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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. - PowerPoint PPT Presentation
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Mem
ber
of
the H
elm
holt
z
Associa
tion
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
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
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
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 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
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-)
+ 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
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)
8
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
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 chemistryvs. parallel flow
2D parallel-radial plasma flow, plus 3D kinetic gas-plasma reactions
Gas inflow
Pump
plasma energy source (arc)
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
[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
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)
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
14
Probe data
Spectroscopic data
Not PSI-2 is upright, but the code’sX-Y coordinates are...
15
B2-EIRENE, for PSI-2, low power, partially recombining plasma: Te (eV)
ElectronTemperatur
Probe data
Spectroscopic data
16
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 position
Te 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
17
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]
18
Axial variation of gas pressure [Pa], w/o plasma
Axial positionsof pumps
EIRENE, nominal pump speeds
measured
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
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
21
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:
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 pumpsquite too high, compared to actual values
P_H2, EIRENE, [Pa]
23
Axial variation of gas pressure [Pa], w/o plasma
Axial positionsof pumps
EIRENE, nominal pump speeds
measured
EIRENE, exp. pumping speeds
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
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
26
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
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 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
28
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
29
B2-EIRENE, PSI-2, H2+ density
H2+ molecular
ion density
Color 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,…
30
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))
31
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
32
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
33
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
)
43210
Internuclear 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
34
> 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/C
M2/
ST
ER
AD
(lo
g s
cale
)
H
H+
H2
H2+
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]
62
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
32
[4] Pospieszczyk,A., Reinhart,M., J. Nucl. Mat 438 (2013)
35
Balmer series spectroscopy in linear devices
Measured Line ratio4.5(typical forPISCES,PSI-2
http://open.adas.ac.uk/adf13
36
EIRENE database
Problem with some ADAS versionsbefore 2000 (stillonline)
H + e H* +e
H+ + e H* +….
37
e + H2+ H* + H
38
e+H3+ H*+..
e+H2 H* +..
39
H- +.. H* + ..Labels referto EIRENE onlineA&M database:www.hydkin.de
40
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)
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 (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
Thank you for your attention!