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C. Salmagne 1 , D. Reiter 1 , P. Börner 1 , M. Baelmans 2, W. Dekeyser 1,2

Tokamak edge transport studies using linear plasma devices. 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.

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C. Salmagne 1 , D. Reiter 1 , P. Börner 1 , M. Baelmans 2, W. Dekeyser 1,2

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  1. Tokamak edge transport studies using linear plasma devices C. Salmagne1, D. Reiter1, P. Börner1, M. Baelmans2, W. Dekeyser1,2 M. Reinhart1, S. Möller1, M. Hubeny1, B. Unterberg1,O. Marchuk1 Special thanks to C. Brandt1,3 and the PISCES-A team 1 – ForschungszentrumJülich GmbH, IEF-4,Association EURATOM – Jülich, 52428 Jülich, Germany 2 - Department of Mechanical Engineering, KatholiekeUniversiteit Leuven, Celestijnenlaan 300A, 3001 Leuven, Belgium 3 - Center for Energy Research, University of California at San Diego, La Jolla, CA, USA 21st International Conference on Plasma Surface Interactions in Controlled Fusion Devices Kanazawa, Japan, May 26-30 2014

  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. Relative importance of plasma flow forces • over chemistry and PWI: I edge region  II divertor div(nv║)+div(nv┴)= ionization/recombination/charge exchange div(nv║)+div(nv┴)= ionization/recombination/charge exchange I: midplain • parallel vs. • (turbulent) • cross field • flow • parallel vs. • chemistry • and PWI • driven flow II: target • Dominant friction: p + H2, detachment

  4. Relative importance of plasma flow forces • over chemistry and PWI: I edge region  II divertor div(nv║)+div(nv┴)= ionization/recombination/charge exchange div(nv║)+div(nv┴)= ionization/recombination/charge exchange I: midplain • parallel vs. • (turbulent) • cross field • flow • 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. • parallel vs. • chemistry • and PWI • driven flow II: target • Linear plasma devices • often operate in the • advection-reaction dominated regime • Dominant friction: p + H2, detachment

  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 (H2, H2(v), H2*) • Molecular Ions (H2+, H3+, H-) • 2D fluid flow (Navier Stokes Eqs. • for magnetized plasmas: “Braginskii”) • r, Θ, ignore toroidalΦ 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 • + Impurities: He, C, W, Be, ….,+ their ions and hydride-molecules

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

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

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

  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: 1017 m-3 < n < 1020 m-3, Te < 30 eV MFP of electrons indicate that fluid approximation is likely to be marginally valid (test bed for parallel electron kinetics)

  11. 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 [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)

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

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

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

  16. PSI-2, 2500 W, 0.03 Pa, 70 sccm, Te (eV) • Langmuir Probe, Te • B2-EIRENE, PSI-2 • Te at probe position • Te at spectr. position • 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) • Ti, (D+) temperature (not measured) • Minor radius, cm • B2-EIRENE electron and ion temperatures (eV), • radial profiles at probe and spectrometer • axial positions, case: 0.03 Pa

  17. B2-EIRENE, PSI-2, neutral gas pressure [Pa] • Pump 1: 600 l/s D2 • Experiment: • 0.033 Pa • 0.02 • Pa • Pump 2: 1320 l/s D2

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

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

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

  21. Distinct from tokamaks: • In the linear devices, andin 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 • Gas Pressure PH2 • Plasma conditions: ne, Te, vi, Qe,i, …

  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_H2, EIRENE, [Pa]

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

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

  26. Less clear experimental plasma density information: 1) Probe data 2) Balmer line ratio • B2-EIRENE, PSI-2, electr. density • 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 (ne, Te) • sometimes way out of • code results, even if • probe plasma flux (Jsat) is • matched. Exp. Data: [4],[5] • ne at spectr. position • ne at probe position • B2-EIRENE electron densities (cm-3), • radial profiles at probe and spectrometer • axial positions, case: 0.03 Pa • bring on Thomson scattering ! • For the time being: PH2 (exp.=calculated), scan arc power fraction to plasma, • to match Jsat, rely on spectroscopy to sort out Te, ne • [4] Pospieszczyk et al, J. Nucl. Mat, 438 (2013) [5] Reinhart et al, Trans. Fus. Sci. Techn 63 (2013)

  27. Robust trends & interpretation of spectroscopy • 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 Te, ne. • try first “modeling answers” to: • 1st : what is the positive charge carrier? H+ or H2+ or H3+ • -- H3+ is often dominant ion in very low density/temperature plasmas • 2nd : is plasma detachment in PSI-2 similar to tokamak divertor • detachment? • -- role of H- and of vibrational kinetics of H2 • -- Molecular assisted recombination MAR, etc…

  28. B2-EIRENE , PSI-2, electron density • Plasma (electron) • density • Log scale in colours • Plasma • density, • Log scale • Probe • 5e18 • m-3 • Spectrometer • Log scale, 1017 to 1019 m-3

  29. B2-EIRENE, PSI-2, H2+ density • H2+ molecular • ion density • Color code: • Log (Density cm-3) • Color code • reduced by • factor 10 as • compared to • ne profile. • H3+ and H- still • “not visible” • even then • (black picture) • Colour Scale: • X 10 • H2+ is the key player in hydrogen plasma chemistry: MAR, H3+ formation,…

  30. Competition: H2 + H2+ H3+ + H e + H2+  H + H* (or  H + H+) For H3+ concentration: R= ne/nH2 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)) • Ratio D2+/D+: 1e-2 • Ratio D3+/D+: 1e-3 • Ratio D-/D+: 1e-5 • B2-EIRENE iteration cycles • B2-EIRENE @ PSI-2: D3+, D2+ and D- stay minority • (confirmed even under 10 times lower plasma densities than here, • as seen from code density scans (but D- and D3+ physics in EIRENE • is quite “reduced” only compared to specialized A&M codes).

  31. B2-EIRENE, PSI-2: plasma pressure [Pa] • Plasma • Pressure • In divertors: • ║ pressure drop • = “detachment”. • Do we have • “divertor • detachment” here? • Detachment in tokamak divertors: ║ pressure drop by: • p+H2 friction, (Lyman opacity  ne higher,)  3 body vol.recomb., • Little or no MAR (p+H2(v) H+H2+, then e+ H2+  H + H) • Kukushkin, Kotov et al, B2-EIRENE (SOLPS) 1995-2014

  32. B2-EIRENE @ PSI-2 Recombination channels, volumetric rates cm-3s-1 • e+H+  H + hʋ • e+e+H+  H + e • e+H2(v) H + H- • H- + p  H + H • p+H2(v)  H2+ + H • e+H2+  H + H • x 2000 • Volumetric rates (cm-3/s) • Log scale color code: 1013 – 1017 for MAR, 1012 – 5 1013 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)

  33. H2 molecule, status in present • SOLPS-ITER code • More complete modes are • available  identify „as simple • as possibel“ model for edge codes • 13.6 eV • Resonance ! • H*+H initiallycompiled 1997 • Courtesy: K. Sawada, Shinshu Univ. Jp.

  34. Post-Processing B2-EIRENE PSI-2 • Line of sight integration of side-on emissivity Ph/s/cm2/sterad • across full B2-EIRENE solution, at axial “spectrometer position” • (absolute radiances, line ratios: similar to PSI-2 exp. (within 50%) [4] • H2+ >H > H2 >H- >H+ • H2+ > H > H2 >H+>H- >H3+ • > H3+ • 62 • 32 • Big surprises in side-on emissivity • contributions. Very low density species • can have dominant contribution. • Highly case-dependent, perhaps • Unpredictable without transport codes • central • r=0.5cm • at Te-peak • r=2.3 cm • boundary • r=3.5 cm • [4] Pospieszczyk,A., Reinhart,M., J. Nucl. Mat 438 (2013)

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

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

  37. e + H2+ H* + H

  38. e+H3+ H*+.. • e+H2 H* +..

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

  40. Inter • stellar clouds MAst • MAST • PISCES-A • Role of H2+, H3+ in PISCES-A, by mass spectroscopy: • E. Hollmann, A. Pigarov, PoP 9, (2002) • 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 H+ H2+, H3+ H* • H‾ H2 H

  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 D2+ nor D3+ (same as in tokamaks) -- minority ions D2+ 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 ne, as in PSI-2) -- sensitivity to surface vibrational kinetics (EleyRideal 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. Thank you for your attention!

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