Transport in three-dimensional magnetic field:

examples from JT-60U and LHD

Katsumi Ida and LHD experiment group and JT-60 group

14th IEA-RFP Workshop

April 26-28, 2010Padova Italy

OUTLINE１ Magnetic structure near the rational surface(Nesting, stochastic magnetic flux, magnetic island)

2 Transport in nesting flux surface near magnetic island 2-1 radial electric field structure at magnetic island 2-2 electron-ITB and magnetic island

3 Transport in stochastic magnetic flux surface 3-1 Flattening of temperature profile with low shear 3-2 Heat pulse propagation experiment

4 Transport in magnetic island 4-1 cold pulse propagation in magnetic island 4-2 peaked temperature profile in magnetic island

5 Summary

Magnetic structure near the rational surface

stochastization

Nesting magnetic island(confinement?)

Healing of magnetic island

transition

Flattening of Te

transition transition

No Te flattening

Flattening of Te stochastization but NOT Flattening of Te stochastization Heat flux parallel to magnetic field is much larger than Heat flux perpendicular to magnetic field.

The stochastization can be identified by the pulse propagation experiment.Fast pulse propagation is the evidence of stochastization of magnetic flux surface.

Flattening of Te

Heat flux perpendicular to magnetic field

Heat flux parallel to magnetic field

Transport in nesting magnetic flux surface near rational surface and

magnetic island

0

0.02

0.04

0.06

Wp

(MJ)

Electron temperature profiles of ITB plasma in LHD2.0 2.0

1.5 1.5

1.6 : 1.9et s t s

t s e t s

PWp

Wp P

ITB is characterized by the peaked Te profiles and the increase of Te(0) is larger than the increase of heating power significant reduction of e

0

2

4

6

8

10

0 0.2 0.4 0.6 0.8 1

PECH

/ne=4.4

PECH

/ne=3.0

PECH

/ne=0

PECH

/ne=1.5

Te(k

eV)

02468

Te(0

) (k

eV)

0

1

2

0 1 2 3 4

Pec

h, Pnb

i (M

W)

time (s)

NBI

ECH

NBI

Te = 2 kev @ PECH/ne =1.5Te = 8keV @ PECH/ne =4.4

K.Ida et al., Plasma Phys Control Fusion 46 (2004) A45

0.1

1

10

100

1000

0 0.2 0.4 0.6 0.8 1

PECH

/ne=4.4

PECH

/ne=3.0

PECH

/ne=1.5

PECH

/ne=0

e /(T

e3/2

/B2 )

(m2 s-1

keV

-3/2

T2 )

Normalized e profiles

Thermal diffusivity normalized by Te3/2/B2 is reduced close to 0.1 (m2s-1keV-3/2T2) at

the ITB region both in LHD and JT60U.However, the radial profiles of normalized e are quite different (e keeps decreasing toward the plasma center in LHD, while it has a minimum at = 0.35 in JT60U)

No ITB

0.01

0.1

1

10

100

1000

0.0 0.2 0.4 0.6 0.8 1.0 e /(T

e3/2

/B2 )

(m2 s-1

keV

-3/2

T2 )

JT60UITB

LHD

ITB

Er structure near the rational surface

-6

0

-6

0

-6

0

-6

0

-6

0

3.8 3.9 4.0 4.1

Er(k

V/m

)

R(m)

9cm

4cm

1cm

260A

500A

690A

900A

1200A

Radial electric field , Er, shear are observed at the boundary of magnetic island as well as the ITB.

Er near =1 surfaceEr near the = 1/3 surface

This Er shear may contribute the reduction of thermal diffusivity at the boundary of magnetic island

-5

0

5

10

15

0 0.2 0.4 0.6 0.8 1 1.2

Er(k

V/m

)

= 1/3

No Island

Increase the size of magnetic island

=1

K.Ida et al., Phys Rev Lett 88 (2002) 015002

K.Ida et. al., Phys Rev Lett 91 (2003) 085003

Cold pulse propagation near rational surface

0

1

2

3

0 0.2 0.4 0.6 0.8 1

Before Injection+2ms+6ms+10ms

Te (

keV

)

Large delay time inside the ITBJump of delay time at the boundary of ITB suggests the more reduction of transport at the boundary (near rational surface)

Electron ITB plasma with the foot point locating near the rational surface

0 0.01 0.02 0.03

= 0.09

0.17

0.29

0.34

0.43

0.57

t-t0 (s)

#38834

Te

0.5

KeV 0

0

0

0

0

0

insi

de th

e IT

Bou

tsid

e th

e IT

B

0

5

10

15

0.0 0.2 0.4 0.6 0.8 1.0

Del

ay T

ime

(ms)

insideITB

outsideITB

=1/2

K.Ida et. al., Phys Plasmas 11 (2004) 2551

ITB formation with/without magnetic island

0

1

2

3

4

0 0.2 0.4 0.6 0.8 1

Te(k

eV)

rho

reduced 2/1 island

with 2/1 island

The magnetic island contribute rather than suppress the formation of ITB

with 2/1 magnetic island Clear ITB formation

Cancel 2/1 magnetic island no ITB formation

Electron temperature profile with and without 2/1 magnetic island

0

1

2

3

4

1.9 1.95

Te (

keV

)

Time (s)

0.016

0.255

=

0.581

0.408

LHD #43108

without 2/1 island Ctr.

on-axis ECH

MECH

(a)

0

1

2

3

4

1.90 1.95

Te (

keV

)

Time (s)

0.016

0.255

=

0.581

0.408

LHD #43101with 2/1 islandCtr.

on-axis ECH

MECH

(b)

no 2/1 island with 2/1 island

2/1 ialsnd

K.Ida et. al., Phys Plasmas 11 (2004) 2551

Transport in stochastic magnetic flux

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

2 4 6 8

time(sec)

Ip(kA)

co-NBI ctr-NBI

= 0.83

0.70

0.58

0.470.370.29

(a)

-200

-100

0

2 4 6 8time(sec)

Ip(kA)

co-NBIctr-NBI

= 0.83

0.700.58

0.470.370.29

(b)

Magnetic shear is controlled by NBCD

Co to ctr Ctr to co

Weak magnetic shear

strong magnetic shear

Co= increase iotaCtr=decrease iota

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0.0 0.2 0.4 0.6 0.8 1.0

T

e(ke

V)

ctr to co

co to ctr

strong shearweak shear

= 0.5 ctr to coco to ctr

The flattening of electron temperature profile is observed in the discharge with the switch of NBI from of co- to counter, where the magnetic shear becomes weak.

0.0

0.5

1.0

0

1

2

3

4

(/)

d/d

dT

e/d

(keV

)

@=0.5

with island

no island

B C

D

low shear

high shear

@=0.5

ctr to co-injection

ctr to co-injection

co to ctr-injection

co to ctr-injectionA

stochastization

0

1

2

0 1

Te(k

eV)

4.5sec=0.5

A

0 15.5sec=0.5

B

0 16.5sec

=0.5

C

0 17.5sec

=0.5

D

-0.04

-0.02

0.00

0.02

3 4 5 6 7 8 9

T(k

eV)

time (s)

= 0.43

There is no MHD instability observed at the onset of temperature flattening.

The temperature fluctuations in the frequency range of 0.8 - 1.2kH appears afterwards with a partial temperature flattening

Bifurcation phenomena of magnetic island

no island Stochastization

Nested magnetic islandwith interchange mode

transition

K.Ida et al., Phys. Rev. Lett, 100 (2008) 045003

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.0 0.2 0.4 0.6 0.8

"isl

and

wid

th"

(/)d/d

no island

shrinking

healingisland growingt<50ms

0.0

0.2

0.4

0.6

4.6 4.8

wid

th

time (sec)

50ms(b)

stochastization

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

-0.5 0.0 0.5 1.0 1.5

dTe/d

(k

eV)

(@ =

0.5

)

(/)d/d

positive shear

with island

co to ctr

ctr to co

no island

negativeshear

(a) /A = 10-2

interchange mode

10-3

stochastization

Relation of island width to magnetic shear

Clear hysteresis is observedIn the relation between island width and magnetic shear

Island healing island stochastization: no interchange modestochastization nesting island healing interchange mode is excited

K.Ida et al., Phys. Rev. Lett, 100 (2008) 045003

Heat pulse propagation

Heat pulse propagation has been studied with modulation electron cyclotron heating

The direction of NBI is switched from co- to counter- during the discharge

Edge iota decreases and central iota increases, which results in weaken the magnetic shear.

Flattening of electron temperature and modulation amplitude is observedModulation amplitude on-axis decreasesModulation amplitude off-axis increases

Heat pulse propagates very quickly towards the plasma edge.

Nesting and stochastic magnetic flux surface

Finite temperature gradientStandard pulse propagation

Zero temperature gradientVery fast pulse propagation

Zero temperature gradientSlow pulse propagation

（ mountain shape ）

Nesting magnetic flux surface Stochastic magnetic flux Nesting magnetic island

Transport in magnetic island

Pellet injection experiment in LHD

-0.5

0.0

0.5

3.0 3.5 4.0

Z (

m)

R (m)

TESPEL

cold pulseoutside islnad

cold pulse inside island

Pulse propagation inside the magnetic island is much slower than that outside the magnetic island

Small solid pellet (TESPEL) is injected near the X-point of the magnetic island

Inside magnetic island outside magnetic island

Cold pulse propagation in magnetic island

Significant time delay propagating from the boundary of magnetic island to the center of O-point is observed in the magnetic island where the Te profile is flat.

The effective thermal diffusivity inside the magnetic island is smaller than that outside by an order of magnitude.

S.Inagaki et al., Phys Rev. Lett 92 (2004) 05500

Heat pulse propagation in magnetic island

Heat pulse due to MECH (modulation electron cyclotron heating) shows inward/outward propagation inside the magnetic island.

M.Yakovlev et. al., Phys Plasmas 12 (2005) 09250

Peaked Ti profile in magnetic island

0

0.02

0.04

0.06

0.08

0.1

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

r/a

t = 7.27s

magnetic islnad0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

jt60umcxrs_tir@049578

r/a

6.465s

7.265s

7.015s

magnetic islnad

0

0.01

0.02

0.03

0.04

0.05

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

r/a

t = 6.43s

magnetic islnad

Peaked Ti profile is observed inside the magnetic island after the back-transition from H to L mode

Summary

1 Transport near the magnetic islandLarge radial electric field shear is observed at the boundary of magnetic island.The magnetic island (not the rational surface) would contribute the formation of internal transport barrier.

2Transport in the stochastic magnetic fluxBifurcation phenomena are observed in the stochastization of magnetic flux surface (a sudden flattening of Te profile in the core region of r/a < 0.4) at the low magnetic shear of 0.15. The stochastization of magnetic flux is confirmed by the very fast heat pulse propagation in the temperature flat region. (The propagation is slow in the nesting magnetic island)

3 Transport inside the magnetic islandCold pulse propagation experiment shows good confinement insode the magnetic island Peaked temperature profile observed inside the magnetic island after the back-transition from H-mode also suggests good confinement of magnetic island.