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

17. April 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

17. April 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.

17. April 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

17. April 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: m -3 < n < m -3, T e < 30 eV  MFP of electrons indicate that fluid approximation is likely to be valid

17. April 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

17. April  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 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),

17. April Simulation of PSI-2  Summary of existing results:  [1] Kastelewicz, H., & Fussmann, G. (2004). Contributions to Plasma Physics, 44(4),  [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

17. April 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]

17. April  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

17. April 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

17. April Extension of the numerical model  Extension of the neutral particle model using a collisional radiative model an metastable states  Incorporation of parallel electric currents

17. April 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] x Model I x Model II x Refinement

17. April 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

17. April  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

17. April 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

17. April 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.

17. April  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

17. April 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

17. April 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

17. April 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.

17. April Thank you for your attention!

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

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