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Application of a multiscale transport model for magnetized plasmas in cylindrical configurationWorkshop on Plasma Material Interaction Facilities

| Christian Salmagne1, Detlev Reiter1, Martine Baelmans2, Wouter Dekeyser2

1 Institute of Energy and Climate Research - Plasma Physics, Forschungszentrum Jülich GmbH2 Dep. of Mechanical Engineering, K.U.Leuven, Celestijnenlaan 300 A, 3001 Heverlee, Belgium

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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

Midplane

Target

Target

Plasma source

Aspect ratio:a/R=∞

topol.equiv.

Direct use of B2-EIRENE (SOLPS) for PSI-2 is possible, but the coordinates have to be adapted

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

Tokamak MAST

linear toroidal

radial radial

polar toroidal

axial poloidal

PSI-2

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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)

Boundary conditions, grid and used parameters

[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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First results did not match old results „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]

Reproducing existing results

FLIM = 0,8

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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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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

Plasma density and temperature also change strongly

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

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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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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

Extension of the neutral Model: MAR

Model [1]

Model I

Model II

Ratio Model I / Model II

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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

[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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Normalized current density:

Normalized heat flux density:

Heat flux and electric current behave exactly asexpected when the potential is changed

Incorporation of parallel electric currents:Code verification

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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 stilllarger 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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Continuity equation:

Parallel momentum equation:

Radial momentum equation:

Governing equations

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Electron and ion energy equations:

Governing equations