high performance operational limits of tokamak and helical

1

a) National Institute for Fusion Science, Toki, Gifu 509-5292, Japanb) Japan Atomic Energy Research Institute, Naka, Ibaraki 311-0193, Japan

Kozo Yamazakia and Mitsuru Kikuchib

High Performance Operational Limits of

Tokamak and Helical Systems

ITC-12/APFA701December 11(TUE) ~ 14(FRI), 2001

Ceratopia, Toki City, Japan

2

1. Introduction2. Achieved operational domain3. Equilibrium Properties4. Confinement5. Stability Limit6. Density Limit7. Steady-State Operation8. Reactor Prospect9. Summary

Outline

3

INTRODUCTIONFor the realization of attractive fusion reactors,

plasma operational boundaries should be clarified, and be extended to the higher performance limit.

There are several plasma operational limits:(1) confinement Limit ,(2) stability Limit,(3) density limit, and (4) pulse-length limit.

Here we would like to discuss on a variety of toroidal plasma operational limits focusing on thesimilarities and differences between TOKAMAK and HELICAL systems.

4

Maximum Parameters Achieved

Electron TemperatureTe (keV) 25

(ASDEX-U,JT-60U)) 10 (LHD)

Ion TemperatureTi (keV) 45 (JT-60U) 5.0 (LHD)

Confinement timeτE (s)

1.21.1

(JET)(JT-60U,NS) 0.36 (LHD)

Fusion Triple Productni τE Ti (m

-3・s･keV) 15x1020 (JT-60U) 0.22x1020 (LHD)Stored Energy

Wp (MJ)1711

(JET)(JT-60U,NS) 1.0 (LHD)

Beta Valueβ (%)

40 (toroidal)12 (toroidal)

(START)(DIII-D) 3.0 (average) (LHD,W7-AS)

Line-Averaged Densityne (1020m-3) 20 (Alcator-C) 3.6 (W7-AS)

Plasma Durationτdur

2 min3 hr. 10min.

(Tore-Supra)(Triam-1M)

2 min1 hour

(LHD)(ATF)

TOKAMAK HELICAL

5

Normalized parameters

Operation Regime and Reactor Requirements

0.01

0.1

1

10

<bet

a>

.001 .01 .1

<rho>

ASDEX AUG CMOD COMPASS D3D JET JFT2M JT60U PBXM PDX TCV

TOK

重ね合わせプロット

0.001

0.01

0.1

1

10

100

<nu>

.001 .01 .1

<rho>


TOK


0.01

0.1

1

10

<bet

a>

.001 .01 .1

<rho>

ATFCHSFFHRHELEHSRLHDMHRSPPSW7-AW7-AS

STELL


0.001

0.01

0.1

1

10

100

<nu>

.001 .01 .1

<rho>


STELL


*ρ

β

*ρ

*ν*ν

SSTR

SSTR

MHR

MHR

HELICALTOKAMAK

*ρ *ρ

β

22

22/5*

*

/~/

)/(~/

)/(~/

BnTBnkT

Tnaa

aBTa

thei

s

=

=

=

β

εννν

ρρ

LHD high-beta

DIII-D high-beta

FFHR

FFHR

6

Similarities and Differences between Tokamak and Helical Systems

STANDARD TOKAMAK STANDARD HELICAL

Plasma BoundaryShape

2D 3D

Magnetic FieldComponents

Toroidal (m,n)=(1,0)Toroidal (1,0) +Helical

(L,M)+ Bumpy (0,M) Ripples

Plasma Currents External + BS CurrentsNo net toroidal current

or BS Current

q-profileNormal or

Reversed shear profileFlat or

Reversed shear profile

DivertorPoloidal divertor

2DHelical or island divertor

3D


Magnetic shearSubstantial Shear orShearless in the core

Substantial Shear

Magnetic Well Well in whole region Hill near edge

Radial Electric Fielddriven by toroidal rotation

& grad-pdriven by non ambipolar

loss (Helical Ripple)Toroidal Viscosity Small Large (Helical Ripple)

grad-j, grad-pgrad-j drivengrad-p driven

grad-p dominant

Island, Ergodicity near separatrix Edge Ergodic Layer

PhysicsProperties

Equilibrium

7

QA

QP

QO

QH

M=2 M=3

Core Symmetry

Quasi Omunigenity

Quasi Axi-Symmetry

Quasi Helical Symmetry

Quasi Poloidal Symmetry

Helical Divertor

Edge Symmetry

M=4

M=5

M/L=10/2M/L=4/1

Advanced Plasma Shapes

StandardTokamak

StandardHelical

M=0(n=0)

Larger M

8

Magnetic Shear / WellTokamak:Shear is changed

by current profile.Magnetic well.

Helical:A variety of shears

by helical coil.Magnetic hill near edge.

Flat or Reversed Shear

Normal or Reversed Shear

0

0.5

1

1.5

2

0 0.2 0.4 0.6 0.8 1

1/q

rho

TJ-II

LHD

JT-60U Normal Shear

W7-AS

JT-60U Current Hole

9

Confinement Scaling LawsComparing between ITER ELMy-H Database and

stellarator Database adding LHD data

0.001

0.01

0.1

1

10

tau_

exp

.001 .01 .1 1 10

tau_IPB98(y)


STELL


0.001

0.01

0.1

1

10TA

UTO

T

.001 .01 .1 1 10

IPB98(y)


TOK


0.001

0.01

0.1

1

10

TA

UTO

T

.001 .01 .1 1 10

tau_ISS


TOK


0.001

0.01

0.1

1

10

tau_

exp

.001 .01 .1 1 10

tau_ISS95


STELL


40.03/2

80.051.059.065.021.295 08.0 ιτ BnPRa eISSE

−=

97.023.008.041.063.093.10365.0 IBnPR eELMYE ετ −=

95ISSEτ

ELMYEτ

10.050.083.0 ** −−−∝ νβρττ BELMYE

04.016.071.095 ** −−−∝ νβρττ BISSE

EXPEτ

EXPEτ EXP

Eτ

EXPEτ

Reactor

Reactor

HELICALTOKAMAK

10

Positive electric field driven by ripple loss in low density regimepredicted by Neo-Classical Theory

Er shear driven by toroidal rotaion and grad-p (JT-60U,Shirai)

0.1

1

10

χ [m

2 /s]

χiN C

-2

-1

0V

φ [1

05 m

/s]

-40

-20

0

0 0.5 1

Er [

kV/m

]

r/a

Vφ

Er

ITB

ITB

χe

χi

HELICALTOKAMAK

Radial Electric Field & ITB

NC-ITB (CHS, Minami & Fujisawa)

11

•

• •

Targets

Baffles

Titanium evaporators

•

•

Island DivertorPoloidal Divertor Helical Divertor

Short connection lengthRather clean separatrixRemote radiation

LHD W7-AS, LHDITER

HELICALTOKAMAK

0 105 R (m)

Island, Ergodicity and Divertor

12 3.6 3.7 3.8

Magnetic Axis Position (m)

Equilibrium limit

unstable

Experiment

6

4

2

0V

olum

e A

vera

ged

Bet

a (%

)

0

1.0

2.0

3.0

0 0.2 0.4 0.6 0.8 1.0

Rax

=3.6m Rax

=3.75m

β t (%)

ρ

V''=0

Unstable Region

Mercier DIagram

DI=0

N

0

1

2

3

4

5

0 0.2 0.4 0.6 0.8 1 1.2

β

εβp

H-mode

high-βp mode large p0/<p>

high-βN medium p0/<p>

qedge/q0=4

qedge/q0=6

PBX-M

T-11JT-60U

TFTRASDEX

ITER

DIII-D

DIII-D

1 2 30

2

4

6

8

10

12

βN =3.5

Stability

Normalized current I/aB (MA/m/T)

Tokamak Helical

LHD

Ideal beta agrees with Ideal MHD

Resistive beta agrees with NTM & TM, RWM theories

Beta obtained beyond Mercier mode

Global mode is still marginal.

JT-60U

grad-j dominant or grad-p dominant ?Stability Limits

13

Mode structure

0

0. 5

1

2

3

4

5

6

7

0 0 . 5 1ρ

p

q

m=3m=4

m=5

m=6

m=7

0 0.5 10

1

ρξr

ρ(=√ψ)

(JT-60U, Takeji)ERATO-J code

(LHD, Nakajima)CAS3D code

Low-n mode isinterchange-like.

High-n mode isballooning-like.

HELICALTOKAMAKGlobal mode driven by grad-j

Localized mode driven by grad-p

14

max

imu

m

β N

Position of conductor : rw /a

n=1

n=2n=3

n=4

0 .0

1 .0

2 .0

3 .0

4 .0

5 .0

6 .0

1 .2 1 .4 1 .6 1 .8 2 .0 2 .2 2 .4 2 .6

unstable

stableBallooning mode is stable in the area : βN < 6.

0 .0

0 .2

0 .4

0 .6

0 .8

1 .0

2 . 0

2 . 5

3 . 0

3 . 5

4 . 0

4 . 5

0 . 0 0 .2 0. 4 0. 6 0 . 8 1 . 0

p(ρ

) q(ρ

)

ρ

p(ρ)

q (ρ)

(JT-60SC,Kurita)

Tokamak HelicalMode is localized andthere is no strong wall effect on pressure-driven mode, but substantial effects on BS current-driven external mode.

(LHD,Cooper)

Terpsichore

Effects of Wall

Kink-ballooning modes driven by grad-j & grad-p can be easily stabilized by the fitted wall.

Stable

Unstable (b/a>1.2)

15

Operational Density Regime

1e+18

1e+19

1e+20

1e+21

NEB

AR

1e+18 1e+19 1e+20 1e+21

nGR


TOK


1e+18

1e+19

1e+20

1e+21

NEB

AR

1e+18 1e+19 1e+20 1e+21

ncr


TOK


1e+18

1e+19

1e+20

1e+21

NEB

AR

1e+18 1e+19 1e+20 1e+21

nGR

ATFCHSHELELHDW7-AW7-AS

STELL


1e+18

1e+19

1e+20

1e+21

NEB

AR

1e+18 1e+19 1e+20 1e+21

ncr

ATFCHSHELELHDW7-AW7-AS

STELL


radiation collapseleading to current disruption

radiation collapseslow plasma decay

HelicalTokamak

LHDn_ LHDn_

GRn_ GRn_

EXPn_

EXPn_

EXPn_

EXPn_

2_20 25.0mm

TMWLHD aR

BPn =

2_20m

MAGR a

In

π=

16

WVII- A Team,Nucl. Fusion 20 (1980) 1093.

Fujita et al., IEEE Transaction on Plasma SciencePS-9 (1981) 180.

Disruption-Free in Helical System ?

W7-A JIPP T-IITearing mode, even NCTM,can be stabilizedin helical system?

m/n=1/1Wex/a=0.085

LHD

Tokamak - Helical Hybrid(Current Carrying Stellarator)

17

NB Current Drivein JT-60U RS Elmy H-mode

(80% bootstrap current fraction)

~1keV long pulse operation In LHD (ICRF 0.8MW)

Steady-state OperationI p(

MA)

0

1

4 6 8 10 12

Full non-inductive CD Ip

time (s)

Ibs

Ibeam

LH Current Drivein Triam-1M (3hr.10min.)

Tokamak Helical

(Triam-1M,Sakamoto，

this conference)

18

0

5

10

15

20

25

30

1970 1975 1980 1985 1990 1995 2000 2005 2010

R(m)

Year

FFHR-1

MHR-S

QP#1

MSRH-H

U-M

T-1

HSR

CT6

SPPS

QA#1MHR-C

Progress on Reactor DesignsLower-aspect designs are explored.

Helical

Tokamak SSTR

SSTRARIES-RS

A-SSTR2

19

Operational Limits


Confinement Gyro-BohmGyro-Bohm (Grobal)

Helical Ripple Effect (Local)

Beta LimitKink-Ballooning ModeResistive Wall Mode

Neoclassical Tearing Mode

Low-n Pressure-DrivenMode

Density LimitRadiation & MHD

CollapsesRadiation Collapse

Pulse-Length LimitRecycling Control

Resistive Wall ModeNeoclassical Tearing Mode

Recycling ControlResistive mode (?)

Beyond limitThermal collapse

Current disruption Thermal collapse

20

Summary

● For realization of attractive fusion reactors, better confinement and longer-pulsed operations should be achieved in addition to burning plasma physics clarification.

●In tokamak systems, critical issue is to avoid disruption and to demonstrate steady-state operation.●In helical systems, high performance discharges should be demonstrated with reliable divertor, and compact design concepts should be developed.

● Each magnetic concepts should be developed complementally focusing on above critical issues keeping their own merits, for realization of attractive reactors and forclarification of common toroidal plasma confinement physics.

high performance operational limits of tokamak and helical

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