Mitglied der HelmholtzGemeinschaft Application of a multiscale transport

Mitglied der Helmholtz-Gemeinschaft Application of a multiscale transport model for magnetized plasmas in cylindrical configuration Workshop on Plasma Material Interaction Facilities 16 October 2021 1 Institute 2 Dep. | Christian Salmagne 1, Detlev Reiter 1, Martine Baelmans 2, Wouter Dekeyser 2 of Energy and Climate Research - Plasma Physics, Forschungszentrum Jülich Gmb. H of Mechanical Engineering, K. U. Leuven, Celestijnenlaan 300 A, 3001 Heverlee, Belgium

Outline 0. Motivation 1. Using the ITER divertor code B 2 -EIRENE for PSI-2 2. Simulation of PSI-2 3. Extension of the numerical model 4. Summary & Outlook 16 October 2021 2

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 B 2 -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. 16 October 2021 3

1. Using the ITER divertor code B 2 -EIRENE for PSI-2 § PSI-2 Jülich § Using the B 2 -EIRENE code for a linear device § Governing equations § Boundary conditions, grid and used parameters 16 October 2021 4

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 e. V § MFP of electrons indicate that fluid approximation is likely to be valid 16 October 2021 5

Use of B 2 -EIRENE code for a linear device Plasma source Midplane topol. equiv. Aspect ratio: a/R=∞ Direct use of B 2 EIRENE (SOLPS) for PSI-2 is possible, but the coordinates have to be adapted linear toroidal radial polar toroidal axial poloidal polar (toroidal) coordinates are neglected (symmetry is assumed) Target Tokamak MAST 16 October 2021 PSI-2 6

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: 1 cm decay length in Te, TI and n § Parameters: § § Pumping rate: 3500 l/s Neutral influx(D 2): 6. 32 x 1019 s-1 Anomalous diffusion: Din = 3. 0 m 2/s; Dout = 0. 2 m 2/s Perpendicular heat conduction: κe, in= 5. 0 m 2/s; κe, out= 11. 0 m 2/s § Source next to anode at given temperature (Te = 15 e. V; TI = 5 e. V) 16 October 2021 [1] Kastelewicz, H. , & Fussmann, G. (2004). Contributions to Plasma Physics, 44(4), 352 -360 7

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 16 October 2021 8

Summary of existing results § Modeling activities in Berlin with former B 2 -EIRENE Version SOLPS 4. 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] 16 October 2021 9

Reproducing existing results § First results did not match old results FLIM = 0, 8 § „flux limiter“ was introduced into B 2 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] 16 October 2021 10

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 16 October 2021 11

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 16 October 2021 12

Refinement 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 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 16 October 2021 13

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 16 October 2021 14

Model [1] Extension of the neutral Model: MAR Ratio Model I / Model II 16 October 2021 § 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 15

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 16 October 2021 16

Incorporation of parallel electric currents § In “extended B 2” [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 16 October 2021 [3] Baelmans, M. (1993). Code Improvements and Applications of a two-dimensional Edge Plasma Model for toroidal Fusion Devices. Katholieke Universiteit Leuven. 17

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 16 October 2021 18

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 16 October 2021 19

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 16 October 2021 20

4. Summary & Outlook § Summary § Numerical model was rebuild and old numerical and experimental results were reproduced using the ITER divertor code B 2 -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. § B 2 -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. 16 October 2021 21

THANK YOU FOR YOUR ATTENTION! 16 October 2021 22

Governing equations § Continuity equation: § Parallel momentum equation: § Radial momentum equation: 16 October 2021 23

Governing equations § Electron and ion energy equations: 16 October 2021 24