2010/01/18

Integrated Tokamak Code: TASK

A. Fukuyama

Department of Nuclear Engineering, Kyoto University

AcknowledgmentsM. Honda, H. Nuga, and BPSI working group

Outline

1. Integrated Simulation of Fusion Plasmas

2. Integrated Tokamak Modeling Code: TASK

3. Transport Modeling

4. Source Modeling

5. ITER Modeling

6. Summary

Integrated Simulation of Toroidal Plasmas

• Why needed?– To predict the behavior of burning plasmas in tokamaks

– To develop reliable and efficient schemes to control them

• What is needed?– Simulation describing:◦ Whole plasma (core & edge & divertor & wall-plasma)◦ Whole discharge

(startup & sustainment & transients events & termination)◦ Reasonable accuracy (validation by experiments)◦ Reasonable computer resources (still limited)

• How can we do?– Gradual increase of understanding and accuracy

– Organized development of simulation system

Simulation of Tokamak Plasmas

Broad range of time scale:100GHz ∼ 1000s

Broad range of Spatial scale:10 μm ∼ 10m

1mm

1m

1Hz1kHz1MHz1GHz

LH

EC

ICMHD Transport

Turbulence

Heating

TIME

LENGTH NBI

One simulation code nevercovers all range.

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

Integrated simulation combining modeling codesinteracting each other

Integrated Tokamak Simulation

Desired Features of Integrated Modeling Code

• Modular structure: for flexible extension of analyses

– Core modules (equilibrium, transport, source, stability)

– Various levels of models (quick, standard, precise, rigorous)

– New physics models (easier development)

• Standard module interface: for efficient development-of modules

• Interface with experimental data: for validating physics models

• Unified user interface: for user-friendly environment

• Scalability in parallel processing of time consuming modules

• High portability• Open source of core modules

• Visualization included

Integrated Modeling Activities

• Japan: BPSI (Burning Plasma Simulation Initiative)

– Research collaboration among universities, NIFS and JAEA◦ Framework for code integration◦ Physics integration◦ Advanced computing technology

• EU: ITM-TF (EFDA Task Force: Integrated Transport Modeling)

– Code Platform Project: code interface, data structure

– Data Coordination Project: verification and validation

– Five Integrated Modeling Projects: EQ, MHD, TR, Turb., Source

• US: FSP (Fusion simulation project) — a part of SciDAC

– Simulation of Wave Interactions with Magnetohydrodynamics (SWIM)

– Center for Plasma Edge Simulation (CPES)

– Framework Application for Core-Edge Transport Simulations (FACETS)

• ITER: IMEG (Integrated Modeling Expert Group)

BPSI: Burning Plasma Simulation Initiative

Research Collaboration of Universities, NIFS and JAEA

• Targets of BPSI– Framework for collaboration of various plasma simulation codes

– Physics integration with different time and space scales

– Advanced technique of computer science

All Japan collaboration Integrated code development

Integrated Modeling Code: TASK

• Transport Analysing System for TokamaK

• Features– Core of Integrated Modeling Code in BPSI◦ Modular structure◦ Reference imprementation of standard data set and interface

– Various Heating and Current Drive Scheme◦ EC, LH, IC, AW, NB

– High Portability◦ Most of library routines included (except LAPACK, MPI, MDS+)◦ Original graphic libraries (X11, Postscript, OpenGL)

– Development using CVS (Version control)

– Open Source: http://bpsi.nucleng.kyoto-u.ac.jp/task/)

– Parallel Processing using MPI Library (partially)

Components of the TASK Code

• Developed since 1992, now in Kyoto UniversityBPSD Data Exchange Standard data set, Program interfaceEQ 2D Equilibrium Fixed boundary, Toroidal rotationTR 1D Transport Diffusive transport, Transport modelsTX 1D Transport Dynamic Transport, Rotation and ErFP 3D Fokker-Planck Relativistic, Bounce-averagedWR 3D Ray Tracing EC, LH: Ray tracing, Beam tracingWM 3D Full Wave IC: Antenna excite, Alfven EigenmodeDP Wave Dispersion Dielectric tensor, Arbitrary f (u)

FIT3D NBI Physics Birth, Orbit width, DepositionPL Utilities Interface to BPSD and profile databaseLIB Libraries Common libraries, MTX, MPI

GSAF Graphics Original graphic library for Fortran

• TASK3D: Extension to 3D Helical Plasmas (NIFS and Kyoto U)

Original Structure of the TASK code

Present Structure of TASK and Related Codes in BPSI

Inter-Module Collaboration Interface

• Role of Module Interface– Data exchange between modules: BPSD◦ Standard dataset: Specify set of data◦ Specification of data exchange interface: set/get/load/save

– Execution control: BPSX◦ Specification of execution control interface:

initialize, setup, exec, visualize, terminate◦ Uniform user interface: parameter input, graphic output

• Role of data exchange interface– Keep present status of plasma and device– Save into file and load from file– Store history of plasma– Interface to experimental data base

Policies of BPSD

• Minimum and Sufficient Dataset

– To minimize the data to be exchanged– Mainly profile data– Routines to calculate global integrated quantities◦ separately provided

• Minimum Arguments in Interfaces

– To maximize flexibility– Use derived data type or struct– Only one dataset in the arguments of an interface

• Minimum Interfaces

– To make modular programming easier– Use function overloading

Data Exchange Interface: BPSD

• Standard dataset: Specify data to be stored and exchanged

– Data structure: Derived type (Fortran95): structured type

e.g.

time plasmaf%timenumber of grid plasmaf%nrmaxnumber of species plasmaf%nsmaxsquare of grid radius plasmaf%s(nr)plasma density plasmaf%data(nr,ns)%pnplasma temperature plasmaf%data(nr,ns)%pt

• Specification of API:– Program interface

e.g.

Set data bpsd set data(plasmaf,ierr)Get data bpsd get data(plasmaf,ierr)Save data bpsd save(ierr)Load data bpsd load(ierr)

BPSD Standard Dataset (version 0.6)

Category Name EQ TR TX FP WR WM DPShot data bpsd shot type – – – – – – –Device data bpsd device type in in in in1D equilibrium data bpsd equ1D type out in in in2D equilibrium data bpsd equ2D type out in in in in1D metric data bpsd metric1D type out in in in2D metric data bpsd metric2D type out in in in inPlasma species data bpsd species type in in in in inFluid plasma data bpsd plasmaf type in out out i/o inKinetic plasma data bpsd plasmak type out inTransport matrix data bpsd trmatrix type i/oTransport source data bpsd trsource type i/o i/o i/o out outDielectric tensor data bpsd dielectric type in in outFull wave field data bpsd wavef type in outRay tracing field data bpsd waver type in outBeam tracing field data bpsd waveb type in outUser defined data bpsd 0/1/2ddata type – – – – – – –

Execution Control Interface

• BPSX: not yet decided

– Monolithic integrated code– Script-driven element codes– MPI-2 driven element codes

• Example of element codes for TASK/TRTR INIT Initialization (Default value)TR PARM(ID,PSTR) Parameter setup (Namelist input)TR SETUP(T) Profile setup (Spatial profile, Time)TR EXEC(DT) Exec one step (Time step)TR GOUT(PSTR) Plot data (Plot command)TR SAVE Save data in fileTR LOAD load data from fileTR TERM Termination

Equilibrium Analysis

• Shape of an axisymmetric plasma: poloidal magnetic flux ψ(R,Z)

• Grad-Shafranov equation

R∂

∂R1R∂ψ

∂R+∂2ψ

∂Z2 = −μ0R2dp(ψ)

dψ− F(ψ)

dF(ψ)dψ

– Pressure profile: p(ψ)

– Poloidal current density profile: F(ψ)

– Plasma boundary shape (fixed boundary) orPoloidal coil current (free boundary)

determines the poloidal plasma shape.

• Coupling with transport analysis– Input: p(ψ), q(ψ) = F

dVdψ

⟨1

R2

⟩– Output: Metric quantities, Flux surface averaged quantities

Various Levels of Transport Modeling

Transport Modeling 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:

– Continuity equation and equation of motion for plasma density

– Flux-averaged fluid equation

– Plasma rotation and transient phenomena

• Kinetic transport equation: TASK/FP:

– Gyrokinetic equation for momentum distribution function

– Bounce-averaged Fokker-Plank equation

– Modification of momentum distribution

Diffusive Transport Equation: TASK/TR

• Transport Equation Based on Gradient-Flux Relation:

Γ =↔M · ∂F/∂ρ

where V: Volume, ρ: Normalized radius, V ′ = dV/dρ

– Particle transport

1V ′∂

∂t(nsV

′) = − ∂∂ρ

(V ′〈|∇ρ|〉nsVs − V ′〈|∇ρ|2〉Ds

∂ns∂ρ

)+ S s

– Toroidal momentum transport

1V ′∂

∂t(nsuφsV

′) = − ∂∂ρ

(V ′〈|∇ρ|〉nsuφsVMs − V ′〈|∇ρ|2〉nzμs∂uφs

∂ρ

)+ Ms

– Heat transport

1V ′5/3

∂

∂t

(32nsTsV

′5/3)= − 1

V ′∂

∂ρ

(V ′〈|∇ρ|〉3

2nsTsVEs − V ′〈|∇ρ|2〉nsχs∂Ts

∂ρ

)+ Ps

– Current diffusion

∂Bθ∂t=∂

∂ρ

[η

FR0〈R−2〉R0

μ0

F2

V ′∂

∂ρ

(V ′BθF

⟨|∇ρ|2R2

⟩)− η

FR0〈R−2〉〈J · B〉ext

]

Transport Processes

• Neoclassical transport– Collisional transport in an inhomogeneous magnetic field

– Radial diffusion: usually small compared with turbulent diffusion

– Enhanced resistivity: due to trapped particles

– Bootstrap current: toroidal current driven by radial pressure gradient

– Ware pinch: Radial particle pinch driven by toroidal electric field

• Turbulent transport– Various transport models: GLF23, CDBM, Weiland, · · ·

• Atomic transport: charge exchange, ionization, recombination

• Radiation transport– Line radiation, Bremsstrahlung, Synchrotron radiation

• Parallel transport: along open magnetic field lines in SOL plasmas

Turbulent Transport Models

• CDBM model: current diffusive ballooning mode turbulence model

– developed by K. Itoh et al.– Marginal stability condition of the current diffusive ballooning mode

including turbulent transport coefficients as parameters

• GLF23 model: Gyro-Landau-Fluid turbulence model

– developed by Waltz and Kinsey (GA)– Linear growth rate from gyro-Landau-fluid model (ITG, TEM, ETG)

– Evaluate transport coefficients based on mixing length estimate

– Calibrate coefficients by the linear stability code GKS

– Calibrate coefficients by the nonlinear turbulence code GYRO

• Weiland model:– developed by J. Weiland– Based on ITG turbulence model

GLF23 Transport Model

Linear growth rate from gyro-Landau-fluid model

Calibrate coefficients by the nonlinear turbulence code GYRO

Good agreement with experimental data

CDBM Transport Model: CDBM05

• Thermal Diffusivity (Marginal: γ = 0)

χTB = F(s, α, κ, ωE1)α3/2 c2

ω2pe

vA

qR

Magnetic shear s ≡ rq

dqdr

Pressure gradient α ≡ − q2Rdβdr

Elongation κ ≡ b/a

E × B rotation shear ωE1 ≡ r2

svA

ddr

ErB

• Weak and negative magnetic shear,Shafranov shift, elongation,

and E × B rotation shearreduce thermal diffusivity.

s − α dependence ofF(s, α, κ, ωE1)

0.0

0.5

1.0

1.5

2.0

2.5

-0.5 0.0 0.5 1.0

F ωE1

=0.2

ωE1

=0.3

ωE1

=0.1

ωE1

=0

s - α

F(s, α, κ, ωE1) =

(2κ1/2

1 + κ2

)3/2

×

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎩

11 +G1ω

2E1

1√2(1 − 2s′)(1 − 2s′ + 3s′2)

for s′ = s − α < 0

11 +G1ω

2E1

1 + 9√

2s′5/2√2(1 − 2s′ + 3s′2 + 2s′3)

for s′ = s − α > 0

TFTR #88615 (L-mode, NBI heating)

DIII-D #78316 (L-mode, ECH and ICH heatings)

Comparison of Transport Models: ITPA Profile DB

Deviation of Stored EnergyCDBM CDBM05

GLF23 Weiland

1D Dynamic Transport Code: TASK/TX

• Dynamic 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)◦ Energy transport equations

– Maxwell’s equations– Slowing-down equations for beam ion component– Diffusion equations for two-group neutrals

• Self-consistent description of plasma rotation and electric field– Equation of motion rather than transport matrix

• Quasi-neutrality is not assumed.

Model Equation of Dynamic Transport Simulation

• Flux-surface-averaged multi-fluid equations:∂ns∂t=− 1

r∂

∂r(rnsusr) + S s

∂

∂t(msnsusr)=−1

r∂

∂r(rmsnsu

2sr) +

1rmsnsu

2sθ + esns(Er + usθBφ − usφBθ) −

∂

∂rnsTs

∂

∂t(msnsusθ)=− 1

r2

∂

∂r(r2msnsusrusθ) + esns(Eθ − usrBφ) +

1r2

∂

∂r

(r3nsmsμs

∂

∂rusθr

)

+FNCsθ + F

Csθ + F

Wsθ + F

Xsθ + F

Lsθ

∂

∂t

(msnsusφ

)=−1

r∂

∂r(rmsnsusrusφ) + esns(Eφ + usrBθ) +

1r∂

∂r

(rnsmsμs

∂

∂rusφ

)

+FCsφ + F

Wsφ + F

Xsφ + F

Lsφ

∂

∂t32nsTs=−1

r∂

∂rr

(52usrnsTs − nsχs ∂

∂rTe

)+ esns(Eθusθ + Eφusφ)

+PCs + P

Ls + P

Hs

Typical Ohmic Plasma Profiles at t = 50ms

JFT-2M like plasma composed of electron and hydrogenR = 1.3 m, a = 0.35 m, b = 0.4 m, Bφb = 1.3 T, Ip = 0.2 MA, S puff = 5.0 × 1018 m−2s−1

γ = 0.8, Zeff = 2.0, Fixed turbulent coefficient profile

0.0 0.2 0.4 0.6 0.8 1.0−8

−6

−4

−2

0

Er(r) [kV/m]

0.0 0.2 0.4 0.6 0.8 1.0−0.20.00.20.40.60.8

Eθ [mV/m]

0.0 0.2 0.4 0.6 0.8 1.00.000.040.080.120.160.20

Eφ [kV/m]

0.0 0.2 0.4 0.6 0.8 1.00.00

0.04

0.08

0.12

Bθ [T]

0.0 0.2 0.4 0.6 0.8 1.00.0

0.4

0.8

1.2

Bφ [T]

0.0 0.2 0.4 0.6 0.8 1.00.000.050.100.150.200.250.30

ne [1020m-3]

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

Te [keV]

0.0 0.2 0.4 0.6 0.8 1.00.00.10.20.30.40.5

Ti [keV]

0.0 0.2 0.4 0.6 0.8 1.00

4

8

12 n01 [1014m-3]

0.0 0.2 0.4 0.6 0.8 1.00

2

4

6

8

n02 [1010m-3]

0.0 0.2 0.4 0.6 0.8 1.00123456

uer [m/s]

0.0 0.2 0.4 0.6 0.8 1.0−16

−12

−8

−4

0ueθ [km/s]

0.0 0.2 0.4 0.6 0.8 1.0−500−400−300−200−100

0ueφ [km/s]

0.0 0.2 0.4 0.6 0.8 1.00.000

0.015

0.030

0.045De [m2/s]

0.0 0.2 0.4 0.6 0.8 1.0012345

χe=χi=μe=μi [m2/s]

0.0 0.2 0.4 0.6 0.8 1.00123456

uir [m/s]

0.0 0.2 0.4 0.6 0.8 1.00.00.20.40.60.81.0

uiθ [km/s]

0.0 0.2 0.4 0.6 0.8 1.00.000.050.100.150.200.25

uiφ [km/s]

0.0 0.2 0.4 0.6 0.8 1.00

1

2

3

4 q

0.0 0.2 0.4 0.6 0.8 1.00.00.51.01.52.02.5

jφ [MA/m2]

Density Profile Modification Due to NBI Injection

Modification of n and Er profile depends on the direction of NBI.

Co/Counter with Ip: Density flattening/peaking

0.0 0.2 0.4 0.6 0.8 1.0−16−12−8−404

Er [kV/m]

0.0 0.2 0.4 0.6 0.8 1.00.0

0.1

0.2

0.3

0.4

ne [1020m-3]

0.0 0.2 0.4 0.6 0.8 1.00.00.20.40.60.81.0

Te [keV]

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

Ti [keV]

0.0 0.2 0.4 0.6 0.8 1.0−3000−2000−1000

010002000

ubφ [km/s]

0.0 0.2 0.4 0.6 0.8 1.00.00.51.01.52.02.5

uer [km/s]

no NBIcocounter

0.0 0.2 0.4 0.6 0.8 1.0−25−20−15−10−505

ueθ [km/s]

0.0 0.2 0.4 0.6 0.8 1.0−600−500−400−300−200−100

0ueφ [km/s]

0.0 0.2 0.4 0.6 0.8 1.00

1

2

3

4q

0.0 0.2 0.4 0.6 0.8 1.00.00.51.01.52.02.5

jφ [MA/m2]

0.0 0.2 0.4 0.6 0.8 1.00.0

0.4

0.8

1.2

uiθ [km/s]

0.0 0.2 0.4 0.6 0.8 1.0−80

−40

0

40

80uiφ [km/s]

Toroidal Rotation Due to Ion Orbit Loss

• Ion orbit loss near the edge region drives toroidal rotation

Ref. M. Honda et al., NF (2008) 085003

Source Modeling

• Heat and momentum sources:

– Alpha particle heating:◦ sensitive to fuel density and momentum distribution

– Neutral beam injection:◦ birth profile, finite size orbit, deposition to bulk plasma

– Waves:◦ IC (∼ 50 MHz): fuel ion heating, current drive, rotation drive(?)◦ LH (∼ 10 GHz): current drive◦ EC (∼ 170 GHz): current drive, pre-ionization

• Particle source– Gas puff, recycling:

– Neutral beam injection:

– Pellet injection: penetration, evaporation, ionization, drift motion

Wave Modeling

• Ray tracing: EC, LH

– Spatial evolution of ray position and wave number

– Wave length λ much less than scale length L: λ � L

– Beam size d is sufficiently large (Fresnel condition): L � d2/λ

• Beam tracing: EC

– New variables: beam radius, curvature of equi-phase surface

• Beam propagation: EC

– Under development: Time evolution of E(r, t) e iωt

• Full wave analysis: IC, AW, MHD

– Stationary Maxwell’s equation as a boundary problem

– Wave length λ comparable with scale length L

– Evanescent region, strong absorption, coupling with antenna

Wave Dispersion Analysis : TASK/DP

• Various Models of Dielectric Tensor↔ε (ω, k; r):

• Analytic model– Resistive MHD model– Collisional cold plasma model– Collisional warm plasma model– Kinetic model (Maxwelian, non-relativistic)– Drift-kinetic model (Maxwellian, inhomogeneity)– Hamiltonian formulation (cyclotron, bounce, precession)

• Numerical integrateion– Kinetic model (Relativistic, Maxwellian)– Kinetic model (Relativistic, arbitrary f (u))– Drift-kinetic model (Inhoogeneity, arbitrary f (u))– Hamiltonian formulation (arbitrary f (u)))

Ray Tracing: TASK/WR

• Geometrical Optics– Wave length λ � Characteristic scale length L of the medium

– Plane wave: Beam size d is sufficiently large◦ Fresnel condition is well satisfied: L � d2/λ

• Evolution along the ray trajectory τ– Wave packet position r, wave number k, dielectric tensor K

– Ray tracing equation:drdτ=∂K∂k

/∂K∂ω

dkdτ= − ∂K

∂r

/∂K∂ω

– Equation for wave energy W, group velocity ug, damping rate γ

∇ · (ugW)= −2γW

Beam Tracing: TASK/WR

• Beam size perpendicular to the beam direction: first order in ε

• Beam shape : Hermite polynomial: Hn)

E(r) = Re

[∑mn

Cmn(ε2r)e(ε2r)Hm(εξ1)Hn(εξ2) e i s(r)−φ(r)

]

– Amplitude : Cmn, Polarization : e, Phase : s(r) + iφ(r)

s(r) = s0(τ) + k0α(τ)[rα − rα0 (τ)] +

12sαβ[r

α − rα0 (τ)][rβ − rβ0(τ)]

φ(τ) =12φαβ[rα − rα0 (τ)][rβ − rβ0(τ)]

– Position of beam axis : r0, Wave number on beam axis: k0

– Curvature radius of equi-phase surface: Rα = 1/λsαα– Beam radius: dα =

√2/φαα

• Gaussian beam : case with m = 0, n = 0

R1

R2

d1

d2

Beam Propagation Equation

• Solvable condition for Maxwell’s equation with beam fielddrα0dτ=

∂K∂kα

dk0α

dτ= − ∂K

∂rα

dsαβdτ= − ∂2K

∂rα∂rβ− ∂2K∂rβ∂kγ

sαγ − ∂2K∂rα∂kγ

sβγ − ∂2K∂kγ∂kδ

sαγsβδ +∂2K∂kγ∂kδ

φαγφβδ

dφαβdτ= −

(∂2K∂rα∂kγ

+∂2K∂kγ∂kδ

sαδ

)φβγ −

(∂2K∂rβ∂kγ

+∂2K∂kγ∂kδ

sβδ

)φαγ

• By integrating this set of 18 ordinary differential equations, we obtaintrace of the beam axis, wave number on the beam axis, curvature ofequi-phase surface, and beam size.• Equation for the wave amplitude Cmn

∇ · (ug0|Cmn|2)= −2

(γ|Cmn|2

)Group velocity: ug0, Damping rate: γ ≡ (e∗ · ↔ε A · e)/(∂K/∂ω)

Full wave analysis: TASK/WM

• magnetic surface coordinate: (ψ, θ, ϕ)

• Boundary-value problem of Maxwell’s equation

∇ × ∇ × E = ω2

c2↔ε · E + iωμ0 jext

• Kinetic dielectric tensor: ↔ε– Wave-particle resonance: Z[(ω − nωc)/k‖vth]– Fast ion: Drift-kinetic[

∂

∂t+ v‖∇‖ + (ud + uE) · ∇ + eα

mα(v‖E‖ + ud · E)

∂

∂ε

]fα = 0

• Poloidal and toroidal mode expansion

– Accurate estimation of k‖• Eigenmode analysis: Complex eigen frequencywhich maximize wave

amplitude for fixed excitation proportional to electron density

Fokker-Planck Analysis : TASK/FP

• Fokker-Planck equationfor multi-species velocity distribution function: fs(p‖, p⊥, ψ, t)

∂ fs∂t= E( fs) +C( fs) + Q( fs) + L( fs)

– E( f ): Acceleration term due to DC electric field

– C( f ): Coulomb collision term

– Q( f ): Quasi-linear term due to wave-particle resonance

– L( f ): Spatial diffusion term

• Bounce-averaged: Trapped particle effect, zero banana width

• Relativistic: momentum p, weakly relativistic collision term

• Nonlinear collision: momentum and energy conservation

• Multi-species: conservation between species

• Three-dimensional: spatial diffusion (neoclassical, turbulent)

ITER Modeling Needs

based on Dr. Campbell’ talk at Cadarache, Sept 2007

• Plasma scenario development:– Preparation for operation

• Detailed design of auxiliary systems:

– H&CD, Diagnostics, Fueling, · · ·• Design of plasma control system:

– Development and optimization of integrated control strategies

• Preparation of ITER operational programme:

– End-to-end scenario development

– Detailed pulse definition

• Experimental data evaluation:

– Pulse characterization and physics analysis

– Refinement of operation scenario and performance predictions

Analysis of EC propagation in ITER

4 5 6 7 8-4

-2

0

2

4ABS POWER

0.0 0.2 0.4 0.6 0.8 1.00

1

2

3

4

5

6

7

8

ABS WEIGHT POWER

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

BB = 5.300RR = 6.200RA = 2.000RKAP = 1.700

Q0 = 1.000QA = 3.000RF = 1.700E+05NPHII= -0.1177

PA(1) = 0.0005PZ(1) = -1.0000PN(1) = 0.8000PNS(1) = 0.0100

PTPR(1)= 20.0000PTPP(1)= 20.0000PTS(1) = 0.0500MODELP1= 25.

PA(2) = 2.0000PZ(2) = 1.0000PN(2) = 0.4000PNS(2)= 0.0050

PTPR(2)= 20.0000PTPP(2)= 20.0000PTS(2) = 0.0500MODELP2= 1.

Analysis of IC propagation in ITER

• Minority heating in D phase: D + H

Radial profile Wave electric field Pabs by minority ion

ITER Plasma Transport Simulation with CDBM05

• Inductive operation– Ip = 15 MA

– PNB = 40 MW on axis

– βN = 2.65Time evolution Radial profile

• Hybrid operation– Ip = 12 MA

– PNB = 33 MW on axis

– βN = 2.68Time evolution Radial profile

Alfven Eigenmode Analysis by TASK/WM

• Alfven eigenmode driven by alpha particles– Calculated by the full wave module TASK/WM

– Toroidal mode number: n = 1

– TAE is stable: Eigen mode frequency = (95.95 kHz, −1.95 kHz)

Alpha particle density

Alfven continuum frequency Alfven eigenmode structure

ITER Inductive Operation

• 15 MA Current rise in 70 s

• Behavior of plasma depends on timing of heating

Future Plan of the TASK code

Remaining Issues in Tokamak Plasma Modling

• Pedestal temperature: modeling of L/H transition

• Transport barrier formation: turbulence transport model

• ELM physics: nonlinear behavior of ELM on transport

• Nonlinear MHD events: modeling of plasma profile change

• Energetic-ion driven phenomena:coupling of Alfven mode and drift waves

• Kinetic analysis of transport and MHD phenomena:non-Maxwellian distribution

• Wave physics: full wave analysis of Bernstein waves

• Divertor plasma: plasma-wall interaction

• Start up: Rapid change of equilibrium and control

and so on...

Summary

• Integrated modeling of burning plasmas is indispensable forexploiting optimized operation scenario of ITER and reliable de-sign of DEMO.

• Discussion on international collaboration for the developmentof integrated ITER modeling is on going.

• There are many remaining issues in constructing compre-hensive integrated code; especially, L/H transition mechanism,turbulent transport model, ELM physics, nonlinear MHD events,energetic particle driven phenomena and plasma wall-interactions.

• Solving those remaining issues requires not only large-scalecomputer simulations but also intensivemodeling efforts basedon experimental observations.