Observation of avalanche-like transport in Heliotron J and JT-60U plasmas

The avalanche type of transport can induce a long-radial transport and thus can contribute to the global profile formation. In this study, we observed the heat perturbations exhibiting avalanche-like transport in the stellarator/heliotron device, Heliotron J, and the tokamak device, JT-60U. We found that the electron heat propagation in Heliotron J is mainly generated from the heating source region. The relatively high value of the Hurst exponent, which is a signature of avalanches, depends on the total heating power. On the other hand, the electron and ion heat avalanches measured in JT-60U tend to spread from the local peak of the temperature gradient and are not influenced by the heating source profiles. The contrasting features of avalanches in stellarator/heliotrons and tokamaks potentially imply the difference in the temperature profile formation, such as the presence of stiffness.


Introduction
Turbulent transport is universally important in stellarator/heliotron and tokamak plasmas.The power degradation of confinement observed in both devices indicates the common physics underlying toroidal plasmas [1].However, the transport in stellarator/heliotrons and tokamaks are not completely identical, particularly in the context of a stiffness.Here, we define the stiffness as a condition of the marginal Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.stable, i.e. the profiles whose gradients are very close to the instability threshold everywhere [2].The stiffness is typically observed in tokamaks.Independent of the heating source profiles, the inverse temperature gradient scale length, 1/L T = −∇T/T, is kept constant over a wide radial region [3,4].A slight change of 1/L T , despite the significant variation in heating power, indicates the presence of a critical gradient that drives the turbulent transport.On the other hand, stiff profiles are hardly observed in stellarator/heliotron plasmas.The temperature profile is easily changed following to the heating source depositions [5], and 1/L T is monotonically decreased towards the core, implying the degradation of the confinement as the temperature increases [6].Note that the lack of stiffness is still reported in W7-X [5,7], which was designed to optimize the reduced neo-classical transport.
The stiffness is typically explained by the critical gradient model [2], in which the transport coefficients are nonlinearly dependent on the local plasma parameters.However, the nonlocal dependence of the transport coefficient is reported in the experiment, both from tokamak and stellarator/heliotron plasmas [8].The critical gradient model also encounters difficulty when the profile gradient is below the marginality.The avalanching transport is proposed to describe the submarginal to the near-marginal profiles by the intermittent transport events [9][10][11][12][13][14]. Once the local gradient exceeds the instability threshold, the transport occurs to relax the gradient and redistributes heat to the neighbors, triggering the correlated transport event.Therefore, avalanches can drive the longradial transport, which could demonstrate the non-local phenomena.The avalanches are considered to contribute to the global profile formation including the stiffness profile [15][16][17] to the submarginal profile [18,19].Therefore, investigating the avalanches in both stellarator/heliotrons and tokamaks is important to understand the different transport features observed between the devices.
Here we report the characteristics of heat avalanches observed in Heliotron J (stellarator/heliotron) and JT-60U (tokamak).The heating power scan experiment is performed, and the electron heat transport is investigated in Heliotron J and JT-60U.The analysis revealed the propagation of the electron temperature perturbation that exhibits avalanche-like transport.The parameter dependence of avalanches is compared in both devices.Using conditional averaging, the ion heat perturbation is investigated in JT-60U.When the avalanche occurs, the ion heat perturbation significantly relaxes the ion temperature gradient.We also discuss the impact of the avalanche-driven transport fluxes on the profile formations.

Experimental setup
Heliotron J is a stellarator/heliotron device that is composed of 5 types of coil systems.The flexible magnetic field configurations can be achieved by adjusting coil currents.The experiment is performed with the standard magnetic field configuration, which is preferable to achieve both the MHD stability and reduced ripple loss.The deuterium plasma is produced with an average major radius of R = 1.2 m, an average minor radius of a = 0.17 m, and a magnetic field strength at the magnetic axis of B = 1.25 T. In order to avoid the MHD instability generated by the low-order rational surface, the safety factor (q) profile is flat in the whole plasma radius, which is shown in figure 1.The plasma heating is provided by the Electron Cyclotron Heating (ECH), with a second harmonic X-mode of 70 GHz.While the electron temperature reaches ∼1 keV, the ion temperature is ∼200 eV even during the Neutral Beam Injection (NBI) heating [20].Since the magnetic field of Heliotron J is not explicitly optimized like W7-X, the transport of ion-scale could be influenced by the large neo-classical transport.Thus, we investigate only the electron heat transport in Heliotron J.The temporal evolution of electron temperature is measured by the Electron Cyclotron Emission (ECE) radiometry.The The radial profile of the safety factor q for Heliotron J and JT-60U.16-channel ECE radiometry detects the 2nd harmonics of the ECE signal from the low magnetic-filed side that is covering at ρ = 0.0-1.0,where ρ indicates a normalized minor radius, ρ = r/a.However, certain channels could not be used for analysis due to the saturation of the detectors, the influence of large ECH noise, or measurement points being located beyond the last closed flux surface.Using the ECE radiometry, the heating power dependence of electron temperature perturbations is analyzed.
JT-60U is a large tokamak device whose major and minor radii are R = 3.3 m and a = 0.83 m, respectively.The deuterium plasma is confined with a toroidal magnetic field strength of 3.7 T. The plasma heating is provided by the NBI.During a current ramp-up phase, the tangential NBI starts to heat the plasma with a balanced-torque injection.Because the current diffusion is suppressed by the NBI heating, the negative magnetic-shear q profile is sustained, which is shown in figure 1.The main plasma heating is performed by the perpendicular NBI, which starts just before the current flattop phase.The power of perpendicular NBI is changed on a shot-by-shot to investigate the heating power dependence of electron and ion heat transport.The electron temperature perturbation is observed by the 12-channel ECE radiometry, which detects the 2nd harmonics of the ECE signal from the low field side.The measurement location of ECE is limited at ρ = 0.4-0.7.The ion temperature perturbation is measured by the Charge Exchange Recombination Spectroscopy (CXRS), which measures the spectral line of carbon impurity (C VI, 529.05 nm).Because the exposure time and the sampling period are 2.5 ms, the conditional sampling technique is used to investigate the ion temperature fluctuation, which will be explained in section 3.3.

Experimental results
In this section, we present the experimental observation of the heat perturbations during the steady state phase.In Heliotron J, only electron heat transport is analyzed, whereas in JT-60U, both electron and ion heat transports are examined.The heating power scan experiments in both devices are explained in section 3.1.The characteristics of electron heat perturbation in Heliotron J and JT-60 U are described in section 3.2.The ion heat perturbation in JT-60U is shown in section 3.3.

Heating power scan experiment
The heating power scan experiment is operated by ECH in Heliotron J and by NBI in JT-60U, respectively.For both devices, the power degradation of confinement is observed.As shown in figures 2(a) and (b), the total heating power dependence of diamagnetic stored energy (W dia ) is shown.The lineaveraged electron density is also shown in the figures, which is approximately constant with ≈ 1 × 10 19 m −3 .As the heating power increases, W dia is saturated, which is expressed by the curve fit represented by red lines.The fitting curves show dependencies of W dia ∝ P 0.3 ECH for Heliotron J and W dia ∝ P 0.5 NBI for JT-60U.The results indicate the degradation of energy confinement time to the heating power, i.e. τ E ≈ W dia /P ECH ∝ P −0.7

ECH
for Heliotron J and τ E ≈ W dia /P NBI ∝ P −0.5

NBI
for JT-60U.The plasma profiles are shown in figure 3.In the case of Heliotron J, the heating deposition of the ECH is calculated by the ray-tracing code, TRAVIS.As shown in figure 3(a), the onaxis ECH is provided with a total heating power of 113, 192, 247, and 287 kW.Despite the increase of the ECH power, electron temperature profiles shown in figure 3(b) are almost similar, which is measured by a Thomson scattering system.The T e gradient peaks around ρ ≈ 0.5 and shows a little increase even when the ECH power is more than doubled, as shown in figure 3(c).The normalized inverse scale length of the T e gradient, R/L Te , is also insensitive to the heating power, as shown in figure 3(d).Note that the monotonical decrease of R/L Te from the edge to the core indicates the exhibition of the dome-shaped profile, which indicates the degradation of confinement as the temperature increases towards the core [6,21].Usually, the profile stiffness is associated with R/L Te maintained at a constant value which corresponds to an instability threshold over a wide radial region.Therefore, the domeshaped electron temperature profile in Heliotron J is not considered stiff, and its gradient is subcritical to a threshold.
In the case of JT-60U, both electron and ion heat transports are considered.As shown in figures 3(e) and (i), electron and ion heating source profiles are estimated from the NBI and Joule current.The deposition profile of NBI is calculated by the Monte-Carlo code, OFMC.Since the acceleration energy of NBI is 80 keV, ion heating is predominant.In addition to the NBI, the electron heating source includes the Joule current, which contributes to heating electrons at ρ ≈ 0.6.Similar to Heliotron J, the electron temperature measured with a Thomson scattering system is hardly changed against the increase of the NBI power, which is shown in figure 3(f ).The ion temperature measured with CXRS also exhibits similar profiles, as shown in figure 3(j).Regarding electron heating, dominant location of heating source changes from the off-axis (ρ ≈ 0.6) to the on-axis (ρ ≈ 0) with the increase of NBI power.Thus, the temperature profile is hardly changed either by the heating power or by the heating location.Both the gradients of electron and ion temperature are approximately peaked at ρ ≈ 0.5, which are shown in figures 3(g) and (k).The normalized inverse scale length of the temperature gradients, R/L Te and R/L Ti , are shown in figures 3(h) and (l).In contrast to Heliotron J, R/L Te and R/L Ti in JT-60U are both peaked at ρ ≈ 0.6-0.7,indicating that the dome-shaped profile does not appear.The peak location of R/L Ti at ρ ≈ 0.7 coincides with the location of q min , which could be potentially related to the reduction of the turbulence near q min [22].However, some experiment indicates that the reversed magnetic shear is not a sufficient condition for the enhanced confinement [23].Thus, the coincidence of peak location of R/L Ti and q min is not clearly understood.Importantly, the value of R/L Ti takes constant at ρ ≈ 0.3-0.5, which is a signature of the stiffness.In this sense, the temperature profiles in Heliotron J and JT-60U are qualitatively different.Note that the temperature corrugation can be seen in figure 3(k).The corrugation potentially implies the presence of the E × B staircase, in which avalanches dominate the transport [24].However, this is beyond the scope of this work and remains for future study.

Electron heat perturbations in Heliotron J and JT-60U
In this subsection, we show the characteristics of electron temperature fluctuations measured by ECE diagnostic.Normalized electron temperature fluctuations, Te / Te , are observed in Heliotron J and JT-60U with the sampling frequency of 1 MHz and 50 kHz, respectively.Figures 4(a) and (b) show waveforms of Te / Te , which are low-pass filtered by 2 kHz.The waveforms are arranged as Te / Te + ρ.In the case of Heliotron J, the fluctuation intermittently shows radial correlation.Especially, the void ( Te / Te < 0) at t ≈ 0.265 s appears in the whole radial region.It was found that the average radial correlation length increases with the heating power [25].The amplitude of Te / Te is pronounced in the region at ρ < 0.3, which corresponds to the location of the ECH deposition.On the other hand, Te / Te in JT-60U seems to exhibit anti-phase between ρ < 0.55 and ρ > 0.55, which can be seen in figure 4(b).At t ≈ 5.105 s, the void ( Te / Te < 0) appears in ρ > 0.55, while the bump ( Te / Te > 0) appears in ρ < 0.55.The boundary location of ρ ≈ 0.55 is approximately coincident with the peak of the electron temperature gradient, which is shown in figure 2(g).The simultaneous appearance of voids and bumps becomes significant with the heating power increase [17].
To study the propagation of electron temperature fluctuation, the causal relation between ECE signals is investigated by the transfer entropy analysis [26]   T ρ ref =0.95→ρ others .Thus, the net information flows from core to edge direction, indicating that the electron temperature fluctuation propagates from core to edge.The significant information propagates from ρ = 0.13 to 0.95 within 0.2 ms, which accounts for a propagation speed of ≈0.7 km s −1 .This is consistent with the result obtained by the cross-correlation analysis [25].Note that the time scale of 0.2 ms is shorter than the time constant of the lowpass filter of 3 kHz, however, the transfer entropy calculated with data filtered by 10 kHz lowpass shows an identical time scale, 0.2 ms.The radial propagation speed of 0.7 km s −1 is approximately one-third of the diamagnetic drift velocity, which is calculated as V diamag.= T e /eBa ≈ 2 km s −1 .This is a typical speed of avalanches observed in a flux-driven simulation [16].On the other hand, the radial outward propagation (ρ = 0.42 to 0.72) is not significant in JT-60U plasma, as shown in figure 3(b).The information propagation can be seen for the transfer entropy representing ρ ref = 0.57, where the reference point is close to the peak of the electron temperature gradient.The outward propagation of information can be seen from ρ = 0.57 to 0.72 within 1 ms.This corresponds to the propagation speed of ≈120 m s −1 , which is consistent with the crosscorrelation analysis [17].From the analysis, we found that the electron temperature fluctuation in Heliotron J propagates from core to edge with an one-third of the diamagnetic drift velocity, while the electron temperature fluctuation in JT-60U propagates from the local peak of the electron temperature gradient with an order of few tenths of diamagnetic drift velocity (V diamag.= T e /eBa ≈ 1 km s −1 ).Note that the latter is consistent with the previous observations in tokamaks [13,14]].
As studied in previous works [17,25], electron temperature fluctuation exhibits a long-temporal correlation, which is a signature of avalanches.The long-temporal correlation, or long-term memory, can be revealed when a Hurst exponent takes a value within 0.5 < H < 1 [11,12].The Hurst exponent is estimated by the rescaled range statistics (R/S) [11,12] during a steady state phase (line-averaged density varies within 10%).The R/S ratio of a temporal signal X is defined as, R(n) S(n) = max(0,W1,W2,...,Wn)−min(0,W1,W2,...,Wn) √ , where is the cumulative deviations from the mean.Here, X (n) and S (n) are the mean and variance of the signal X.The Hurst exponent can be derived from the exponent of the expected value of the R/S ratio, i.e.The Hurst exponent increases from 0.8 (P ECH = 113 kW) to 0.98 (P ECH = 287 kW).On the other hand, the Hurst exponent in JT-60U is evaluated as 0.9, independent of the heating power.
Next, we show the Hurst exponent as a function of the heating power density and the electron temperature gradient.In the case of Heliotron J, the Hurst exponent does not simply correlate to the local heating power density nor local electron temperature gradient, which is shown in figures 7(a) and (b).The Hurst exponent seems to depend on the total power of the ECH.At the ECH source region, where the heating power density is ≈10 MW m −3 , the Hurst exponent is ≈0.9 except for the lowest heating power, P ECH = 113 kW.As the total heating power increases, the value of the Hurst exponent higher than 0.9 expands toward the edge region, where the heating power density is lower.In the case of JT-60U, the Hurst exponent scatters to the local heating power density and total heating power, which is shown in figure 7(c).However, the Hurst exponent tends to decrease abruptly at the local maximum of the temperature gradient, ≈12 keV m −1 , as shown in figure 7(d).In other words, the Hurst exponent is kept high value except at the peak location of the electron temperature gradient.Since   heating power in Heliotron J and on the electron temperature gradient in JT-60U, respectively.This can be also found by the radial profiles of the Hurst exponent in Heliotron J and JT-60U, as shown in figure 8.
The Root Mean Square (RMS) of the normalized electron temperature fluctuation (f < 2-3 kHz), which is above the thermal noise and indicates the amplitude of avalanches, is shown in figure 9.In Heliotron J, the RMS increases with the increase of the local heating power density, as shown in figure 9(a).As the heating power density decreases, where the outside of the ECH source region, the RMS increases with the total ECH power.On the other hand, the RMS in JT-60U seems to depend on the electron temperature gradient, rather than the heating power density, which is shown in figures 9(c) and (d).
As the temperature gradient decreases, the RMS decreases.The parameter dependency of the RMS of electron temperature fluctuation is similar to that of the Hurst exponent.Note that the RMS of normalized electron temperature fluctuation in Heliotron J is larger than that in JT-60U.As shown in figure 5, the radial propagation of avalanche is faster in Heliotron J. Thus, the larger amplitude of avalanches could be related to the higher propagation speed, which is suggested in [12].

Ion heat perturbations in JT-60U
The ion heat perturbation that exhibits avalanching transport is investigated in JT-60U.As shown in figure 10, the bursty increase of density fluctuation, which is measured by an Omode reflectometer, is synchronized to the electron temperature perturbation that exhibits large avalanche events [17].As the density fluctuation increases, the electron temperature decreases at ρ ≈ 0.6.Although the sampling rate of the CXRS is 2.5 ms, the ion temperature perturbation at ρ ≈ 0.6 is also synchronized to the burst of the density fluctuation, which is shown in figure 10(b).
Using the conditional averaging technique, the temporal resolution of the ion temperature fluctuation is improved.The bursty increases of density fluctuation are used as the reference signal of the conditional averaging.As shown in figure 11, the conditional averaging is provided by taking the relative time difference of the measurement of many samples with respect to the reference events.For smoothing, we applied a low-pass filter with a cutoff frequency of 0.4 kHz to the sampled data.The origin of the relative time, τ = 0 s, is defined as a rising edge of the bursty increase of the density fluctuation.The temporal evolution of profiles of reconstructed ion temperature fluctuation is shown in figure 12. Before the occurrence of avalanche events (τ < 0 ms), ion temperature fluctuation develops to increase the temperature gradient at ρ ≈ 0.48, indicated by a green dashed line.After the occurrence of large avalanche events (τ > 0 ms), ion temperature fluctuation evolves to relax the enhanced temperature gradient, i.e. the bump occurs at ρ < 0.48 and the void occurs at ρ > 0.48, simultaneously.The enhancement and subsequent relaxation of the ion temperature gradient at ρ ≈ 0.48 approximately coincides with the peak of the local temperature gradient, as shown in figure 3(k).The  change of the ion temperature gradient by the avalanche events accounts for ≈2 keV m −1 .Therefore, the avalanche events significantly impact the temperature profile formation.Note that the reconstructed ion temperature fluctuation cannot be obtained in the case of 8 and 10 MW heating, because of the low level of signal-to-noise ratio.

Discussion
As shown in figure 2, the power degradation of the confinement is observed both in Heliotron J and JT-60U.In addition, both devices exhibit similar temperature profiles that are insensitive to the heating power, which is shown in figure 3.Although R/L T profiles suggest the existence of the stiffness in JT-60U but not in Heliotron J, the profile similarity (or profile consistency [27]) is obtained independent to the condition of the stiffness.In this sense, the profile similarity is just a necessary condition of the stiffness but is not a sufficient condition of it.In other words, the profile similarity can be achieved even when the average profiles maintain a gradient below the critical value.One of the explanations for such a submarginal profile is addressed by the Self-Organized Criticality (SOC) system, which is dominated by the avalanching transport [18,19].The heating power dependences of the Hurst exponent and RMS of the temperature fluctuation in Heliotron J suggest the enhancement of the avalanche for maintaining the profile similarity, potentially leading to power degradation.On the other hand, in JT-60U, the avalanche activities are not affected by either the heating power or the heating source deposition.The latter can be seen by comparing the electron (P e ) and ion (P i ) heating power profiles, which are shown in figures 3(e) and (i).Although P e peaks at ρ ≈ 0.6 and P i peaks at ρ ≈ 0, the electron and ion heat avalanches are both found to relax the temperature gradient at ρ ≈ 0.5.The insensitivity of avalanches to the heating source profile reminds us of the feature of similar shapes of profiles observed in the off-axis heating in tokamaks [1].
Considering the impact of avalanching transport, the amount of avalanche-driven electron heat flux is roughly estimated.For Heliotron J, in the case of 287 kW heating, the surface integral of avalanche-driven heat flux per second ≈ 45 kW, where f, ∆τ, A indicate the frequency and pulse width of avalanches, and plasma surface, respectively.Here, Te / Te ∼ 1.5% is estimated as the time-averaged amplitude of avalanche components (0.1k < f < 3 kHz), and thus the frequency of avalanches is determined as f = 1.5 kHz.The evaluated heat flux of Q ∼ 45 kW accounts for approximately 16% of the electron heating power at ρ = 0.6, P e = 280 kW.For JT-60U, in the case of 11 MW heating, the surface integral of avalanche-driven heat flux per second at ρ = 0.6 is, Q ∼  ( 65 m 2 ) ≈ 0.18 MW.The evaluated heat flux of Q ∼ 0.18 MW accounts for approximately 20% of the electron heating power at ρ = 0.6, P e = 0.9 MW.Although the calculation is not rigorous, it is suggested that the avalanching transport is not negligible both in Heliotron J and JT-60U.Note that the electron heat flux driven by large avalanche events is evaluated more precisely in JT-60U by using the energy conservation equation, and we evaluated that it reaches ∼10% of total transport, which is effective in keeping a constant profile [17].
It is worth to mention that the numerical studies indicate the importance of avalanche-driven transport.Flux-driven gyrokinetic [28] and gyrofluid [29] simulations indicate that avalanches drive a significant amount of heat flux, accounting approximately 50% of the total transport.To confirm the simulation, more accurate experimental estimation of avalanchedriven fluxes is necessary.In general, the direct measurement of avalanche-driven heat flux is quite challenging, because of the simultaneous measurements of radial flow fluctuation and electron temperature fluctuation are required.The other technique is calculating the energy balance equation with heating source profiles, which was demonstrated in [17].In this case, the time derivative of electron temperature fluctuation that exhibiting avalanching transport is required.Thus, it is necessary to distinguish avalanches from the electron temperature fluctuation in the ECE signal, which is inevitably influenced by thermal noise.We consider that the pattern extraction algorithm should be improved to extract avalanches form the signal, as well as the improvement of the ECE measurement with high SNR.Note that in [17], we used the conditional averaging only on the large avalanche events, excluding the small scale of avalanches.Therefore, the estimated electron heat flux in [17] is just a fraction of the total avalanchedriven transport.Improvements in the analysis are necessary for more accurate estimations.

Summary
The avalanche-like heat transport is studied during the heating power scan experiments in Heliotron J and JT-60U.The ECH and NBI are used for the main heating in Heliotron J and JT-60U, respectively.Despite the increase in the heating power, we observed similar temperature profiles in both devices.The electron heat avalanches in Heliotron J are measured using ECE diagnostic.The transfer entropy analysis provides that the temperature perturbation clearly propagates from the core to the edge with an one-third of the diamagnetic drift velocity.The Hurst exponent depends on the total ECH power, rather than the local heating power density or the local temperature gradient.In JT-60U, we observe electron and ion heat avalanches using ECE and CXRS diagnostics.The electron heat avalanches originate from the peak of the temperature gradient, which propagates with an order of a few tenths of a diamagnetic drift velocity.The Hurst exponent tends to be independent of the heating power but abruptly decreases with an increase of the temperature gradient.It was found that the large avalanche events relax the ion temperature gradient significantly.The different characteristics of avalanches, i.e. place of origin, propagation velocity, and dependence of the Hurst exponent, could help to understand the different profile formations observed in stellarator/heliotrons and tokamaks.

Figure 1 .
Figure 1.The radial profile of the safety factor q for Heliotron J and JT-60U.

Figure 2 .
Figure 2. The diamagnetic stored energy W dia and the line-averaged electron density ne as a function of the heating power of (a) ECH in Heliotron J and (b) NBI in JT-60U.The red curve shows the approximate scale dependence of W dia on the heating power.

Figure 3 .
Figure 3.The radial profiles of heating source, plasma temperature, temperature gradient, and the normalized inverse temperature gradient scale length for (a)-(d) electrons in Heliotron J, (e)-(h) electrons in JT-60U and (i)-(l) ions in JT-60U, respectively.The electron temperature profile in Heliotron J is averaged in the steady state phase.The temperature profiles of JT-60U are time slices at t = 5.2 s.
. The transfer entropy quantifies the direction of information flow between two temporal signals, X and Y.When the information transfers from Y to X, the transfer entropy is defined as, T Y→X = ∑ p (x n+1 , x n−k , y n−k ) log 2 p(xn+1|x n−k ,y n−k ) p(xn+1|x n−k ) .Here, p (a, b, c) indicates a Probability Distribution Function (PDF) calculated as a histogram with a discrete section of m bins for each argument.The number of bins for p (a, b, c) is m 3 , and p(a|b) shows a conditional PDF.The number k implies a time lag in the temporal history of the signal.Because the data record length of ECE is limited for both devices, the PDF is obtained with m = 2 to obtain statistically significant results.The transfer entropy T Y→X indicates the improvement in predicting signal X by incorporating the temporal history of both signals X and Y, as compared to using only signal X.Note that T X→X = 0 from the definition.The transfer entropy is calculated on the electron temperature fluctuation filtered by lowpass 3 kHz.As shown in figure 5(a), the transfer entropy representing ρ ref = 0.13 indicates the propagation of information from ρ = 0.13 to other locations, T ρ ref =0.13→ρ others , as a function of the time lag.For comparison, the transfer entropy representing ρ ref = 0.95, T ρ ref =0.95→ρ others , is shown in figure 5(b).The contour plots show that the magnitude of T ρ ref =0.13→ρ others is much larger than

Figure 4 .
Figure 4. Temporal evolution of normalized electron temperature fluctuations, which are low-pass filtered by 2 kHz, in (a) Heliotron J and (b) JT-60U.The normalized electron temperature fluctuations are arranged with adding the offset as Te Te + ρ, where ρ indicates the normalized minor radius of the ECE measurements.

Figure 5 .
Figure 5.The transfer entropy of electron temperature fluctuation in (a) and (b) Heliotron J and (c) and (d) JT-60U.The direction of information flow is represented as a reference location ρ ref , which is indicating Tρ ref →ρ others .
) and (b) indicate the R/S ratio of electron temperature fluctuation in Heliotron J and JT-60U as a function of a time lag τ , which is calculated by multiplying n by a sampling time of signal X.Because the short time scale component (less than ∼1 ms) of the ECE signal is contaminated by the thermal noise, we investigate the Hurst exponent at 1 < τ < 10 ms.In the case of Heliotron J, the slope of the logarithmic scale plot increases with the heating power.

Figure 6 .
Figure 6.The R/S ratio of electron temperature fluctuation with different heating power in (a) Heliotron J and (b) JT-60U.

Figure 7 .
Figure 7.The Hurst exponent as a function of the electron heating power density and the electron temperature gradient for (a) and (b) Heliotron J and (c) and (d) JT-60U, respectively.

Figure 9 .
Figure 9.The Root Mean Square (RMS) of the normalized electron temperature fluctuation as a function of the electron heating power density and the electron temperature gradient for (a) and (b) Heliotron J and (c) and (d) JT-60U, respectively.

Figure 10 .
Figure 10.Temporal evolution of (a) electron density fluctuation measured by the reflectometer and (b) electron and ion temperature measured by the ECE and the CXRS, respectively.

Figure 11 .
Figure 11.Schematic picture of the conditional averaging method on the CXRS data.

Figure 12 .
Figure 12.Temporal evolution of profiles of normalized ion temperature fluctuation.The relative times of avalanche events are shown in right.