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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

Tokamak edge transport studies using linear plasma devices

21st 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, Germany2 - Department of Mechanical Engineering, Katholieke Universiteit Leuven, Celestijnenlaan 300A, 3001 Leuven, Belgium3 - Center for Energy Research, University of California at San Diego, La Jolla, CA, USA

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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

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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 fieldflow

parallel vs.chemistry and PWIdriven flow

div(nv║)+div(nv┴)= ionization/recombination/charge exchange

Dominant friction: p + H2, detachment

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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 fieldflow

parallel vs.chemistry and PWIdriven flow

div(nv║)+div(nv┴)= ionization/recombination/charge exchange

Dominant friction: p + H2, 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 threeprocesses.

Linear plasma devices often operate in theadvection-reaction dominated regime

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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

ElectronsHyd. Ions: H+

Neutral atoms (H, H*)Neutral molecules (H2, H2(v), H2*)

Molecular Ions (H2+, H3

+, 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

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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

Plasma temperature in KCourtesy: S. Lisgo

Step 1: consider an up down symmetric double null tokamak. Example: MAST (UK)

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Midplane

Target

Target

Plasma source

Aspect ratio:R/a=0

Pitch:Bpol/Btor=∞

topol.equiv.

A quite counterintuitive interpretation of coordinates,but avoids duplicating programming work

polar (toroidal) coordinates are neglected (symmetry is assumed)

Tokamak

linear tokamak

radial radial

polar toroidal

axial poloidal

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

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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 chemistryvs. parallel flow

2D parallel-radial plasma flow, plus 3D kinetic gas-plasma reactions

Gas inflow

Pump

plasma energy source (arc)

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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)

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[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

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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

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B2-EIRENE for PSI-2, low power, partially recombining plasma (2500 W, 0.03Pa)

ElectronTemperatur

inputparameters: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

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Probe dataSpectroscopic data

Not PSI-2 is upright, but the code’sX-Y coordinates are...

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B2-EIRENE, for PSI-2, low power, partially recombining plasma: Te (eV)

ElectronTemperatur

Probe data

Spectroscopic data

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PSI-2, electron temperature profile

0.00E+00

1.00E+00

2.00E+00

3.00E+00

4.00E+00

5.00E+00

6.00E+00

7.00E+00

8.00E+00

9.00E+00

0 1 2 3 4 5 6

radius (cm)

eV

Te at Langmuir probe Te at spectrometer Ti at Langmuir probe Ti at spectrometer

Pospieszczyk, A. et al., J. Nucl. Mat, 438 (2013) Paper P3-097PSI-conf. 2012, Aachenand:M.Reinhart et al, Trans. Fus. Sci. Techn. 63(May 2013)

PSI-2, 2500 W, 0.03 Pa, 70 sccm, Te (eV)Langmuir Probe, Te B2-EIRENE, PSI-2

Te at probe positionTe at spectr. position

Minor radius, cm

Ti, (D+) temperature (not measured)

B2-EIRENE electron and ion temperatures (eV),radial profiles at probe and spectrometer axial positions, case: 0.03 Pa

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0.02 Pa

Pump 2: 1320 l/s D2

Pump 1: 600 l/s D2

Experiment:0.033 Pa

B2-EIRENE, PSI-2, neutral gas pressure [Pa]

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Axial variation of gas pressure [Pa], w/o plasma

Axial positionsof pumps

EIRENE, nominal pump speeds

measured

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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.

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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 loweredpumping speed165 l/s

Effective pumping speedfrom exp. w/o plasma 330 l/s

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Plasma conditions: ne, Te, vi, Qe,i, …

Gas

Pre

ssur

e P

H2

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:

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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 pumpsquite too high, compared to actual values

P_H2, EIRENE, [Pa]

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Axial variation of gas pressure [Pa], w/o plasma

Axial positionsof pumps

EIRENE, nominal pump speeds

measured

EIRENE, exp. pumping speeds

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•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”.

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Plasmadensity,Log scale

B2-EIRENE, PSI-2, electron density

Plasma (electron)densityLog scale in colours

~5e18m-3

Probe

Spectrometer

“plausible“ fromother considerations

Colour code 1e11 – 1e13 cm-3

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PSI-2, ion density profile

0.E+00

1.E+12

2.E+12

3.E+12

4.E+12

5.E+12

6.E+12

7.E+12

0 1 2 3 4 5 6

radius (cm)

#/cm

**3

at Langmuir probe at spectrometer

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

ne at probe position

ne at spectr. positionB2-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 ofcode results, even ifprobe plasma flux (Jsat) 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: PH2 (exp.=calculated), scan arc power fraction to plasma, to match Jsat, rely on spectroscopy to sort out Te, ne

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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…

Robust trends & interpretation of spectroscopy

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Plasmadensity,Log scale

B2-EIRENE , PSI-2, electron density

Plasma (electron)densityLog scale in colours

5e18m-3

Probe

Spectrometer

Log scale, 1017 to 1019 m-3

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B2-EIRENE, PSI-2, H2+ density

H2+ molecular

ion densityColor codereduced by factor 10 as compared tone profile.

H3+ and H- still

“not visible”even then(black picture)

Color code:

Log (Density cm-3)

Colour Scale: X 10

H2+ is the key player in hydrogen plasma chemistry: MAR, H3

+ formation,…

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ratio of minority ion densities to electron density

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

0 50 100 150 200 250 300

no. of timesteps

D2+/D+D3+/D+D-/D+

B2-EIRENE iteration cycles

Ratio D2+/D+: 1e-2

Ratio D3+/D+: 1e-3

Ratio D-/D+: 1e-5

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 EIRENEis quite “reduced” only compared to specialized A&M codes).

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))

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PlasmaPressure

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+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

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B2-EIRENE @ PSI-2 Recombination channels, volumetric rates cm-3s-1

Volumetric rates (cm-3/s) Log scale color code: 1013 – 1017 for MAR, 1012 – 5 1013 for EIRDominant role of MAR in PSI-2, same code that predicts its absence in ITERMAR in lin. Devices: NAGDIS, Ohno et al, PRL 81 (1998)

x 2000

e+H+ H + hʋe+e+H+ H + e

e+H2(v) H + H-

H- + p H + Hp+H2(v) H2

+ + He+H2

+ H + H

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initially compiled 1997

H2 molecule, status in presentSOLPS-ITER code

13.6 eVResonance ! H*+H

Courtesy: K. Sawada, Shinshu Univ. Jp.

35

30

25

20

15

10

5

0

Pote

ntia

l En

ergy

(eV

)

43210Internuclear Distance (A)

H2

X1g+

b3u+

X2g+

H2+

n=3n=4

E,F1g+

a3g+

B1u+

C1u

c3u

H++ H

H + H

More complete modes areavailable identify „as simpleas possibel“ model for edge codes

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> H3+

Balmer_delta

1.E+07

1.E+08

1.E+09

1.E+10

1.E+11

1.E+12

1.E+13

1 2 3 4 5 6 7 8

no. of LOS#/

S/CM

2/ST

ERAD

(log

sca

le)

HH+H2H2+H-H3+total

Post-Processing B2-EIRENE PSI-2 Line of sight integration of side-on emissivity Ph/s/cm2/steradacross full B2-EIRENE solution, at axial “spectrometer position”(absolute radiances, line ratios: similar to PSI-2 exp. (within 50%) [4]

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centralr=0.5cm

at Te-peakr=2.3 cm

boundaryr=3.5 cm

H2+ >H > H2 >H- >H+ H2

+ > H > H2 >H+ >H- >H3+

Big surprises in side-on emissivitycontributions. Very low density species can have dominant contribution. Highly case-dependent, perhaps Unpredictable without transport codes

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[4] Pospieszczyk,A., Reinhart,M., J. Nucl. Mat 438 (2013)

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Balmer series spectroscopy in linear devices

Measured Line ratio4.5(typical forPISCES,PSI-2

http://open.adas.ac.uk/adf13

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EIRENE database

Problem with some ADAS versionsbefore 2000 (stillonline)

H + e H* +e

H+ + e H* +….

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e + H2+ H* + H

38

e+H3+ H*+..

e+H2 H* +..

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H- +.. H* + ..Labels referto EIRENE onlineA&M database:www.hydkin.de

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H*

H+

H

H2+, H3

+

H2

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

Interstellar clouds

Role of H2+, H3+ in PISCES-A, by mass spectroscopy: E. Hollmann, A. Pigarov, PoP 9, (2002)

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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 (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

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Thank you for your attention!