On the interplay between MHD instabilities and turbulent transport in magnetically confined plasmas

The interplay between MHD and turbulence is an interesting topic in magnetically confined plasma and solar plasma. The experimental observations made recently, shown below, suggest coupling and interplay between MHD and turbulence in magnetically confined toroidal plasmas. (1) Turbulence spreading into the magnetic island, (2) there is a self-organized change in topology and turbulence in the magnetic island, (3) the flow is damped by a stochastic magnetic field, (4) the trigger mechanism for the MHD bursts, (5) MHD bursts have an impact on the ion velocity distribution and potential, and (6) turbulence exhausts are created at the MHD burst event. In this paper, experimental evidence for the interplay between MHD and turbulence in toroidal plasmas is reviewed. The physics mechanism of the interplay and a possible link to astrophysical plasma physics are also discussed.


Introduction
The interplay between MHD and turbulence is an interesting topic in magnetically confined plasma and solar plasma research. The fast reconnection of magnetic fields in solar flares is well known; however, the mechanism is not fully understood. Turbulence in the current sheet is a strong candidate for explaining fast reconnection in solar flares [1,2]. In magnetically confined plasmas, MHD instabilities and electrostatic turbulence have been investigated independently. No coupling between the electrostatic turbulence and MHD instability is assumed.
However, recent experimental observations, shown below, suggest coupling and interplay between MHD and turbulence in magnetically confined toroidal plasmas [3], turbulence spreads into the magnetic island [4], there is a self-organized change in topology and turbulence in the magnetic island [5], the flow is damped by a stochastic magnetic field [6], the trigger mechanism for the MHD bursts [7], the MHD bursts have an impact on the ion velocity distribution and potential [8,9], and turbulence exhausts are created at the MHD burst event [10]. Evidence for the interplay between MHD and turbulence in toroidal plasma is reviewed and the physics mechanism of the interplay is also discussed in section 2. For example, in the heat pulse experiment in the DIII-D tokamak plasma, the turbulence increase occurs after the arrival of the heat pulse with a significant delay at the X-point, while it occurs before the radial propagation of the heat pulse at the O-point of the magnetic island. This is due to the turbulence spreading from the X-point to the O-point of the magnetic island faster than the heat pulse, determined by the transport time scale inside the magnetic island. In the D-IIID tokamak, two states of magnetic islands are observed. The 'high-accessibility' state is when the heat pulse propagating from outside a magnetic island can penetrate the magnetic island, while the 'low-accessibility' state is when penetration of the heat pulse into the magnetic island is prevented at the boundary. Oscillations between these states are self-regulated and the change in magnetic topology, such as the stochastization of the magnetic field at the boundary of the magnetic island, is one possible mechanism for this self-regulated oscillation. Self-regulated oscillation of the topology and transport inside the magnetic island is observed owing to the interplay between the MHD and turbulence. In Large Helical Device (LHD) helical plasma, anomalous flow damping is observed related to the stochastic magnetic field in the plasma core, which suggests interplay between MHD and turbulence in plasma.
More recently, a strong MHD burst is found to have been triggered by nonmodal (no toroidal and no poloidal periodic number) localized plasma deformation. Here, nonmodal means that there is no clear helical structure characterized by the loworder toroidal and poloidal periodic number usually expressed by n/m at the rational surface. The nonmodal perturbation has a solitary structure and is highly localized in the toroidal and poloidal direction. The perturbation with a solitary structure is observed near the plasma edge when the edge localized mode (ELM) activities are excited, and is also known as a finger structure [11,12]. This MHD burst causes the distortion of ion velocity distribution and a large potential due to energetic ion loss. This MHD burst also causes the rapid radial propagation of turbulence from the plasma core to the SOL region. This is also clear evidence for the interplay between MHD and turbulence. A new experimental result on the impact of an MHD burst on plasma flow and turbulent transport as evidence for interaction between MHD and turbulence is discussed in section 3. Figure 1 shows a diagram of the physics elements of the interactions between the topology and MHD, as well as interactions between turbulence and plasma flow. The interaction between the flow shear of parallel, E×B flow and zonal flow has been discussed since strong E×B flow shear was found in the pedestal region in the H-mode plasma. The flow shear contributes to the suppression of the turbulence shearing effect, and flow shear is recognized to be a key element in the feedback loop of edge formation and the internal transport barrier. Recently, work on the interaction between topology and MHD concluded that the plasma selforganizes by triggering an internal bifurcation of magnetic island chains [13,14]. However, there are few experiments to have reported on the interactions between turbulence and topology or MHD and the interaction between topology and MHD in the toroidal plasma.
MHD instability causes a change of magnetic topology in the plasma. The magnetic island and the stochastic magnetic field are topology effects commonly observed in a toroidal plasma. The oscillations are observed in the magnetic probe signal or temperature due to the plasma rotation. The oscillation frequency is finite in the laboratory frame but zero in the plasma frame. Therefore, when the plasma does not have rotations, the oscillations owing to this topology effect disappear. In contrast, the MHD has a characteristic magnetic field oscillation frequency in the plasma frame and sometimes grows nonlinearly, triggering the collapse of the plasma. Energeticparticle-driven modes, edge-localized mode (ELM), the sawtooth crash and disruptions are included in this category.

Turbulence spreading into magnetic island
In the local transport model, the turbulence level in the plasma is assumed to be determined by the local plasma parameters such as temperature and density, their gradients, the magnetic field and the potential structure (the magnetic shear and radial electric field shear). However, various nonlocal phenomena that cannot be explained by the local transport model have been observed in experiments in toroidal plasma [15]. These experimental results are evidence that the local closure of the flux-gradient (turbulence-gradient) relation has been violated. Several of the mechanisms causing the violation of these relations have been proposed in theory. The coupling between the turbulence of meso-or long-range correlation and micro turbulence have been proposed to explain the strong core-edge coupling of turbulence and transport observed in experiment. In the avalanche model, the strong nonlinearity of the growth rate of micro-scale turbulence can cause the simultaneous fast radial propagation of both micro-turbulence and gradients, and consequently in ballistic transport and super diffusion. Turbulence coupling and turbulence spreading are the most likely mechanisms to cause nonlocal transport. It was recently shown that turbulence spreading from the pedestal region to the scrape off layer (SOL) is expected to be beneficial in broadening the SOL power decay length [16][17][18][19][20][21]. Therefore, the experimental identification of turbulence spreading becomes one of the crucial issues in edge transport.
In spite of the importance of turbulence spreading, there are only a few measurements on turbulence. This is because the separation of the turbulence origin (spreading turbulence and locally driven turbulence) is impossible in the usual turbulence measurements. The novel analysis of turbulence to distinguish its origin from the modulation of bias was reported in TJ-II. The time evolution of free turbulent energy á ñ n 2 (where ñ=n− á ñ n ) is obtained from the radial part of the continuity equation by neglecting cross-field coupling and damping as well as the effect of background flows as [22]  The angular brackets á ñ ... indicate a running average over a time interval much larger than the turbulence correlation time. The first term is a product of the turbulent particle flux and density gradient and the second term is the diffusion of turbulent energy. With the normalization of the local turbulence amplitude, á ñ n 2 , two rates of turbulence are defined. One is the rate of turbulence drive due to the density gradient as and the other is the rate of turbulence spreading due to the turbulence intensity gradient as These two quantities have quite a different response to edge biasing as seen in figure 2. The negative edge bias of the voltage of −380 V and the modulation frequency of 40 Hz during the discharge (bias is off-on-off-on-off, about 1180-1240 ms). The rate of turbulence locally driven, ω D inside LCFS (r<r 0 ), is significantly reduced during the on phase of edge biasing, while the reduction of the rate outside LCFS (r>r 0 ) is moderate. In contrast, the rate of the turbulence spreading, w S is significant outside LCFS (r>r 0 ), although there is almost no impact inside LCFS (r<r 0 ). The experimental data clearly shows the locally driven turbulence is suppressed at the plasma edge by the E×B shear produced by edge biasing, while the turbulence spreading observed in the SOL region is suppressed by E×B shear at the plasma boundary. This experiment suggests that the E×B flow shear suppresses the turbulence spreading from the core to the SOL.
The other approach to identify spreading turbulence is the measurement of the turbulence response in the region where the local driven turbulence is expected to be small. The magnetic island is an ideal region for spreading turbulence because there should be no driven turbulence inside the large magnetic island in which the temperature and the density flattening region are larger than the correlation length of microturbulence. Magnetic islands define a unique region in the plasma because the temperature and density gradients which drive the turbulence are much weaker inside than outside the magnetic island [23]. Since the heat propagation inside the magnetic island is relatively slow [24,25], turbulence can propagate faster than the heat pulse if there is turbulence spreading [26,27] from the X-point (or boundary) to the O-point of the magnetic island. In order to identify the spreading turbulence, the phase relation between the micro turbulence intensity measured with beam emission spectroscopy (BES [28,29]) and the electron temperature measured with electron cyclotron emission (ECE) was investigated in the X-point and the O-point of the magnetic island in the heat pulse experiment produced by modulated electron cyclotron heating (MECH) in DIII-D [4].    Poincaré maps of the magnetic field at the X-point and O-point of the magnetic island, as well as the direction of heat pulse propagation and density fluctuation propagation indicated with arrows, are plotted in figure 4. Here, the perturbation fields are calculated using the Fourier analysis module in the trip3d code [30]. In general, the electron temperature becomes constant on a magnetic flux surface because the propagation speed of heat pulse parallel to the magnetic field is an order of the electron thermal velocity and much higher than the propagation speed perpendicular to the magnetic field. In contrast, the density fluctuation is not constant on a magnetic flux surface and has poloidal asymmetry. In the normal nested magnetic flux surface, the radial propagation speed of the heat pulse is equal to that of the density fluctuation. However, near the X-point of the magnetic island, the effective radial propagation speed of the heat pulse (the projection of parallel heat pulse propagation to the radial direction) becomes much higher than the speed of the density fluctuation propagating across the magnetic flux surface. Therefore, the heat pulse propagates to the X-point of the magnetic island before the turbulence. In the O-point, the heat pulse propagates from the boundary of the magnetic island of the O-point slowly due to the low level of fluctuation inside the magnetic island (due to the lack of locally driven turbulence). However, turbulence propagating from the X-point to the O-point is faster than the heat pulse and causes a negative turbulence perturbation delay time (turbulence increases before the heat pulse). This is clear evidence of turbulence propagation from the X-point to the O-point of the magnetic island.

Bifurcation of turbulence spreading at the boundary of the magnetic island
The amount of heat flux propagating through the X-point or O-point depends on the velocity of heat pulse propagation at the X-point or O-point region. As the heat pulse propagation becomes slow inside the magnetic island (O-point), the modulation amplitude decreases. Because the heat pulse propagates at the boundary of the O-point, the delay time of the heat pulse peaks at the O-point of the magnetic island [5].
There is a clear relation between the propagation speed (delay time) and a reduction of the modulation amplitude [31]. A large reduction of the modulation amplitude is a result of gradual heat pulse propagation due to the low turbulence level. Therefore, by measuring the modulation amplitude at the O-point of the magnetic island, one can estimate the level of transport and turbulence inside the magnetic island.
The time evolutions of the electron temperature measured with ECE at the O-point phase and the X-point phase of the magnetic island in DIII-D are plotted in figure 5. In this experiment, the toroidal phase of the resonant magnetic field perturbation (RMP) is flipped by 180 degrees during the discharge. Here, the O-point (X-point) phase stands for the phase when the O-point (X-point) of the magnetic island is located at the toroidal location of the ECE measurements. The heat pulse is produced by the modulation ECH and the modulation amplitude of the heat pulse is evaluated by ECE measurements. As seen in figure 5, the modulation amplitude at the X-point phase is larger than the modulation amplitude at the O-point phase. In the O-point phase, the flattening of the electron temperature is observed near 0.4 keV. There is periodic change in the modulation amplitude in the O-point phase, which shows that the reduction of the modulation amplitude is oscillating. One is a phase with a moderate reduction of modulation amplitude and the other has a significant reduction of modulation amplitude. The former is called a high-accessibility heat pulse state and the latter is called a low-accessibility heat pulse state. Figures 5(b), (c) show the contour of the electron temperature modulation amplitude in time and space at the transition: (b) from high to low accessibility states, and (c) from low to high accessibility states. In the high accessibility states, the modulation amplitude gradually decreases from the boundary of the magnetic island (ρ=0.64 and ρ=0.8) to the O-point (ρ=0.72) of the magnetic island. In contrast, the modulation amplitude sharply drops to a low level (1% of temperature). The time scale of the transition from high accessibility states to low accessibility states is 4 ms and the back transition from high to low accessibility states is 7 ms.
In general, a magnetic island is surrounded by a layer of stochastic magnetic field. Stochastization of the magneticfield, i.e., magnetic braiding or the appearance of the secondary magnetic island [32][33][34][35], can occur when the island size reaches a critical value. The width of the magnetic island in DIII-D is 15% of the minor radius and large enough to expect the appearance of a stochastic layer surrounding the magnetic island. When the stochastic layer surrounding the magnetic island appears, the second derivative of temperature decreases due to the enhancement of the effective radial transport. Since the E×B flow shear is roughly proportional to the second derivative of temperature, the E×B flow shear decreases with the appearance of a stochastic layer. Because the E×B flow shear plays an important role in preventing the turbulence spreading, the stochastisation of the field outside the island should increase the rate of turbulence spreading into the island. Therefore, the change of the stochastic layer surrounding the magnetic island is a candidate for the bifurcation of the turbulence spreading state inside the magnetic island. Figure 6 shows a possible image of the electron temperature profile at the X-point and O-point of the magnetic island to explain the bifurcation of the high and low accessibility state of the magnetic island by a simultaneous change in the E×B flow shear, as well as turbulence spreading at the boundary of the magnetic island. Turbulence measurements in the bias experiment in TJ-II suggest that turbulence spreading is reduced by the E×B flow shear [22]. In theory, external E×B shearing is expected to hinder turbulence spreading [36] and turbulence spreading is also proposed to be one of the candidates for the nonlocal transport mechanism [15,37]. These theoretical and experimental results support the working hypothesis that the transition from a high to a low accessibility state is due to the change in the suppression of turbulence spreading by the E×B flow shear at the boundary of the magnetic island where the second derivative of the electron temperature becomes significantly large.
The width of the stochastic region at the boundary of the magnetic island except for the X-point region is smaller than the correlation length of the turbulence. However, at the X-point, the width of the stochastic region can be larger than the correlation length of the turbulence and should also have an impact on the turbulence. The suppression of turbulence spreading results in an increase of the second derivative of temperature (sharp boundary of magnetic island) and the narrow width of the stochastic region (W s ) at the X-point. The increase of the second derivative of the temperature ( ¶ ¶ T r 2 2 ) contributes to the enhancement of the E×B flow and causes positive feedback. The reduction of the stochastic region width at the X-point of the magnetic island contributes to the reduction of turbulence spreading (narrow turbulence spreading window) from the X-point to the O-point of the magnetic island. Therefore, the low accessibility state is characterized by a strong E×B shear, a sharp boundary (large ¶ ¶ T r 2 2 ), and a narrow stochastic region (a small W s ) at the X-point of the magnetic island (turbulence shielding state). In contrast, the high accessibility state is characterized by weak E×B shear, a broad boundary (small ¶ ¶ T r 2 2 ), and a wide stochastic region (large W s ) at the X-point of the magnetic island (turbulence penetration state). These two  states can be bifurcated because of the feedback process through the interplay between the E×B shear, the stochastic magnetic field and the turbulence shielding.

Flow damping due to stochastic magnetic field
Because the interplay between the stochastic magnetic field and plasma flow is important, how the stochastic magnetic field affects the plasma flow is an interesting issue. A heliotron plasma has a significant advantage in this study, because a large stochastic region up to 60% of the plasma minor radius can be produced in the plasma core without a disruption. In general, the magnetic flux surface becomes nested when the magnetic shear is large enough, while the magnetic flux surface becomes dominated by the lowest order magnetic island (e.g. 2/1 for i = 0.5) when the magnetic shear is small. Therefore, the control of the magnetic shear is key to producing a large region with a stochastic magnetic field near a rational surface. Tangential neutral beams have been widely used as a convenient noninductive current drive tool in toroidal plasma, which is called the neutral beam current drive (NBCD). Because of the conservation of poloidal flux linking the plasma, the total current can only change on a resistive time scale. Therefore, when the NBI drives current to the plasma edge, this must induce a loop voltage that drives a compensating current in the opposite direction in the plasma core. In the high-temperature plasma, this compensating current can exceed the noninductive current by the NBCD locally, especially in the case of the off-axis NBCD. In LHD, this compensating current in the opposite direction becomes large enough to change the rotational transform, ι, in the direction opposite to NBCD (e.g. decrease ι for co-NBCD and increase ι for counter-NBCD) near the magnetic axis in the discharge where the direction of the off-axis NBCD is exchanged in the middle of the discharge. The exchange of the NBCD in the opposite direction with each other (the NBCD direction switch) has been used to change the magnetic shear at half the radius of the plasma in LHD [38]. When the direction of the NBCD is switched from the co-direction (parallel to equivalent plasma current direction) to the counter-direction (anti-parallel to equivalent plasma current direction), the edge ι decreases due to the counter NBCD, but the central ι increases due to the inductive current. Then the magnetic shear at half of the plasma minor radius decreases after the beam switch from co-to counter-NBCD.
Toroidal flow velocities at , which indicates that the magnetic flux surface in the core becomes stochastic [39,40]. Later in the discharge, the toroidal rotation velocity begins to increase after t=6.7 s and partially recovers. The radial profile of the heat pulse delay time peaks at the rational surface (r eff /a 99 =0.5), which indicates the disappearance of a stochastic magnetic field region and the appearance of a magnetic island. Figure 7(c) shows the radial profile of the onset of stochastization of the magnetic field. The stochastization of the magnetic field is initiated at the rational surface of ι=0.5 located at r eff /a 99 =0.5. The region of the stochastic magnetic field expands both inward and outward, and the region of the stochastic magnetic becomes 20% of the minor radius in 10 ms, which is called partial stochastization. The outward propagation of the stochastic magnetic field stops at r eff /a 99 =0.6 due to the higher magnetic shear towards the plasma periphery. However, the inward propagation of the stochastic magnetic field continues until the stochastic magnetic field region expands to the magnetic axis in 40 ms, which is called a full stochastization. Figure 7(d) shows the radial profile of a radial electric field before stochastization (with a nested magnetic flux surface) and after the stochastization of magnetic field. The positive radial electric field in the core region (r eff /a 99 <0.4) decreases and the negative radial electric field outside this region increases after stochastization of the magnetic field. The change in the radial electric field is more significant near the rational surface, where the dominant modes are resonant, while the flattening of the electron temperature is observed in the whole core region. This observation is consistent with the fact that the transport enhancement due to the stochastization of magnetic field is ambipolar, except for the region near locations where the dominant modes are resonant [41].
The radial propagation of stochastic magnetic field is considered to be due to the consequence of interplay between stochastization and plasma flow damping. The stochastization of the magnetic field causes strong flow damping. The plasma flow is also expected to play a role in preventing the magnetic field from becoming stochastic. Therefore, once the plasma flow starts to decrease due to enhanced damping from stochastization, the region of flow damping and stochastization expands due to the positive feedback until the stochastic region reaches the plasma axis. In contrast, when the stochastic region starts to shrink, the plasma flow recovers due to the external torque input. The stochastic region disappears and the magnetic island appears or is completely healed (stochastization healing [42]).

Interplay between turbulence and MHD
Energetic particle-driven MHD instabilities have been studied intensively in nuclear fusion research [43][44][45][46]. MHD instability driven by energetic particles often shows nonlinear characteristics and can cause a minor collapse of the helical plasma [47,48]. In LHD, various MHD instabilities driven by energetic particles are observed when high-power neutral beams (∼30 MW) are injected into a low-density (∼1×10 19 m −3 ) target plasma [49,50]. The minor collapse of the plasma associated with the burst of oscillation of the magnetic field observed with magnetic probe arrays is characterized by the sudden decrease of the neutron emission rate, central ion temperature, and kinetic energy of the plasma [51,52].

Energetic particle-driven MHD collapse
Toroidal Alfven eigenmodes (TAEs) driven by energetic particles are widely observed in tokamaks and helical plasma when the fast ion pressure gradient is large enough [53][54][55].
Recently, the abrupt onset of a perturbation with tongue-shaped topology (localized in the poloidal and toroidal directions), leading to the sudden redistribution of energetic ions and MHD burst associated with the sudden increase of plasma rotation, was brought about by changing the radial electric field. This new type of MHD burst is characterized by a unique trigger mechanism. It is triggered by the tongue-shaped deformation that appears between the low order of a rational surface. The MHD instability causing the tongue-shaped deformation is highly nonlinear, grows within one cycle and triggers the redistribution and loss of energetic trapped ions, which are indicated by a sharp jump of RF intensity. The plasma starts to rotate after the loss of ions and the MHD burst starts due to the resonance between the mode frequency and the precession frequency of the trapped particle.
As seen in figures 8(a)-(c), the repeated burst of the magnetic field perturbation with a large amplitude is observed with magnetic probes at a toroidal angle of 90, 198 and 270 degrees [56], called an MHD burst in the LHD. The similar magnitude of the oscillation amplitude in these three probes indicates that the MHD perturbations are rotating toroidally. However, the magnetic perturbation amplitude in the 198 degree probes is much smaller than those in the 90 and 270 degree probes between the MHD burst. This indicates that the MHD oscillation between the MHD burst is caused by the standing wave. Figures 8(d)-(e) are expanded plots of magnetic perturbations from 4 ms before to 4 ms after the collapse, which is indicated by the sharp increase of the RF signal. The frequency of the MHD oscillation and MHD burst is ∼5 kHz, which is lower than the typical MHD frequency of toroidal Alfven eigenmodes (TAEs) in the LHD (∼70 kHz [55]). Unlike the MHD burst driven by TAEs, the start of the MHD burst is associated with plasma rotation driven by the loss of energetic ions [7]. The MHD burst is not the cause of energetic ion loss but the result of plasma rotation driven by energetic ion loss. The oscillation of the magnetic field in 90 and 270 degree probes is out of phase and has an n=1 structure. Therefore, the mode between MHD bursts is n=1 stationary mode. In contrast, the MHD burst (0-2 ms after the collapse) shows a phase delay in the toroidal direction and indicates that this is the n=1 rotating mode. It should be noted that the perturbation of the magnetic field 0.1 ms before the collapse indicated by the vertical dashed line does not have an n=1 structure and the perturbation of the magnetic field is localized poloidally and toroidally. Figure 8(f) shows the contour of displacement of the equi-temperature surface evaluated from d  T T e e measured with an ECE signal. Here the positive value (red) stands for outward displacement, while the negative value (blue) stands for inward displacement. The positive displacement indicated with red starts between two rational surfaces of ι=0.5 at r eff /a 99 =0.5 and ι=1 at r eff /a 99 =0.9. The positive displacement propagates outward and then propagates inward. Negative displacement (blue) is also observed just after the outward displacement. The outward propagation of positive displacement is called tongue formation, and the inward propagation of positive and negative displacement is called tongue collapse [7].
These displacements at the tongue formation and collapse are much more significant than the displacement at the rational surfaces (r eff /a 99 =0.5 and 0.9.) and are not localized but are radially propagating. The displacement of tongue-shaped deformation reaches up to 2 cm at the end of the formation, which is much larger than the displacement (0.2 ∼ 0.5 cm) observed at the two rational surfaces of ι=0.5 and 1.0 [57]. The tongue-shaped deformation typically quickly decays within one or a few cycles, while the displacement at the rational surface continues to oscillate. It should be noted that the perturbation of the magnetic field is correlated to the oscillation localized in the rational surface of ι = 1 at r eff /a 99 =0.9, as seen in a few cycles in t=−3.5 ms. The perturbation of the magnetic field due to the tongue-shaped deformation has a comparable magnitude to that of the MHD oscillation localized at r eff /a 99 =0.9, although the displacement of the tongue-shaped deformation is four times the displacement localized at the ι=1.0 rational surface.

Impact of tongue collapse on ion velocity distribution
The MHD burst triggered by the tongue collapse has a strong effect on plasma velocity distribution and alters the effective ion temperature and effective toroidal rotation velocity. At each MHD burst, the abrupt increase of effective ion temperature and an increase of effective toroidal rotation velocity in the counter-direction is observed, as seen in figures 9(a)-(c). The change of effective ion temperature and effective toroidal rotation velocity is within 1 ms and much faster than the transport time scale. This is due to the redistribution of ions in space, where the hot ions and countertraveling ions in the core region ( ) move outward in a short time associated with tongue formation and collapse. The increase of effective ion temperature and effective toroidal rotation velocity shows the relaxation in the ion-ion collision time scale.
The radial profiles of effective ion temperature and effective toroidal rotation velocity 4 ms before and 1 ms after the tongue collapse are plotted in figures 9(d)-(e). The increase of effective ion temperature is 0.5 keV and relatively constant in space, and the ion temperature gradient is almost unchanged. Before the tongue collapse the effective toroidal rotation velocity is co-directional (parallel to the equivalent plasma current direction) and it is in the counter-direction after the tongue collapse. The rapid change in the effective toroidal rotation velocity is the consequence of outward movement of counter-traveling particles, because the time scale of the change is much faster than the time scale of the momentum transport.
In order to investigate the mechanism for the rapid change of effective ion temperature and effective toroidal velocity, the distortion of the ion velocity distribution from the Maxwell-Boltzmann distribution is evaluated by the moment analysis of ion velocity distribution measured with charge exchange spectroscopy viewing the plasma toroidally [58]. The zeroth to the 4th moment of the ion velocity distributions are defined as  figure 10. Here τ is the relative time with respect to the tongue collapse indicated by the sharp increase of RF intensity. After the tongue collapse, the 1st moment (M 1 ) and the square root of the 2nd moment show the rapid change, which is consistent with the rapid increase of the effective toroidal rotation velocity in a counter-direction and the rapid increase of the effective ion temperature. Before the tongue collapse, the 3rd moment is close to zero, which shows that the ion distribution has a Maxwell-Boltzmann distribution. After the tongue collapse, the M 3 value drops to −0.15 and recovers to zero within 1-2 ms. The change is much larger than the error bar of the measurements. M 4 −3 also shows a significant drop to −0.2 after the tongue collapse, and the negative M 4 −3 indicates the increase of epithermal ions due to the outward shift of hot ions towards the plasma edge. This negative M 4 −3 also recovers to zero within 1-2 ms due to the thermalization of ion distribution through ion-ion collisions.
The outward shift of ions causes an intense negative radial electric field in the core region. The change in the radial electric field is measured with charge exchange spectroscopy, while the timing of the loss of ions is monitored by the RF probe. The RF intensity measured with the RF probe is a good time indicator of the ion loss, because the high-frequency instability is excited when the iron in the hot core is exhausted at the plasma edge. Therefore, the intensity of RF radiation probes is used as a timing indicator for energetic ion loss from the plasma [59] in this work because the RF probe has a high time resolution and is sensitive to the high-frequency RF signals excited by the loss of energetic ions at the plasma edge [60,61]. Large poloidal flow in the electron diamagnetic direction and a sharp increase of RF intensity is observed at each MHD burst as seen in figures 11(a)-(c).
The radial profile of the poloidal rotation velocity and the radial electric field shows the large negative electric field well at r eff /a 99 =0.9, while the radial electric field before the tongue collapse is positive as seen in figures 11(d)-(e). The change in radial electric field near the plasma edge (r eff /a 99 >0.8) is mainly contributed by the change in poloidal flow in the electron diamagnetic direction, while the change in radial electric field further inside the plasma is contributed by the increase of toroidal flow in the counter-direction. The radial electric field outside the plasma boundary (r eff /a 99 =1) is almost unchanged. The change of the radial profile of the radial electric field to a more negative value clearly shows the loss of bulk ions associated with the tongue collapse.

Turbulence exhaust driven by MHD collapse
It is interesting to investigate the impact of MHD collapse on turbulence. The Doppler reflectometer is a useful tool for measuring the density fluctuation near the plasma boundary. Frequency-hopping Doppler reflectometers have been installed in the LHD and the frequency is set to 30 GHz in this experiment [62,63]. The location of the measurement (reflection point) can be scanned from the edge stochastic region to the nested region inside during the discharge where the edge density gradually decreases in time. The analysis technique of the radial scan of the reflection point of the Doppler reflectometer using the density ramp up/down in time has been applied in the LHD experiments. This method is recognized to be a useful technique to measure the radial profile of the density fluctuation amplitude and perpendicular velocity near the plasma edge [64]. Figure 12 shows the time evolution of the perpendicular velocity at the edge stochastic region (r eff /a 99 >0.95) and inside the plasma (r eff /a 99 <0.95). The contour of the fluctuation level integrated low-frequency (30-150 kHz) turbulence and high-frequency (150-490 kHz) turbulence are also plotted. When the reflection point is in the edge stochastic region, the positive spikes of the intensity of high frequency ( f=150-490 kHz) micro-turbulence are observed at the tongue collapse event. In contrast, the slight decrease of highfrequency micro-turbulence is observed at the nested flux region inside the plasma (r eff /a 99 <0.95). It should be pointed out that there is no change in turbulence intensity at a lower frequency range ( f=30-150 kHz).
The time evolution of the perpendicular velocity of the stochastic region and the nested region inside shows the change of perpendicular velocity in the electron diamagnetic direction. This data indicates the formation of negative radial electric field consistent with the negative poloidal flow measured with charge exchange spectroscopy. The formation of a negative electric field is transient and lasts only 2 ms. As seen in the spectrum in the stochastic region (r eff /a 99 >0.95) plotted in figures 12(d)-(e), only the micro-turbulences in the frequency region above 150 kHz increase rapidly within 0.15 ms after the collapse. This rapid increase of turbulence observed is due to the rapid avalanche-like radial propagation process [65][66][67][68] into the SOL rather than the change in locally driven turbulence associated with changes in the temperature or density gradients in the SOL.

Discussion
As an example of interplay between the turbulence and the topology, the following experimental evidence has been reported in a toroidal plasma. Turbulence spreading from the X-point to the O-point of the magnetic island is identified from the phase delay between the heat pulse and the turbulence response. The bifurcation of magnetic island states can  be explained by the interplay between turbulence spreading and stochastization at the X-point of the magnetic island. The radial propagation of the stochastic magnetic field towards the magnetic axis of the helical plasma can also be explained by the interplay between the plasma flow and stochastization of the magnetic field.
The experimental evidence for two states of a magnetic island provides a new insight into understanding the radial flux of (surface-averaged) heat transport in the presence of magnetic islands during RMP experiments. This understanding can be further improved and it may be possible to achieve better control of the heat transport in discharges with RMP fields by using the heat pulse propagation technique as a tool to identify the state of the magnetic island. Turbulence spreading observed in the magnetic island also gives a new insight into turbulence spreading physics, which is necessary for better understanding of the turbulence in the SOL, where the spreading turbulence dominates locally driven turbulence. Because the turbulence in the SOL is beneficial for the broadening of the power decay length, deeper understanding of SOL turbulence is essential for better control of the SOL decay length in future devices. Exploration of the impact of magnetic field stochastization on turbulence spreading and flow damping is a new research field. The former is important in understanding the complicated plasma response of particle and heat transport to the RMP field and the latter is indispensable to understand the response of plasma flow to RMP fields, where partial stochastization is expected. Better understanding of the impact of RMP fields on plasma flow is essential for more reliable predictions of the power threshold of the L-to H-mode transition in future devices.
The strong impact of energetic-particle-driven MHD instability has been observed. MHD bursts are triggered by tongue formation and collapse. This tongue collapse has an impact on ion velocity distribution and causes distortion from the Maxwell-Boltzmann distribution. The distortion has been found in experiments with a significant transient change in skewness and kurtosis of the ion velocity distribution. The tongue collapse also enhances the loss of the bulk ions of epithermal ions and produces a negative radial electric field, exciting the MHD instability at the plasma edge. The turbulence exhaust by the tongue collapse is also observed in the Doppler reflectometer. This interplay between MHD and turbulence is essential for integrated understanding for various phenomena in toroidal plasma.
Understanding the impact of MHD instabilities driven by energetic particles on plasma flow and turbulence becomes more important for future devices, because an increased fraction of energetic particles is expected in burning plasmas. Because of the strong coupling between plasma rotation and the plasma potential in toroidal plasma, the plasma rotation can be driven by energetic ion losses triggered by MHD instabilities. Once the plasma starts to rotate, another MHD instability can be excited by the resonance between the mode frequency and the precession frequency of the trapped particles. This is an example of where an MHD instability drives another MHD instability through the plasma flow which is determined by the momentum transport. Therefore, the interplay between MHD and transport is key physics in understanding the situation where various MHD modes appear one after the other during the discharge in the plasma when the fraction of the beam beta is high [16,69].