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1 第 12 回若手研究会那珂核融合研究所 2009 年 3 月 日 原子力機構におけるトカマク統合 コードの開発と最近の研究成果 林伸彦 本多充 清水勝宏 濱松清隆 滝塚知典 小関隆久 星野一生 原子力機構
2 Introduction Issues of fusion burning plasmas: Control of plasmas with strong complexity and autonomy Multi-scale Physics Consit of the wide spacial scale and the time scale Consist of complexibility and self-organization Recurring Process Bulk plasma determines a-heating profile, -heating profile determines the bulk plasma profile Nonlinearity: multi equilibrium point, bifurcation, discontinuity Steady-state control -heating external heating: Reduction of heating power for the control Bootstrap current externally driven current: Reduction of CD and momentum input for the control Existence of the steady state solution, controllability, stiffness
3 Background To progress the research of burning plasma, it is necessary to understand complex features of the advanced tokamak plasmas. Because, in the steady state, plasma has very wide time scale and spatial scale, and it has complex physics such as turbulence, transport, MHD, wave-particle interaction, plasma-wall interaction, atomic and molecular physics, and so on [s] - Timescales High freq. wave EC, LH, IC Turbulence MHD event Island evolu. Current diffus. Energy confinement Discharge, Plasma-wall Exploration and understand of the complex plasma are big issues. High confinement, high beta, high bootstrap fraction, high radiation fraction, control of ash and impurity, -heating, etc. Control of the complex plasma are also serious issues. Strong coupling of each physics mechanism, i.e. autonomous plasmas Modeling and integration of models are useful means for the understand and the prediction of the burning plasma.
4 Strategy of Modeling / Integration of model To make the integrated model, validation is necessary based on the fundamental researches of experiment and simulation. JT-60 high beta steady state experiments - High confinement - High beta - High bootstrap fraction - High radiation fraction - Control of ash and imp. - Plasma-wall interaction - High energy particles etc. Simulation based on the first principle - Turbulence simulation - MHD simulation - Divertor simulation Validation of Modeling and Integration Modelling and Integration of model of Transport models, MHD models, Particle models, CD/Heating model, etc Core plasma model Edge/Pedestal model SOL/Divertor model Understand and prediction of the complex plasma
5 Integrated modeling in JAEA Core plasma Edge/pedestal SOL/Divertor Momentum Wave Core MHD stability: Sawtooth, NTM Heat/particle transport: ITB Current drive Wave-particle interaction -Heating, Energetic particles Pedestal transport: ETB Edge MHD stability: ELM SOL transport, recycling SOL/Divertor plasma transport Neutral particles Impurity particles Interaction with wall, A & M Plasma rotations Radial electric field J B torque RF Heating: IC Alfvén Eigenmode: TAE, RSAE Fokker-Planck TOPICS-IB: TOPICS extended to the Integrated modeling for Burning plasma SONIC: SOLDOR/ NEUT2D/ IMPMC TASK: DP/FP WM/TX Burning plasma integrated code
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7 Integrated modeling in JAEA Core plasma Edge/pedestal SOL/Divertor Momentum Wave Core MHD stability: Sawtooth, NTM Heat/particle transport: ITB Current drive Wave-particle interaction -Heating, Energetic particles Pedestal transport: ETB Edge MHD stability: ELM SOL transport, recycling SOL/Divertor plasma transport Neutral particles Impurity particles Interaction with wall, A & M Plasma rotations Radial electric field J B torque RF Heating: IC Alfvén Eigenmode: TAE, RSAE Fokker-Planck TOPICS-IB: TOPICS extended to the Integrated modeling for Burning plasma SONIC: SOLDOR/ NEUT2D/ IMPMC TASK: DP/FP WM/TX Burning plasma integrated code
8 TOPICS-IB (TOPICS extended to Integrated simulation for Burning plasmas) TOkamak Prediction and Interpretation Code System - 1D transport & 2D MHD equilibrium - Time-dependent / Steady-state analysis of JT-60U experiment - Simulation with transport model Neoclassical : MI method or NCLASS, Anomalous : CDBM, GLF23, MMM95 Components and Related codes - NB & High energy particle : 1D or 2D FP, 3D Monte-Carlo (OFMC) - EC : Ray tracing & Relativistic FP (EC-Hamamatsu) - MHD : Kink / Ballooning / Peeling (MARG2D) - Impurity : 1D transport (IMPACT), 2D Monte-Carlo (IMPMC) - Neutral : 2D Monte-Carlo - Radiation : Synchrotron (CYTRAN) - SOL / Div. : Five-point model (D5PM), 2D Fluid & Monte-Carlo (SONIC) Recent works - Core-SOL-div. integration for ELM study (loss & cycle) (Hayashi, IAEA08) - Integration with 1d1v FP code of particles (Ozeki, Hamamatsu, JSPF08)
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10 Simulation of ELM energy loss and cycle 1.5D core transport ( TOPICS ) ELM model Linear MHD stability ( MARG2D ) Core neutrals (2D Monte-Calro) Newly integrated for density dynamics SOL-divertor (D5PM) Neutral model
11 Integrated modeling reproduces the collisionality dependence of ELM energy loss. ELM energy loss in the follwoing ELMs deviates a little from that at first ELM, but the collisionality dependence is almost the same. As found in the first ELM (H-modeWS07), the following physics cause the dependence. - Electron : Bootstrap current broadens the region of ELM enhanced transport and SOL parallel conductive transport decreases the SOL temperature in the low collisionality. (NF07) - Ion : Ti > Te in the low collisionality due to the ineffectiveness of equipartition, which enhances ion convective and CX losses. Reduction of total energy loss is comparable with that in experiments.
12 Integrated Simulation of ELM Energy Loss and Cycle in Improved H-mode Plasmas ( Hayashi, IAEA08 ) - Integrated code TOPICS-IB clarified that steep pressure gradient inside the pedestal top broadens the region of ELM enhanced transport and enhances the ELM energy loss. - Transport model of pedestal neoclassical transport connected to SOL parallel transport reproduces the experimentally observed collisionality dependence of inter-elm transport. Inter-ELM energy confinement time agrees with JT-60U scaling HH98y2~1.3
13 Energetic particle loss by AE modes E MA/1.7T, E NNB ~390 (kev) P NNB Frequency (khz) Neutron emission rate (10 15 n/s) reduction rate (MW) amplitude (a. u.) (1) (3) RSAE TAE measurement calculation (A) (1) 2 > q mn > time (s) (B) weak AEs AE modes in a weak shear plasma w/w A RSAE r/a r/a (A) Sn reduced in 20~30% when AE modes existed. Degradation of high energy particles (B) Measured Sn was close to the OFMC calculation: ~ classical confinement w/w A (3) q mn < 1.5 q mn = 1.4 TAE Reduction rate of Sn increased in AE mode flucuation Plausible candidate is MHD resonance particle loss.
14 Simulation of Autonomous and Recurrence Process Heating / CD Impurity transport Edge pedestal / Divertor plasma Fusion reaction Core Plasma Heating He ash TOPICS code -particle birth -particle transport F-P code P AE mode Anomalous transport (AE code)
15 -particle birth and transport model by K.Hamamatsu f (v,,t) : Velocity distribution function of alphas t f (v,,t) + 1 D v, D NC (v, ) D NC (v, ) = ( ) f + V AN ( v, )f D(v, ) = D NC (v, ) + D AN (v, ) D AN (v, )&V AN (v, ) C j ( f ) S(v, ) L( f ) : Neo-classical like diffusion 2 2 b, b = 1 + eff 2v cos p, eff = (v), = R 0, (v) v : velocity, : minor radius = C j ( f ) + S(v, ) L( f ) j 2D Fokker-Planck Equation : Anomalous diffusion & convection model of the resonance with MHD instability : Collision term colliding with j-th bulk plasma n s ( ) and T s ( ) are calculated by TOPICS-IB : Particle source by fusion reaction and NBI : Loss term removes slowed down particles L( f ) = f (v,,t) th ( ) exp m v 2, T ash ( ) is constant. =3 in this case th ( ) : thermal collison time : Pitch angle scat. time
16 Simulation of F-P equation for fixed background Effects of the anomalous transport on the -particle pressure/heating Assumption: : neo-classical like -diffusion, the anomalous by the MHD fluctuation and zero flow velocity Time trace and profiles for the simulation with (red) and without(green) anomalous On of anomalous: p max > p on Off of anomalous: p max < p off
17 Integrated simulation results Critical gradient of pressure (2.0) (1.0) (1.5) (0.5)
18 Integrated modeling in JAEA Core plasma Edge/pedestal SOL/Divertor Momentum Wave Core MHD stability: Sawtooth, NTM Heat/particle transport: ITB Current drive Wave-particle interaction -Heating, Energetic particles Pedestal transport: ETB Edge MHD stability: ELM SOL transport, recycling SOL/Divertor plasma transport Neutral particles Impurity particles Interaction with wall, A & M Plasma rotations Radial electric field J B torque RF Heating: IC Alfvén Eigenmode: TAE, RSAE Fokker-Planck TOPICS-IB: TOPICS extended to the Integrated modeling for Burning plasma SONIC: SOLDOR/ NEUT2D/ IMPMC TASK: DP/FP WM/TX Burning plasma integrated code
19 Integrated Divertor Code for Fusion Reactor To investigate the power and particle control in tokamak reactor, integrated divertor codes have been developed. The MC approach has an advantage to the flexibility of modelling. Plasma: Fluid Gyro-motion ==> Erosion Neutrals ==> Methane breakup Kinetic effect ==> Thermal force Plasma: Fluid prediction Neutrals: Monte Carlo Impurities: MC Interpretation Neutrals: Monte Carlo Impurities: Fluid But should solve MC problems, Long CPU, MC noise, Steady-state.
![Integrated Divertor Code in JAEA The elaborate impurity Monte Carlo code (IMPMC) has been successfully combined with divertor code [1].](/docs-images/99/143067569/images/20-0.jpg "D ion [2] PARASOL PIC + Monte Carlo - Kinetic effect - Collision - Sheath, Drift - Transport etc. SONIC [3] D neutral C impurity interaction [1] K. Shimizu, et al., 17th PSI (2006). [2] T.")
20 Integrated Divertor Code in JAEA The elaborate impurity Monte Carlo code (IMPMC) has been successfully combined with divertor code [1]. D ion [2] PARASOL PIC + Monte Carlo - Kinetic effect - Collision - Sheath, Drift - Transport etc. SONIC [3] D neutral C impurity interaction [1] K. Shimizu, et al., 17th PSI (2006). [2] T. Takizuka, et al., 15th PSI (2002). [3] H. Kawashima, et al., Plasma Fusion Res (2006). IMPMC uses (1) Diffusion model using Langevin analytical solution to extend time step, (2) MPI with many particles to reduce MC noise, (3) Particle reduction scheme to obtain steady state.
21 Simulation of X-point MARFE with SONIC To reduce the high heat load onto the divertor plate, the control method for impurity retention in the divertor region should be established. SONIC simulations reproduced the formation of X-point MARFE in JT-60U discharge with high heating NBI power. MW/m P NBI attached D 2 puff JT-60U experiment (PNB=15~20MW) time detached Xp MARFE dome attached plasma detached plasma X-point MARFE SONIC simulation (PNB=15MW) Hydrocarbons sputtered from the dome contribute to the enhanced radiation near the X-point.
22 Plan of integration core transport i, Q i, Q e TOPICS, TASK hierarchical coupling SlimCS PWI 1. Coupling with core transport 2. Including plasma wall interactions EDDY IMPMC SOLDOR NEUT2D MD simulation species-elements integration SONIC hierarchical coupling
23 EDDY/IMPMC Simulation Plasma ion irradiation on material surfaces Dynamic erosion and deposition processes Impurity transport in near-surface plasma dissociation processes of hydrocarbons: 700 reactions! C x H y,x=1,2,3 (R.K.Janev, D.Reiter, Rep.FZ-Juelich, Jul-3966 (2002); Jul-4005 (2003)) for Methane Breakup Model EDDY CH 4 Chemical erosion C x H y C x H y H Carbon tile Redeposited layer Comparison with the observed erosion distribution: a small sticking of hydrocarbons and erosion yield of on the outer divertor plate. To investigate migration of carbon in large scale and contamination process into the main plasma, EDDY IMPMC
![9 10 20 m -3, T ed = 17 ev) number density 1/16 [1/mm 2 ] EDDY/ IMPMC CD 4 => C + CD 4 => C + In detached plasma, simple model is](/docs-images/99/143067569/images/24-4.jpg "relatively good approximation simple ionization sticking coef. = 0.")
24 Comparison with Simple Methane Breakup detached inner divertor (n ed = m -3, T ed = 1.7 ev) attached outer divertor (n ed = m -3, T ed = 17 ev) number density 1/16 [1/mm 2 ] EDDY/ IMPMC CD 4 => C + CD 4 => C + In detached plasma, simple model is relatively good approximation simple ionization sticking coef. = 0.2 C => C + C => C + In attached plasma, the methane breakup can not be simplified The dome with a small sticking coefficient enhances the contam- ination of carbon into the main plasma.
25 Integrated modeling in JAEA Core plasma Edge/pedestal SOL/Divertor Momentum Wave Core MHD stability: Sawtooth, NTM Heat/particle transport: ITB Current drive Wave-particle interaction -Heating, Energetic particles Pedestal transport: ETB Edge MHD stability: ELM SOL transport, recycling SOL/Divertor plasma transport Neutral particles Impurity particles Interaction with wall, A & M Plasma rotations Radial electric field J B torque RF Heating: IC Alfvén Eigenmode: TAE, RSAE Fokker-Planck TOPICS-IB: TOPICS extended to the Integrated modeling for Burning plasma SONIC: SOLDOR/ NEUT2D/ IMPMC TASK: DP/FP WM/TX Burning plasma integrated code
26 M. Honda and A. Fukuyama, J. Comp. Phys. 227 (2008) 2808 TASK/TX Electron Thermal ion two-fluid equations NCLASS viscosity Continuity equation Equation of motion Thermal transport equation Two-group neutrals Beam ion TF ripple untrapped trapped Diffusion equation Continuity equation Equation of motion Continuity equation source profile Maxwell s equations background background OFMC draw orbit EPOC
27 Toroidal rotation induced by charge separation Motivation 1) Ionization of fast neutrals from NB produces electrons and fast ions. 2) Owing to the toroidal drift, the trapped ion especially deviates from the birth flux surface. 3) The charge separation continues as long as NB is injected, causing local charge imbalance. 4) A radial current flows in the bulk plasma to maintain quasi-neutrality. 5) A resultant j B torque drives the toroidal rotation. TASK/TX simulations with OFMC have reproduced the toroidal rotation by charge separation due to near perpendicular NBI. have clarified that horizontally-injected NB (case (a)) drives the rotation most efficiently. important Banana width and magnetic field at birth position TASK/TX results with source profiles by OFMC JT-60U-like parameters M. Honda et al., 2008 Fusion Energy Conf., TH/P8-15
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31 Summary Core integrated code TOPICS-IB - Core-SOL-div. integration for study of ELM loss & cycle - Integration with 1d1v FP code for study of AE modes effect on particle confinement Divertor integrated code SONIC - IMPMC-EDDY integration for study of methane breakup effect on X-point MARFE Two-fluid core code TASK/TX - TASK/TX -OFMC integration for study of toroidal rotation induced by charge separation of fast ions (due to ripple & perpendicular NBI).
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SUMMARY Japan is one of the most earthquakeprone country in the world, and has repeatedly experienced serious major damages. No matter how serious the impact of earthquake disasters, each and every time,