Proceedings of ITC/ISHW2007

Physics Mechanisms of Toroidal Rotation Profile andProperties of Momentum Transport in JT-60U
M. Yoshida, Y. Kamada, H. Takenaga, Y. Sakamoto, H. Urano,
N. Oyama, G. Matsunaga, and the JT-60 TeamJapan Atomic Energy Agency, 801-1, Mukoyama, Naka 311-0193, JapanThe roles of the elements determining the toroidal rotation velocity (Vt) profile, i.e. the momentum transport,
the external momentum input, and the intrinsic rotation are found by the transient momentum transport analysis.
The perturbation techniques enable us to evaluate the momentum diffusivity () and the convection velocity (Vconv),
and to calculate Vt profiles driven by external torque input by neutral beams (NBs). The measured Vt profiles at low
heating power are almost reproduced by  and Vconv. At higher heating power, the CTR directed (anti-parallel tothe plasma current, Ip) intrinsic rotation, which is locally determined by the local pressure gradient is observed in
the core region. This rotation increases with increasing the pressure gradient in CO and CTR rotating L-mode
plasmas. Concerning the momentum transport,  increases with increasing heating power, and decreases withincreasing Ip. In the H-mode plasmas,  is smaller than that in the L-mode under similar experimental conditions. It
is found that  separated from non-diffusive term increases with increasing the heat diffusivity (i), and -Vconv
increases with increasing  in H-mode plasmas.
Keywords: toroidal rotation velocity, intrinsic rotation, momentum transport, L-mode, H-mode.

1. Introduction
The Burning plasma is the self-regulating system,
where the pressure, rotation, and current profiles arestrongly linked to each other [1]. The JT-60 project hasaddressed major physics issues towards the understanding
and the operation of the burning steady-state plasmas, andpromoted an integrated research project focusing on therotation. In many present-day tokamak experiments, thetoroidal rotation velocity (Vt) is driven by external
momentum input from neutral beam (NB) injection.
However, in future burning plasma experiments, theexternal momentum input from the auxiliary heating is
expected to be small. Intrinsic toroidal plasma rotations
generated by the plasma itself have recently become thesubject of intense interest and investigation in themagnetically confined tokamak plasma research, sincesuch an intrinsic rotation could dominate the total plasma
rotation in future devices [2]. Therefore, the criticalimportance of understanding the physical mechanisms
determining the Vt profile including the intrinsic rotation,and controlling Vt profile has been increasingly
recognized for next step devices.
It is now widely recognized that the rotation and its
radial shear play essential roles in determining
magnetohydrodynamic stability at a high plasma pressure,author’s e-mail: journal@jspf.or.jp

such as the stabilization of the resistive-wall mode [3, 4],
and in the suppression of turbulence leading to enhanced
confinement, such as the transport barrier formation [5, 6].
However, the mechanism determining rotation profile is
not understood well. Because the Vt profiles are
determined by various mechanisms. The worldwide
progress in understanding the physics of momentum
transport and rotation has been made experimentally[7-12] and theoretically [13-15]. As for the elements
determining the Vt, characteristics of momentum
transport which consists of diffusive (the toroidal
momentum diffusivity, ) and non-diffusive (theconvection velocity, Vconv) terms [7, 12], the external
momentum input and the intrinsic rotation [8-11] havebeen reported individually. However, the understandingof rotation mechanisms with integrating all of the terms(the momentum transport, the external momentum input
and the intrinsic rotation) remains an open issue despite
its urgency towards the next step devices. This is due
mainly to an experimental difficulty in evaluating the
diffusive term of the momentum transport, thenon-diffusive term of that and the intrinsic rotation
separately.
In order to address this issue, we have applied theperturbation techniques developed in our recent works [7,Proceedings of ITC/ISHW200712], which enable us to evaluate  and Vconv separately.
As a novel momentum source, fast ion losses due to thetoroidal field ripple, which locally induce a toroidal
rotation in the direction antiparallel to the plasma current,
i.e. the counter (CTR) direction in the peripheral region
through the formation of an inward electric field havebeen used [7]. This momentum source is found by a beam
perturbation experiment and orbit following Monte Carlo(OFMC) code [16]. The effects of the ripple loss of fastions on the toroidal rotation are also investigated by using
data with and without ferritic steel tiles (FSTs) [16]. The
characteristics of the  and the Vconv, and the correlations
between , Vconv and i are investigated by Ip and heating
power scans in L- and H-mode plasmas. We haveseparately identified the roles of the momentum transport
and the intrinsic rotation on Vt profiles in the CO (in the
direction to the plasma current, Ip), and CTR rotating
L-mode plasmas. In this paper, negative sign of Vt
designates CTR-directed rotation and positive sign of Vt
CO-directed rotation, and the momentum balance
equation is solved using a cylindrical model for toroidal
momentum with flux surface averaged parameters.

2. Neutral beams in JT-60U
In JT-60U [17], NBs of various injection geometries
are installed. They consist of; two tangential beams
directing the same direction as that of the plasma current(CO-NBs), two tangential beams directing opposite to theplasma current (CTR-NBs) and seven near perpendicularbeams as shown in Fig. 1(a). The injection angle oftangential beams is 36 degree and that ofnear-perpendicular neutral beam (PERP-NB) is 75 degreewith respect to the magnetic axis. The deuterium beam
acceleration energy is about 85 keV, and the input power
per injected unit is about 2 MW. The plasma rotation in
the toroidal direction is varied using a combination ofthese NBs. In addition such a direction, one of eachtangential beams in the same direction is almost on-axis

Fig.1 (a) Neutral beam (NB) system on JT-60U (b) A
poloidal cross-section with NB trajectories.

deposition and the other is off-axis deposition, four of
PERP-NBs are almost on-axis deposition and the others
are off-axis deposition as shown in Fig. 1(b).

3. Driving source of CTR rotation
In JT-60U, CTR rotation is observed with PERP-NB
injections in the case with large ripple loss condition. In
this section, the effects of the ripple loss of fast ions andthe location of the driving source of CTR rotation areinvestigated in an L-mode plasma.
The relation between Vt in the peripheral region(r/a~0.9) and the ripple loss power is investigated by NB
power and the toroidal field ripple (with and without
FSTs) scans, as shown in Fig. 2(a). In this data set, IP, thetoroidal magnetic field (BT), the plasma volume (Vol.),and the line averaged electron density ( ne ) are kept
almost constant (Ip=1.15 MA, BT=2.6 T, the safety factor
at 95% flux surface, q95~4.1, Vol.~65 m3,
ne ~ 1.5  2  1019 m3 ). Each arrow indicates the change
in Vt by installing FSTs under the condition of almost
same absorbed power (solid arrow: PABS~1.4-1.8 MW,
dotted arrow: PABS~2.8-3 MW). As shown in Fig. 2(a), it
is recognized that the systematic dependence of CTR
rotation on the ripple loss of fast ions can be obtained byusing data with and without FSTs.
In order to confirm the location of the driving sourceof CTR rotation, beam perturbation techniques [7] are

Fig.2 (a) Vt dependence on the ripple loss power. (b)Response of Vt to modulated beams. Profiles of (c)phase delay, (d) modulated amplitude, fast ion loss.

Proceedings of ITC/ISHW2007

Fig.4 Data (solid circles) and reproduced Vt profile(solid lines) (a) with CO-NBI, (b) with CTR-NBI.

Fig.3 Profiles of (a) the toroidal momentum diffusivity(), (d) the convection velocity (Vconv), and (c) Vt
from calculation and measurements.
applied in an L-mode plasma. In this experiment, theplasma with low IP (IP=0.87 MA, BT=3.8 T, q95=8.2) andlarge volume (Vol.=72 m3) was selected in order toenhance ripple losses. In order that the central region isfree from direct external momentum input, off-axis
PERP-NBs (the injected power PIN=3.9 MW) are injectedwith a square wave modulation at 2 Hz into the discharge.
As mentioned above, the injection angle of PERP-NBs is
75 degree with respect to the magnetic axis. For thepurely PERP-NB injections (i.e. with no external
momentum input), one unit of CO PERP-NB and that of
CTR PERP-NB are injected simultaneously. Figure 2(b)shows the waveforms of modulated Vt at r/a=0.87 and0.23 (solid lines), and the total injected power. Each trace
is fitted to a sinusoidal function at the modulation
frequency (dotted lines). The radial profiles of the phasedelay  and of the amplitude of the modulated part of thetoroidal rotation velocity Vt0 are shown in Figs. 2(c) and2(d), respectively. The phase delay is taken from the startof NB injection. Using OFMC code [16], the profile ofthe prompt fast ion loss is also shown in Fig. 2(d). Large
amplitude and small phase delay are recognized in the
peripheral region (0.7<r/a<0.9), and this region agrees
with the location at which fast ion losses take place.
Therefore, we conclude the fast ion losses due to thetoroidal field ripple induce CTR rotation in the edge
region.

4. Evaluation of momentum transport coefficients
The toroidal momentum balance equations are
written as

n i Vt=   M + S ,tn V
M = mi  i t + mi Vconv n i Vt ,
r
mi

(1)
(2)

where mi, ni, M and S are the ion mass, the ion density,

the toroidal momentum flux and the toroidal momentum
source, respectively [7, 12]. In this paper, ions are definedas the main (deuterium) and impurity ions, assuming thatthe toroidal rotation velocity of the main ions is same asthat of the carbon impurity ions, which is measured by
the charge exchange recombination spectroscopy [18].
We can express the modulated n iVt assuming
nicV˜t >> n˜ iVt c , n˜ iV˜t as follows (the validity of thisassumption in this experiment is shown later),V˜t ( r,t ) = Vt0 ( r ) sin(t   ( r )) ,(3)

From equations (1)-(3), the time-independent solution of and Vconv can be obtained [12].
Figures 3(a) and 3(b) show  and Vconv as evaluatedfrom above mentioned modulation analysis (i.e.  and Vt0
profiles in Figs. 2(c) and 2(d)) assuming that the
momentum source in the core region (0.2<r/a<0.65) is
negligible (the momentum flux due to the modulated
PERP-NBs, M on the left-hand side of equation (2) is oneorder of magnitude smaller than -miniVt/r andmiVconvniVt at r/a~0.6). These transport coefficients in theregion r/a>0.7 are not evaluated, because the driving
source of CTR rotation is localized near the peripheral
region as shown in Fig. 2(d).
The solid lines in Fig. 3(c) show Vt profiles
calculated from equations (1) and (2) using transportcoefficients in Figs. 3(a) and 3(b) with the boundary
condition at r/a~0.65. Experimental data is also shownwith solid circles. As shown in Fig. 3(c), Vt profile in thecore region can be reproduced by momentum transportconsidering  and Vconv.
In Fig. 3(c), we compared the measured Vt profile tocalculation from equations (1) and (2) using transportcoefficients for a PERP-NBs injected L-mode plasma.
We also treat the plasmas in which the external
momentum source is injected, in order to investigate
whether the toroidal rotation in the core region isdominated by the momentum transport with thecoefficients. Experimental data (solid circles) in L-mode
plasmas with one unit of CO tangential NB (IP=1.2 MA,
BT=3.8 T,  N=0.39, q95=5.7 and n e=1.2x1019 m-3) andthat of CTR tangential NB (IP=0.87 MA, BT=3.8 T,

Proceedings of ITC/ISHW2007
N=0.34, q95=8.2 and n e=1.6x1019 m-3) are shown in
Figs. 4(a) and 4(b), respectively. In both plasmas, one
unit of PERP-NB is injected for the CXRS measurements[18]. Toroidal momentum source (torque) density profiles(dashed line) are also shown. The solid lines show Vt
profiles evaluated by the above-mentioned equations (1)and (2). In the both cases, the toroidal rotation profiles
almost agree with calculations. The toroidal rotation
profiles in the presence and absence of external torquehave been explained by the momentum transport in thecore region.

5. Characteristics of   and Vconv
Parameter dependences of the momentum transportcoefficients (i.e.  and Vconv) evaluated above-mentioned
method are shown in this section. Experiments have been
carried out to investigate the momentum transport as theheating power is varied under otherwise similar
conditions. As shown below, the degradation of
momentum confinement with increasing heating power isobserved similar to thermal confinement: the absorbed
power range varied over the range 2.4 MW<PABS<10.7
MW. Over the entire power range, L-mode phase wasmaintained due to the high power threshold at the highBT=3.8 T. The operation regimes in L-mode plasmas areN=0.39-1, pol*=0.03-0.05 and *=0.07-0.14. Here, N is
the normalized , pol* is the ion poloidal Larmor radiusnormalized to the minor radius, and * is the effective
electron collision frequency normalized to the bounce
frequency. As noted above, these L-mode plasmas satisfy
L-mode scaling in JT-60U [19]. Other plasma parameters
for this series of discharges were Ip=1.5 MA, q95=4.2,
=0.3 and Vol.=74 m3. The profiles of  and Vconv
during this heating power scan are shown in Figs. 5(a)and 5(b), respectively. The momentum diffusivity 
increases systematically with increasing the heating
power, and the shape of  is nearly identical.
Non-diffusive inward flux exists and has maximum value

10

(a)

6.4 MW
6.0 MW1

2.4 MW

outward0-10

inward(b)

Vconv (m/s),  (m2/s)

 (m 2/s)
Vconv (m/s)

PABS

10 ~10.7 MW

40
20

at r/a~0.6. The dependences of  and Vconv at r/a=0.6 onabsorbed power are shown in Fig. 5(c). The momentum
diffusivity at r/a=0.6 roughly scaled linearly with heating
power in this data set. The data in H-mode phase is alsoplotted in Fig. 5(c). The momentum diffusivity in the
H-mode is smaller than in L-mode by factor of 2-3.

6. Relation between   ,  i and Vconv
In this section, the relations between , i, Vconv in
H-mode plasmas are denoted by Ip and PABS scans.
After separating the diffusive and convective terms,
the relation between  and i is found for the fast time.
Figures 6(a)-6(c) illustrate the radial profiles of , Vconv,
i in a Ip scan, where BT also varies so that q95~4.3 issame value (Ip/BT=1.2/2.8, 1.5/3.8, 1.8/4 MA/T). For
these plasma discharges, two units of CO tangential NB
and PERP-NBs are injected with PABS=7.2-8.9 MW.
Other plasma parameters for this series of discharges
were =0.35 and n e=2.0-2.5x1019 m-3. The momentum
diffusivity  decreases with increasing Ip over the wholeradius. Also Vconv and i decrease with increasing Ip. The
dependences of the 1/ and 1/i at r/a=0.6 and the energy
confinement time E on Ip are also shown in Fig. 6(d).
These coefficients are almost proportional to Ip, and thecoefficients are similar value (1/~0.12 Ip, 1/i~0.14 Ip,
E~0.15 Ip).
The comparison of  and i in the Ip scan is shownin Figs. 7(a) and 7(b). Figure 7(a) is the data from theprofile data (0.25<r/a<0.6) shown in Figs. 6(a), and 6(b).
The relation at fixed radius (r/a=0.5, 0.6) is shown in Fig.
7(b). A similar data set during the heating power scan isshown in Figs. 7(c) and 7(d), where two units of CO
tangential NBs and PERP-NBs are injected at constant(c)
L-mode
H-mode

0
-20
-40
0

Vconv

r/a=0.6
10
15
PABS (MW)5

0 0.2 0.4 0.6 0.8 1
r/a

Fig.5 Profiles of (a)  and (b) Vconv during a heating
power scan in L-mode plasmas. (c) Dependence of and Vconv at r/a=0.6 on absorbed power.

Fig 6 Profiles of (a) , (b) Vconv and (c) i during an Ip
scan in H-mode plasmas. (c) Dependence of 1/ and1/i at r/a=0.6 and E on Ip.

Proceedings of ITC/ISHW2007(b) 401.2 MA
1.5 MA
1.8 MA20

/i~1

10
0

0

2

4 6 8 10i (m2/s) (m 2/s)(c)40 0.25<r/a<0.630

/i~1-3

4.8 MW
6.0 MW
8.4 MW
10 MW

20
10
0

0

2

4 6 8 10i (m 2/s)

 r/a=0.5
 r/a=0.6

30
 (m2/s)

30

20
10

/i~1

00

2

4 6 8 10i (m 2/s)(d) 4030
 (m2/s) (m 2/s)(a)40 0.25<r/a<0.6

20

 r/a=0.5
 r/a=0.6

and  for the first time. Figures 8(a) and 8(b) show thecorrelation between -Vconv and  from the profile data in
the region 0.25<r/a<0.6, and from the data at fixed radius(r/a=0.5, 0.6). The inward convection velocity (-Vconv)
increases with increasing  over a wide range of radii foreach discharge and at fixed radius in PABS and Ip scans.
This finding of the correlation between  and Vconv cancontribute to the understanding of the anomalous
momentum transport.

/i~2-3

7. Intrinsic rotation

10
0
0

2

4 6 8 10i (m 2/s)

Fig.7 Relation of  and i (a), (b) during the Ip scan,and (c), (d) during the heating power scan in H-mode
plasmas. (a), (c) are the data from the profile, (b), (d)are the data at r/a=0.5, 0.6.
Ip=1.2 MA. Other plasma parameters for this series ofdischarges were =0.34 and n e=1.8-2.2x1019 m-3. One
can see that  increases with increasing i. This tendency
is observed over a wide range of radii for each discharge.
In the case of the conventional steady-state analyses
without considering Vconv, the evaluated  tended to bemuch smaller than i. However, in this study,  is closeto i by analyzing both the diffusive and convective terms.
This means that the momentum diffusivity is alsoanomalous in a similar level with the heat diffusivity.
We have also found the correlation between Vconv

Fig.8 Correlation between Vconv and  (a) from theprofile data for each discharge, and (b) at r/a=0.5, 0.6
in H-mode plasmas.

In section 4, the Vt profiles in the case with andwithout external momentum input can be almost
reproduced by momentum transport calculations with and Vconv. However, not all measured Vt can be explainedwith the momentum transport model including  andVconv, the boundary condition of Vt, and the external
momentum input by NBs. In this section, thecharacteristics of the Vt profiles, which cannot be
explained with the momentum transport model, areinvestigated.
Figure 9(a) shows the radial profile of the measured
Vt (open circles) in the case with a higher heating power
PABS=11 MW L-mode plasma. The solid line in Fig. 9(a)shows the calculated Vt from the momentum transport
equations using  and Vconv with the boundary condition(setting the measured Vt equal to the calculated one at
r/a~0.65) [7]. Although the measured Vt agrees with thecalculation in the region 0.45<r/a<0.65, the measured Vt
deviates from the calculated one in the CTR-direction in
the core region 0.2<r/a<0.45. These results mean that themeasured Vt cannot be explained with the momentum
transport model including momentum transport

Fig.9 (a) Profiles of the measured Vt (open circles) andthe calculated one (solid line), (b) and gradPi in thecase of higher PABS=11 MW L-mode plasma.

Proceedings of ITC/ISHW2007

Vt (km/s)

50
40

PABS=2.4 MW=6.0 MW
=6.4 MW=11 MW
CTR-rotating

30
CTR
20
CO
10
0
L-modeCTR-10
44-6 10 -3 10
0
gradPi (Pa/m)

Fig.10 -Vt is plotted against the gradPi in a heating
power scan for L-mode (Ip=1.5 MA, BT=3.8 T).
coefficients, the boundary condition of Vt, and theexternal momentum input by NBs. In such plasma, thelarge pressure gradient (gradPi) is observed in the coreregion (0.2<r/a<0.45) as shown in Fig. 9(b).
In order to investigate the relation between theincrease of CTR rotation and the gradPi, the difference
between the measured Vt and the calculated one, i.e.
Vt=Vt(measurement)-Vt(calculation)=intrinsic rotationin the region 0.3<r/a<0.6 is plotted against the gradPi in
the heating power scan in Fig. 10. The symbols denoteVt at r/a=0.3, 0.4, 0.5 and 0.6. In these plasmas, thelarger values of gradPi are obtained in the core region. As
shown in Fig. 10, Vt in L-mode plasmas grows withincreasing gradPi in all cases. This tendency is almost thesame, even the direction of the Vt is different (CO- andCTR-rotating plasmas), over a wide range of  which
varies by about one order of magnitude radially (~1-30m2/s) and by about a factor of three (~1-3 m2/s) (in theheating power scan) at fixed radius (r/a~0.4). These
results indicate gradPi affects the intrinsic rotation evenin L-mode plasmas, and the local gradPi affects the local
value of the intrinsic rotation. This good correlation
between the local intrinsic rotation velocity and the local
gradPi indicates that the gradPi appears to cause thevalue of the local intrinsic rotation velocity. The proper
evaluation of the momentum coefficients enables us toevaluate the intrinsic rotation.

8. Summary
The elements determining the Vt profile have been
identified, and the roles of these elements on Vt profile
are also found. The fast ion losses due to the toroidal field
ripple induce CTR rotation in the edge region. As a novel
momentum source, this edge localized momentum source

has been used for the transient momentum transport
analysis. The  and Vconv have been separately evaluatedusing the transient momentum transport analysis. We
have found that , which separated from the convective
term increases with increasing i. The -Vconv increases
with increasing  over a wide range in radii. At low
plasma pressure, the steady Vt profiles with CO andCTR-NBIs can be almost reproduced by calculations with
 and Vconv. On the other hand, At higher plasmapressure, the intrinsic rotation (Vt) increases withincreasing gradPi in CO-, CTR-rotating L-mode plasmas.
The results indicate that the local gradPi appears to cause
the local value of intrinsic rotation.

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