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17. April 2015 Mitglied der Helmholtz-Gemeinschaft Application of a multiscale transport model for magnetized plasmas in cylindrical configuration Workshop on Plasma Material Interaction Facilities | Christian Salmagne 1, Detlev Reiter 1, Martine Baelmans 2, Wouter Dekeyser 2 1 Institute of Energy and Climate Research - Plasma Physics, Forschungszentrum Jülich GmbH 2 Dep. of Mechanical Engineering, K.U.Leuven, Celestijnenlaan 300 A, 3001 Heverlee, Belgium

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17. April 20152 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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17. April 20153 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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17. April 20154 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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17. April 20155 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: 10 17 m -3 < n < 10 20 m -3, T e < 30 eV MFP of electrons indicate that fluid approximation is likely to be valid

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17. April 20156 Use of B2-EIRENE code for a linear device Midplane 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 lineartoroidal radial polartoroidal axialpoloidal PSI-2

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17. April 20157 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 T e,T I and n „Vacuum-boundary“ and anode: 1cm decay length in T e,T I and n Parameters: Pumping rate: 3500l/s Neutral influx(D 2 ): 6.32 x 10 19 s -1 Anomalous diffusion: D in = 3.0m 2 /s; D out = 0.2 m 2 /s Perpendicular heat conduction: κ e,in = 5.0 m 2 /s; κ e,out = 11.0 m 2 /s Source next to anode at given temperature (T e = 15 eV; T I = 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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17. April 20158 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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17. April 20159 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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17. April 201510 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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17. April 201511 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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17. April 201512 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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17. April 201513 Extension of the neutral model Model [1]: neutral model as used in [1] Model I: Collisional radiative model for H 2 + and H 2 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]274.81.21 x 10 20 Model I224.21.45 x 10 20 Model II318.91.73 x 10 20 Refinement

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17. April 201514 Extension of the neutral Model: Recombination Reaction rates show that H 2 + -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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17. April 201515 H 2 + -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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17. April 201516 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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17. April 201517 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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17. April 201518 Normalized current density: Normalized heat flux density: Heat flux and electric current behave exactly as expected when the potential is changed Incorporation of parallel electric currents: Code verification

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17. April 201519 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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17. April 201520 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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17. April 201521 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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17. April 201522 Thank you for your attention!

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17. April 201523 Continuity equation: Parallel momentum equation: Radial momentum equation: Governing equations

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17. April 201524 Electron and ion energy equations: Governing equations

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