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, 2010
Padova Italy
OUTLINE
１ 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
Nesting
magnetic island
(confinement?)
Heat flux
perpendicular to
magnetic field
Healing of
magnetic
island
Flattening of Te
Heat flux parallel
to magnetic field
transition
transition
No Te flattening
transition
stochastization
Flattening
of Te
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.
Transport in nesting magnetic flux
surface near rational surface and
magnetic island
Electron temperature profiles of ITB plasma in LHD
Pe
Wpt  2.0 s
 1.6 :
Wpt 1.5 s
Pe
Wp (MJ)
0.06
t  2.0 s
10
 1.9
t 1.5 s
T (keV)
0.04
e
0.02
P
8
ECH
/n =4.4
e
PECH/ne=3.0
PECH/ne=1.5
6
PECH/ne=0
4
ech
P ,P
nbi
e
(MW) T (0) (keV)
0
2
8
6
4
2
0
0
0
NBI
NBI
2
ECH
1
0
0
1
0.2
0.4

0.6
0.8
1
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 ce
DTe = 2 kev @ PECH/ne =1.5
DTe = 8keV @ PECH/ne =4.4
2
3
4
time (s) K.Ida et al., Plasma Phys Control Fusion 46 (2004) A45
T )
e
3/2
e
PECH/ne=3.0
1
PECH/ne=1.5
PECH/ne=0
0.1
2 -1
0.1
10
1
0.01
0.0
LHD
JT60U
ITB
e
e
c /(T
/n =4.4
ECH
100
2
P
/B ) (m s keV
10
ITB
c /(T
2 -1
/B2) (m s keV
No ITB
100
1000
3/2
e
-3/2 2
1000
-3/2
T2)
Normalized ce profiles
0
0.2
0.4

0.6
0.8
1
0.2
0.4

0.6
0.8
1.0
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 ce are quite different
(ce keeps decreasing toward the plasma center in LHD, while it has a minimum at 
= 0.35 in JT60U)
Er structure near the rational surface
Er near i =1 surface
Er near the i = 1/3 surface
-6
i = 1/3
5
-6
Er(kV/m)
0
-5
0
0.2
0.4
0.6

260A
i=1
0
r
E (kV/m)
10
0.8
1
1.2
500A
1cm
0
-6
690A
4cm
0
9cm
K.Ida et. al., Phys Rev Lett 91 (2003) 085003 -6
Radial electric field , Er, shear are
observed at the boundary of magnetic
island as well as the ITB.
No
Island
0
15
900A
0
-6
1200A
Increase the
size of
magnetic
island
4.1
4.0
3.9
This Er shear may contribute the reduction 3.8
R(m)
of thermal diffusivity at the boundary of K.Ida et al., Phys Rev Lett 88 (2002) 015002
magnetic island
Cold pulse propagation near rational surface
Before Injection
+2ms
+6ms
+10ms
e
T (keV)
2
Electron ITB plasma with the foot point
locating near the rational surface
15
outside
1
0
0.2
0.4

0.6
 = 0.09
0.17
0
0.29
0
0.34
0
0.43
0
0.57
0
0.01 0.02
t-t (s)
0
0.03
outside the ITB
T
e
0.5 KeV
0
0
10
0.8 1
#38834
inside the ITB
0
Delay Time (ms)
3
5
ITB
i =1/2
inside
0 ITB
0.0 0.2 0.4 0.6 0.8 1.0

K.Ida et. al., Phys Plasmas 11 (2004) 2551
Large delay time inside the ITB
Jump of delay time at the boundary of ITB 
suggests the more reduction of transport at the
boundary (near rational surface)
ITB formation with/without magnetic island
no 2/1 island
with 2/1 island
Electron temperature 4 LHD #43108
(a) without 2/1 island
profile with and without
Ctr.
2/1 magnetic island
 = 0.016
2
0.255 0.408
Te(keV)
e
3
2/1 ialsnd
2
0
0.2
0.4
0.6
rho
2
0.581
1
MECH
reduced 2/1 island
0
1.9
0
0.581
1
1
0.255 0.408
e
with 2/1 island
T (keV)
4
T (keV)
3
4 LHD #43101
(b) with 2/1 island
Ctr.  = 0.016
3
0.8
1 Cancel
MECH
on-axis ECH
Time (s)
1.95
2/1 magnetic island
 no ITB formation
0
1.90
on-axis ECH
Time (s)
1.95
with 2/1 magnetic island
 Clear ITB formation
K.Ida et. al., Phys Plasmas 11 (2004) 2551
The magnetic island contribute rather than suppress the
formation of ITB
Transport in stochastic magnetic flux
Magnetic shear is controlled by NBCD
(a)
(b)
i
0.9  = 0.83
0.8
Co= increase iota
Ctr=decrease iota
 = 0.83
0.7 0.70
0.6
0.58
0.5
0.47
0.4 0.37
0.3 0.29
1.5
i
1.0
0.70
0.58
0.47
0.37
0.29
Ip(kA)
0.2
0
Ip(kA)
0.1
co-NBI
0.0
2
4
ctr-NBI
6
time(sec)
8
ctr-NBI
2
4
-100
co-NBI
-200
6
8
time(sec)
Co to ctr
Ctr to co
Weak magnetic
shear
strong magnetic
shear
Te(keV)
1.0
co to ctr
0.5 i = 0.5
0.0 weak shear
ctr to co
-0.5
co to ctr
-1.0
-1.5
0.0
0.2
ctr to co
strong shear
0.4

0.6
0.8
1.0
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.
A
dTe/d (keV)
4
i=0.5
i=0.5
i=0.5
i=0.5
4.5sec
5.5sec
6.5sec
7.5sec
0
0
10
10
1
10




ctr to co-injection
2
A
(/i)di/d
D
co to ctr-injection
1 @i=0.5
B
0
@i=0.5
C
stochastization
high shear
ctr to co-injection
co to ctr-injection
0.5
0.02
0.00
-0.02
-0.04
3
no island
no island
with island
 = 0.43
4
Stochastization
transition
Nested magnetic island
with interchange mode
There is no MHD instability observed at
the onset of temperature flattening.
low shear
0.0
T(keV)
Bifurcation phenomena
of magnetic island
1
3
1.0
D
C
B
Te(keV)
2
The temperature fluctuations in the
frequency range of 0.8 - 1.2kH appears
afterwards with a partial temperature
flattening
5
6
7
time (s)
8
9
K.Ida et al., Phys. Rev. Lett, 100 (2008) 045003
Relation of island width to magnetic shear
Island healing  island stochastization:
no interchange mode
stochastization  nesting island  healing
interchange mode is excited
/A = 10
2.5 positive negative
shear
shear
2.0
1.5 no island
1.0
0.5
0.0
-0.5
with
island
0.0
-2
10
0.6
-3
0.5
ctr to co
co to ctr
interchange
mode
stochastization
0.5
1.0
(/i)di/d
0.6
(b)
1.5
stochastization
width D
3.0
(a)
"island width" D
e
dT /d (keV) (@i = 0.5)
3.5
Clear hysteresis is observed
In the relation between island
width and magnetic shear
50ms
0.4
0.2
0.4
shrinking
0.3
0.0
4.6
4.8
time (sec)
0.2
island
growing
0.0 Dt<50ms
0.1
0.0
no island
0.2
0.4
(/i)di/d
healing
0.6
0.8
K.Ida et al., Phys. Rev. Lett, 100 (2008) 045003
Heat pulse propagation
The direction of NBI is
switched from co- to counterduring the discharge
Edge iota decreases and central
iota increases, which results in
weaken the magnetic shear.
Heat pulse propagation has been studied with
modulation electron cyclotron heating
Flattening of electron temperature and modulation
amplitude is observed
Modulation amplitude on-axis decreases
Modulation amplitude off-axis increases
Heat pulse propagates very quickly towards the plasma
edge.
Nesting and stochastic magnetic flux surface
Finite temperature gradient
Standard pulse propagation
Zero temperature gradient
Very fast pulse propagation
Nesting magnetic flux surface
Stochastic magnetic flux
Zero temperature gradient
Slow pulse propagation
（ mountain shape ）
Nesting magnetic island
Transport in magnetic island
Pellet injection experiment in LHD
Z (m)
0.5
0.0
Small solid pellet (TESPEL) is injected near the
X-point of the magnetic island
cold pulse
outside islnad
TESPEL
-0.5
cold pulse
inside island
3.0
3.5
R (m)
Pulse propagation
inside the magnetic
island is
much slower than that
outside the magnetic
island
Inside magnetic island
4.0
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
M.Yakovlev et. al., Phys Plasmas 12 (2005) 09250
Heat pulse due to MECH (modulation
electron cyclotron heating) shows
inward/outward propagation inside the
magnetic island.
Peaked Ti profile in magnetic island
Peaked Ti profile is observed inside the
magnetic island after the back-transition from H
to L mode
0.05
0.04
8
delta Te
magnetic islnad
0.02
0.01
7.015s
0
magnetic islnad
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
r/a
0.08
delta Te
4
6
0.1
7.265s
t = 6.43s
0.03
6.465s
2
i
T (keV)
10
12
jt60umcxrs_tir@049578
t = 7.27s
0.06
0.04
0.02
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
r/a
magnetic islnad
0
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
r/a
Summary
1 Transport near the magnetic island
Large 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.
2 Transport in the stochastic magnetic flux
Bifurcation 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 island
Cold pulse propagation experiment shows good confinement insode the magnetic
island
Peaked temperature profile observed inside the magnetic island after the backtransition from H-mode also suggests good confinement of magnetic island.