--- H 3. Towards a H --- H H H 2. CR model for transport codes: application to linear plasma devices. D. Reiter, R. K.

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1 Member of the Helmholtz Association Towards a H --- H H H H 3 + CR model for transport codes: application to linear plasma devices D. Reiter, R. K. Janev Forschungszentrum Jülich GmbH, IEF-4, Association EURATOM Jülich, Jülich, Germany 2 nd IAEA RC meeting, Atomic and Molecular Data for State-resolved Moelling of Hydrogen and Helium and their Isotopes in Fusion Plasmas, IAEA, Vienna, July 2013

2 Ratko Janev, Detlev Reiter: H,H2,H3 data compilation. Mostly cross sections, few rate coefficients Today: 471 references, Almost all data fitted. Last report: New edition: summer 2013

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4 Outline News from FZ Jülich: shutting down TEXTOR in 2013 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 4

5 TEXTOR: started operation in 1984, will be shut down end of 2013 EIRENE Monte Carlo Code was originally developed for TEXTOR (my phd: ), but quickly then used for many other fusion devices B2-EIRENE was developed originally for TEXTOR (and INTOR) ( ) but quickly then used for many other fusion devices. Now embedded in SOLPS suit of edge codes. 5

6 Detlev Reiter Institute of Energy Research Plasma Physics Association EURATOM FZJ No 6

7 A new laboratory for PFC materials under extreme loads Refurbished Hot Material Laboratory: controlled area, Hot Cells November 22 nd, 2012 Institut für Energie- und Klimaforschung Plasmaphysik, Forschungszentrum Jülich, Nr. 7

8 JULE-PSI Steady state linear plasma generator with target analysis and exchange chamber, inside Hot Cell Loading conditions (deuterium plasmas), with target biasing q = MW m -2, simulation of transients by laser irradiation (120 J / 4 ms) n e = m -3 T e up to 20 ev (T i ~ 0.5 T e ) E ion = ev (biasing) G ion = m -2 s -1 F = m -2 in 4 h D flow channel ~ 6 cm Institut für Energie- und Klimaforschung Plasmaphysik, Forschungszentrum Jülich, Nr. 8

9 EIRENE: Simulations of transport in unstructured 3D configurations 1985: TEXTOR, ALT-II Pumplimiter ~ 100 surfaces 2011: Optimization of Monte Carlo by approaches from image processing 2012: JULE PSI tetrahedrons 2013: Assessment of gas flow : Gas Pressure (Pa) from target recycling JULE-PSI Target recycling

10 Outline News from FZ Jülich: shutting down TEXTOR in 2013 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 10

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

12 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 +, He +, He ++ Neutral atoms (H,D,He) Neutral molecules (H 2, H 2 (v)) H*, H 2 *, He*,.. Molecular Ions (H 2+, H 3+, H - ) 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 Fast (collisional) relaxation, treated in quasi steady state with other species Minority (?) species, treated in post processing, no effect on others. + Impurities: He, C, W, Be,.,+ their ions and hydride-molecules

13 ITER, B2-EIRENE simulation, fully detached, T e field hotter than 1 Mill deg.

14 Why? A rich hydrogen plasma chemistry is the dominant effect in divertor detachment. Divertor codes (ITER, DEMO, ) have to get this right, at least Use linear plasma devices to focus edge simulations on this issue Hydrogen chemistry model verification? Assess similarity of linear divertor simulators to real tokamak divertors, by applying same simulation code to both. Next: How hard can it be to use an established tokamak divertor code as is for a linear device? (here: B2-EIRENE, vs. solps4.3, ITER)

15 Step 1: consider an up down symmetric double null tokamak. Example: MAST (UK) H atom density H line emission experimental checks. Courtesy: S. Lisgo Plasma temperature in K H atom density, log scale, cm -3

16 Use of B2-EIRENE code for a linear device Midplane Plasma source Direct use of B2- EIRENE (SOLPS) for PSI-2 is possible, but the coordinates have to be adapted in a quite counter-intuitive way linear toroidal Target topol. equiv. Aspect ratio: R/a=0 Pitch: B pol /B tor = radial polar axial radial toroidal poloidal polar (toroidal) coordinates are neglected (symmetry is assumed) Tokamak MAST Target PSI-2 16

17 Upstream: Gas inflow plasma energy source (arc) Plasma generation, different from outer midplane in tokamaks, but can be prescribed (e.g. as boundary condition) Downstream: (1D) parallel multi-species plasma flow in transition regime between kinetic and fluid Pump PMI, sheath, plasma chemistry vs. parallel flow

18 For a 2D tokamak divertor code (e.g. SONIC, B2-EIRENE (SOLPS), UEDGE, etc ) a linear plasma device is just a zero aspect ratio, infinite field pitch, tokamak upstream, symmetry plane, (?) plasma source downstream divertor plasma sink

19 The PSI-2 Jülich device 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: m -3 < n < m -3, T e < 30 ev MFP of electrons indicate that fluid approximation is likely to be valid 19

20 B2-EIRENE (SOLPS4.3), for PSI-2, low power, partially recombining plasma (2500 W, 0.03Pa) Electron Temperatur input parameters: H.Kastelewicz... CPP (2004) New runs: SOLPS4.3 New pumping configuration, Gas inlet, reduced, 70sccm Low input power (2500 W)

21 Probe data Spectroscopic data

22 B2-EIRENE (SOLPS4.3), for PSI-2, low power, partially recombining plasma Electron Temperatur Probe data Spectroscopic data

23 PSI-2, 2500 W, 0.03 Pa, 70 sccm, ev Langmuir Probe, T e B2-EIRENE, PSI-2 case 9 PSI-2, electron temperature profile 9.00E E E E+00 Te at probe position Te at spectr. position 5.00E E+00 Pospieszczyk, A. et al., Paper P3-097 PSI-conf. 2012, Aachen JNM and: Reinhart, A. et al., Trans. of Fus. Sci. and Techn. 63 May 2013, p E E E+00 T i, (D + ) temperature 0.00E Minor radius, cm radius (cm) Te at Langmuir probe Te at spectrometer Ti at Langmuir probe Ti at spectrometer B2-EIRENE electron and ion temperatures (ev), radial profiles at probe and spectrometer axial positions, case: 0.03 Pa

24 B2-EIRENE (SOLPS4.3), for PSI-2 case-9 Pump 1: 600 l/s D Pa Experiment: 0.03 Pa Pump 2: 1320 l/s D 2

25 B2-EIRENE (SOLPS4.3), for PSI-2, case 9 ~5e18 m -3 Plasma (electron) density Log scale in Plasma colours density, Probe Log scale Spectrometer M.Reinhart el al.

26 #/cm**3 PSI-2, 2500 W, 0.03 Pa, 70 sccm, Less clear experimental plasma density information: 1) Probe data 2) Balmer line ratio 3) Stark broadening (Paschen) 4) Rotational temperature See: M. Reinhart et al. B2-EIRENE plasma density is roughly consistent with Balmer, Stark and rot. Temp. Measurement and YACORA fitting. Simulations indicate: No strong axial variation in n e (except very near to the target) 7.E+12 6.E+12 5.E+12 4.E+12 3.E+12 2.E+12 1.E+12 B2-EIRENE, PSI-2 case 9 PSI-2, ion density profile ne at probe position 0.E radius (cm) at Langmuir probe ne at spectr. position at spectrometer B2-EIRENE electron densities (cm -3 ), radial profiles at probe and spectrometer axial positions, case: 0.03 Pa

27 For experimentally given gas inlet, arc power, pumping speeds, PSI-2 vacuum vessel configuration,. B2-EIRENE (ITER SOLPS version) finds very close Te, gas pressure and plausible plasma densities. Taking this simulation, try careful first modeling answers to: 1 st : what is the positive charge carrier? H + or H 2 + or H 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

28 B2-EIRENE (SOLPS4.3), for PSI-2, case 9 5e18 m -3 Plasma (electron) density Log scale in Plasma colours density, Probe Log scale Spectrometer Log scale, to m -3

29 B2-EIRENE (SOLPS4.3), for PSI-2, case 9 Color code: Log (Density cm-3) H 2 + molecular ion density Scale: X 10 Color code reduced by factor 10 as compared to n e profile. H 3 + and H - still not visible even then (black picture)

30 ratio of minority ion densities to electron density 1.E-01 1.E-02 Ratio D 2+ /D + : 1e-2 1.E-03 1.E-04 1.E-05 Ratio D 3+ /D + : 1e-3 D2+/D+ D3+/D+ D-/D+ 1.E-06 1.E-07 Ratio D - /D + : 1e no. of timesteps B2-EIRENE iteration cycles B2-EIRENE: D 3+, D 2 + and D - stay minority (confirmed even under 10 times lower plasma densities then here, as seen from code density scans).

31 B2-EIRENE (SOLPS4.3), for PSI-2 Color code: Log (Density cm-3) Neutral gas density Atomic comp. Log scale, to m -3

32 B2-EIRENE (SOLPS4.3), for PSI-2 case-9 Color code: Log (Density cm-3) Pump 1 Neutral gas density Molec. Neutral comp. gas H 2 (v=0) density Molecular comp. Pump 2 Log scale, to m -3

33 Color code: Log (Density cm-3) Neutral gas density Molec. comp. H 2 (v=1) Vibr. states v=2,3, are even much less populated Log scale, to m -3

34 Simplifying matters a bit. The density n M of a species M is determined by n 1 n 2 {production of M rate coefficient} =n plasma n M {loss of M rate coefficient} assuming that the M is produced by collisions between species 1 and 2, and destroyed by collisions with plasma (electrons). n M =n 1 n 2 /n plasma x {production of M rate coefficient} {loss of M rate coefficient} Example: M =H 3 +: production: H 2 + H 2 + H H losses: e + H + 3 H 2 +H(n=2) Dissociative recombination, or H+H+H very fast, unless n e very low Caution: Real life is a bit more complicated, non-linearities are involved,. Not yet proven if B2-EIRENE could produce large H + 3 densities, if the conditions would be appropriate for that (never done so far)

35 BUT: Whether a species M has a large effect on plasma or not, depends only on its production rate, not on its loss rate Very minor species can have large effects E.g. p+ H 2 (v=4) H H MAR (with H 2 + precurser) E.g. H 2 + H 2 + H 3 + H 2 + H(n=2) H(n=3) Balmer alpha

36 B2-EIRENE (SOLPS4.3), for PSI-2, case-1 (Berlin) 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 high, 3 body vol.recomb., no MAR

37 B2-EIRENE PSI-2 case 9b, 9 ev arc, double pump 2 Recombination channels, volumetric rates cm -3 s -1, x 2000 Log scale color code: for MAR, for EIR 37

38 #/S/CM2/STERAD (log scale) Post-Processing B2-EIRENE PSI-2 case 9: Line of sight integration of side-on emissivity Ph/s/cm 2 /sterad across full B2-EIRENE solution, at axial spectrometer position H + > H + 2 >H > H 2 >H - >H + 3 H + 2 > H > H 2 >H + >H - >H Balmer_delta E+13 1.E+12 1.E+11 1.E+10 1.E+09 1.E+08 H H+ H2 H2+ H- H3+ total 1.E no. of LOS central r=0.5cm at Te-peak r=2.3 cm boundary r=3.5 cm Big surprises in side-on emissivity contributions. Very low density species can have dominant contribution. Highly case-dependent, unpredictable without transport codes 38

39 ..recent correction in our H,H2,H3.. Database (1 5 scaled from 1 4 Crosses: CCC (Bray, Ralchenko) Dashed: 1993 NF supplement, IAEA Solid lines: new fits Dotted: Johnson

40 Last RCM: see talk by D. Wuenderlich/U Fantz: Problems matching data between R matrix and Johnson semi-empirical formula. The unphysical bump near n=5 disappears, if CCC cross sections are used for excitation to lower n states, rather than the 1993 IAEA data collection. CCC: Bray et al Johnson, semi-empirical) 2002 R Matrix calculations: cross sections lost, only rate coefficients kept (ADAS)

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 the current ITER divertor design code B2-EIRENE (version: SOLPS4.3). Low power partially recombining PSI-2 plasma conditions are well 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 fundamentally different processes (at least for low n e, as in PSI-2) -- sensitivity to surface vibrational kinetics (Eley Rideal process) Outlook: (distinct from tokamaks) Classical drifts and currents are currently introduced. Direct comparison to spectroscopic data is underway simulations of PSI-2 plasmas with synthetic fluctuating backgrounds (blobby transport) to practice for far scrape off layer tokamak modeling 41

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43 3d drift fluid Turbulence simulation CCD camera

44 K: orginal PSI-2 discharge conditions, see Kastelevizcz, Salamagne

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47 Density x 5, compare spectroscopy with and without fluctuations.

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49 Line ratios ok, but total line emissivity is affected by fluctuations (1D,t) CR Models? Our HYDKIN online CR model is either 1D or t-dep)

50 Thank you for your attention! 50

51 Boundary conditions, grid and used model parameters Boundary conditions: Walls perpendicular to the field lines: Sheath conditions Axis of the cylinder: vanishing gradients in T e,t I and n Vacuum-boundary and anode: 1cm decay length in T e,t I and n Parameters: Pumping rate: 3500l/s Neutral influx(d 2 ): 6.32 x s -1 Anomalous diffusion: D in = 3.0m 2 /s; D out = 0.2 m 2 /s Perpendicular heat conduction: κ e,in = 5.0 m 2 /s; κ e,out = 11.0 m 2 /s Source next to anode at given temperature (T e = 15 ev; T I = 5 ev) [1] Kastelewicz, H., & Fussmann, G. (2004). Contributions to Plasma Physics, 44(4),

52 Edge/divertor code simulation of PSI-2 Summary of previous results: [1] Kastelewicz, H., & Fussmann, G. (2004). Contributions to Plasma Physics, 44(4), [2] Vervecken, L. (2010). Extended Plasma Modeling for the PSI-2 Device. Master thesis. KU Leuven [3] Salmagne et al., Report JUEL-4340, April 2012 (ISSN ) 2 nd PMIF, (2011), Juelich, C. Salmagne et al Reproduction of previous numerical and experimental results [2] Dependency on kinetic flux limiter need plasma diagnostic at least at two axial positions to constrain the code model [3] Ambipolarity constraint (j=0) relaxed to j r =0, div(j )=0, target biassing simulations enabled [3] 52

53 Numerical tool for the edge plasma transport: B2-EIRENE code package version: SOLPS4.3: ITER.org (Cadarache) FZ Juelich jointly developed and applied: since about 15 years Self-consistent description of the magnetized plasma, and neutral particles produced due to surface and volume recombination and sputtering see B2: a 2D multi species (e, H +, He +,++, C , ) plasma fluid code Plasma flow Parameters CR codes: HYDKIN A&M data Computational Grid Source terms (Particle, Momentum, Energy) EIRENE: a 3d3v Monte-Carlo multi-species kinetic transport code, incl. radiation transfer. (H,H*,H 2,H 2 (v),h 2 *,H -,H 2+, ) (anything that moves on straight lines between collisions)

54 Governing equations Continuity equation: Parallel momentum equation: Radial momentum equation: 54

55 Governing equations Electron and ion energy equations: 55

56 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 56

57 Potential Energy (ev) H 2 molecule, status in present ITER divertor code E [ev] 16 compiled 1997 H 2 + More complete models available, still need to be integrated 35 compiled since E,F B C 13.6 ev a Resonance b! Singlet v=14 v=3 v=2 v=1 v=0 H 2 c n=3 n=2 Triplet system Courtesy: K. Sawada, for He, He + : T. Fujimoto, M. Goto H 2 + H 2 X 2 g + 1 b 3 u + X 1 g + a 3 g + B 1 u + 2 c 3 u C 1 u E,F 1 + g Internuclear Distance (A) 3 H + + H H*+H n=4 n=3 H + H 4

58 Achieved so far: (L. Vervecken, 2010, Chr. Salmagne 2011) Magnetic grid generation for linear devices re-developed Modelling results from Berlin SOLPS4 (version 1997) reproduced with current ITER SOLPS version (comparison to experiment: H.K., loc.cit.) Some more refined physics activated now in SOLPS4.3 (version 2009 from ITER design review) parallel electr. currents, electr. biasing ( redistribution of power found, 45% increase of target power) first MAR studies (molecular kinetics), neutral-neutral interaction, ( only marginally important in PSI-2, apparently) First experiments in H plasmas for code benchmark: June 2011 (planned) Next, depending on experimental results and availability of students: Drifts and currents (incremental approach) kinetic ions? kinetic electrons (eedf)? More complex chemistry, (hydrogen, hydrocarbons,.) Radiation transport

59 B2-EIRENE modelling for PSI-2 linear plasma device H. Kastelewicz, D. Reiter et al., 23 rd EPS (Kiev), p II-803 (1996) and 24 th EPS (Berchtesgaden), p IV-1805 (1997), reports, conf. proceeding,. Summary of all this: H. Kastelewicz, G. Fussmann Plasma Modelling for the PSI Linear Plasma Device Contrib. Plasma Physics 44 No.4, (2004), then stopped due to retirement of H.K. (2005- ) B2-EIRENE modelling activities at FOM, for Pilot-PSI, and Magnum PSI M. Baeva et al, (PSI 2006 Hefei, Plasma Sci. and Tech., 10, No.2 April 2008), R. Wieggers et al. (see EPS 2008, Hersonissos, and PSI 2010, San Diego) PSI-2 modelling revived in 2010 (joint master student program in TEC) L. Vervecken, M. Baelmans, D. Reiter Extended Plasma Modelling for the PSI-2 Device, (until June 2010), Chr. Salmagne, D. Reiter, M. Baelmans, W. Dekeyer (until Sept. 2011) D. Allerts, M. Baelmans, D. Reiter (until Sept. 2012) Mainly: Edge code training purposes

60 Strong, intermittend fluctuations in PSI-2 (see D. Reiser talk) Do these affect recycling, impurity transport, or can we just use averaged values? No answer today, but 1 st steps to quantify this (Thesis: Samad Mekkaoui, now guest scientist at IEK-4, planned: EFDA fellowship ) Next three slides: Samad s thesis defense, March 2012, Univ. Marseille

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62 Construct from experim. observations (or from Dirk s ATTEMPT simulations) a synthetic stochastic fluctuation model for EIRENE: multivariate Gamma PDF

63 (here: strongly idealized slab model, for which analytic solution exists) Note from Detlev: This agreement is not a surprise, because EIRENE solves the same analytic equation. But it is a verification of both the code and the analytic solution.

64 Note for myself Turb. free = stationary background, no fluctuations in time, but in space maybe a profile, e.g. from B2. This is original eirene background. a=0, with fluctuations, i.e.: this is a case WITH turbulence, But: correl. Length is very small relative to mfp, So: densities in neighboring cells are essentially independent, and averaging then (using ergodic theorem) gives the same solution as in truly turbulence free case. Non trivial conclusion that this is the same, but it is. A=inf: essentially homogeneous plasma (relative to mfp), but entire plasma (spatially const) is fluctuating in time. Strongest effect. Applicable if mfp very short relative to size of turb. structure., e.g. H2

65 PSI-2, standard case 70 sccm at gas inlet, no gas puff high density

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69 #/cm**3 PSI-2, 70 sccm at gas inlet, no gas puff, Te=15eV, Ti=5eV in arc, ni via Eirene 1.E+13 1.E+12 1.E+11 1.E+10 1.E+09 1.E+08 1.E+07 1.E+06 1.E+05 1.E+04 1.E+03 1.E no. of timesteps D D+ D2(v=0) D2+ D3+ D-

70 #/cm**3 PSI-2, 70 sccm at gas inlet, no gas puff, Te=15eV, Ti=5eV in arc, ni via Eirene 1.E+13 1.E+12 1.E+11 1.E+10 1.E+09 D D+ D2(v=0) D2+ D3+ 1.E no. of timesteps