Mitglied der Helmholtz-Gemeinschaft
Application of a multiscale transport
model for magnetized plasmas in
cylindrical configuration
Workshop on Plasma Material Interaction Facilities
13. April 2015
1 Institute
2 Dep.
| Christian Salmagne1, Detlev Reiter1, Martine Baelmans2, Wouter Dekeyser2
of Energy and Climate Research - Plasma Physics, Forschungszentrum Jülich GmbH
of Mechanical Engineering, K.U.Leuven, Celestijnenlaan 300 A, 3001 Heverlee, Belgium
Outline
0. Motivation
1. Using the ITER divertor code B2-EIRENE for
PSI-2
2. Simulation of PSI-2
3. Extension of the numerical model
4. Summary & Outlook
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0. Motivation
 Linear plasma device PSI-2 has been transferred from Berlin
to FZJ last year.
 The modeling activities carried out in Berlin are not usable
anymore and are rebuild in Jülich, using the ITER divertor
code B2-EIRENE.
 Modeling of PSI-2 creates the possibility of an additional
analysis of a plasma that resembles the edge plasma of a
Tokamak in important points.
 That gives the opportunity to verify and improve the Code
with another type of experiment.
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1. Using the ITER divertor code
B2-EIRENE for PSI-2
 PSI-2 Jülich
 Using the B2-EIRENE code for a linear device
 Governing equations
 Boundary conditions, grid and used parameters
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PSI-2 Jülich
 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 valid
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Use of B2-EIRENE code for a linear device
Plasma source
Midplane
topol.
equiv.
Aspect
ratio:
a/R=∞
Direct use of B2EIRENE (SOLPS)
for PSI-2 is
possible, but the
coordinates have to
be adapted
linear
toroidal
radial
radial
polar
toroidal
axial
poloidal
polar (toroidal)
coordinates are
neglected (symmetry
is assumed)
Target
Target
Tokamak MAST
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PSI-2
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Boundary conditions, grid and used
parameters
 First aim: Reproduction of radial profiles using all existing
information about the simulation from Berlin [1]
 Boundary conditions:
 Walls perpendicular to the field lines: Sheath conditions
 Axis of the cylinder: vanishing gradients in Te,TI and n
 „Vacuum-boundary“ and anode: 1cm decay length in Te,TI and n
 Parameters:




Pumping rate: 3500l/s
Neutral influx(D2): 6.32 x 1019 s-1
Anomalous diffusion: Din = 3.0m2/s; Dout = 0.2 m2/s
Perpendicular heat conduction: κe,in= 5.0 m2/s; κe,out= 11.0 m2/s
 Source next to anode at given temperature
(Te = 15 eV; TI = 5 eV)
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[1] Kastelewicz, H., & Fussmann, G. (2004). Contributions to Plasma Physics, 44(4), 352-360
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2. Simulation of PSI-2
 Summary of existing results:
 [1] Kastelewicz, H., & Fussmann, G. (2004). Contributions to Plasma
Physics, 44(4), 352-360
 [2] Vervecken, L. (2010). Extended Plasma Modeling for the PSI-2
Device. Master thesis. KU Leuven
 Reproduction of existing numerical and experimental results
 Dependency on kinetic flux limiter
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Summary of existing results
 Modeling activities in Berlin with former B2-EIRENE Version
SOLPS4.0, 1995, Summary can be found in [1]
 In [2] the model was rebuild, old results could already be
partially reproduced.
 Figures: Radial profiles at two different positions, Coefficients
for anomalous transport adapted to fit experiment
[1]
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Reproducing existing results
 First results did not match old results
FLIM = 0,8
 „flux limiter“ was introduced into B2 to compensate kinetic
effects
 Parallel heat conductivity is limited to:
with parameter FLIM
 Different values of FLIM found in old input
 It is not possible to reconstruct, which value was used in [1]
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Dependency on kinetic flux limiter
 Dependency on the flux limiter indicates the importance of
kinetic effects
 Additional free parameter influencing the parallel transport
 Experimental values at at least two axial positions needed
 Values for the flux limiter can be obtained using the comparison
with experimental data or a complete kinetic model of PSI-2
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3. Extension of the numerical model
 Extension of the neutral particle model using a collisional
radiative model an metastable states
 Incorporation of parallel electric currents
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Refinement
Extension of the neutral model
 Model [1]: neutral model as used in [1]
 Model I: Collisional radiative model for H2+ and H2
 Model II: Vibrationally excited states treated as metastable
 Particle and heat fluxes on the neutralizer plate strongly
depend on the used model
Heatflux [W]
Particle flux [s-1]
Model [1]
274.8
1.21 x 1020
Model I
224.2
1.45 x 1020
Model II
318.9
1.73 x 1020
 Plasma density and temperature also change strongly
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Extension of the neutral
Model: Recombination
 Reaction rates show that
H2+-MAR is the most
important
recombination channel
 Most recombination takes
place at neutralizer and
cathode
 3 body recombination
and radiative
recombination are
unimportant in the model
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Model [1]
Extension of the neutral
Model: MAR
Ratio Model I / Model II
Model I
Model II
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 H2+-MAR rates also
depend on the used
model
 With Model I rates are
overestimated in the
target chamber and
underestimated at the
anode
 Vibrationally excited
states have to be
modeled as metastable
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Incorporation of parallel electric currents
 The plasma potential is not calculated and the potential drop is
only important for the heat flux, and thus for the boundary
condition for the electron energy.
 For equal electron and ion temperatures it can be approximated
as:
 Since the variation with the temperatures is small, the potential
drop is provided as a constant input parameter
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Incorporation of parallel electric currents
 In “extended B2” [3] currents are incorporated. Then, the
potential drop depends on the current and changes to:
 That also changes the electron energy flux
 In this version the possibility to set the wall potential for each
wall differently exists.
 That makes it possible to bias the neutralizer wall
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[3] Baelmans, M. (1993). Code Improvements and Applications of a two-dimensional Edge Plasma Model for
toroidal Fusion Devices. Katholieke Universiteit Leuven.
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Incorporation of parallel electric currents:
Code verification
 Normalized current density:
 Normalized heat flux density:
 Heat flux and electric
current behave exactly as
expected when the
potential is changed
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Incorporation of parallel
electric currents
 When no potential is
applied, the direction of
the current is
depending on the radial
position
 The direction of the
electric currents can be
influenced by changing
the potential at the
neutralizer plate
 Direct influence of
strong current densities
on the electron
temperature can be seen
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Incorporation of parallel electric currents
 Ion temperature and plasma density do not change
significantly
 Electric current on the neutralizer plate changes and reaches a
saturation for negative potentials of the neutralizer
 Heat flux on the wall also changes and has a minimum near
the floating potential
 Minimal heat flux still
larger than in case of
disabled currents
 Heatflux not minimal,
if total current vanishes
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4. Summary & Outlook
 Summary
 Numerical model was rebuild and old numerical and experimental results
were reproduced using the ITER divertor code B2-EIRENE.
 A dependency on the kinetic flux limiter was found.
 The neutral particle model was improved and it was shown that the correct
treatment of the vibrationally excited states is crucial in the model.
 B2-EIRENE can account for parallel electric currents in a linear machine
 Outlook:
 Classical drifts and diamagnetic currents will be introduced.
 Experimental data is needed to compare target biasing effects and to cope
with the dependency on the kinetic flux limiter.
 Neutral particle simulation can be further extended. The model of the
reactions at the walls has to be checked.
 Impurities will be introduced.
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Thank you for your attention!
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Governing equations
 Continuity equation:
 Parallel momentum equation:
 Radial momentum equation:
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Governing equations
 Electron and ion energy equations:
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