11 Progress of Steady-state Tokamak towards Fusion Energy Utilization in the Later Half of 21st...

11

Progress of Steady-state Tokamak Progress of Steady-state Tokamak towards Fusion Energy Utilization in towards Fusion Energy Utilization in

the Later Half of 21st Centurythe Later Half of 21st Century

Progress of Steady-state Tokamak Progress of Steady-state Tokamak towards Fusion Energy Utilization in towards Fusion Energy Utilization in

the Later Half of 21st Centurythe Later Half of 21st Century

2008 International Workshop on Frontiers in Space and Fusion Energy SciencePlasma and Space Science Center, National Cheng Kung University

November 6-8November 6-8JAEAJAEA

M. KikuchiM. Kikuchi

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1. Y2008 is anniversary year for 50 years of Fusion Research1. Y2008 is anniversary year for 50 years of Fusion Research

22nd IAEA Fusion Energy Conference held at Geneva last month22nd IAEA Fusion Energy Conference held at Geneva last month

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2. Fusion Research is a project to realize Sun on the Earth2. Fusion Research is a project to realize Sun on the Earth

Galaxy

Sun

ITER

QuantityITERSunRatioDiameterCentral tempCentral densityCentral press.Power densityReactionPlasma massBurn time const16.4m140x104km~1/108200Mdeg15Mdeg10~1020/m 3~1032/m 31012~5atm~1012atm~1011~0.6MW/m3~0.3W/m3DT reactionpp reaction0.35g2x1030kg1/6x10 33200s1010years1015~2x106Plasma temperature of ITER is more than 10 time of center of Sun.520Mdeg much higher than that of ITER was already achieved at JT-60U in 1996 so that we are confident to achieve such high plasma temperature in ITER.

4

New Stone Age Bronze/Iron Ages

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3. A BIG transition in population and energy consumption at 20003. A BIG transition in population and energy consumption at 2000

Question to 21st Century : Can we sustain large population & energy consumption w/o fossil fuels.Question to 21st Century : Can we sustain large population & energy consumption w/o fossil fuels.

Fossil Era will end in a momentFossil Era will end in a moment

5

4. Industrial Revolution is needed to reduce of CO4. Industrial Revolution is needed to reduce of CO22 emission emission

Revolution in energy user sectors (Transportation(CAR), Industry(Steel), Living)Revolution in energy sources (Fossil to Renewables & Nuclear)

12

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Toyako summit(July,2008)

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5. Role of Fusion in the JAEA Vision toward low Carbon Society 5. Role of Fusion in the JAEA Vision toward low Carbon Society

http://www.jaea.go.jp/02/press2008/p08101601/index.html (in Japanese)

In October 16, JAEA press-released a vision to reduce CO2 emission of Japan to 1/10 in 2100.Point is importance of consideration on later half of this century. This is not a prediction, which is difficult.

RenewablesHydroFusionFissionCoalNat. Gas

RenewablesHydroFusionFissionCoalNat. Gas

Fusion will not enter energy market in first half of this centuryFirst quarter is ITER Era.Second quarter is DEMO Era.If ITER&DEMO are successful, we could move to commercialization in second half of this century.It is important to make non-negligible contribution to energy.

Fusion will not enter energy market in first half of this centuryFirst quarter is ITER Era.Second quarter is DEMO Era.If ITER&DEMO are successful, we could move to commercialization in second half of this century.It is important to make non-negligible contribution to energy.

DEMO: Load map by Fusion Forum of Japan

DEMO: Load map by Fusion Forum of Japan

M ton CO2M ton CO2

Electricityproduction by sourcesElectricityproduction by sources

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6. Fusion has many attractive features as energy sources6. Fusion has many attractive features as energy sources

M. Kikuchi, N. Inoue, "Role of Fusion Energy for the 21 Century Energy Market and Development Strategy with International Thermonuclear Experimental Reactor ", 18th World Energy Congress, Buenos Aires, 2001.

3. In case of nuclear accident, radiological toxic hazard potential of T from Fusion is less than 1/1000 of that of 131I from Fission.

3. In case of nuclear accident, radiological toxic hazard potential of T from Fusion is less than 1/1000 of that of 131I from Fission.

LWR(TRU)LWR(TRU)

FusionFusion

Coal ashCoal ash

5. CO2 emission from fusion is small and comes only during construction.

5. CO2 emission from fusion is small and comes only during construction.

4. Total radiological toxic hazard potential of Fusion waste decays within 100years to the level of coal ash.

4. Total radiological toxic hazard potential of Fusion waste decays within 100years to the level of coal ash.

8

7. Magnetic Fusion Research7. Magnetic Fusion Research

Major magnetic confinement configurations Tokamak and HelicalMajor magnetic confinement configurations Tokamak and Helical

HelicalIntrinsically steady Research issue: Confinement improvement at high T

HelicalIntrinsically steady Research issue: Confinement improvement at high T

TokamakShort pulse (<30s) confinement is good Research issue : Steady-state operation

TokamakShort pulse (<30s) confinement is good Research issue : Steady-state operation

Plasma currentPlasma current

Primary currentPrimary current

Lawson DiagramLawson Diagram

Thermal transport at low *Thermal transport at low *

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80% bootstrap fraction in JT-60 is a basis for this concept

80% bootstrap fraction in JT-60 is a basis for this concept

8. Steady-state Tokamak Reactor8. Steady-state Tokamak Reactor

To resolve pulsed nature of Tokamak system, use of bootstrap current and active current drive is essential.

To resolve pulsed nature of Tokamak system, use of bootstrap current and active current drive is essential.

M. Kikuchi, M. Azumi, PPCF 37(1995)1215M. Kikuchi, M. Azumi, PPCF 37(1995)1215

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9. What is bootstrap current ?9. What is bootstrap current ?

M. Kikuchi, M. Azumi, PPCF 37(1995)1215M. Kikuchi, M. Azumi, PPCF 37(1995)1215

In toroidal magnetic confinement system, particles with small v // are trapped by the magnetic mirror (trapped particles) and have larger radial excursion with their “banana orbit”. This radial excursion produces shift of e. velocity distribution function counter to plasma current. Then, collisional diffusion across the trapped-untrapped boundary produces particle flow to untrapped region. This current can be a large fraction of plasma current, say 75% in SSTR.

Mechanism of bootstrap current generationMechanism of bootstrap current generation

Parallel momentum and heat momentum equationsParallel momentum and heat momentum equations

Generalized Ohm’s LawGeneralized Ohm’s Law

Bootstrap Current FractionBootstrap Current Fraction

Jbs~dP/dr/Bp

Ibs/Ip~0.670.5p

p=20<P>/Bp2

Jbs~dP/dr/Bp

Ibs/Ip~0.670.5p

p=20<P>/Bp2

11

M. Kikuchi, M. Azumi, PPCF 37(1995)1215M. Kikuchi, M. Azumi, PPCF 37(1995)1215 T. Oikawa, et al., NF41(2001)1575T. Oikawa, et al., NF41(2001)1575

€

F = Jbd ⋅B / Jfast ⋅B

M, L: viscous and friction matrixSb : momentum and heat momentum source

10. Beam driven current10. Beam driven current

The bootstrap current is driven by pressure gradient, which is difficult to control. So, some part of the plasma current have to be controlled by the external means, either NBI or RF(ex.ECCD).

Generalized Ohm’s LawGeneralized Ohm’s Law

Beam-driven current Beam-driven current

Stacking factorStacking factor

JT-60U and N-NBIJT-60U and N-NBI JT-60U and N-NBIJT-60U and N-NBI

CD with Te and EbCD with Te and EbDriven current up to 1MA

agrees with TheoryDriven current up to 1MA

agrees with Theory

CD =RICDne/PCD~5x1019Am-2/W is required for SSTRCD =RICDne/PCD~5x1019Am-2/W is required for SSTR

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Reversed shear is first proposed by Ozeki (1992) as MHD stable operation mode for the Steady-state Tokamak.T. Ozeki et al., 14th IAEA Conf. Wurzburg, Germany, IAEA-CN-56/D-4-1(1992) See also, T. Ozeki et al., PPCF 39(1997)A371

Original steady-state operation mode is normal shear mode with q(0)>1.5-2 for the ballooning mode stability.

This requires wall stabilization, which led to strong activity of RWM stabilization of “toroidal” plasma (note : RWM can not be stabilized in ideal cylindrical plasma due to slipping of plasma with respect to the mode).

RS plasma is ideally stable if dP/dr at qmin is small. -- Closely related to position of ITB ---

RS plasma is ideally stable if dP/dr at qmin is small. -- Closely related to position of ITB ---

High confinement regimeHollow J profile

Internal Transport BarrierPlasma Pressure

plasmaRS regime

11. Current Profile control11. Current Profile control

13

Current Hole (CH) is an extreme case of RS configuration with q(0)CH has been stably sustained above current diffusion time.

Central axisPlasma Cross- sectionCurrent densityCurrent Hole

T. Fujita et al., P.R.L. 87(2001)245001N.C. Hawkes et al., P.R.L. 87(2001)115001T. Fujita et al., P.R.L. 87(2001)245001N.C. Hawkes et al., P.R.L. 87(2001)115001

12. Current Hole as unique Structure Formation in Tokamak12. Current Hole as unique Structure Formation in Tokamak

These experiments led to many PRLl works such as Huysmans2001, Martynov2003, Wang2004, Rodrigues 2005&2007 These experiments led to many PRLl works such as Huysmans2001, Martynov2003, Wang2004, Rodrigues 2005&2007

An explanation of CH by equilibria with negative current, Rodrigues 2007Question still arise why CD at CH is difficult with this equilibria.

CH has merit to increase bootstrap current by Jbs~1/Bp dependence and elongation by lower li.CH has demerit of a particle loss with lower Bt ripple. Reactor application not well assessed.

CH has merit to increase bootstrap current by Jbs~1/Bp dependence and elongation by lower li.CH has demerit of a particle loss with lower Bt ripple. Reactor application not well assessed.

14

L-modeL-mode

Pressure Profile Hollow J profileHollow J profile

Pre

ssu

re P

rofi

le

Normal J ProfileNormal J Profile

Pre

ssu

re P

rofi

le

H-modeH-mode Reversed shear modeReversed shear modeHigh p modeHigh p mode

J P

rofi

le

J P

rofi

le

High p H-modeHigh p H-mode RS H-mode RS H-mode ETB : edge transport barrierITB: internal transport barrier

ETB : edge transport barrierITB: internal transport barrier

There are many improved modes starting from Wagner’s H-mode. “ITB” is accepted as common phenomena after Koide’s PRL 94.

[1] Y. Koide, M. Kikuchi et al., PRL72(1994)3662, Naming of “ITB”[2] R. Nazikian, K. Shinohara et al., PRL94(2005)135002, “Turbulence de-correlation during ITB formation”

13. Families of Improved Confinement Modes in Tokamak13. Families of Improved Confinement Modes in Tokamak

“ITB” is associated with Turbulence de-correlation as measured in ITB of JT-60U.

“ITB” is associated with Turbulence de-correlation as measured in ITB of JT-60U.

“ITB” is local relaxation of “long radial correlation”“ITB” is local relaxation of “long radial correlation”

15

[1] Y. Kishimoto et al., POP 3(1996)1289- Semi-global ITG inclined by Bloch angle- Critical temp. gradient model =0(- Intermittent transport induced by vortex dissipation

[3] F. Ryter et al., PRL(2005) Critical temperature Tc in electron transport in AUG.

[3] F. Ryter et al., PRL(2005) Critical temperature Tc in electron transport in AUG.

Sand collapse in sand hill and Bernard cell are typical examples of self-organized criticalitySand collapse in sand hill and Bernard cell are typical examples of self-organized criticality

14. Understanding of L-mode : 14. Understanding of L-mode : SSelf elf OOrganized rganized CCriticalityriticality

“Self-organized criticality” is a common phenomena in Nature

[2] K. Miki,Y. Kishimoto et al., PRL(2007)145003- Explanation of Dimits shift by GAM dynamics- New intermittent transport by GAM below Dimits shift

Critical temperature gradient also exists on ion (see JET IAEA08)

Critical temperature gradient also exists on ion (see JET IAEA08)

Features of SOC same with L-mode1. Profile resilience to keep SOC2. Intermittent transport3. Long correlation length4. May explain offset-linear scaling

Hea

t F

lux

Temperature Gradient

Critical Temperature Gradient Model

(dT/dr) crit

center surface

Pre

ssu

re

L-mode





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R= 0

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R=1800Chandraseckhar, Hydrodynamic and Hydromagnetic stability

P. Bak, Phys. Rev. A38(1988)364

M. Kikuchi et al., Nuclear Fusion 27(1987)1239

M. Kikuchi et al., Nuclear Fusion 27(1987)1239

16

High p mode: Koide IAEA94

RS mode: Fujita NF38(1998)207

ua(1)

u//a b

ua

(Diamagnetic flow)

(Parallel flow)

ua(1) = u⊥a(1) + u//ab

ÅEErυEB

15. Toroidal symmetry plays important role in Tokamak15. Toroidal symmetry plays important role in Tokamak

<R2a>=0

<R2a>=0

Toroidal symmetryToroidal symmetry

<(F/B)ba>=<B-

1(bxa>

<(F/B)ba>=<B-

1(bxa>

(=o(/L)2)

Mn(d/dt)<RV>=<R2a>=o(/

L)2)

Mn(d/dt)<RV>=<R2a>=o(/

L)2)

Easier to drive plasma rotation and hence ExB shear turbulence suppression

Impurity Toroidal Rotation:

Er can be calculated as,

17

16. Gyro-kinetic PIC/ Vlasov simulation clarifies turbulence16. Gyro-kinetic PIC/ Vlasov simulation clarifies turbulence

Zonal flow dynamicsUse of canonical Maxwellian is essential for Zonal flow simulation

Y. Idomura, et al, NF43(2003)234 (2006 NF prize nominees)

Global ETG turbulence simulation clarifyShear-less ETG : Zonal flow due to 2D turbulence (HM-equation) Y. Idomura, Physics of Plasmas 13(2006)080701With shear : ETG mode coupling to produce streamer

Full f Vlasov, source-driven ITG simulation Y. Idomura et al., 22nd IAEA FEC (2008)LTi/R kept constant and 1/f spectrum in L-mode : SOC QuickTime˛ Ç∆

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p

17. MHD Regime of exploitation changed to high 17. MHD Regime of exploitation changed to high pp regime regime

3

2

1

0

0 5 10

t (%)

t=NIp/aBtt=NIp/aBt

pt=N2/4pt=N2/4

Poloidal p=4Pdv/Ip

2

Poloidal p=4Pdv/Ip

2

High beta pulsedHigh beta pulsed

High beta poloidal steadyHigh beta poloidal steady

N~3.3(No wall-limit)

N~4.5(wall stabilization)

Steady-state requires operation at high poloidal Steady-state requires operation at high poloidal beta to increase bootstrap current fractionbeta to increase bootstrap current fraction

Steady-state requires operation at high poloidal Steady-state requires operation at high poloidal beta to increase bootstrap current fractionbeta to increase bootstrap current fraction

This constraint led to advanced tokamak research This constraint led to advanced tokamak research to move to high beta poloidal and hence high q.to move to high beta poloidal and hence high q.

This constraint led to advanced tokamak research This constraint led to advanced tokamak research to move to high beta poloidal and hence high q.to move to high beta poloidal and hence high q.

To achieve high power density for the reactor, beta To achieve high power density for the reactor, beta regime above no-wall limit is required.regime above no-wall limit is required.

To achieve high power density for the reactor, beta To achieve high power density for the reactor, beta regime above no-wall limit is required.regime above no-wall limit is required.

19

18. Kinetic Alfven Wave and Stabilization of Resistive Wall Mode18. Kinetic Alfven Wave and Stabilization of Resistive Wall Mode

Early1990’s, wall stabilization was thought to be difficult. Why?Reasons :[1] Wall is not ideal wall but is resistive wall.[2] Ideal MHD can not be stabilized by plasma rotation for resistive wall since RWM is attached to wall while plasma is rotating (slipping of plasma w.r.t. mode. Wall condition Br=0 will not work.( Say, [1] C.G. Gimblett, N.F. 26(1986)617 : Ideal MHD plasma will not be stabilized by rotation with Resistive wall)

Non-ideal effect to damp the RWM is required.[1] Hasegawa-Chen , Kinetic Alfven Wave(KAW) (1974, first proposed as heating method)

Plasma rotation

Stabilization of RWM

RWM is fixed to wallRWM is fixed to wall





KAW(>me/mi)KAW(>me/mi)

Mechanism of Kinetic Damping:- Mode conversion of Shear Alfven wave to Kinetic W (KAW)r =k//vA .-KAW have parallel electric field and wave can be damped by the Landau damping.A. Hasegawa, Liu Chen, Phys. Fluids 19(1976)1924.

Sound Wave Damping: gives too weak damping

Mechanism of Kinetic Damping:- Mode conversion of Shear Alfven wave to Kinetic W (KAW)r =k//vA .-KAW have parallel electric field and wave can be damped by the Landau damping.A. Hasegawa, Liu Chen, Phys. Fluids 19(1976)1924.

Sound Wave Damping: gives too weak damping

20

0

0.2

0.4

0.6

0.8

1

-60 -40 -20 0 20

C

Vt( / ) =km s at q

N

-no wall

x

xx

xx

x

N

-ideal wall

DIII-DJT-60U

H. Reimerdes et al. (DIII-D) , PRL98(2007)055001M. Takechi et al. (JT-60U) , PRL98(2007)055002H. Reimerdes et al. (DIII-D) , PRL98(2007)055001M. Takechi et al. (JT-60U) , PRL98(2007)055002

C=(-NW)/(W-NW)C=(-NW)/(W-NW)

19. Resistive Wall Mode can be stabilized by V19. Resistive Wall Mode can be stabilized by Vcc/V/VAA~0.3%~0.3%

21

20. Reactor relevant high bs discharge was achieved at low q20. Reactor relevant high bs discharge was achieved at low q





Y. Sakamoto et al., IAEA08Y. Sakamoto et al., IAEA08

















22

21. Plasma rotation changes MHD operator to non-Hermitian21. Plasma rotation changes MHD operator to non-Hermitian

Linear MHD operator without flow : t2 = Ls

Ls is a self-adjoint and stability can be judged by the sign of energy integral.

Linear MHD operator without flow : t2 = Ls

Ls is a self-adjoint and stability can be judged by the sign of energy integral.

Linear MHD operator with flow : t2+2(u)t = (Ls+LD)

Ld = [(u)u-u(u)] is self-adjoint, but 2(u)t is

not.Stability can not be judged by the sign of energy integral.Initial value problem (Aiba, IAEA 2008), or Laplace transform (Hirota).

Linear MHD operator with flow : t2+2(u)t = (Ls+LD)

Ld = [(u)u-u(u)] is self-adjoint, but 2(u)t is

not.Stability can not be judged by the sign of energy integral.Initial value problem (Aiba, IAEA 2008), or Laplace transform (Hirota).

E. Frieman and M. Rotenberg, Reviews of Modern Physics 32(1960)898E. Frieman and M. Rotenberg, Reviews of Modern Physics 32(1960)898

Frieman-Rotenberg EquationFrieman-Rotenberg Equation

Standard MHD EquationStandard MHD Equation

23

N. Oyama et al, PPCF49(2007)249 ： ELM can be soften by toroidal rotation.

N. Oyama et al, PPCF49(2007)249 ： ELM can be soften by toroidal rotation.

Energy loss is excessive for Type I ELM, and may shorten the divertor life time of ITER. Grassy ELM regime is preferable.Energy loss is excessive for Type I ELM, and may shorten the divertor life time of ITER. Grassy ELM regime is preferable.

a

c

H BurstH BurstChange in Stored Energy

Change in Stored Energy

Toroidal Rotation profile

Toroidal Rotation profile

Vt/2R (kHz)Vt/2R (kHz)

q~6.5,~0.55, p~0.84-1.88q~6.5,~0.55, p~0.84-1.88

Rotation sheard/dq<120kHz

Rotation sheard/dq<120kHz

Issue : asymmetry in rotation direction and off-set Issue : asymmetry in rotation direction and off-set

22. ELM change its character by Rotation22. ELM change its character by Rotation

24

N. Aiba, S. Tokuda et al., IAEA2008N. Aiba, S. Tokuda et al., IAEA2008

Solve F-R eq. for peeling mode as initial value problem

Solve F-R eq. for peeling mode as initial value problem

[t2-Ut] = (f)-g

[t2-Ut] = (f)-g

M. Furukawa, S. Tokuda, PRL94(2005)175001M. Furukawa, S. Tokuda, PRL94(2005)175001

Flow shearFlow shear

Stabilization by flow shearStabilization by flow shear

Ballooning mode equation with flowBallooning mode equation with flow

/A0 of the infinite-n

ballooning mode at s=0.78.

Dependence of /A0 on 1/nEigenfunctions of the n=500 mode.(up: static, down M0=0.29)

23. Ballooning/Peeling Mode changes by rotation shear23. Ballooning/Peeling Mode changes by rotation shear

25

NTM suppression by ECCD becomes crucial for SSTRNTM suppression by ECCD becomes crucial for SSTR

Since steady-state tokamak best utilizes the bootstrap current, NTM (Neoclassical Teaing Mode) becomes important issue.Since steady-state tokamak best utilizes the bootstrap current, NTM (Neoclassical Teaing Mode) becomes important issue.

Z. Chang et al., PRL74(1995)4663 - First measurement of NTM

ITER : e* ~ 0.03 , 1ce JT-60U : e* ~ 0.03 , 1ce DIII-D : e* ~ 0.03 , 2ce AUG : e* ~ 0.16 , 2ce

Completely suppressed by ECRF using the auto-tracking EC mirror system for the first time in JT-60U ( Isayama, NF03).

Completely suppressed by ECRF using the auto-tracking EC mirror system for the first time in JT-60U ( Isayama, NF03).

24. Steady-state Tokamak subject to NTM24. Steady-state Tokamak subject to NTM

NTM : local loss of P at magnetic island leads to the loss of bootstrap current, which de-stabilizes tearing mode.NTM : local loss of P at magnetic island leads to the loss of bootstrap current, which de-stabilizes tearing mode.

1.5

3.0

2.0

1.0

Bootstrap current

1.00.0 r/a

P

q

Loss of bootstrap current due to island formation

26

Early injection is effective for NTM suppression (Nagasaki, NF03, NF05) Early injection is effective for NTM suppression (Nagasaki, NF03, NF05)

JECCD~0.5Jbs can stabilize NTM with Optimum ECCD (Isayama, NF07) JECCD~0.5Jbs can stabilize NTM with Optimum ECCD (Isayama, NF07)

Late injectionReal-time FB on

•

Early injectionReal-time FB off

••

GGJPolarizationClassicalBootstrapECCD

€

0

η

dW

dt= k

c′ Δ W( ) ∇ ρ

2

+ kBSμ

0L

qjBS

∇ ρ

Bp

W

W2

+ Wd

2− k

GGJεs

2

βp

Lq

2

ρsL

p

1 −1

q2

⎛

⎝ ⎜

⎞

⎠ ⎟ ∇ ρ

2 1

W

€

− kpolε

s

1 . 5

βp

ρpiL

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⎛

⎝ ⎜

⎞

⎠ ⎟

2

∇ ρ2 1

W3

− kECμ

0

Lq

ρs

∇ ρ

Bp

ηEC

IEC

a2

1

W2

kBS

~ 4-5, kGGJ

< 10, kpol

~ 1, kEC

~ 3-4, Wd ~ 0.02

NTM behavior of JT-60U can be explained by Modified Rutherford Equation (Hayashi, NF03)NTM behavior of JT-60U can be explained by Modified Rutherford Equation (Hayashi, NF03)

25. NTM Physics 25. NTM Physics

Hysterisis nature

27

q

r/a

r

RS configuration in some cases becomes unstable to DTM (Double Tearing Mode) . Three distinct linear and non-linear behaviors were identified, which depend on proximity of 2 rational surfaces.

RS configuration in some cases becomes unstable to DTM (Double Tearing Mode) . Three distinct linear and non-linear behaviors were identified, which depend on proximity of 2 rational surfaces.



(a) strongly coupled DTM( r = 0-0.16 )

(a) strongly coupled DTM( r = 0-0.16 )

(c) weakly coupled DTM( r > 0.32 )

(c) weakly coupled DTM( r > 0.32 )

t(pa)

m/n=3/1

6/2 9/3

(b) nonlinearly destabilized DTM( r = 0.16-0.32 )

(b) nonlinearly destabilized DTM( r = 0.16-0.32 )

t(pa)

m/n=3/1

6/29/3

kin

eti

c e

ne

rgie

s

t(pa)

m/n=3/1

9/36/2

Linear mode structure

Y. Ishii et al., P.R.L.89(2002)205002

26. Three Different DTM regimes in RS Tokamak26. Three Different DTM regimes in RS Tokamak

28

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Point reconnection : Triangular deformation of the inner island forms the localized current structure (current point)Point reconnection : Triangular deformation of the inner island forms the localized current structure (current point)

lin in the explosive growth phase weakly depends on nl


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kinetic energy of 3/1

magnetic energy of 3/1magnetic energy of 3/1-mode

=3x10-6

=5x10-6

=1x10-5

=2x10-5

27. New Reconnection Process associated with DTM27. New Reconnection Process associated with DTM

29





28. Alfven Eigen Modes (TAE, EAE, NAE, RSAE)28. Alfven Eigen Modes (TAE, EAE, NAE, RSAE)

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2004 Award for Excellence in Plasma Physics Research Recipient

2004 Award for Excellence in Plasma Physics Research Recipient

Shear Alfven wave resonance: =k//VA, N=ck/

Shear Alfven wave resonance: =k//VA, N=ck/

Toroidal coupling of m and m+1 produces frequency range Alfven resonance is prohibited.

[ (k2//m- (VA) (k2

//m+1- (VA)-2 (VA=0k//m=(n-m/q)/R

k//m=- k//m+1 --> q=(m+1/2)/n

Toroidal coupling of m and m+1 produces frequency range Alfven resonance is prohibited.

[ (k2//m- (VA) (k2

//m+1- (VA)-2 (VA=0k//m=(n-m/q)/R

k//m=- k//m+1 --> q=(m+1/2)/n

Spinor : sin(m)+sin((m+1)) =sin[(m+0.5)]cos(0.5Mobius band ( periodic with two circulation) can not resonate.

Spinor : sin(m)+sin((m+1)) =sin[(m+0.5)]cos(0.5Mobius band ( periodic with two circulation) can not resonate.

Kramer PRL98;EAE,NAEKramer PRL98;EAE,NAE





Kimura NF98;TAE q<1(tornado)Kimura NF98;TAE q<1(tornado)

ShinoharaNF02;ALEShinoharaNF02;ALE

ShinoharaNF01; Slow Freq. Sweeping, Fast FSShinoharaNF01; Slow Freq. Sweeping, Fast FS

Ishikawa NF07 EP transportIshikawa NF07 EP transport

shear Alfven Eigen mode can be destabilized by the coupling with Energetic

Particles if the pressure gradient is high enough.

)/eBr 1

shear Alfven Eigen mode can be destabilized by the coupling with Energetic

Particles if the pressure gradient is high enough.

)/eBr 1

Takechi PoP05;RSAETakechi PoP05;RSAE

30

To increase bs fraction

To increase bs fraction High p H /Imp H(1994)High p H /Imp H(1994)

RWMRWM

High N above no-wall lim

High N above no-wall lim

NTMNTM

Troyon scaling(1984)Troyon scaling(1984)

ELMELM

Rotation driveRotation drive

Kinetic dampingKinetic damping

ITB(Internal Transport Barrier)

ITB(Internal Transport Barrier)

Er shear Er shear

RMPRMP

29. Interlink among Steady-state Tokamak Physics29. Interlink among Steady-state Tokamak Physics

Steady-state Tokamak Reactor (~1990)Steady-state Tokamak Reactor (~1990)

Plasma currentPlasma current High BetaHigh Beta Energetic ParticleEnergetic ParticleConfinementConfinement DivertorDivertor

BS current(1971)BS current(1971)NICDNICD

Power~IpnePower~Ipne

High p operationHigh p operation

NBCDNBCD ECCDECCD

fbs~pfbs~p

To reduce power required for SSTo reduce power required for SS

To increase power density

To increase power density

Compensation of lost bs current

Compensation of lost bs current

AEAE

Ideal MHDIdeal MHD

RS/C HoleRS/C Hole

AEAE

H-mode(1982)H-mode(1982)

ETBETB

TAEShear-Alfven

Resonance Gap

TAEShear-Alfven

Resonance Gap

DTMDTM

31

30. JT-60 shut down and new Generation devices in Asia30. JT-60 shut down and new Generation devices in Asia

32

Summary[1] Steady-state tokamak is an important concept in tokamak confinement.

[2] This has to be realized under the large bootstrap fraction, say, 75%.

[3] Simultaneous achievement of current drive, reactor relevant confinement, MHD stability is key to achieve SSTR.

[4] Progress of understanding is remarkable and many new interesting processes came in and theoretical predictability was greatly improved.

[5] But further research is needed to develop consistent reactor scenario.

Summary[1] Steady-state tokamak is an important concept in tokamak confinement.

[2] This has to be realized under the large bootstrap fraction, say, 75%.

[3] Simultaneous achievement of current drive, reactor relevant confinement, MHD stability is key to achieve SSTR.

[4] Progress of understanding is remarkable and many new interesting processes came in and theoretical predictability was greatly improved.

[5] But further research is needed to develop consistent reactor scenario.

33

2.2 Generalized Ohm’s Law in Tokamak2.2 Generalized Ohm’s Law in Tokamak

Parallel momentum and heat momentum balance equations

Flux surface average

Linear force-flow relation

Thermodynamic forces

Generalized Ohm’s Law

Ref. M. Kikuchi, M. Azumi, PPCF 37(1995)1215Ref. M. Kikuchi, M. Azumi, PPCF 37(1995)1215

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2.4 Resistivity and Bootstrap current 2.4 Resistivity and Bootstrap current

ResistivityResistivity

Hirshman-Hawryluk-Birge NF17(1977)611

M. Kikuchi, M. Azumi, PPCF 37(1995)1215

Bootstrap currentBootstrap current Zarnstorff 1990Kikuchi 1990

L31, L32 are calculated by L and M Generalized Ohm’s LawGeneralized Ohm’s Law

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