2010/01/18

Integrated Tokamak Code: TASK

A. Fukuyama
Department of Nuclear Engineering, Kyoto University
Acknowledgments
M. 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
LENGTH

1m

Heating
LH
EC

IC
MHD

Transport
NBI

Turbulence

1mm

1GHz

1MHz

1kHz

1Hz

Energetic Ion Confinement
Transport BarrierCore Transport

MHD Stability

Non-Inductive CD

Turbulent Transport

RF Heating

Impurity Transport

NBI Heating

SOL Transport

Neutral Transport

Divertor Plasma

Plasma-Wall Int.

TIME

One simulation code never
covers all range.

Blanket, Neutronics, Tritium,
Material, Heat and Fluid Flow

Integrated simulation combining modeling codes
interacting 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 University
BPSD Data ExchangeStandard data set, Program interface
EQ 2D Equilibrium
Fixed boundary, Toroidal rotation
TR 1D Transport
Diffusive transport, Transport models
TX 1D Transport
Dynamic Transport, Rotation and Er
FP 3D Fokker-Planck Relativistic, Bounce-averaged
WR 3D Ray Tracing
EC, LH: Ray tracing, Beam tracing
WM 3D Full Wave
IC: Antenna excite, Alfvén Eigenmode
DP Wave Dispersion Dielectric tensor, Arbitrary f (u)FIT3D NBI Physics
Birth, Orbit width, Deposition
PL Utilities
Interface to BPSD and profile database
LIB 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%time
number of grid
plasmaf%nrmax
number of species
plasmaf%nsmax
square of grid radius plasmaf%s(nr)plasma density
plasmaf%data(nr,ns)%pn
plasma temperature plasmaf%data(nr,ns)%pt• Specification of API:
– Program interfacee.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)
CategoryName
EQ TR TX FP WR WM DP
Shot data
bpsd shot type
– – – ––––
in in in in
Device data
bpsd device typeout in in in
1D equilibrium data
bpsd equ1D type
out
in in
in in
2D equilibrium data
bpsd equ2D type
1D metric data
bpsd metric1D type out in in in
in in
in in
2D metric data
bpsd metric2D type out
in in in in
inPlasma species data
bpsd species typein out out i/oin
Fluid plasma data
bpsd plasmaf type
outinKinetic plasma data
bpsd plasmak typei/oTransport matrix data bpsd trmatrix typei/o i/o i/o out out
Transport source data bpsd trsource typeinin outDielectric tensor data bpsd dielectric typein outFull wave field data
bpsd wavef typeinout
Ray tracing field data bpsd waver typeinoutBeam tracing field data bpsd waveb type–––
User 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/TR
TR 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 file
TR LOADload data from file
TR TERM
Termination

Equilibrium Analysis• Shape of an axisymmetric plasma: poloidal magnetic flux ψ(R, Z)• Grad-Shafranov equationdF(ψ)∂ 1 ∂ψ ∂2ψ
dp(ψ)
2+ 2 = −μ0R
− F(ψ)R∂R R ∂R ∂Zdψdψ– Pressure profile: p(ψ)– Poloidal current density profile: F(ψ)– Plasma boundary shape (fixed boundary) or
Poloidal coil current (free boundary)determines the poloidal plasma shape.

• Coupling with transport analysis
 
dV 1– Input: p(ψ), q(ψ) = Fdψ 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



∂
1 ∂
∂n s



2
(n
V
V
)
=
−
|∇ρ|n
V
−
V
|∇ρ|
D
s
s s
s
V  ∂t
∂ρ
∂ρ


+Ss

– Toroidal momentum transport



∂u
∂
1 ∂
φs



2
(n
V
+ Ms
u
V
)
=
−
|∇ρ|n
u
V
−
V
|∇ρ|
n
μ
s φs
s φs Msz s
V  ∂t∂ρ∂ρ– Heat transport



1 ∂ 3
5/3
n
T
V
s
s
V 5/3 ∂t 2





3
∂T s
1 ∂


2
V |∇ρ| n sT sVE s − V |∇ρ| n sχ s
=− 
V ∂ρ
2
∂ρ

– Current diffusion







∂
η
R0 F ∂ V Bθ∂Bθ=∂t∂ρ FR0R−2 μ0 V  ∂ρ F
2



|∇ρ|
R2

2





η
J · Bext−
FR0R−2+ Ps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 GYROGood agreement with experimental data

CDBM Transport Model: CDBM05
s − α dependence ofF(s, α, κ, ωE1)

• Thermal Diffusivity (Marginal: γ = 0)
χTB = F(s, α, κ, ωE1) α3/2

2.5

c vA
ω2pe qR2

ω E1=02.0

ω E1=0.1
1.5

Magnetic shear
Pressure gradientElongation

ω E1=0.2

F

r dq
s≡
q dr

1.0

dβ
α≡ −q Rdr
κ ≡ b/aω E1=0.3

0.5

2

0.0
-0.5


F(s, α, κ, ωE1) =• Weak and negative magnetic shear,
Shafranov shift, elongation,

reduce thermal diffusivity.

0.5

1.0

s-α

r2 d EE × B rotation shear ωE1 ≡svA dr rB

and E × B rotation shear

0.0

×

2κ1/2
1 + κ2

3/2

⎧
1
1
⎪
⎪
⎪
⎪
1 + G 1ω2E1 2(1 − 2s )(1 − 2s + 3s2)⎪⎪⎪⎪⎨ for s = s − α < 0√ 5/2⎪⎪
1
1 + 9 2s⎪⎪√⎪⎪
1 + G 1ω2E1 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 Energy
CDBM
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:∂n s
1 ∂(rn su sr ) + S s
=−
∂t
r ∂r
1∂
∂
1
∂
(m sn su sr )=−(rm sn su2sr ) + m sn su2sθ + e sn s(Er + u sθ Bφ − u sφ Bθ ) − n sT s
∂t
r ∂r
r
∂r


1 ∂ 2
∂
∂
1 ∂
u
sθ
(m sn su sθ )=− 2 (r m sn su sr u sθ ) + e sn s(Eθ − u sr Bφ) + 2
r3 n s m sμ s
∂t
r ∂r
r ∂r
∂r r
C
W
X
L
+F NC
sθ + F sθ + F sθ + F sθ + F sθ




1∂
∂
∂
1∂
m sn su sφ =−(rm sn su sr u sφ) + e sn s(Eφ + u sr Bθ ) +rn sm sμ s u sφ
∂t
r ∂r
r ∂r
∂r
X
L
+F Csφ + F W
sφ + F sφ + F sφ



5
∂ 3
∂
1∂
n sT s =−ru sr n sT s − n sχ s T e + e sn s(Eθ u sθ + Eφu sφ)∂t 2r ∂r 2∂r+PCs + PLs + PHs

Typical Ohmic Plasma Profiles at t = 50 ms
JFT-2M like plasma composed of electron and hydrogen

R = 1.3 m, a = 0.35 m, b = 0.4 m, Bφb = 1.3 T, I p = 0.2 MA, S puﬀ = 5.0 × 1018 m−2s−1
γ = 0.8, Zeﬀ = 2.0, Fixed turbulent coefficient profile
0
−2
−4
−6

Er(r) [kV/m]−8
0.0 0.2 0.4 0.6 0.8 1.0
0.30
0.25
0.20
0.15
0.10
20 -3
0.05 ne [10 m ]0.00
0.0 0.2 0.4 0.6 0.8 1.0
6
5
4
3
2
1
0
6
5
4
3
2
1
0

uer [m/s]

0.8
0.6
0.4
0.2
0.0
Eθ [mV/m]−0.2
0.0 0.2 0.4 0.6 0.8 1.0

0.20

0.8

0.5

0.6
0.4
0.2

Te [keV]0.0
0.0 0.2 0.4 0.6 0.8 1.0

0.12

0.08

0.8

0.08
0.04

Eφ [kV/m]

0.00
0.0 0.2 0.4 0.6 0.8 1.0

0.04

8

4

4

2

Ti [keV]

0.0 0.2 0.4 0.6 0.8 1.0
1.0
0.8
0.6
0.4
0.2 uiθ [km/s]
0.0
0.0 0.2 0.4 0.6 0.8 1.0

0.25
0.20
0.15
0.10
0.05 uiφ [km/s]
0.00
0.0 0.2 0.4 0.6 0.8 1.0

4

−4

8

0.3
0.1

n01

[1014m-3]

0.0 0.2 0.4 0.6 0.8 1.0

0.030

6

0

n02 [1010m-3]
0.0 0.2 0.4 0.6 0.8 1.0

5De[m2/s]

χe=χi=μe=μi [m2/s]

4
3
2

0.015

1

0.000
0.0 0.2 0.4 0.6 0.8 1.00

0.0 0.2 0.4 0.6 0.8 1.0

2.5

q

3

2.0

jφ [MA/m2]

1.5

2

1.0

1
0

Bφ [T]

0.0
0.0 0.2 0.4 0.6 0.8 1.0

0.4

0.045

ueθ [km/s]

0.4

12

0
−100 ueφ [km/s]
−200
−300
−400
−500
0.0 0.2 0.4 0.6 0.8 1.00Bθ [T]

0.00
0.0 0.2 0.4 0.6 0.8 1.00−16

0.0 0.2 0.4 0.6 0.8 1.0

1.2

0.0
0.0 0.2 0.4 0.6 0.8 1.0−12uir [m/s]

0.12

0.2

−8

0.0 0.2 0.4 0.6 0.8 1.0

0.16

0.5
0.0 0.2 0.4 0.6 0.8 1.0

0.0
0.0 0.2 0.4 0.6 0.8 1.0

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
ne [1020m-3]

Er [kV/m]

4

0.4

0

0.3

−4
−8

0.2

−12

0.1

−16
0.0 0.2 0.4 0.6 0.8 1.0

0.0
0.0 0.2 0.4 0.6 0.8 1.0

ubφ [km/s]

2000
1000
0
−1000
−2000
−3000
0.0 0.2 0.4 0.6 0.8 1.0

q
4
3
2
1
0

0.0 0.2 0.4 0.6 0.8 1.0

uer [km/s]

2.5
no NBI
2.0
co
1.5
counter
1.0
0.5
0.0
0.0 0.2 0.4 0.6 0.8 1.0

Te [keV]

1.0
0.8
0.6
0.4
0.2
0.0
0.0 0.2 0.4 0.6 0.8 1.0

u [km/s]

5 eθ
0
−5
−10
−15
−20
−25
0.0 0.2 0.4 0.6 0.8 1.0

jφ [MA/m2]

2.5
2.0
1.5
1.0
0.5
0.0
0.0 0.2 0.4 0.6 0.8 1.0uiθ [km/s]
1.2

Ti [keV]
0.6
0.4
0.2
0.0
0.0 0.2 0.4 0.6 0.8 1.0

ueφ [km/s]

0
−100
−200
−300
−400
−500
−600
0.0 0.2 0.4 0.6 0.8 1.0
80
40

0.8

0

0.4

−40

0.0
0.0 0.2 0.4 0.6 0.8 1.0

uiφ [km/s]−80
0.0 0.2 0.4 0.6 0.8 1.0

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 numberL– Wave length λ much less than scale length L: λ– Beam size d is sufficiently large (Fresnel condition): L• Beam tracing:

d2/λ

EC

– New variables: beam radius, curvature of equi-phase surface• Beam propagation:EC– Under development: Time evolution of E(r, t) e i ωt

• 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 ↔
 (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 λCharacteristic scale length L of the medium– Plane wave: Beam size d is sufficiently large◦ Fresnel condition is well satisfied: Ld2/λ• Evolution along the ray trajectory τ– Wave packet position r, wave number k, dielectric tensor K– Ray tracing equation:∂K  ∂K
dr
=
dτ
∂k ∂ω
∂K  ∂K
dk
= −
dτ
∂r ∂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 
• Beam shape : Hermite polynomial: Hn)
E(r) = Re

Cmn( 2 r)e( 2 r)Hm(ξ1 )Hn (ξ2 ) e i s(r)−φ(r)mn– Amplitude : Cmn, Polarization : e, Phase : s(r) + i φ(r)s(r) =10ααs0(τ) + kα(τ)[r − r0 (τ)] + sαβ[rα − r0α(τ)][rβ − r0β(τ)]21
φ(τ) = φαβ[rα − r0α(τ)][rβ − r0β(τ)]
2– Position of beam axis : r0, Wave number on beam axis: k0– Curvature radius of equi-phase surface: Rα = 1/λsααR1– Beam radius: dα =2/φαα

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

R2

d1
d2

Beam Propagation Equation• Solvable condition for Maxwell’s equation with beam field
∂K
dr0α
=
dτ
∂kα
∂K
dkα0
= − α
dτ
∂r
dsαβ
∂2 K
∂2 K
∂2 K
∂2 K
∂2 K
= − α β − β sαγ − α sβγ − γ δ sαγ sβδ + γ δ φαγ φβδdτ∂r ∂r∂r ∂kγ∂r ∂kγ
∂k ∂k
∂k ∂k
 2
 2


2
2
dφαβ
∂K
∂K
∂K
∂K
+
s
−
+
sβδ φαγ
= −
φ
αδ
βγ
α
γ
γ
β
γ
γ
dτ
∂r ∂k
∂k ∂kδ∂r ∂k∂k ∂kδ

• 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∗ · ↔
 A · e)/(∂K/∂ω)Full wave analysis: TASK/WM• magnetic surface coordinate: (ψ, θ, ϕ)• Boundary-value problem of Maxwell’s equation
ω2 ↔
∇ × ∇ × E = 2  · E + i ωμ0 jextc
• Kinetic dielectric tensor: ↔
– Wave-particle resonance: Z[(ω − nωc)/k vth]
– Fast ion: Drift-kinetic





eα
∂
∂
(v E + ud · E)
+ v ∇ + (ud + uE) · ∇ +fα = 0∂tmα∂ε• Poloidal and toroidal mode expansion– Accurate estimation of k

• Eigenmode analysis: Complex eigen frequency which maximize wave
amplitude for fixed excitation proportional to electron density

Fokker-Planck Analysis : TASK/FP• Fokker-Planck equation
for multi-species velocity distribution function: f s(p , p⊥, ψ, t)∂ fs= E( f s) + C( f s) + Q( f s) + L( f s)∂t
– 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
BB = 5.300
RR = 6.200
RA = 2.000
RKAP = 1.700

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

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

4

PTPR(1)= 20.0000
PTPP(1)= 20.0000
PTS(1) = 0.0500
MODELP1= 25.
8PA(2) = 2.0000
PZ(2) = 1.0000
PN(2) = 0.4000
PNS(2)= 0.0050

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

ABS POWER

7
6
5
4

2

3
2
1
0
0.0
0.2
0.4
ABS WEIGHT POWER
1.4

0

0.6

0.8

1.0

0.6

0.8

1.0

1.2
1.0
0.8

-2

0.6
0.4
0.2
-4
4

5

6

7

8

0.0
0.0

0.2

0.4

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 = 2.65
Time evolution

Radial profile• Hybrid operation– Ip = 12 MA– PNB = 33 MW on axis
– βN = 2.68
Time evolution

Radial profileAlfvén Eigenmode Analysis by TASK/WM• Alfvén 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)
Alfvén continuum frequency
Alpha particle density

Alfvén 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 MHD events:

nonlinear behavior of ELM on transportmodeling of plasma profile change• Energetic-ion driven phenomena:
coupling of Alfvén mode and drift waves• Kinetic analysis of transport and MHD phenomena:
non-Maxwellian distribution• Wave physics:• Divertor plasma:• Start up:
and so on...

full wave analysis of Bernstein waves
plasma-wall interaction
Rapid change of equilibrium and control

Summary• Integrated modeling of burning plasmas is indispensable for
exploiting optimized operation scenario of ITER and reliable design of DEMO.

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

• There are many remaining issues in constructing comprehensive 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 intensive modeling efforts basedon experimental observations.