Application of a multiscale transport model for magnetized plasmas in cylindrical configuration

1. Application of a multiscale transport model for magnetized plasmas in cylindrical configuration Workshop on Plasma Material Interaction Facilities | Christian Salmagne1, Detlev Reiter1, Martine Baelmans2, Wouter Dekeyser2 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

2. Outline 0. Motivation • Using the ITER divertor code B2-EIRENE for PSI-2 • Simulation of PSI-2 • Extension of the numerical model • Summary & Outlook

3. 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.

4. 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

5. 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

6. Use of B2-EIRENE code for a linear device 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) Plasma source Midplane topol. equiv. Aspect ratio: a/R=∞ Target Target Tokamak MAST PSI-2

7. 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) • [1] Kastelewicz, H., & Fussmann, G. (2004). Contributions to Plasma Physics, 44(4), 352-360

8. 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

9. 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]

10. Reproducing existing results • 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] FLIM = 0,8

11. 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

12. Extension of the numerical model • Extension of the neutral particle model using a collisional radiative model an metastable states • Incorporation of parallel electric currents

13. Extension of the neutral model Refinement • 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

14. 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

15. Model [1] Extension of the neutral Model: MAR • 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 Ratio Model I / Model II Model I Model II

16. 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. 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.

18. Incorporation of parallel electric currents:Code verification • Normalized current density: • Normalized heat flux density: • Heat flux and electric current behave exactly asexpected when the potential is changed

19. 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

20. 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

21. 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.

22. Thank you for your attention!

23. Governing equations • Continuity equation: • Parallel momentum equation: • Radial momentum equation:

24. Governing equations • Electron and ion energy equations: