Integrated Transport Simulation Aiming at Burning Plasmas

Transcription

1 Workshop on Transport and Confinement NIFS University, 2006/11/09 Integrated Transport Simulation Aiming at Burning Plasmas A. Fukuyama and M. Honda Department of Nuclear Engineering, Kyoto University Contents Status of BPSI ans TASK Status of Burning Plasma Simulation (Kessel, IAEA) Advanced transport simulation: TASK/TX (Honda) Summary

2 Burning Plasma Simulation Simulation describing a burning plasma: Whole plasma (core & edge & diverter & wall-plasma) Whole discharge (startup & sustainment & transients events & termination) Reasonable accuracy (validation with experimental data) Reasonable computer resources (still limited) Target of BPSI Framework for collaboration of various plasma simulation codes Physics integration with different time and space scales Advanced technique of computer science

3 Integrated Code Development Based on BPSI Framework Integrated code: TASK and TOPICS NIFS Universities JAEA BPSI TASK/3D TASK TOPICS HINT MEGA GNET GRM OFMC MARG2D - - -

4 TASK Code Features Core of Integrated Modeling Code in BPSI Modular structure Reference data interface and standard data set Various Heating and Current Drive Scheme EC, LH, IC, AW, NB High Portability Development using CVS (Concurrent Version System) Open Source (V1.0: Fortran95, Parallel Processing using MPI Library Extension to Toroidal Helical Plasmas

5 Modules of TASK EQ 2D Equilibrium Fixed/Free boundary, Toroidal rotation TR 1D Transport Diffusive transport, Transport models WR 3D Geometr. Optics EC, LH: Ray tracing, Beam tracing WM 3D Full Wave IC, AW: Antenna excitation, Eigen mode FP 3D Fokker-Planck Relativistic, Bounce-averaged DP Wave Dispersion Local dielectric tensor, Arbitrary f (u) PL Data Interface Data conversion, Profile database LIB Libraries LIB, MTX, MPI Under Development TX Transport analysis including plasma rotation and E r Collaboration with TOPICS EQU Free boundary equilibrium NBI NBI heating

6 Modular Structure of TASK

7 Recent progress in TASK code WM/FP/DP Development of Self-Consistent Wave Analysis EQ/TR Transport Simulation for ITER Benchmark test for ITER Hybrid/SS scenario (Kessel) TX EQU/NBI 3D Dynamical Transport Simulation including Rotation Common Module Interface Collaboration with NIFS

8 Self-Consistent Wave Analysis with Modified f(u) Modification of velocity distribution from Maxwellian Absorption of ICRF waves in the presence of energetic ions Current drive efficiency of LHCD NTM controllability of ECCD (absorption width) Self-consistent wave analysis including modification of f (u)

9 Development of Self-Consistent Wave Analysis Code Development in TASK Ray tracing analysis with arbitrary f (v): Already done Full wave analysis with arbitrary f (v): Completed Fokker-Plank analysis of ray tracing results: Already done Fokker-Plank analysis of full wave results: Almost competed Self-consistent iterative analysis: Preliminary Tail formation by ICRF minority heating Momentum Distribution Tail Formation Power deposition PPERP 10 0 F2 FMIN = E+01 FMAX = E P abs with tail Pabs [arb. unit] P abs w/o tail PPARA p**2 r/a

10 ITER H-mode Scenario

11 ITER Advanced Scenario Hybrid scenario I p = 12 MA, P NB = 33 MW Steady state I p = 6 9MA

12 Benchmark Test for ITER Hybrid Scenario C.E. Kessel et al.: IAEA2006 IT/P1-7 (ITPA/SSO) Codes: CRONOS, ONETWO, TSC/TRANSP, TOPICS, ASTRA

13 Benchmark Test for ITER Steady-State Scenario Codes: TOPICS, CRONOS, TSC/TRANSP

14 Motivation of TASK/TX Transport Simulation including Core and SOL Plasmas Role of Separatrix Closed magnetic surface Open magnetic field line Difference of dominant transport process Transient Behavior of Plasma Rotation Radial Electric Field: Radial force balance, (Poisson equation) Poloidal rotation: Equation of motion Toroidal rotation: Equation of motion Equation of motion rather than transport matrix Analysis including Atomic Processes

15 1D Transport code: TASK/TX Dynamic Transport Equation: Fukuyama et al. PPCF (1994) A set of flux-surface averaged equations Two fluid equation for electrons and ions Continuity equation Equation of motion (radial, poloidal, toroidal) Energy transport equation Neoclassical transport Poloidal viscosity Turbulent transport Ambipolar diffusion through poloidal momentum transfer Thermal diffusivity, Perpendicular viscosity Maxwell s equation, Poisson s equation Slowdown equation for beam component Diffusion equation for neutral particles

16 Transport Model Neoclassical transport Poloidal viscosity radial transport, resistivity, bootstrap current, Ware pinch Hirshman and Sigmar NCLASS Turbulent Diffusion Perpendicular momentum exchange between electron and ion Non-bipolar flux (electron flux = ion flux) F W eθ = Fiθ W = e2 B 2 φd e n e T e F W eφ = F W iφ = e2 B 2 φd e T e ( u eθ B ) θ u eφ, B φ ( B θ n e u eθ B ) θ u eφ B φ B φ Perpendicular viscosity, Thermal diffusivity,

17 Model of Scrape-Off Layer Plasma Particle, momentum and ion heat losses along the field line Decay time in a sound velocity time scale ν L = C s 2πqR Electron heat loss Decay time in a thermal diffusion time scale χ ν L = (2πqR) 2 Recycling from diverter Recycling rate: γ 0 = 0.8 fixed density and temperature at diverter Gas puff from wall, NBI, Charge exchange

18 Electron flux Steady State Flux (1) Inertia term in the equation of motion = 0 Radial flux u er = α ν e + ν ei n e m e Ω 2 eφ [ dpe dr + dp ] i dr α E φ α B θ 1 + α F w θ n e m e Ω eφ + 1 ν e u 1 + αω iθ + eφ α B φ ν eb (u 1 + α B θ Ω bφ u iφ ) eφ where α ν e + ν ei B 2 θ ν ei + ν eb B 2, ν eb = n bm b ν n φ e m be e Poloidal neoclassical viscosity ν e Factor α represents parallel neoclassical viscosity First three terms in RHS are neoclassical diffusion, Ware pinch and turbulent diffusion.

19 Steady State Flux (2) Toroidal current { 1 1 e u eφ = E φ + 1 B θ ν e + ν ei ν ei + ν eb 1 + αm e 1 + α B φ n e m e Ω eφ [ dpe dr + dp ] i dr + 1 B θ Fθ w + ν e B θ u 1 + α B φ n e m e 1 + α B iθ φ ( ν eb α ) ( 1 + α ν ei u bφ ν ei + α ) } 1 + α ν eb u iφ The first two terms in RHS are neoclassical resistivity and bootstrap current Similar expression for poloidal rotation Model equations include dominant neoclassical transport.

20 Recent Update of TASK/TX Numerical scheme Finite element method (Linear interpolation, radial variable) Streamline Upwind Petrov-Galerkin (SUPG) method Choice of variables and boundary conditions Improvement of numerical stability Increase of spatial resolution Neoclassical poloidal viscosity Hirshman, Sigmar NCLASS SOL plasma model Electron heat loss: Thermal diffusion

21 Neoclassical Effects Comparison of resistivity and bootstrap current Value Estimated from the steady state flux Value calculated by NCLASS Resistivity Bootstrap current TASK/TX NCLASS 0.12 TASK/TX NCLASS η [Ω m] 10 6 j BS [MA/m 2 ] r/a (a) 0.00 r/a (b)

22 Neoclassical Transport (without turbulent transport) Density Radial electric field n e (r) [10 20 m-3] E r (r) [kv/m] u er (r) [m/s] N 0 (r) [10 14 m -3 ] r/a Radial velocity 0 r/a Neutral density

23 Typical Profiles (D e : fixed parabolic profile) E r (r) [kv/m] n e (r) [10 20 m -3 ] u er (r) [m/s] u ir (r) [m/s] q(r) E θ (r) [mv/m] E φ (r) [V/m] B θ (r) [T] T e (r) [kev] u eθ (r) [km/s] u iθ (r) [km/s] j eφ (r) [MA/m 2 ] T i (r) [kev] u eφ (r) [km/s] u iφ (r) [km/s] B φ (r) [T] SLOW N 0 (r) [10 14 m -3 ] FAST N 0 (r) [10 10 m -3 ] D i (r)+d e (r) [m 2 /s] = χ [m 2 i =μ e = μ i /s]

24 Density Peaking Due to Momentum Input Density peaking was observed in NBI counter injection on JT60-U. Ref. Takenaga et al. (ITPA, 2005) n e ( m -3 ) co-injection : n e (r/a=0.2)/ <n e >=1.4 1 P IN =8.4MW, P ABS =6.3MW, P LOS S FAST /P IN =0.26, H H 98(y,2) =0.8 6 ctr-injection : n e (r/a=0.2)/ <n e >=1.7 4 P IN =10.2MW, P ABS =6.5MW, P LOS S FAST /P IN =0.38, H H 98(y,2) = r/a T e ( kev ) r/a T i ( kev ) r/a

25 Density Peaking Simulation (TASK/TR: old version) Transport model: CDBM (particle diffusivity, thermal diffusivity) NBI 6.5MWwas injected 50 ms after the simulation started. Simulation results n(0) for co injection is 12% higher than that for counter inj. Temperature is higher for counter injection experiments CO CTR

26 Extension to TASK/3D 3D Equilibrium: Interface to equilibrium data from VMEC or HINT Interface to neoclassical transport coefficient codes Modules 3D-ready: WR: Ray and beam tracing WM: Full wave analysis Modules to be updated: TR: Diffusive transport (with an appropriate model of E r ) TX: Dynamical transport (with neoclassical toroidal viscosity) FP: Fokker-Planck analysis (with helical ripple trapping) Modules to be added: (by Y. Nakamura) EI: Time evolution of current profile in helical geometry

27 Future Plan of TASK code Present Status In 2 years In 5 years Equlibrium Fixed/Free Boundary Equilibrium Evolution Start Up Analysis Core Transport 1D Diffusive TR Kinetic TR 2D Fluid TR 1D Dynamic TR SOL Transport 2D Fluid TR Plasma-Wall Interaction Neutral Tranport 1D Diffusive TR Orbit Following Energetic Ions Kinetic Evolution Orbit Following Wave Beam Ray/Beam Tracing Beam Propagation Full Wave Kinetic ε Gyro Integral ε Orbit Integral ε Stabilities Sawtooth Osc. Tearing Mode Systematic Stability Analysis ELM Model Resistive Wall Mode Turbulent Transport CDBM Model Linear GK + ZF Nonlinear ZK + ZF Diagnostic Module Control Module

28 Summary We are developing TASK code as a reference core code for burning plasma simulation based on transport analysis. Preliminary results of self-consistent analysis of wave heating and current drive describing the time evolution of the momentum distribution function and its influence on the wave propagation and absorption have been obtained. Simulations of ITER advanced scenarios requires further benchmark tests Dynamical transport module TASK/TX was significantly improved on the numerical scheme and the transport model. Barrier formation and density modification will be studied. Extension to 3D configuration is on-going in collaboration with Dr. Y. Nakamura and NIFS.

29 Model Equation (1) Fluid equations (electrons and ions) n s t = 1 r r (rn su sr ) + S s t (m sn s u sr )= 1 r r (rm sn s u 2 sr ) + 1 r m sn s u 2 sθ + e sn s (E r + u sθ B φ u sφ B θ ) r n st s t (m sn s u sθ )= 1 r 2 r (r2 m s n s u sr u sθ ) + e s n s (E θ u sr B φ ) + 1 ( r 3 n r 2 s m s μ s r r +F NC sθ ( ) 1 ms n s u sφ = t r + F C sθ + FW sθ + FX sθ + FL sθ r (rm sn s u sr u sφ ) + e s n s (E φ + u sr B θ ) + 1 r r ( ) rn s m s μ s r u sφ ) u sθ r t 3 2 n st s = 1 r +F C sφ + FW sφ + FX sφ + FL sφ ( ) 5 r r 2 u srn s T s n s χ s r T e + e s n s (E θ u sθ + E φ u sφ ) +P C s + P L s + P H s

30 Model Equation (2) Diffusion equation for (fast and slow) neutral particles Maxwell s equation 1 E θ c 2 t n 0 t B θ t = 1 r 1 r r ( ) n 0 rd 0 r r (re r) = 1 ɛ 0 = E φ r, = r B φ μ 0 e s n s u sθ, s B φ t s = 1 r 1 E φ c 2 t e s n s + S 0 r (re φ) = 1 r r (rb θ) μ 0 e s n s u sφ s