Spontaneous rotation as an offdiagonal term of momentum transport

1
Spontaneous rotation as an off-diagonal term of
momentum transport

• K.Ida
• National Institute for Fusion Science
• ITPA Transport at Princeton
• 25 April 2006

1 History and mechanism of spontaneous toroidal
rotation 2 Spontaneous toroidal flow in tokamak
(in JITT TIIU, JFT-2M, JT60U) 3 Spontaneous
toroidal flow in helical system (in Wendelstein
7AS, CHS and LHD) 4 Comparison tokamak ??
helical plasmas experiment ?? theory 5
Summary
Acknowledgement Dr.K.Itoh and JIPP-TIIU,
JFT-2M, JT-60U, CHS, Wendelstein-7AS, and LHD
Group
2
History of spontaneous toroidal rotation
1980 Toroidal rotation of Ohmic plasma CTR
rotation of Ohmic plasma in PLT NF 21 (1981)
1301 PDX NF 23 (1983) 1643 and Alcator
C-mod NF 37 (1997) 421 Early 90 Toroidal
rotation of ICRF plasmas CTR rotation in
JIPP-TIIU NF 31 (1991) 943 Co rotation in JET
PPCF 34 (1992) 863 in Alcator C-mod NF 38
(1998) 75 Mid 90 Non-Diffusive term of
momentum transport in NBI heated Plasmas CTR
rotation in JT-60U NF 34 (1994) 449 in JFT-2M
PRL 74 (1995 ) 1990 CTR Spontaneous toroidal
flow in helical plasma in LHD 2005 Spontaneous
toroidal flow in the plasma with ITB CTR
rotation in JT-60U PRL 72 (1994) 3662, PoP 3
(1996) 1943, NF 41 (2001) 865 CTR rotation in
TFTR PoP 5 (1998) 665 CTR rotation in Alcator
C-mod NF 41 (2001) 277 Early 2000
Spontaneous toroidal flow driven by
ECH CTR rotation in CHS (anti-parallel to
ltErxBqgt) PRL 86 (2001 ) 3040 CTR rotation
driven by ECH plasma in D-IIID PoP 11 (2004)
4323
3
Mechanism driving spontaneous totoidal flow
Spontaneous flow is considered to be off-diagonal
term of transport matrix M
Interference of Flux
K.Itoh, S-I Itoh and A.Fukuyama Transport and
structural formation in plasmas IOP publishing
1999
Pfr - M33 Vf - M31 n - M34 T - M32
Vq
Spontaneous rotation
Diagonal term
Off-diagonal term
When off-diagonal tem is driven by pressure
gradient
Spontaneous rotation is determined by Er
K.Itoh et al., J. Phys. Soc. Jpn 65 (1996) 760
4
What is spontaneous totoidal rotation?
Non-ambipolar loss
ICRF perp NBI ECH
ripple loss
Poloidal rotation
Momentum from NBI
External driven Toroidal rotation
Pressure gradient
Radial force balance
spontaneous Toroidal rotation
ExB force
Er
Anomalous transport
viscosity tensor
The spontaneous toroidal rotation can be defined
as the toroidal rotation not driven by external
toroidal momentum input. It can be driven by
non-ambipolar loss or pressure gradient with the
coupling of ExB force and viscosity tensor.
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Observation of spontaneous toroidal rotation
Spontaneous toroidal rotations in counter
direction (anti-parallel to the direction of
plasma current, contributing negative Er) are
observed both in NBI and NBIICRF heated plasmas
From K.Itoh, et. al. Transport and structural
formation in plasmas page 13 IOP publishing 1999
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Spontaneous toroidal rotation in JFT-2M tokamak
Spontaneous toroidal flow anti-parallel to plasma
current is observed in the NBI discharge in
tokamak PRL74 (1995) 1990
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Non-steady state momentum transport analysis
Momentum transport analysis shows the
non-diffusive term (finite momentum flux at zero
gradient)
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diffusive and non-diffusive viscosity coefficients
Momentum Flux
GM mini- mD dvf /dr mN (vth /Ti)(eEr)
The non-diffusive term is more significant at the
ITB
eEr dTi/dr
Rearranged from Fig.1 in Y.Sakamoto et al., Nucl.
Fusion 42 (2001) 865
diffusive (shear viscosity)
non-diffusive (driving term)
JT-60U
JFT-2M
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q dependence of non-diffusive term (spontaneous
flow) in JFT-2M
The non-diffusive term is proportinal to q value
in JFT-2M J. Phys. Soc. Jpn 67 (1998)
4089 Similar q dependence is observed in Alcator
C-mod Dvf (Wp/Ip) J.E.Rice NF 41 (2001) 277
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Spontaneous toroidal flow with ECH in CHS
NBI ECH
Spontaneous toroidal flow is observed with ECH in
CHS transport barrier in the hot electron mode
PRL 86(2001)3040
NBI
CHS
ECH
NBI
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Spontaneous toroidal rotation
Te
Vq
Vf
Poloidal flow Vq is almost consistent with the
poloidal component of ErxB drift
velocity Toroidal flow Vf is much larger than
the toroidal component of ErxB drift
velocity (Spontaneous toroidal flow is NOT just
toroidal component of ErxB drift velocity )
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Grad-Te dependence of spontaneous flow
Spontaneous flow due to ECH
Spontaneous toroidal flow increases associated
with the increase of positive Er and Te gradient
PRL 86(2001)3040
13
Spontaneous toroidal rotation in CHS
Mod-B
The spontaneous toridal flow driven by ECH is
proportional to the poloidal flow (radial
electric field)
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Spontaneous rotation in LHD
Spontaneous rotation is more visible off the
plasma where the toroidal momentum input is
relatively small
Positive Er
Near center (r lt 0.4) ? NBI driven toroidal
rotation dominant Off center (r gt 0.4) ?
spontaneous toroidal rotation dominant
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Spontaneous toroidal flow in tokamak and helical
JFT-2M tokamak (Erlt0)
Wendelstain 7AS (Er lt 0)
spontaneous rotation in co-direction
spontaneous rotation in ctr-direction
For NBI plasma where the radial electric field is
negative (Erlt0) Tokamak plasmas vf (co)lt vf
(ctr) PRL74 (1995) 1990 Helical plasmas
vf(co)gt vf (ctr) EPS 18B I (1994) p392 The
direction of spontaneous flow is opposite between
tokamak and helical plasmas
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Difference between tokamak and helical system
?Tokamaks (internal current system)
vq
? Helical (external current system)
PPCF 44 (2002) 361
Tokamak negative Er ? counter spontaneous flow
V1.3Er/Bq Helical positive Er ? counter
spontaneous flow V0.16Er/Bq
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Mechanism driving spontaneous totoidal flow
ICRF perp NBI ECH
tangential NBI
Poloidal rotation
Ripple loss
Spontaneous flow is observed in L-mode
Heating
Tokamak
Helical
Radial force balance
VfNET
Pressure gradient
VfNBI
VfNET
VfNBI
VfSPON
VfSPON
ITB
Anomalous transport
Er Er
VfSPON cEr/Bq
VfSPON - cEr/Bq
anti parallel to ltErxBqgt Ctr-rotation for Er gt 0
in CHS and LHD
Localized spontaneous flow in ctr direction is
observed in ITB region in TFTR, JT-60U Alcator
C-mod
parallel to ltErxBqgt Ctr-rotation for Er lt 0
1/Ip dependence is observed in JFT-2M and Alcator
C-mod
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Comparison with theory
Spontaneous rotation driven by pressure gradient
is predicted as
K.Itoh et al., J. Phys. Soc. Jpn 65 (1996) 760
The spontaneous rotation observed in JFT-2M is
1-2 times of theoretical value
The spontaneous rotation is 1 2 of the Alfven
velocity
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Summary
1. Spontaneous toroidal flow is observed
regardless heating method (Ohmic, NBI , ICRF,
ECH) in toroidal plamsas (both in tokamak and
helical) as a results of interference of energy
and momentum flux. 2. Spontaneous toroidal flow
is positive contributing to enhance the Er
(ctr-rotation in negative Er plasma in tokamak
while it is negative contributing to reduce the
Er in helical because of the difference of
viscosity tensor due to symmetry. 3. When the
spontaneous flow is driven by pressure gradient,
the magnitude of the spontaneous flow observed
(vf/vth) is consistent with the theoretical value
of (qR/a)(ri/a) and it is 1 2 of the Alfven
velocity.