核燃焼プラズマ統合コード研究会
7 月 31日 - 8 月 1日 (2003), 京都大学

BPSI

Axisymmetric Tri-Magnetic-Islands Equilibriumof Strongly-Reversed-Shear Tokamak Plasma- An Idea for the Current Hole 滝塚 知典（原研那珂研）ContentConfinement and Transportof RS Plasmas with ITB

Axisymmetric Tri-MagneticIslands (ATMI) Equilibrium

ITB

1

pressure

BS current

0

Wcore

0

r/a

BS current

1

negativecurrent
positivecurrent

Confinement and Transport of RS Plasmas with ITB
T. Takizuka et al., "Energy Confinement Scaling for Reversed-Shear Plasmas withInternal Transport Barrier in JT-60U", Plasma Phys. Control. Fusion 44 (2002) A423.

10Box type ITB5Ti
103ne0Ti

2Te504qneq0.5r/a1(b)5TeBt ≈ 4 T

10(a)Parabolic type ITBWdia (MJ)

15(1019m-3)(keV)

000.5r/a

JT-60U database
L-mode edge, Box type ITB

1012I p (MA)

1.9 MA < Ip < 2.3 MA3051015Pnet (MW)Stored energy depends strongly
on plasma current Ip ( Wdia ~ Ip1.4 ),but little on heating power Pnet( ≡ PNB - dW/dt )(2) Stored energy is devided into L-mode base
part and core part inside ITB.

[WthL = 0.026 M0.3 Ip0.5 Bt0.39 R1.44 a0.92 κ0.88 n190.5 P0.330]

ITB foot1pressureWorking hypotheses(1) Stored energy is govered not by the heat flux
through ITB but by the plasma parameters
around ITB.

Wcore
WthL
0r/a

1

Wdia depends more strongly on Bp,foot than on Ip
Wdia (MJ)

10

Wcore can be expressedby a dimensionally-correct
form without including P :Wcore ~ Bp,f 2 x Vcore

11Ip (MA)100.1 Bp,foot (T)1Energy Confinement Scaling
Wscale = C εf -1 Bp,f 2 Vcore
Analysis of Database
under the above hypotheses

Wcore (MJ)10εf βp,core = const. ( ≈ 1/4 )*Indication of MHD
Equilibrium Limit

1

0.1
0.1

Bt : 2.1 ~ 4.1 T
Ip : 0.8 ~ 2.6 MA
PNB : 4 ~ 19 MW
εf : 0.12 ~ 0.19

1

Wscale (MJ)
r = 0.95, σ = 22 %10Vcore : 9 ~ 25 m3
Wcore : 0.3 ~ 7.7 MJ* Bp,f is measured atthe outer midplane.
When averaged Bp,fused,
εf βp,core > 1/2 .

"Neoclassical transport of ITB" is not inconsistent with the data,
though the core stored energy is independent of Pnetχ ITB ∝ Pnet / (Sf ne0 |dT/dr| ITB )χNEO ∝ εf 0.5 ne0 / Bp,f 2 Ti0 0.5

χ ITB (a.u.)

10

10.1
0.1

1

χNEO (a.u.)

100.1

1

χB (a.u.)

10 0.1

1

χGB (a.u.)

Bohm or GyroBohm transport isinconsistent with the data10

Axisymmetric Tri-Magnetic-Islands (ATMI) Equilibrium- An Idea for the Current Hole T. Takizuka, "Axisymmetric Tri-Magnetic-Islands Equilibrium of Strongly-Reversed-Shear
Tokamak Plasma: An Idea for the Current Hole", J. Plasma Fusion. Res. 78 (2002) 1282;
http://jspf.nifs.ac.jp/RCPDF/

Bp ~ 033.2 3.4 3.6 3.8

R [m]

41.2
10.8
0.6
0.4
0.2
0100
80

j~ 06040

T. Fujita et al., Phys. Rev. Lett.
87 (2001) 245001

200432
1010Ti, Te [keV]

0.04
0.02
0- 0.02j [MA/m2]

0.1
0.08
0.06

q

Bp/Bt

E36639 5.4s

ne [1019 m-3]

Current Hole in JT-60U Tokamak Plasma

00.2 0.4 0.6 0.8

ρ18Ti6Te42000.2 0.4 0.6 0.8

ρ1

Generation of Negative Current andInstability of a Single-Magnetic-Axis (SMA)
Equilibrium with Central Negative Current

JBS0ETJ0Vr
Bp = 0 ; βp , li → ∞Growth of bootstrap Central negative current
current JBS induces in a SMA configuration
negative ET at the destroys the equilibrium.
central region.
Large Shafranof shift∆ ~ ε Λ ( Λ = βp + li/2 - 1 )Bp = 0Even in a cylindrical plasma, central
negative current ina SMA configuration
destabilizes n=0/m=1
resistive MHD mode.

Formation of Three Magnetic Islands (m=2/n=0)
through Nonlinear Evolution of m=1/n=0 Instability (?)

peaks ofpositivecurrent

V
Bp = 0Flow pattern
mixing of positive &negative currents

Unstable Configuration (Z arrangement) andStable Configuration (R arrangement)
under the Current Limit

Unstable Z-ar.
Iv

Stable R-ar.
Zc
Zx

Stability Condition(current limit)

Ic

F+ < F c

F+I+
I-

F+Fv

R

I+

I+/ (r12 + δZ2) < Ic/ Zc2

II+I+Fc

IvIcRI+/ r12 < Ip (Zc - Zx) / Zx Zc2
qATMI /qa > κ12 Zc2/ (Zc - Zx) aκ12 Z
2I+ / I- ≈ (1 + κ12) /κ( see 2 page later )Scenario for the Rotation from Unstable Z-ar.
Configuration to Stable R-ar. Configuration
Rotation is not simply explained by MHD theory.
1. Very small Bp at the central region
2. Large ion-orbit size
3. Large radial electric field E
4. E×B rotation from Z-ar. to R-ar.
5. Closed magnetic surfaces of tri-magnetic islands atstable R-ar.
6. Uniform electrostatic potential on each magnetic surface
7. E×B rotation is on the surface, and stable R-ar. does notchange its magnetic configuration.

Ratio of negative to positive currents in ATMI I- / I+ ≈ 1
r1

2

z1(= κ1 r1 )I+ I-I+R

BxR ∝ 2 I+ z1/ (r12 + z12)

I- / I+

BxR- I- / z1
BxR = 01

I- / I+ ≈ 2 κ12/ (1 + κ12)
001

κ12

Unbalance current flows out through x-point region
by magnetic reconnection process.
Current drive for both co- and ctr- directions is difficultin the current hole region. (ECCD experiment in JT-60U)

SummaryCore Stored Energy : MHD equilibrium limt εf βp,core = const.
Neoclassical Transport at ITB
Axisymmetric Tri-Magnetic-Islands (ATMI) Equilibrium
Generation of central negative ET due to the grouth of JBS
Formation of ATMI configuration through the nonlinear
evolution of m=1/n=0 MHD instability (?)
ExB rotation to the stable R-ar. configuration (?)
Limit of the +/- current ratio

I- /I+ ~ 1

Difficulty of current drive in the ATMI region

Limit of the ATMI current

qATMI /qa > κ12 Zc2/ (Zc - Zx) aqATMI > 40 for the JT-60U parameters

Current Hole is ATMI Equilibrium
Plasma profile in central region is not flat, but wavy along R direction