Benchmarking Fluid and Kinetic Neutral Models for Attached and Detached State M. Furubayashi a , K. Hoshino e , M. Toma a , A. Hatayama a , D. Coster b , R. Schneider c , X. Bonnin d , H. Kawashima e , N. Asakura e , and Y. Suzuki e P3-26 18th International Conference on Plasma Surface Interactions, May 26-30, 2008, Toledo, Spain a Graduate School of Science and Technology, Keio University, Kanagawa, Japan b Max-Planck-Institut fur Plasmaphysik, Garching, Germany d LIMHP-CNRS, Universite Paris 13, Villetaneuse, France c Max-Planck-Institut fur Plasmaphysik, Greifswald, Germany e Naka Fusion Institute, Japan Atomic Energy Agency, Ibaraki, Japan Introduction Simulation Code 3.2 3.6 4.0 4.4 4.8 2.8 2.4 2.0 -1.6 -1.2 -0.8 -0.4 0 0.4 0.8 1.2 1.6 Z(m) R(m) c l N N CX T n v = Neutral Model Neutrals are treated just like ions by B2.5 Neutrals are assumed to have the same temperature as ions Numerical Mesh of JT-60U D + , C + -C 6+ Ion Species EIRENE : Neutral Monte-Carlo code Basic Eq. : Boltzmann Eq. D, D2, C Kinetic Neutral Model Neutral Species : D, C Fluid Neutral Model Neutral Species : B2.5 : 2D Multi Fluid code Basic Equation Ion Continuity Eq. Ion and Electron Momentum Eq. Ion and Electron Energy Balance Eq. Current Continuity Eq. 2 m s / = D 03 . = = c c ^ ^ i e 20 . 2 m s / Transport Model Parallel Transport : Classical Transport Radial Transport : Anomarous Transport Energy Transport Coefficient Diffusion Coefficient ¢ = + () G G G 1 4 2 nv Fig. 1 Numerical Mesh Energy Transport Coefficient Diffusion Coefficient D n n T m cx i in e i N = + ( ) -1 s s Particle Flux G n D n x =- ¶ ¶ Neutral Flux Limiter Diffusion Approximation Boundary Conditions Divertor Plate Bohm Condition Wall Side l T = 1cm Decay Length for n and T G =anC s m -2 s -1 Particle Flux Core Interface Boundary tot Q al i e Q Q ( ) = = 2.5MW Total Energy Input G r = 0 m -2 s -1 Particle Flux Ion Density n D core = · 1.0-3.6 10 19 m -3 -1.2 -1.6 -1.4 2.8 3.0 3.2 3.4 R(m) Z(m) Optimization of Parameters of Fluid Neutral Model Some parameters of the fluid neutral model are changed from the kinetic neutral model to fit the mid-plane profile. Fig. 2 The radial profiles at upstream [4] B2-E : B2-EIRENE run B2-DCHe : "original" B2 run NEW : "optimized" B2 run Follwing recommendations from Ref.[4] are used to fit the mid-plane profile: In addition, to fit the radial profile of the electron density, feedback boundary condition for neutral particles is used for wall side boundary condition. This boundary condition adjusts the incoming neutral flux from the wall to fit the electron density of the outer mid-plane separatrix (1) use a core neutral loss boundary condition rather than a zero flux boundary condition (2) use a neutral flux limiter Conclusion [5] K. Hoshino, et al., J.Nucl. Mater. 48 (2008) 136-140. References [1] R. Schneider, et al., Contrib. Plasma Phys. 46 (2006) 3-191. [2] V. Rozhansky, et al., Contrib. Plasma Phys. 40 (2000) 423-430. [6] V. Rozhansky, et al., Contrib. Plasma Phys. 41 (2001) 328. [3] D. Reiter, et al., J.Nucl. Mater. 220-222 (1995) 987. [4] D. Coster, et al., Phys. Scr. T 108 (2004) 7. Kinetic Neutral Model Fluid Neutral Model (c) ncore = 3.6x10 19 [m -3 ] Distance from Separatrix [cm] Poloidal Electron Energy Flux (x10 5 W m -2 ) 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 0 8 12 16 4 (b) ncore = 1.5x10 19 [m -3 ] Distance from Separatrix [cm] Poloidal Electron Energy Flux (x10 5 W m -2 ) 0 2 4 6 8 10 12 0 8 12 16 4 (a) ncore = 1.0x10 19 [m -3 ] Distance from Separatrix [cm] 0 2 4 6 8 10 12 14 Poloidal Electron Energy Flux (x10 5 W m -2 ) 0 8 12 16 4 Kinetic Neutral Model Fluid Neutral Model (a) ncore = 1.0x10 19 [m -3 ] 0 40 80 120 160 Electron Temperature [eV] 0 8 12 16 4 Distance from Separatrix [cm] (c) ncore = 3.6x10 19 [m -3 ] Distance from Separatrix [cm] 0 2 4 6 8 10 12 Electron Temperature [eV] 0 8 12 16 4 (b) ncore = 1.5x10 19 [m -3 ] 0 30 60 90 Distance from Separatrix [cm] Electron Temperature [eV] 0 8 12 16 4 Atomic Density (Fluid Model) Atomic Density (Kinetic Model) Molecular Density (Kinetic Model) Atomic Density (Kinetic with common background) Molecular Density (Kinetic with common background) Neutral Density [m -3 ] Distance from Separatrix [cm] 10 16 10 17 10 18 10 19 10 20 (a) ncore = 1.0x10 19 [m -3 ] 0 8 12 16 4 Distance from Separatrix [cm] Neutral Density [m -3 ] 10 16 10 17 10 18 10 19 10 20 (b) ncore = 1.5x10 19 [m -3 ] 0 8 12 16 4 Distance from Separatrix [cm] Neutral Density [m -3 ] 10 16 10 17 10 18 10 19 10 20 (c) ncore = 3.6x10 19 [m -3 ] 0 8 12 16 4 Kinetic Neutral Model B2.5-Eirene Fluid Neutral Model B2.5 -1.0 -1.2 -1.4 -1.6 2.8 3.0 3.2 3.4 Molecular Density D2 (m -3 ) R (m) Z (m) -1.0 -1.2 -1.4 -1.6 2.8 3.0 3.2 3.4 Atomic Density D (m -3 ) R (m) Z (m) -1.0 -1.2 -1.4 -1.6 2.8 3.0 3.2 3.4 Atomic Density D (m -3 ) R (m) Z (m) 1e19 7e18 3e18 1e18 7e17 3e17 1e17 7e16 3e16 1e19 7e18 3e18 1e18 7e17 3e17 1e17 7e16 3e16 Kinetic Neutral Model B2.5-Eirene Fluid Neutral Model B2.5 -1.0 -1.2 -1.4 -1.6 2.8 3.0 3.2 3.4 Molecular Density D2 (m -3 ) R (m) Z (m) -1.0 -1.2 -1.4 -1.6 2.8 3.0 3.2 3.4 Atomic Density D (m -3 ) R (m) Z (m) -1.0 -1.2 -1.4 -1.6 2.8 3.0 3.2 3.4 Atomic Density D (m -3 ) R (m) Z (m) Electron Temperature at the Outer Divertor Plate Neutral Density at the Outer Divertor Plate Distribution of Neutrals in the Divertor Region Poloidal Electron Energy Flux at the Outer Divertor Plate Pressure Balance Fig. 3 Electron temperature profiles at the divertor plate with the core density of (a) 1.0x10 19 [m -3 ], (b) 1.5x10 19 [m -3 ], (c) 3.6x10 19 [m -3 ] Fig. 6 Neutral density profiles at the divertor plate with the core density of (a) 1.0x10 19 [m -3 ], (b) 1.5x10 19 [m -3 ], (c) 3.6x10 19 [m -3 ] Fig. 7 Density distribution of neutrals with the core density of 1.0x10 19 [m -3 ] Fig. 8 Density distribution of neutrals with the core density of 3.6x10 19 [m -3 ] Fig. 4 Poloidal electron energy flux profiles at the divertor plate with the core density of (a) 1.0x10 19 [m -3 ], (b) 1.5x10 19 [m -3 ], (c) 3.6x10 19 [m -3 ] Fig. 5 Pressure profiles at the divertor plate with the core density of (a) 1.0x10 19 [m -3 ], (b) 1.5x10 19 [m -3 ], (c) 3.6x10 19 [m -3 ]. The profile at the divertor plate is mapped to the mid-plane along the magnetic field. - When the core boundary density is 1.0x10 19 m -3 , both of the results are in attachment condition. - As the core density increases, the peak of the kinetic model moved outward. - When the core boundary density is 3.6x10 19 m -3 , the kinetic model has a lower energy flux to the divertor, making it easier to realize the detachment condition. - When the core boundary D+ density is 1.0x10 19 m -3 both of the results are in attachment condition. - When the core density is high, the kinetic model is in the detach state. - When the core boundary D+ density is 1.0x10 19 m -3 both of the results were in attachment condition. - When the core density is higher, the kinetic model is in the detach state, and the tendency differed. - At the divertor plate, the density of molecules is higher than atoms. The effect of molecules may be more dominant than atoms. - Kinetic neutral model has a higher density of neutrals, making it easier to detach. - The tendency of the atomic density differs even if use the same common background plasma. - The fluid neutral model has a high density of atoms in the outer-side of the divertor region. - The kinetic neutral model has a higher density of neutrals in the private region. Simulation Result Kinetic Neutral Model (Divertor Plate) Kinetic Neutral Model (Mid-Plane) Fluid Neutral Model (Mid-Plane) Fluid Neutral Model (Divertor Plate) 0 Pressure [Pa] Distance from Separatrix [cm] 50 100 150 200 250 (a) ncore = 1.0x10 19 [m -3 ] 0 2 3 4 1 0 Distance from Separatrix [cm] Pressure [Pa] 50 100 150 200 250 300 350 (b) ncore = 1.5x10 19 [m -3 ] 0 2 3 4 1 Distance from Separatrix [cm] Pressure [Pa] 0 350 (c ) ncore = 3.6x10 19 [m -3 ] 50 100 150 200 250 300 0 2 3 4 1 - Most of the edge plasma transport codes treat neutral particles by a fluid model or a kinetic model. - In this study, benchmarking of the fluid and kinetic neutral model is made by using the 2-D edge plasma code, SOLPS [1]. - Fluid Neutral Model (B2.5) [2] Fluid Model is easier to prove convergence, and simulation cost is low. - Kinetic Neutral Model (B2.5-EIRENE) [3] Kinetic Treatments by the Monte-Carlo method are more exact than the fluid model. - Benchmarks of the kinetic neutral model (B2.5-EIRENE), and the fluid model (B2.5) was done in Ref. [4,5]. However, the benchmark studies of neutral model were limited to the case in detach case. - In this study, benchmark has been made in detach and attach state. To benchmark both detached and attached case we changed the value of the core boundary D+ density in a wide range. - However, in the divertor region, large differences were observed in the plasma profiles. - The value of the electron temperature is higher than the kinetic neutral model. - The energy flux profiles at the divertor plate, matched quite well when both of them are in the attached state, but as the core density increases, the tendency differs. - The pressure profiles at the divertor plate from the fluid model are high, even if the core density is high. Further improvement or optimization of fluid neutral model should be made to reproduce the reasonable divertor characteristics. Otherwise the kinetic neutral model should be used for neutrals to analyze the divertor region especially in the detached state. - Kinetic neutral model and fluid neutral model has been benchmarked under the attached and detached state, using the SOLPS code. - To attain both conditions, we changed the value of the core boundary D+ density in a wide range. - To benchmark the profiles at the divertor region, the upstream profiles are carefully fitted. - Therefore, the fluid model could not reproduce the detachment condition. - To consider the cause, we focused on the neutral profiles. - At the divertor plate, densities of molecules are higher than the density of atoms. The effect of molecules may be more dominant than atoms in the divertor plate. However, the fluid neutral model doesn't consider the molecular effects. - The tendency of the neutral distribution differs. A thin layer of molecules appears in the kinetic neutral model and the fluid model has a higher density of atoms in the outer-side of the divertor region. - The difference in the tendency appears even if we use the same background plasma profiles. - Therefore, we may need to consider the effect of molecules and optimize the neutral source terms, diffusion coefficients, transport coefficients, and the flux limits of ions and neutrals.