Flow damping due to stochastization of the magnetic field

Abstract

The driving and damping mechanism of plasma flow is an important issue because flow shear has a significant impact on turbulence in a plasma, which determines the transport in the magnetized plasma. Here we report clear evidence of the flow damping due to stochastization of the magnetic field. Abrupt damping of the toroidal flow associated with a transition from a nested magnetic flux surface to a stochastic magnetic field is observed when the magnetic shear at the rational surface decreases to 0.5 in the large helical device. This flow damping and resulting profile flattening are much stronger than expected from the Rechester-Rosenbluth model. The toroidal flow shear shows a linear decay, while the ion temperature gradient shows an exponential decay. This observation suggests that the flow damping is due to the change in the non-diffusive term of momentum transport.

ARTICLE

Received 9 Jun 2014 | Accepted 11 Nov 2014 | Published 8 Jan 2015

K. Ida1, M. Yoshinuma1, H. Tsuchiya1, T. Kobayashi1, C. Suzuki1, M. Yokoyama1, A. Shimizu1, K. Nagaoka1,S. Inagaki2, K. Itoh1 & the LHD Experiment Group*

The driving and damping mechanism of plasma ow is an important issue because ow shear has a signicant impact on turbulence in a plasma, which determines the transport in the magnetized plasma. Here we report clear evidence of the ow damping due to stochastization of the magnetic eld. Abrupt damping of the toroidal ow associated with a transition from a nested magnetic ux surface to a stochastic magnetic eld is observed when the magnetic shear at the rational surface decreases to 0.5 in the large helical device. This ow damping and resulting prole attening are much stronger than expected from the RechesterRosenbluth model. The toroidal ow shear shows a linear decay, while the ion temperature gradient shows an exponential decay. This observation suggests that the ow damping is due to the change in the non-diffusive term of momentum transport.

DOI: 10.1038/ncomms6816 OPEN

Flow damping due to stochastization of the magnetic eld

1 National Institute for Fusion Science, Toki, Gifu 509-5292, Japan. 2 Research Institute for Applied Mechanics, Kyushu University, Kasuga 816-8580, Japan. Correspondence and requests for materials should be addressed to K.I. (email: mailto:[email protected]

Web End [email protected] ).

*List of participants and their afliations appear at the end of the paper.

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Stochastization of the magnetic ux surface is expected to be induced when the magnetic islands are overlapped and their width exceeds a threshold in toroidal plasmas. Stochastiza

tion of magnetic surfaces has been considered to be important because this mechanism, caused by perturbation elds, has a strong impact on transport and MHD events, such as a major disruption or an edge localized mode crash. The role of stochasticity in electron and ion heat transport has been studied in reverse eld pinch (RFP) plasmas (in a reversed eld experiment (RFX)1,2 and in the Madison Symmetric Torus (MST)35), where magnetic islands overlap and eld lines are stochastic. In general, good agreement between the electron thermal diffusivity estimated from power balance and the analytic predictions of the RechesterRosenbluth model6 has been reported. However, the role of stochastization of the magnetic eld in plasma ow has not been discussed before, in spite of the importance of ow shear in the turbulence in plasma, which determines the transport in toroidal magnetized plasmas, such as in tokamak, helical and RFP plasmas.

Here we demonstrate that stochastization of the magnetic eld occurs when the magnetic shear at the rational surface decreases in a plasma and the damping of toroidal ow due to the stochastization is stronger than expected by the Rechester Rosenbluth model.

ResultsExperimental set-up. The large helical device (LHD) is a heliotron-type device for magnetic connement of high-temperature plasmas. The LHD has three tangential neutral beams (NBs); two beams are used to change the direction of the plasma current from parallel (co-injection) to anti-parallel (counter-injection) with respect to the equivalent plasma current. The toroidal ow and ion temperature are measured with charge exchange spectroscopy7, while the rotational transform, i/2p, and magnetic shear, s[ (r/i)qi/qr], at the rational surface (i/2p 0.5) are

measured with motional stark effect spectroscopy (MSE)8 in the LHD. There are three kinds of topology of the magnetic eld in the plasma: the rst is nested magnetic ux surfaces, the second is a stochastic magnetic eld and the third is a magnetic island. The magnetic topology is identied by the characteristics of heat pulse propagation produced by modulated electron cyclotron heating (MECH), measured with electron cyclotron emission9. In the nested magnetic ux surfaces, the heat pulse propagates outwards on the time scale of the heat transport. In contrast, the heat pulse propagation becomes very fast due to the propagation along the magnetic eld line in the stochastic region in the plasma.

Observation of ow damping. Figure 1 shows the time evolution of toroidal ow, angular momentum, rotational transform, magnetic shear, and inverse of the electron and ion thermal diffusivity in the discharge, where the direction of the NB injection (NBI) is switched from co-injection to counter-injection (parallel to anti-parallel to the equivalent plasma current, which gives the poloidal eld produced by the external coil current) at t 5.3 s. The vacuum magnetic axis is 3.6 m and the magnetic

eld strength is 2.75 T. The edge rotational transform decreases due to the NB current drive (NBCD) and the central rotational transform increases due to the inductive current; the magnetic shear at the i/2p 0.5 rational surface starts to decrease and

reaches the steady-state value of 0.5 at t 5.8 s after the switch of

the NBI. This decrease of magnetic shear increases the magnetic island width and nally causes stochastization due to the overlapping of magnetic islands with higher modes9,10. The toroidal ow velocity changes its sign from positive (co-rotation) to negative (counter-rotation) and becomes steady state at a central

toroidal ow velocity of 40 km s 1. An abrupt drop of the

toroidal ow velocity is observed at t 6.0 s, although the NBI

continues to be injected until t 7.3 s. The toroidal ow velocity

starts to recover at t 6.7 s. The core angular momentum (reff/

a99o1/2) decreases at the stochastization, which suggests that this ow damping is not due to the increase in perpendicular viscosity but due to the direct loss of angular momentum.

The topology of the magnetic eld is identied by the characteristics of the heat pulse propagation driven by MECH with a frequency of 25 Hz at the plasma center within reff/a99o0.1. Here, reff is the averaged minor radius on a magnetic ux surface and a99 is the effective minor radius in which 99% of the plasma kinetic energy is conned, which is 0.63 m in this

5.75 s

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6.25 s

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6 4

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[afii9836]/(2[afii9843])

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reff/a99 reff/a99

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reff/a99 =0.5

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102 [afii9851]e

[afii9851]i

Figure 1 | Time evolution of ow velocity and other plasma parameters. Time evolution of (a) toroidal ow velocity, Vf, (b) angular momentum in the core (reff/a99o1/2), (c) rotational transform, i/2p, (d) magnetic shear, s, at the rational surface (i/2p 0.5), and (e) inverse of the electron and

ion thermal diffusivity, 1/we, 1/wi, at reff/a99 0.35 in the discharge where

the direction of neutral beam injection (NBI) is switched from co- to counter-injection. Radial proles of delay time of heat pulse produced by modulated electron cyclotron heating (MECH) at three time slices(t 5.45, 6.02, 6.72 s) are also plotted. The error bars of the delay times

are standard deviations. The error bars of toroidal rotation are derived from the uncertainty of the tting parameter of the charge exchange line emission to a Gaussian prole. The error bars of rotational transform and magnetic shear are derived from the standard deviations of the MSE signal.

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discharge. Just after the beam switch at t 5.45 s, the delay time

of the heat pulse indicates that the magnetic topology is characterized by normal nested magnetic ux surfaces as seen in Fig. 1. At t 6.02 s, where abrupt drop of the toroidal ow

velocity is observed, the delay time of the heat pulse propagation shows attening in the plasma core (reff/a99o0.57), which

indicates the change of magnetic topology to a stochastic character (stochastization of the magnetic eld). During the latter period in this discharge, at t 6.72 s, the radial prole of

the delay time shows a small peak at reff/a99B0.5, which indicates

the magnetic island where the heat pulse propagates from the boundary to the O-point of the magnetic island, located at reff/a99B0.5. There are two patterns of heat pulse propagation

observed in the at temperature region: one pattern is a very fast

propagation as seen at t 6.02 s, and the other is simultaneous

propagation at two separate points (reff/a99B0.4 and 0.6) as seen

at t 6.72 s. The former is clear evidence of the stochastization of

the magnetic eld, and the latter is consistent with a magnetic ux surface with a magnetic island. A negative slope of the time delay shows that the heat pulse propagates inward from the boundary of the magnetic island at reff/a99B0.6 to the O-point,

and a peaked delay prole indicates that the heat transport inside the magnetic island is comparable to or even better than that outside of the magnetic island11,12.

Thermal diffusivity and viscosity. In the core plasma of the LHD, the electron thermal diffusivity evaluated from heat pulse is comparable to that evaluated from the power balance in the steady state13. These experimental results suggest that the heat pinch14 or other non-linearities of electron transport are small enough to be neglected in this experiment. Therefore, the effective transport coefcients (electron thermal diffusivity, ion thermal diffusivity and viscosity) are evaluated from the ratio of radial ux normalized by density to gradient for simplicity. Here, the radial ux of electron ion heat transport and momentum transport are calculated from the power deposition and torque proles driven by the MECH and the NBIs. Figure 2 shows the radial proles of toroidal ow velocity, electron temperature, ion temperature and electron density before (t 5.64 s, 5.61 s) and after (t 6.44 s,

6.41 s) the stochastization of the magnetic eld. Before the stochastization, the toroidal ow velocity is very peaked at the plasma centre, because the toroidal viscosity due to helical ripple increases sharply towards the plasma edge and hence signicant damping of the toroidal ow occurs there. After the stochastization, a clear attening of the toroidal ow, ion temperature and electron temperature proles is observed. Since the density prole is already at even before the stochastization, the effect of stochastization on particle transport is not clear in this experiment. The increase of electron density is gradual and not due to the stochastization of the magnetic eld.

Thermal diffusivity (dened as the ratio of the normalized heat ux to the temperature gradient) is evaluated for ion and electron transport, with a correction due to the slowing-down process15. The electron thermal diffusivity (we) at reff/a99 0.35 (reff 0.2 m)

increases by more than one order of magnitude (we 4.11.2 m2 s 1-4102 m2 s 1), while the ion thermal

diffusivity (wi) increases only by a factor of 1.8 (wi 3.80.3 m2 s 1-6.90.9 m2 s 1). The electron and ion

thermal diffusivity in the stochastic region can be evaluated as wsti;e DMue;i using the RechesterRosenbluth model6. Here ue

and ui are the thermal velocities of electron and ion, respectively, and DM is the diffusion of the eld line, dened by 2pr2s=RB2n, rs

is the radius of the resonant surface and Bn ( (RBr)/(rsBf)) is

the normalized perturbation eld16. Then we in the stochastic

region is expected to be much larger than that of the ions by (mi/me)1/2 because of its larger thermal velocity5,17. The thermal diffusivity in the stochastic region wst evaluated from similar discharges9 is 2.50.5 102 m2 s 1 for electrons and

61 m2 s 1 for ions, which is consistent with this experimental observation. The magnitude of the electron thermal diffusivity is comparable to that estimated from the power balance and also predicted by the analytic formula of the RechesterRosenbluth model6 in RFX1 and in MST3 experiments (102103 m2 s 1).

The viscosity coefcient of the toroidal ow (mf) is similar to wi before the stochastization, which indicates that both momentum and ion heat transport are dominated by turbulence transport. However, the increase in mf is by a factor of 5 (mf 4.01.6

m2 s 1-215 m2 s 1), which is much larger than that in ion thermal transport. This fact suggests that the damping of the toroidal ow is not only due to the increase of the viscosity coefcient. Because the toroidal ow velocity is much more peaked in the core region (reff/a99o0.5), where the stochastiza

tion takes place, than the ion and electron temperature, the change in toroidal ow is most signicant at the topology bifurcation from nested ux surface to the stochastic magnetic eld.

Physics mechanism of ow damping. In this section, the physics mechanism of ow damping is discussed. The large effective Prandtl number observed during stochastization (mf/w 3) dis

cussed in the previous section suggests the existence of an additional damping mechanism of the toroidal ow due to stochastization of the magnetic eld. Figure 3 shows radial

20

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6.41 s

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5.64 s

19 m3 )

6.44 s

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reff/a99

Figure 2 | Radial proles of ow velocity, temperatures, and density. Radial proles of (a) toroidal ow velocity, (b) electron temperature, (c) ion temperature and (d) electron density before (t 5.64, 5.61 s) and after

(t 6.44, 6.41 s) the stochastization of the magnetic eld. The solid lines in

the radial proles of electron density are polynomial t curves to data points. The error bars of toroidal rotation and ion temperature are derived from the uncertainty of the tting parameter of the charge exchange line emission to a Gaussian prole. The error bars of electron temperature are derived from the standard deviations of the signal.

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4.0

3.53.02.52.01.51.0

40 30 20 10

0 10

100

5.278 s

5.307 s

reff/a99 =0.53

reff/a99 =0.09

3 s1)

dV /dr(10

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[afii9836]/(2[afii9843])

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decay

5.347 s

5.382 s

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0.1

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0.50.0

0 0.1

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reff/a99

Figure 3 | Decay of ion temperature and ow velocity. Radial proles of (a) ion temperature and (b) toroidal ow velocity in the core region (reff/

a99o0.6) during the stochastization of the magnetic eld. The decay of the ion temperature gradient and the toroidal ow velocity shear at reff/

a99 0.27 are also plotted in log-scale. The solid lines in the radial proles

of ion temperature and toroidal rotation are polynomial t curves to data points and the solid lines in the time evolution of the ion temperature gradient and velocity shear in the log-plot are the exponential curve and linear curve to t data points. The error bars of toroidal rotation and ion temperature are derived from the uncertainty of the tting parameter of the charge exchange line emission to a Gaussian prole.

0

10

20

30

0.2 0.3 0.4 0.5 0.6

reff/a99

20 t0 = 5.28 s

t = 5.30 s

proles of the ion temperature and toroidal ow velocity in the core region of reff/a99o0.6, and the decay of the ion temperature

gradient and the toroidal ow velocity shear during the decay phase at reff/a99 0.27. The ion temperature proles show a

prompt attening after the stochastization (the drops in ion temperature occur earlier and faster over time); however, the toroidal ow velocity proles show a damping after the drop of ion temperature in the time scale of 100 ms. The decay rate of the central ion temperature becomes smaller with time (qTi/qt(5.278

5.307 s)4qTi/qt(5.3075.347 s)BqTi/qt(5.3475.382 s)), while that of the toroidal rotation becomes larger and then constant with time (qVf/qt(5.2785.307 s)oqVf/qt(5.3075.347 s)BqVf/

qt(5.3475.382 s)). There is a clear difference in the decay of the ion temperature gradient and the toroidal ow velocity shear observed. The toroidal ow shear shows a linear decay, while the ion temperature gradient shows an exponential decay, which is indicated by the solid lines in Fig. 3a,b in log-scale. The toroidal ow shear decreases more than the linear curve at tB5.4 s, as seen in Fig. 3b. This experimental observation (linear decay) cannot be explained by the increase in the diffusive term of the momentum transport, which should be proportional to the velocity shear, and it suggests a new damping mechanism.

Radial propagation of stochastization. It is an interesting issue how the stochastic region develops in time during the stochastization. In order to study the radial propagation of stochastization, the radial prole of the time taken for the abrupt drop of toroidal ow velocity is studied. Figure 4 shows the time evolution of the toroidal ow near the i/2p 0.5 surface and magnetic axis, and a

radial propagation of the onset of the ow damping and the radial prole of the rotational transform measured with the MSE. As discussed earlier, the decay of toroidal ow velocity can be tted well with a linear line. Therefore we can derive the onset time of ow damping from the intersection of two lines of linear tting to

the data before (tott) and after (t4tt) the stochastization. Because the time of the stochastization itself is unknown before the tting and the intersection depends on how the data are separated (namely tt), tt is scanned from well before (t 5.26 s)

to well after (t 5.32 s) the stochastization by 60 ms, and the

onset time and its error bars are determined from the average value and standard deviation in this scan. Please note that the onset time is insensitive to tt. These results show that the stochastization starts near the rational surface of i/2p 0.5 at

reff/a99 0.450.55 and propagates radially in two time scales.

1 )

r(kV m

Nested

Stochastization

15 0.0 0.2 0.4

reff/a99

0.6 0.8 1.0

Figure 4 | Radial propagation of stochastization. (a) Time evolution of toroidal ow velocity and two liner tting lines in the case of tt 5.29 s at

reff/a99 0.09 and 0.53 during the stochastization of the magnetic and

radial proles of (b) onset time of ow damping associated with the stochastization of magnetic eld, (c) rotational transform i/2p, and(d) radial electric eld before stochastization (with nested magnetic ux surface) and after the stochastization measured with HIBP in a similar discharge. The onset time (intersections of two lines) is indicated with the arrows in (a). The typical error bar of the measurements of rotational transform in (c) is 0.01. Because the time of the stochastization itself is unknown before the tting and the intersection depends on the separation of the data (namely tt), tt is scanned from well before (t 5.26 s) to well

after (t 5.32 s) the stochastization by 60 ms. The error bars are

determined from the standard deviation in this scan.

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The thickness of the stochastic region increases slowly up to a quarter of the plasma minor radius (reff/a99 0.360.62), and

then a rapid extension of the stochastic region to the magnetic axis takes place. The sudden extension of the stochastic region to the magnetic axis observed in this experiment indicates the nonlinear growth of the perturbation eld causing stochastization, which was proposed in the major disruption or sawtooth crash model16,18.

DiscussionThe change in a radial electric eld associated with stochastization is plotted in Fig. 4d. The positive radial electric eld in the core region (reff/a99o0.4) decreases and the negative radial electric eld outside this region increases after stochastization of the magnetic eld. The change in the radial electric eld is more signicant near the rational surface, where the dominant modes are resonant, while the attening of the electron temperature is observed in the whole core region. This observation is consistent with the fact that the transport enhanced due to the stochastization of magnetic eld is ambipolar except for the region near locations where the dominant modes are resonant19. Although the neoclassical transport is sensitive to the radial electric eld, the effect of the radial electric eld on transport is relatively small because the electron heat transport is dominated by turbulence transport in this plasma.

In this experiment, the abrupt damping of the toroidal ow due to stochastization of the magnetic eld is observed when the magnetic shear drops to 0.5 after the switch of the NBI from co-injection to counter-injection. The stochastization starts near the rational surface of i/2p 0.5 and the stochastic region

develops to the magnetic axis in two time scales: one is a slow increase of the stochastization width and the other is a fast extension to the magnetic axis. After the stochastization of the magnetic eld, the increase of we is much larger than that of the ions (we/wi415) because of the difference in thermal velocity, which is consistent with the RechesterRosenbluth model (B40) (ref. 6). On the other hand, the ow damping observed cannot be explained by this model and there are clear differences in the decay between ion temperature and toroidal ow velocity, which suggests that the damping of ow is due to the change in the non-diffusive term of momentum transport associated with the stochastization of the magnetic eld.

One of the candidates for a new ow damping mechanism is the change in the non-diffusive term of toroidal momentum transport20 due to stochastization of the magnetic eld. The other candidate is a toroidal momentum pinch as a direct electromagnetic effect, which is also proportional to the ion temperature gradient21. Here a stochastization of the magnetic eld may reduce the phase correlation between magnetic vector potential and electrostatic potential, thus resulting in reduction of the momentum pinch. These electromagnetic effects on toroidal momentum transport (momentum pinch) become strong in the plasma with large ion temperature gradient and decrease the effective Prandtl number signicantly (even to negative values in the case of small density gradients). In our experiment, the Prandtl number before the stochastization is close to unity and the momentum pinch effect is expected to be small. After the stochastization, the ion temperature gradient, which causes the momentum pinch, becomes even smaller. This ow damping mechanism is a strong candidate for the angular momentum loss due to the magnetic island disruption in tokamaks, and should also be important in the solar are, where the magnetic stochastization (overlapping of magnetic islands) is one of the candidates to explain the fast time scale of magnetic eld reconnection22,23.

Methods

Large helical device. LHD is a heliotron-type device for magnetic connement of high-temperature plasmas within a magnetic eld, B, of 2.7 T at the magnetic axis in the vacuum eld, with a major radius, Rax, and effective minor radius, reff, of 3.6 and 0.63 m, respectively. In this experiment, the plasma density is 12 1019 m 3

and the central temperature is in the range of 24 keV. The LHD is equipped with three tangential NBs in the opposite injection direction (two counterclockwise and one clockwise) and electron cyclotron heating (ECH). The NBs are applied for both electron and ion heating, while the ECH is applied for electron heating focused at the magnetic axis in the plasma. The NBs are also used to control the magnetic shear with the toroidal current driven by the NB.

NB current drive. NB current drive (NBCD) is one of the useful tools to drive toroidal current. The total plasma current driven by the NB is in the range of

B100 kA (counter-direction) to 50 kA (co-direction), which is only 36% of the equivalent plasma current (1.8 MA) produced by the external helical coils. However, the time scale in the change of total current is longer than the beam pulses, and the inductive current in the direction opposite to the toroidal current due to NBCD in the core region plays an important role in this experiment. Therefore, by switching the direction of the NBCD during the discharge, the magnetic shear near the plasma core can be controlled. In this experiment, the direction of the injected NB switches from parallel (co-direction) to antiparallel (counter-direction) with respect to the equivalent plasma current, and magnetic shear decreases effectively (from 1.3 to 0.5) after the injection of the NB in the counter-direction.

Modulated ECH. The heat pulse propagation experiment is a useful tool for identifying the magnetic topology in toroidal plasmas. In a magnetic ux surface with a magnetic island, the heat pulse shows bi-directional slow propagation. This is because the perturbation is felt simultaneously at two points separated in radius, which can be interpreted as a surface equilibration. On the other hand, the heat pulse shows very fast propagation in the magnetic ux surface with stochastization due to the heat pulse propagation along the magnetic eld in the time scale of thermal velocity. Recently MECH has been applied to investigate the characteristics of heat pulse propagation. In this experiment, MECH with a frequency of 25 Hz focused at the plasma centre is applied.

Thermal diffusivity and viscosity. Thermal diffusivity and viscosity are evaluated from the ratio of the heat ux and momentum ux to the temperature gradient and velocity gradient. The heat ux and momentum ux are calculated from the heating and torque proles from NBs and ECH using the FIT-3D code, where the steady-state solution of the FokkerPlanck equation is solved based on the birth prole of fast ions calculated by the MonteCarlo method with the radial redistribution of fast ions due to prompt orbit effects with a correction due to the slowing-down process.

References

1. Bartiromo, R. et al. Core transport improvement during poloidal current drive in the RFX reversed eld pinch. Phys. Rev. Lett. 82, 14621465 (1999).

2. Innocente, P. et al. Transport and connement studies in the RFX-mod reversed-eld pinch experiment. Nucl. Fusion 47, 10921100 (2007).

3. Biewer, T. M. et al. Electron heat transport measured in a stochastic magnetic eld. Phys. Rev. Lett. 91, 045004 (2003).

4. Sarff, J. S. et al. Tokamak-like connement at a high beta and low toroidal eld in the MST reversed eld pinch. Nucl. Fusion 43, 16841692 (2003).

5. Fiksel, G. et al. Measurement of magnetic uctuation-induced heat transport in tokamaks and RFP. Plasma Phys. Control. Fusion 38, A213A225 (1996).6. Rechester, A. B. & Rosenbluth, M. N. Electron heat transport in a tokamak with destroyes magnetic surfaces. Phys. Rev. Lett. 40, 3841 (1978).

7. Yoshinuma, M. et al. Charge-exchange spectroscopy with pitch-controlled double-slit ber bundle on LHD. Fusion Sci. Technol. 58, 375382 (2010).

8. Ida, K. et al. Measurements of rotational transform with motional stark effect spectroscopy. Fusion Sci. Technol. 58, 383393 (2010).

9. Ida, K. et al. Topology bifurcation of a magnetic ux surface in magnetized plasmas. New J. Phys. 15, 013061 (2013).

10. Ida, K. et al. Bifurcation phenomena of a magnetic island at a rational surface in a magnetic-shear control experiment. Phys. Rev. Lett. 100, 045003 (2008).

11. Inagaki, S. et al. Observation of reduced heat transport inside the magnetic island O point in the large helical device. Phys. Rev. Lett. 92, 055002 (2004).

12. Yakovlev, M. et al. Heat pulse propagation across the rational surface in a large helical device plasma with counter-neutral beam injection. Phys. Plasmas 12, 092506 (2005).

13. Inagaki, S. et al. Comparison of transient electron heat transport in LHD helical and JT-60U tokamak plasmas. Nucl. Fusion 46, 133141 (2006).

14. Luce, T. et al. Inward energy transport in tokamak plasmas. Phys. Rev. Lett. 68, 5255 (1992).

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ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms6816

15. Lee, H. et al. Dynamic transport study of heat and momentum transport in a plasma with improved ion connement in the large helical device. Plasma Phys. Control. Fusion 55, 014011 (2013).

16. Lichtenberg, A. J. et al. The role of stochasticity in sawtooth oscillations. Nucl. Fusion 32, 495512 (1992).

17. Itoh, S.-I. et al. A model of giant ELMs. Plasma Phys. Control. Fusion 38, 527549 (1996).

18. Itoh, K. et al. Model of the major disruption in tokamaks. Nucl. Fusion 32, 18511855 (1992).

19. Terry, P. W. et al. Ambipolar magnetic uctuation-induced heat transport in toroidal devices. Phys. Plasmas 3, 19992005 (1996).

20. Ida, K. et al. Spontaneous toroidal rotation driven by the off-diagonal term of momentum and heat transport in the plasma with the ion internal transport barrier in LHD. Nucl. Fusion 50, 064007 (2010).

21. Mahmood, A., Eriksson, A. & Weiland, J. Electromagnetic effects on toroidal momentum transport. Phys. Plasmas 17, 122310 (2010).

22. Parker, E. N. The solar-are phenomenon and the theory of reconnection and annihilation of magnetic elds. ApJS 8, 177211 (1963).

23. Yokoyama, T. & Shibata, K. What is the condition for fast magnetic reconnection? ApJ 436, L197L200 (1994).

Acknowledgements

This work is partly supported by the Grant-in-Aid for Scientic Research (No. 21224014

and 23246164) of JSPS Japan; by NIFS10ULHH021; and by the collaboration program of

NIFS and RIAM Kyushu University (NIFS13KOCT001).

Author contributions

K.I. proposed and performed the experiments, analysed the data and wrote the

manuscript. M. Yoshinuma. and H.T. provided toroidal ow data and heat pulse pro

pagation data, respectively. T.K. analysed the heat pulse propagation data driven by

MECH. C.S. and M. Yokoyama developed analysis tools to derive the thermal diffusivity

and viscosity. A.S. provided radial electric eld data. K.N. supported the NBCD in this

experiment. S.I. provided the analysis code of the heat pulse propagation. K.I. provided

the theoretical model.

Additional information

Competing nancial interests: The authors declare no competing nancial interests.

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LHD experiment groupT. Akiyama1, M. Emoto1, T. Evans3, A. Dinklage4, X. Du5, K. Fujii6, M. Goto1, T. Goto1, M. Hasuo6, C. Hidalgo7,K. Ichiguchi1, A. Ishizawa1, M. Jakubowski4, K. Kamiya8, H. Kasahara1, G. Kawamura1, D. Kato1, M. Kobayashi1,S. Morita1, K. Mukai1, I. Murakami1, S. Murakami9, Y. Narushima1, M. Nunami1, S. Ohdach1, N. Ohno10,M. Osakabe1, N. Pablant11, S. Sakakibara1, T. Seki1, T. Shimozuma1, M. Shoji1, S. Sudo1, K. Tanaka1, T. Tokuzawa1,Y. Todo1, H. Wang1, H. Yamada1, Y. Takeiri1, T. Mutoh1, S. Imagawa1, T. Mito1, Y. Nagayama1, K.Y. Watanabe1,N. Ashikawa1, H. Chikaraishi1, A. Ejiri12, M. Furukawa13, T. Fujita10, S. Hamaguchi1, H. Igami1, M. Isobe1,S. Masuzaki1, T. Morisaki1, G. Motojima1, K. Nagasaki14, H. Nakano1, Y. Oya15, Y. Suzuki1, R. Sakamoto1,M. Sakamoto16, A. Sanpei17, H. Takahashi1, M. Tokitani1, Y. Ueda18, Y. Yoshimura1, S. Yamamoto14, K. Nishimura1,H. Sugama1, T. Yamamoto1, H. Idei19, A. Isayama7, S. Kitajima20, S. Masamune17, K. Shinohara7, P.S. Bawankar4,E. Bernard1, M. von Berkel1, H. Funaba1, X.L. Huang4, T. Ii1, T. Ido1, K. Ikeda1, S. Kamio1, R. Kumazawa1, C. Moon1,S. Muto1, J. Miyazawa1, T. Ming1, Y. Nakamura1, S. Nishimura1, K. Ogawa1, T. Ozaki1, T. Oishi1, M. Ohno4,S. Pandya4, R. Seki1, R. Sano4, K. Saito1, H. Sakaue1, Y. Takemura1, K. Tsumori1, N. Tamura1, H. Tanaka1, K. Toi1,B. Wieland1, I. Yamada1, R. Yasuhara1, H. Zhang3, O.Kaneko1 and A. Komori1

3General Atomics, San Diego, California, USA. 4Max-Planck-Institut fr Plasmaphysik, Wendelsteinstr. 1, 17489 Greifswald, Germany. 5The Graduate University for Advanced Studies, 322-6 Oroshi, Toki, Gifu 509-5292, Japan. 6Department of Mechanical Engineering and Science,Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan. 7Laboratorio Nacional de Fusion, Asociacion EURATOM-CIEMAT, 28040 Madrid, Spain. 8Japan Atomic Energy Agency, Naka, Ibaraki 311-0193, Japan. 9Department of Nuclear Engineering, Kyoto University, Kyoto 606-8501, Japan. 10Department of Energy Engineering and Science, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan. 11Princeton Plasma Physics Laboratory, PO Box 45, Princeton, New Jersey 08543-0451, USA. 12Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa-shi, Chiba-ken 277-8561, Japan. 13Department of Applied Mathematics and Physics Faculty of Engineering, Tottori University, 4-101 Koyama-Minami, Tottori 680-8552, Japan 14Institute of Advanced Energy, Kyoto University, Kyoto 611-0011, Japan 15Radioscience Research Laboratory, Faculty of Science,Shizuoka University, 836 Oya, Suruga-ku, Shizuoka 422-8529, Japan. 16Plasma Research Center, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japan. 17Kyoto Institute of Technology, Matsugasaki, Sakyo-ku, Kyoto 606-8585, Japan. 18Graduate School of Engineering, Osaka University, 1-1 Yamadaoka, Suita, Osaka 565-0871, Japan. 19Research Institute for Applied Mechanics, Kyushu University, 6-1 Kasuga-kouen, Kasuga, Fukuoka 816-8580, Japan. 20Department of Quantum Science and Energy Engineering, Tohoku University, Sendai 980-8579, Japan.

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