas inlet, arc power, pumping speeds, PSI-2 vacuum vessel configuration, …. … B2-EIRENE finds exact gas pressure, can match J_sat (parameter scan) and finds “plausible” plasma T e, n e. try first “modeling answers” to: 1 st : what is the positive charge carrier? H + or H 2 + or H 3 + -- H 3 + is often dominant ion in very low density/temperature plasmas 2 nd : is plasma detachment in PSI-2 similar to tokamak divertor detachment? -- role of H - and of vibrational kinetics of H 2 -- Molecular assisted recombination MAR, etc… Robust trends & interpretation of spectroscopy

28. 28 Plasma density, Log scale B2-EIRENE, PSI-2, electron density Plasma (electron) density Log scale in colours 5e18 m -3 Probe Spectrometer Log scale, 10 17 to 10 19 m -3

29. 29 B2-EIRENE, PSI-2, H 2 + density H 2 + molecular ion density Color code reduced by factor 10 as compared to n e profile. H 3 + and H - still “not visible” even then (black picture) Color code: Log (Density cm-3) Colour Scale: X 10 H 2 + is the key player in hydrogen plasma chemistry: MAR, H 3 + formation,…

30. 30 B2-EIRENE iteration cycles Ratio D 2 + /D + : 1e-2 Ratio D 3 + /D + : 1e-3 Ratio D - /D + : 1e-5 B2-EIRENE @ PSI-2: D 3 +, D 2 + and D - stay minority (confirmed even under 10 times lower plasma densities than here, as seen from code density scans (but D - and D 3 + physics in EIRENE is quite “reduced” only compared to specialized A&M codes). Competition: H 2 + H 2 +  H 3 + + H e + H 2 +  H + H* (or  H + H + ) For H 3 + concentration: R= n e /nH 2 ratio matters. R needs to be very low (<10 -3 ), like in interstellar clouds, or in some PISCES-A conditions (Hollmann, Pigarov, POP 9, (2002))

31. 31 Plasma Pressure In divertors: ║ pressure drop = “detachment”. Do we have “divertor detachment” here? B2-EIRENE, PSI-2: plasma pressure [Pa] Detachment in tokamak divertors: ║ pressure drop by: p+H 2 friction, (Lyman opacity  n e higher,)  3 body vol.recomb., Little or no MAR (p+H 2 (v)  H+H 2 +, then e+ H 2 +  H + H) Kukushkin, Kotov et al, B2-EIRENE (SOLPS) 1995-2014

32. 32 B2-EIRENE @ PSI-2 Recombination channels, volumetric rates cm -3 s -1 Volumetric rates (cm -3 /s) Log scale color code: 10 13 – 10 17 for MAR, 10 12 – 5 10 13 for EIR  Dominant role of MAR in PSI-2, same code that predicts its absence in ITER MAR in lin. Devices: NAGDIS, Ohno et al, PRL 81 (1998) x 2000 e+H +  H + h ʋ e+e+H+  H + e e+H 2 (v)  H + H - H - + p  H + H p+H 2 (v)  H 2 + + H e+H 2 +  H + H

33. 33 initially compiled 1997 H 2 molecule, status in present SOLPS-ITER code 13.6 eV Resonance ! H*+H Courtesy: K. Sawada, Shinshu Univ. Jp. More complete modes are available  identify „as simple as possibel“ model for edge codes

34. 34 > H 3 + Post-Processing B2-EIRENE PSI-2 Line of sight integration of side-on emissivity Ph/s/cm 2 /sterad across full B2-EIRENE solution, at axial “spectrometer position” (absolute radiances, line ratios: similar to PSI-2 exp. (within 50%) [4] 6262 central r=0.5cm at Te-peak r=2.3 cm boundary r=3.5 cm H 2 + >H > H 2 >H - >H + H 2 + > H > H 2 >H + >H - >H 3 + Big surprises in side-on emissivity contributions. Very low density species can have dominant contribution. Highly case-dependent, perhaps Unpredictable without transport codes 3232 [4] Pospieszczyk,A., Reinhart,M., J. Nucl. Mat 438 (2013)

35. 35 Balmer series spectroscopy in linear devices Measured Line ratio 4.5 (typical for PISCES, PSI-2 http://open.adas.ac.uk/adf13

36. 36 EIRENE database Problem with some ADAS versions before 2000 (still online) H + e  H* +e H + + e  H* +….

37. 37 e + H 2 +  H* + H

38. 38 e+H 3 +  H*+.. e+H 2  H* +..

39. 39 H - +..  H* +.. Labels refer to EIRENE online A&M database: www.hydkin.de

40. 40 H* H+H+ H H 2 +, H 3 + H2H2 H‾  Linear devices provide many advantages for very detailed, high resolution, spectroscopy (H, D, T) (good access, exposure time,…)  Easy interpretability is not one of them. Bring on Thomson scattering at PSI-2 MAst MAST PISCES-A Inter stellar clouds Role of H2+, H3+ in PISCES-A, by mass spectroscopy: E. Hollmann, A. Pigarov, PoP 9, (2002)

41. 41 Summary  Divertor codes can be used “as is” directly for linear devices, by regarding the latter as “zero-aspect ratio infinite-pitch torus” (full mathematical analogy of transport equations and B-field configuration)  2D PSI-2 numerical model was developed for B2-EIRENE.  Low power partially recombining PSI-2 plasma conditions can be replicated by the code: -- positive charge carrier is D +, not D 2 + nor D 3 + (same as in tokamaks) -- minority ions D 2 + and D - are dominant players for plasma recombination (MAR) (distinct from tokamaks)  plasma detachment in tokamak divertors and in linear devices are different atomic/molecular processes (at least for low n e, as in PSI-2) -- sensitivity to surface vibrational kinetics (Eley Rideal process) (distinct from tokamaks) Outlook:  Classical drifts and currents are currently introduced in PSI-2 runs. Probably easier than in tokamaks, due to near orthogonality of relevant coordinates  simulations of PSI-2 plasmas with synthetic fluctuating backgrounds (blobby transport) to practice for far scrape off layer tokamak modeling

42. 42 Thank you for your attention!