integrated modelling and simulation of toroidal...
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Integrated Modelling and Simulation of Toroidal Plasmas
Atsushi Fukuyama Department of Nuclear Engineering, Kyoto University
!!!
7th ITER International School on High performance computing in fusion science
Aix-Marseille University, Aix-en-Provence, France 2014-08-28
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Outline
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1. Integrated modelling of toroidal plasmas
2. Data exchange in integrated simulation
3. Integrated tokamak modelling code TASK
4. Various level of transport modelling
5. Full wave analysis in toroidal plasmas
6. Summary
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Integrated Simulation of Toroidal Plasmas
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In order to ! predict the performance of future fusion devices ! optimize their operation scenario ! contribute to acceptable design of DEMO reactor
We need a reliable tool to describe Whole plasma ! core, edge, scrape-off layer, divertor
plasmas, and plasma-wall interactions
Whole discharge period ! startup, sustainment, probabilistic
incidents, and shut down
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Use Case of Integrated Modelling
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Device design phase Prediction of performance Specification of components
Before experiment Prediction of time evolution Optimization of operation scenario
During experiment Real time analysis Between shot analysis
After experiment Systematic analysis of experimental data Validation of physics models
Next device Conceptual design Development of control system
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Modelling of Toroidal Plasmas
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Energetic Ion Confinement
Transport Barrier
MHD Stability
Turbulent Transport
Impurity Transport
SOL Transport
Divertor Plasma
Core Transport
Non-Inductive CD
RF Heating
NBI Heating
Neutral Transport
Plasma-Wall Int.
Blanket, Neutronics, Tritium,
Material, Heat and Fluid Flow
1mm
1m
1Hz1kHz1MHz1GHz
LHEC
ICMHD Transport
Turbulence
Heating
TIME
LENG
TH NBI
Broad range of time scale 100 GHz ~ 1000 s
Broad range of spatial scale: 10 "m ~ 10 m
Various phenomena in toroidal plasmas
One simulation code cannot cover all range.
Wide range of time scale, spatial scale, and understanding ! Integrated simulation combining modelling codes ! Various levels of physics model
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Structure of Integrated Modelling
GT5D
MEGA
MD
HINT2
Fixed boundary
Free boundary
Time evolution
Diffusive transport
Dynamic transport
Kinetic transport
MHD stability
Kinetic stability
Ray/beam tracing
Full wave
Kinetic model
Fluid model
Particle orbit
Equilibrium:
Core Plasma Transport:
Global Stability:
Source:
Peripheral Plasma Transport:
Turbulent Transport
Plasma Deformation
Neutral Transport
Impurity Transport
Pellet
Neoclassical Transport
Wave: IC, LH, EC
Magnetic Island
Turbulent Transport
Plasma-Wall Interaction
Integrated Modeling
Rotation, Anisotropy
Energetic Particles
Control model
Diagnostic model
Neutral Transport
Impurity Transport
Radiation Transport
Linear Stability
Pellet ablation
NBI
Radiation Transport
Collisional Transport
Particle model
3D MHDEquilibrium
Turbulence Simulation
Nonlinear MHD
Turbulence Simulation
Material Simulation 6
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Structure of Toroidal Plasma Simulation
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device data
coil current
Equilibrium
pressure prof.current prof.
1D equ. data
2D equ. data
Coretransport
Global instability
spatial prof.density, rotation,
temperature
Wave structure
wave field
Velocity distrib. fnc.
spatial prof.heating, fueling, driven current
Coil control
Pellet & NBI injection
profile modification
Peripheraltransport
particle, energyflux
edge densitytemperature
deposition prof.
device data
device data
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Desired features of Integrated CodeModular structure ‣ Easier maintenance of components
•Addition of new models, update of old models ‣ Various levels of analyses:
•Quick, Standard, Precise, Rigorous
Unified interface ‣ Data set for information exchange ‣ Program interface for data exchange ‣ File interface for data storage ‣ User interface for easier learning
High usability ‣ Portability: Various computational environment ‣ Source accessibility: More user, easier maintenance ‣ Visualization: Understanding of phenomena
High performance ‣ Parallel processing for large-scale and fast computation 8
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Integrated Modelling Activities
JA: BPSI ‣ Burning Plasma Simulation Initiative ‣ Data structure and data interface: BPSD ‣ Execution control interface: BPSX
EU: ITM TF ‣ Integrated Tokamak Modelling - Task Force ‣ Data model: CPO (Consistent Physical Objects) ‣ Code interface: UAL (Universal Access Layer)
ITER: IM Programme ‣ IMAS: Integrated Modelling Analysis Suits ‣ IM standards and guideline ‣ ITER Data model
•Data exchange between modules
•Description of device (coils, actuators, diagnostics)
•Experimental and simulation data storage9
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Data exchange between components: BPSD
Purpose ‣ Standard dataset: Specify set of data ‣ Specification of data exchange interface: initialize, set, get ‣ Specification of file i/o interface: save, load
Policy of BPSD ‣ Minimum and Sufficient Dataset •To minimize the data to be exchanged •Mainly profile data •Routines to calculate global quantities ‣ Minimum Arguments in Interfaces •To maximize flexibility •Use structured data •Only one dataset in the arguments of an interface ‣ Minimum Kinds of Interfaces •To make modular programming easier •Use function overloading
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BPSD Data Exchange Interface
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BPSD Standard Dataset
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BPSD Code Interface
bpsd_set_data(data,ierr): ‣ Copy data into internal dataset
bpsd_get_data(data,ierr): ‣ Copy of interpolate data fram internal dataset
•If nrmax=0, copy data;
•otherwise interpolate for given mesh.
bpsd_save(ierr): ‣ Save all BPSD data into a file ‣ Name of the file is optional.
bpsd_load(ierr): ‣ Load all BPSD data from a file ‣ Name of the file is optional.
Interface for history archiving is under consideration.13
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Several Approaches on Workflow
Monolithic code approach: original approach ‣ Memory-based data exchange •Template: call bpsd_get_data • calculation • call bpsd_set_data
Command approach: for script and workflow tool ‣ File-based data exchange •Template: call bpsd_load ← bpsddata • call bpsd_get_data • calculation • call bpsd_set_data • call bpsd_save → bpsddata
Pre- and post- process approach: no modification of the code ‣ Data conversion •Template pre-process: bpsddata → input file • run code • post-process: output file → bpsddata 14
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Integrated Modelling Code: TASK
Core of Integrated Modelling Code in BPSI ‣ Modular structure for easier maintenance ‣ Reference implementation of BPSD and BPSX
Various Heating and Current Drive Scheme ‣ EC, LH, IC, AW, NB
High Portability ‣ Most of library routines included ‣ Original graphic libraries (X11, Postscript, OpenGL, SVG)
Development using CVS (Version control for collaboration)
Open Source: http://bpsi.nucleng.kyoto-u.ac.jp/task/
Parallel Processing using MPI and PETSc
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Transport Analyzing System for tokamaK
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Present Structure of the TASK code and related codes
Developed since 1992, now at Kyoto University16
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Present Structure of TASK3D for Helical Plasmas
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EQ
TR
BPSD
WR
2D fixed-/free-boundary equlibrium
JT-60U Exp. Data
LHD Exp. Data
Profile Database
Simulation DB
TX
FP
WM
WF
1D dynamiccal transport
1D kinetic transport (3D FP)
Ray and beam tracing
Full wave analysis (multi mode)
Wave dispersion
FIT3D NBI analysis (birth, orbit, deposit)
EI
ER
DCOM/NNW
Helical current evolution
Helical radial electric field
Neoclassical coefficient database
1D diffusive transport
DataInterface
GNET Drift-Kinetic equation solver
PL
TASK
3D
TASK
MIPS 3D equilibrium and MHD stability
EX
DP
EG
Full wave analysis (FEM)
2D anisotropic pressure equilibrium
Linear microinstability
KITES 3D equilibrium
International Tokamak Profile
DB
T2 2D dynamiccal transport
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Various Levels of Transport Modelling
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Transport Modelling in the TASK code
Diffusive transport equation: TASK/TR ‣ Diffusion equation for plasma density ‣ Flux-Gradient relation ‣ Conventional transport analysis
Dynamical transport equation: TASK/TX: ‣ Two-fluid equation and Maxwell’s equation ‣ Flux-averaged fluid equation ‣ Plasma rotation and transient phenomena
Kinetic transport equation: TASK/FP: ‣ Drift-kinetic equation for momentum distribution function ‣ Bounce-averaged Fokker-Plank equation ‣ Time evolution of momentum distribution
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Diffusive Transport Equation: TASK/TR
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Transport processes
Neoclassical transport ‣ Collisional transport in a nonuniform magnetic field ‣ Radial diffusion, enhanced resistivity, bootstrap current,
Ware pinch
Turbulent transport ‣ Various transport models ‣ GLF23, CDBM, Bohm/gyro Bohm, TGLF, ··· Atomic transport ‣ charge exchange, ionization, recombination
Radiation transport ‣ Line radiation, Bremsstrahlung, Synchrotron radiation
Parallel transport ‣ along open magnetic field lines in SOL plasmas
Sources ‣ Particle: gas puff, NBI, pellet ‣ Momentum: NBI, waves ‣ Heat: NBI, waves, fusion reaction
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Heat Transport Simulation of ITER Scenarios
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1D Dynamical Transport Code: TASK/TX
Dynamical Transport Equations (TASK/TX) ‣ M. Honda and A. Fukuyama, JCP 227 (2008) 2808 ‣ A set of flux-surface averaged equations ‣ Two fluid equations for electrons and ions
•Continuity equations
•Equations of motion (radial, poloidal and toroidal)
•Heat transport equations ‣ Maxwell’s equations ‣ Slowing-down equations for beam ion component ‣ Diffusion equations for three-group neutrals
Self-consistent description of plasma rotation and electric field ‣ Equation of motion rather than transport matrix
Quasi-neutrality is not assumed.
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Dynamical Transport Equation in TASK/TX (1)
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Dynamical Transport Equation in TASK/TX (2)
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Typical Ohmic Plasma Profiles at t = 50 ms
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Density Profile Modification Due to NBI Injection
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Toroidal Rotation Due to Ion Orbit Loss
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Kinetic Integrated Modelling: Motivation
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Better understanding of burning plasmas
‣ Behavior of energetic particles
•generation, transport excitation
Analysis of momentum distribution function
‣ Consistent analysis of heating and current drive
•both bulk and energetic components
•all heating schemes
‣ Influence of energetic particles on heating processes
•propagation and absorption of waves
•fusion reaction rate
‣ Modification of momentum distribution due to radial transport
Modelling based on momentum distribution function is required.
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Fokker-Planck Analysis in TASK/FP
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Kinetic Transport Modelling: TASK/FP
Multi species conservation between species
Three dimensional 2D in momentum, 1D in radial
Bounce averaged trapped particle effect
Nonlinear collision momentum and energy conservation
Relativistic weakly relativistic collision term
Fusion reaction velocity integral
Parallel processing using parallel matrix solver PETSc library
Finite orbit size under development
Induced EM fields under development
Fokker-Planck analysis of distribution function
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Multi-Species Fokker-Planck Analysis
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Analysis of Multi-Scheme Heating in ITER Plasma
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Momentum Distribution Functions (t = 1 s)
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Power Transfer between Species
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Simulation with Radial Transport
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Dependence on Radial Diffusion model
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Full Wave Analysis
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Full wave analysis: TASK/WM
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ICRF Waves in a Helical Plasma
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TAE Analysis with TASK/WM
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RSAE Excitation by Energetic Particles
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Progress in Full Wave Analysis
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Full wave analysis by FEM: TASK/WF3D/WF2D
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EC waves in a small-size ST
‣ R=0.22 m, a=0.16 m, B0=0.072 T ‣ f=5 GHz, nφ=8, ν/ω=0.001 O - X - UHR
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Integral Formulation of Wave-Particle Interaction
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Variable Transformation
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Kernel Functions
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One-Dimensional Analysis
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Issues in Kinetic Integrated Modeling
Modeling of transport process ‣ Turbulent transport coefficients with velocity
dependence ‣ Finite orbit size effects (Neoclassical transport) ‣ Coupling with toroidal electric field (Faraday’s law) ‣ Keeping charge neutrality (Gauss’s Law)
Kinetic full wave analysis ‣ Integral form of dielectric tensor including finite gyro
radius effects ‣ Gyro kinetic dielectric tensor for coupling with drift
waves
Coupling with other components ‣ Equilibrium including kinetic effects •Anisotropic pressure, and flow ‣ Modeling of diagnostics •Validation by direct comparison
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Summary
Integrated modelling of toroidal plasmas is required for understanding the physics of experimental observations and predicting the performance of future devices.
For large scale integrated simulation, development and spread of a standard data model is essential. Several efforts to develop infrastructures for integrated modelling are under way.
We have been developing the integrated modelling suites TASK which includes several levels of transport modelling and full wave analysis of toroidal plasmas.
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