Member of the Helmholtz Association
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 – 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
21st International Conference on Plasma Surface Interactions in Controlled Fusion Devices
Kanazawa, Japan, May 26-30 2014
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
2
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
II: target
parallel vs.
(turbulent)
cross field
flow
parallel vs.
chemistry
and PWI
driven flow
Dominant friction: p + H2, detachment3
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
In tokamak edge, all three phenomena
are active everywhere
parallel vs.
(turbulent)
cross field
flow
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
II: target
parallel vs.
chemistry
and PWI
driven flow
Dominant friction: p + H2, detachment4
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
2D fluid flow (Navier Stokes Eqs.
for magnetized plasmas: “Braginskii”)
r, Θ, ignore toroidal Φ dependence
Electrons
Hyd. Ions: H+
3D3V multi species kinetic transport,
Neutral atoms (H, H*)
Typically formulated as Boltzmann eq.,
Neutral molecules (H2, H2(v), H2*) Often solved by Monte Carlo Integration
+,
+,
-
Molecular Ions (H2 H3 H )
Minority species, treated in quasi steady
state (QSS) with other species
+ Impurities: He, C, W, Be, ….,+ their ions and hydride-molecules
5
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
6
Step 1: consider an up down symmetric
double null tokamak. Example: MAST (UK)
Plasma temperature in K
Courtesy: S. Lisgo
For 2D edge codes: a linear device is a
“0 aspect ratio -- infinite pitch torus” .
Plasma source
A quite
counterintuitive
interpretation of
coordinates,
but avoids
duplicating
Midplane
programming
work
topol.
equiv.
linear
radial (toroidal)
radial
polar
coordinates are
polar
toroidal
neglected (symmetry is
axial
poloidal
assumed)
Aspect
ratio:
R/a=0
Target
tokamak
Pitch:
Bpol/Btor=∞
Target
Tokamak
PSI-2
Capitalize on general curvilinear metric formulation, already in place in edge codes
8
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
9
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)
10
 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)
11
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
12
B2-EIRENE for PSI-2, low power, partially
recombining plasma (2500 W, 0.03Pa)
Te, radial-axial
Colours:
Electron
0 – 15 eV
input
parameters:
H.Kastelewicz et al..
CPP (2004)
Temperatur New runs:
New pumping
configuration,
Gas inlet,
70sccm
Low arc power
(2500 W)
13
Not PSI-2 is upright, but the code’s
X-Y coordinates are...
Probe data
Spectroscopic data
14
B2-EIRENE, for PSI-2, low power, partially
recombining plasma: Te (eV)
Electron
Temperatur
Probe data
Spectroscopic data
15
PSI-2, 2500 W, 0.03 Pa, 70 sccm, Te (eV)
Langmuir Probe, Te
B2-EIRENE, PSI-2
PSI-2, electron temperature profile
9.00E+00
8.00E+00
Te at probe position
7.00E+00
Te at spectr. position
6.00E+00
eV
5.00E+00
4.00E+00
3.00E+00
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)
2.00E+00
Ti, (D+) temperature
(not measured)
1.00E+00
0.00E+00
0
1
2
3
Minor radius, cm
radius (cm)
Te at Langmuir probe
Te at spectrometer
4
Ti at Langmuir probe
5
6
Ti at spectrometer
B2-EIRENE electron and ion temperatures (eV),
radial profiles at probe and spectrometer
axial positions, case: 0.03 Pa
16
B2-EIRENE, PSI-2, neutral gas pressure [Pa]
Pump 1: 600 l/s D2
0.02
Pa
Experiment:
0.033 Pa
Pump 2: 1320 l/s D2
17
Axial variation of gas pressure [Pa], w/o plasma
measured
EIRENE, nominal pump speeds
Axial positions
of pumps
18
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%
19
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
20
Gas Pressure PH2
Distinct from tokamaks:
 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
Plasma conditions: ne, Te, vi, Qe,i, …
21
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]
22
Axial variation of gas pressure [Pa], w/o plasma
measured
EIRENE, nominal pump speeds
EIRENE, exp. pumping speeds
Axial positions
of pumps
23
•
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”.
24
B2-EIRENE, PSI-2, electron density
Plasma (electron)
density
Log scale inPlasma
colours
density,
Log scale
Probe
~5e18
m-3
Spectrometer
“plausible“ from
other considerations
Colour code 1e11 – 1e13 cm-3
25
Less clear experimental plasma density
information: 1) Probe data 2) Balmer line ratio
PSI-2, ion density profile
B2-EIRENE, PSI-2,
electr. density
7.E+12
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
6.E+12
5.E+12
#/cm**3
B2-EIRENE plasma can be
made roughly consistent with
Balmer line ratio fitting
(see below).
4.E+12
3.E+12
ne at probe position
2.E+12
1.E+12
0.E+00
0
1
2
3
4
5
6
radius (cm)
at Langmuir probe
at spectrometer
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)
26
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…
27
B2-EIRENE , PSI-2, electron density
Plasma (electron)
density
Log scale inPlasma
colours
density,
Log scale
Probe
5e18
m-3
Spectrometer
Log scale, 1017 to 1019 m-3
28
B2-EIRENE, PSI-2, H2+ density
Color code:
H2+ molecular
ion density
Log (Density cm-3)
Colour Scale:
X 10
Color code
reduced by
factor 10 as
compared to
ne profile.
H3+ and H- still
“not visible”
even then
(black picture)
H2+ is the key player in hydrogen plasma chemistry: MAR, H3+ formation,…
29
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 of minority ion densities to electron density
1.E-01
Ratio D2+/D+: 1e-2
1.E-02
1.E-03
Ratio D3+/D+: 1e-3
D2+/D+
D3+/D+
D-/D+
1.E-04
1.E-05
1.E-06
Ratio D-/D+: 1e-5
1.E-07
0
50
100
150
no. of timesteps
200
250
300
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).
30
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
31
B2-EIRENE @ PSI-2
Recombination channels, volumetric rates cm-3s-1
e+H+
 H + hʋ
e+e+H+  H + e
e+H2(v)  H + HH- + 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 32
ITER
MAR in lin. Devices: NAGDIS, Ohno et al, PRL 81 (1998)
H2 molecule, status in present
SOLPS-ITER code
More complete modes are
available  identify „as simple
as possibel“ model for edge codes
initially compiled 1997
E [eV]
35
H2+
16
14
E,F
C
a
B
c
n=2
10
13.6 eV
8
Resonance
!
b
6
v=14
4
··
·
2
v=3
v=2
v=1
v=0
0
Singlet
H2 Triplet system
Courtesy: K. Sawada, Shinshu Univ. Jp.
Potential Energy (eV)
12
30
n=3
3
+
3
a g c u
25
H2
+
2
X g
20
+
+
H+H
H*+H
15
1
10
3
b u
H2
5
1
X g
0
0
1
C u
+
1
+
1
B u E,F g
n=4
n=3
+
H+H
+
2
3
Internuclear Distance (A)
4
33
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+ > H3+
H2+ > H > H2 >H+ >H- >H3+
Balmer_delta
32
62
#/S/CM2/STERAD (log scale)
1.E+13
1.E+12
H
H+
H2
H2+
HH3+
total
1.E+11
1.E+10
1.E+09
1.E+08
1.E+07
1
2
3
4
5
6
7
8
no. of LOS
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)
Big surprises in side-on emissivity
contributions. Very low density species
can have dominant contribution.
Highly case-dependent, perhaps
Unpredictable without transport codes
34
Balmer series spectroscopy in linear devices
http://open.adas.ac.uk/adf13
Measured
Line ratio
4.5
(typical for
PISCES,
PSI-2
35
Problem with some
ADAS versions
before 2000 (still
online)
EIRENE database
H + e H* +e
H+ + e  H* +….
36
e + H2+  H* + H
37
e+H3+  H*+..
e+H2  H* +..
38
H-
+..  H* + ..
Labels refer
to EIRENE online
A&M database:
www.hydkin.de
39
H+
MAst
MAST
H2+, H3+
H‾
H*
H
Inter
stellar
clouds
H2
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
40
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 41
Thank you for your attention!
42