Characteristics of electron internal transport barrier in Heliotron J

The formation of an electron internal transport barrier (eITB) has been observed for the first time with centrally focused electron cyclotron heating (ECH) microwaves injected into plasma in Heliotron J. When the heating power per electron density ( P ECH / n ¯ e ) exceeds a threshold of 250 × 10 − 19 kW m 3 , transient increases of both the central Te and the core Te gradients are observed. A neoclassical (NC) calculation using the Sugama–Nishimura moment method predicts that the large positive radial electric field (Er) is formed in the core region. Heat transport analysis shows a significant reduction of the effective electron thermal diffusivity in the plasma with the eITB related to that without the eITB. The large gap between the experimentally obtained effective thermal diffusivity and the NC thermal diffusivity suggests that the suppression of anomalous transport contributes to the core improved confinement of the eITB plasma. The electron cyclotron emission measurement shows both the transient increase and the hysteresis phenomena during the eITB formation.


Introduction
The electron internal transport barrier (eITB) formation has been observed in several stellarator/heliotron devices [1][2][3][4]. It is thought that the eITB is characterized by the transitions between the 'ion root' (with a small magnitude of radial electric field (E r ), usually negative) and the 'electron root' (with a large positive E r ) that are based on a bifurcation mechanism [5]. According to this feature, in LHD and CHS, a large positive E r in the core region and a transient formation of a peaked electron temperature (T e ) profile with a density and a heating power threshold are observed when an eITB is formed [6,7].
The effects of the magnetic field configuration on eITB formations, particularly in terms of the effective helical ripple ( eff ) [5] and magnetic islands [8][9][10], have been observed. In contrast, the mechanism of the effect of such a magnetic configuration is not well studied. Various types of stellarator/ heliotron devices exploit unique concepts for the optimization study of the helical configuration. While LHD and CHS have a strong variation of ι (strong shear) to reduce the island width, Heliotron J, TJ-II, HSX, and W7-X have almost flat ι profiles (shearless) close to (but outside) large order rationals, where the density of the rational numbers is smaller. A comparative study between these stellarator/heliotron devices can contribute to the elucidation of the mechanism of magnetic field configuration effect on the eITB physics.
Heliotron J belongs to the extended family of the 'quasiisodynamic symmetric optimization' devices, where a continuous L=1 helical winding is used instead of modular coils. The helical-axis heliotron creates a vacuum magnetic well in the entire confinement region by using an advanced three-dimensional (3D) magnetic axis. Heliotron J is a medium-sized helicalaxis heliotron device (the averaged plasma major radius is = R 1.2 m, the averaged minor radius is = a 0.17 m, and the averaged magnetic field strength at the magnetic axis is = B 1.35 T ax ) with an = L M 1 4 helical coil, where L and M are the pole number and pitch numbers of the helical coil, respectively [11,12]. The Boozer magnetic field spectrum is varied with two sets of toroidal coils, inner vertical coil, outer vertical coil, and external vertical coil connected to the helical coil. This flexible helical axis heliotron device allows the study of core confinement in a wide configuration space. This research aims at identifying the eITB formation and revealing the detailed characteristics of the eITB in the helical-axis heliotron configuration, namely the unique configuration of Heliotron J. The characteristics are investigated from the profiles of T e and E r , formation condition, and heat transport by using an advanced electron cyclotron heating (ECH) system and various diagnostics and by comparing the obtained results to those for the other helical devices. The research of eITB physics in the helical-axis heliotron configuration contributes to expand the variety of configuration research in the stellarator/heliotron devices. Section 2 discusses the eITB profile characteristics in Heliotron J. An eITB formation condition is investigated in terms of n e in section 3, and the estimation of a neoclassical (NC) E r using the Sugama-Nishimura moment method [13,14] is described in section 4. In section 5, the heat transport of the eITB is analyzed using the experimental results and the experimental heat transport and the NC heat transport are compared. Section 6 illustrates temporal dynamics during the eITB formation using the electron cyclotron emission (ECE) measurements. Finally, conclusions are presented in section 7.
2. Typical characteristics of plasma with peaked temperature profile in Heliotron J Plasmas are produced and heated by ECH in Heliotron J. The ECH system of Heliotron J can continuously vary the injection power P ECH during a single discharge. The continuous control enables the investigations of the plasma response for wide heating power range, which is useful for studying of the dynamics of plasma transport. While ECH modulation techniques are used in the heat pulse propagation experiments, few experimental results have been reported for plasma dynamics with continuously varied ECH. The continuously varied ECH enables the investigations of the transition and back-transition for the eITB regime during a single shot. Due to the NC bifurcation characteristics of the helical plasma, hysteresis during eITB formation has been reported for E r in CHS [15] and W7-AS [16]. The continuously varied ECH is also effective for studying hysteresis phenomena.
A peaked T e profile is observed with an on-axis ECH. Here, we show the typical peaked and non-peaked T e plasmas obtained in a single plasma discharge by changing P ECH . The second-harmonic 70 GHz ECH beam with the extraordinary mode is perpendicularly injected in the experiment. The parallel refractive index || N is set to approximately 0.0 and the magnetic field strength is adjusted such that the EC power absorption can be peaked on the axis. In this heating condition, the electron cyclotron driven current (ECCD) is nearly zero and the bootstrap current of only several kA is observed. The vacuum central iota is i p( ) 0 2 0.56 and the magnetic configuration is set to avoid placing the low order resonances in the core region. In this experiment, P ECH is controlled by temporally changing the gyrotron beam voltage for a constant n e plasma. Figure 1(a) shows the time evolution of the lineaveraged electron densityn e , the plasma stored energy W p dia , and P ECH . In the ECH power control experiment, P ECH is controlled to be gradually reduced from 330 to 120 kW after t=210 ms under the constant~´n 1.0 10 m e 19 3 . W p dia slightly decreases as P ECH is reduced. Figures 1(b) and (c) show the typical T e and n e profiles with P ECH values of 175 and 240 kW, respectively. Here, the T e and n e profiles are measured using a Nd:YAG laser Thomson scattering (YAG-TS) system [17,18]. In this plasma condition, the n e is sufficiently high for neglecting the effects of the high energy electrons on the T e measurement. The n e profiles are nearly identical for the two heating power cases. On the other hand, different T e profile shapes are observed during the P ECH change. The maximum value of central T e [ ( )] T 0 e reaches 1.5 keV with P ECH =240 kW with the steep T e gradient of 30 keV m -1 at = r a 0.2. A high T e region is created around the center ( < r a 0.3). Moreover, the reduction of P ECH results in a decreased T e gradient in the core region ( < r a 0.3), while the T e in the outer region ( > r a 0.3) is almost identical for the two heating power cases.

Density threshold for eITB formation
To explore the conditions for the formation of the peaked T e profiles, we investigate the density dependence on central T e and the T e gradient. In this experiment, we control n e by changing gas-puff fueling under a constant P ECH . Figure 2 Here, the T e profiles are fitted using the following function 3 , while the T e variation of the peripheral region is small. The T e gradient at the core region shows the same transient increase as that shown by T e . Whenn e is below the threshold density (´--1.1 1.3 10 m 19 3 ), the T e gradient at = r a 0.1 increases from approximately 20 to approximately -80 keV m 1 . In contrast, the gradient at = r a 0.3 is nearly constant at approximately -10 keV m 1 . The difference in the T e gradient responses for the n e change between the core and peripheral regions shows that there is a clear difference of the transport characteristics between the two regions. The difference between the T e profiles is also observed in the ECH power control experiment described in section 2. The findings that both higher P ECH and lower n e contribute to the formation of the peaked profile are consistent with the predictions that the ion-electron root transition occurs in the collisionless regime and in a plasma with a high T T e i ratio, respectively. The transient increase of both T e and T e gradient suggest that these phenomena have bifurcation nature explained by the NC theory. In LHD, the large size of helical device (R 3.6 m), the clear transition of T e and T e gradient have also been observed, while the normalized threshold value ofP n ECH e for the eITB formation is larger (approximately´-700 10 kW m 19 3 ) than that of Heliotron J (approximately´-250 10 kW m 19 3 ) [19,20]. The much higher helical field ripple in the core region caused by the strong helical axis of Heliotron J (factor of 25 compared to LHD) could increase the ripple transport of the electrons and decreaseP n ECH e at which the eITB formation occurs.  eff , which indicates the property of the NC helical ripple transport in the 1/ν regime, is a candidate for understanding the differences between the threshold values [5]. Table 1 or 0.004) shows that larger  eff corresponds to smaller threshold values and therefore easier eITB formation. While the explanation is certainly plausible, in CHS which has nearly the same magnetic configuration as that of LHD, the threshold value ofP n ECH é -260 10 kW m 19 3 is nearly the same as that of Heliotron J [21]. Furthermore, a comparison of CHS ( r = shows that the trend in the threshold values is opposite to the order expected based on  eff . Therefore, additional factors that determine the threshold value may exist, such as the presence of a magnetic island. For LHD [22] and TJ-II [23], the effects of the magnetic island on plasma flow, turbulence, and heat transport were investigated, and it was reported that the existence of a magnetic island triggers the eITB formation. The effects of a magnetic island on the eITB formation are also under investigation in Heliotron J.

Estimation of a NC radial electric field
In stellarator/heliotron devices, the NC theory predicts a large E r in the core region in an eITB plasma, with the experimental results supporting the NC predictions [5]. A NC calculation is conducted using the moment method (Sugama-Nishimura's method) [13,14] to estimate the E r value for the peaked profile. The magnitude of the NC ambipolar E r is reported to be in good agreement with the measured E r in stellarator/ heliotron devices.
We calculate E r using the T e and n e profiles with the peaked T e plasma, as shown in figure 1 . In this calculation, we assume the ion temperature profile as = -( ) ( ( ) ) T r r a 150 1 i 1.57 1.11 (in eV), the typical profile of the Heliotron J plasma whose validity has been previously confirmed by charge exchange recombination spectroscopy (CXRS) [26]. Due to the nonlinear dependence of the NC particle fluxes on E r in the helical plasma, E r is determined by the ambipolar condition as follows: where Γ represents the particle flux of the plasma species with 'e' for electrons and 'i' for ions. In figures 5(a)-(c), the calculated G i and G e are plotted as a function of E r at = r a 0.17, 0.5 and 0.77 for the peaked T e plasma. At = r a 0.77 ( figure 5(a)), the ambipolarity provides the ion-root E r . An increase of T e in the core region leads to the rapid growth in G e . When T e reaches a value larger than that in the radial inner region, the second solution for a large positive E r appears (the third solution appears simultaneously but is thermodynamically unstable) ( figure 5(b)). This solution is called the electron root. A further increase in core T e at = r a 0.17 leads to the further growth in G e and only the electron root appears (figure 5(c)). Figure 6(b) shows the radial profiles of the theoretically expected ambipolar E r of both the peaked and non-peaked plasmas. For both plasmas, only the electron root (large positive E r ) is predicted in the core region ( < r a 0.3), while the electron and ion roots are predicted to coexist in the outer region ( < < r a 0.3 0.6). The experimentally obtained T e profile is sufficient for considering the ion-electron root transition. A large positive E r (12 kV m -1 ) is expected for the peaked T e profile while the value of E r is nearly half (5 kV m -1 ) for that of the non-peaked T e profile, as shown in figure 6(b). The Bohm and gyro-Bohm mixed transport model with theÉ B shear flow effect has already been compared to the helical and tokamak experimental ITBs [27,28]. The most widely accepted explanation for the ITB formation relies on the suppression of TEM or ITG turbulence due to theÉ B shear flow. The turbulence suppression may occur when theÉ B flow shearing rate wÉ B exceeds the linear growth rate of these turbulences. In our case (figure 6), it is possible that the wÉ B of the peaked T e plasma exceeds these growth rates while the positive E r is formed.  This calculation result and measured T e profile suggest that (1) the large positive E r similar to that observed in other stellarator/heliotron devices can form in Heliotron J and (2) the E r is sufficiently large for suppressing both the NC transport and the turbulence.

Heat transport analysis using experimental results
The analysis of heat transport characteristics is indispensable for identifying eITB. We estimate the electron thermal diffusivities for the ECH power control experiment. The effective electron thermal diffusivity (c e eff ) profiles are evaluated using the T e and n e profiles obtained from the YAG-TS measurement and the single-pass ECH deposition profiles Q ECH for the cases of P ECH ∼ 240 and 175 kW (figure 7). c e eff is defined as follows: Here, the Q ECH is calculated using the TRAVIS ray-tracing code [29,30]. TRAVIS is a ray-tracing code for ECH/ECCD and ECE diagnostics in arbitrary 3D magnetic configurations. The code has been applied and validated for Heliotron J [30]. The T e gradient does not increase while the P ECH increases, suggesting the degradation of peripheral confinement. This phenomenon is well known as the feature of power degradation in the L-mode confinement. The transport analysis shows a clear reduction of c e eff for < r a 0.3 in the highly peaked T e profile case suggesting improved confinement in the core region.
A comparative study of experimental and NC theory results provides more detailed information about the transport properties of the peaked T e plasma. For this purpose, the NC calculation is performed using the method described in section 4, which considers the calculated E r . In this calculation, we discuss the plasmas in the ECH power control   The c e NC of the peaked plasma is lower than that of the non-peaked plasma in the core region ( < r a 0.3). However, the difference of c e NC between the peaked and nonpeaked plasmas in the core region ( < r a 0.3) is small compared to that of c e eff . c e NC and c e eff are plotted in figure 7(b). In the core region, c e NC for the peaked plasma is approximately 1/7 times smaller than c e eff for the peaked plasma. As the experimentally obtained c e eff contains the effects of both NC and anomalous transport, the difference in c e eff between the peaked and non-peaked plasmas is attributed to the reduction of the anomalous transport in the core region.

Evaluation of turbulence suppression
To quantitatively evaluate the degree of reduction of anomalous transport, we investigate the dependence of c e eff on T e . 3 2 decreases as the T e gradient increases, suggesting that the heat transport inside the foot point is smaller than that predicted by the T e dependence of gyro-Bohm scaling.
In the previous section, we discussed the following topics that are recognized as the typical features of a helical eITB: (1) the reduction of thermal diffusivity, (2) the formation of a large positive E r , (3) the transient formation with a threshold value, and (4) the reduction of turbulence. In Heliotron J, the reduction of the thermal diffusivity is predicted by the NC calculation. Experimental analysis in this section shows the reduction of the anomalous transport. Beam emission spectroscopy measurements  [32] will be used in future studies to confirm the reduction of the turbulence. These characteristics are similar to those obtained from the NC theory and experimental observation in LHD, CHS, and W7-AS [19]. According to the discussions of (1)-(4), the peaked profile in Heliotron J is confirmed to be the eITB.

Hysteresis feature of T e between back and forth transition
The temporal dynamics during the eITB formation are investigated. Figure 9(a) shows the time evolution ofn e , W p dia , and P ECH . In this experiment, n e is controlled to decrease until 210 ms and increase after that. The time evolution of T e is obtained from the ECE diagnostic using a multichannel radiometer in the experiment. In the ECE measurement, the optical depth of the emission is greater than 2 within 30% of the plasma minor radius so that the radiation temperature corresponds to T e near the core of Heliotron J. The time evolutions of T e ofr a 0.1, 0.5, and 0.95 are also shown in figure 9(b). The eITB was observed at 210 ms (figure 9(c)) in low n e while it disappears at 260 ms (figure 9(d)) due to the increase in n e . The time evolution of the ECE signal in the core region (r a 0.1) has the same tendency as the change in the T e profile measured using YAG-TS. When n e decreases, the ECE signal in the core region transiently increases at around 195 ms. When n e increases, the ECE signal transiently decreases at around 235 ms. The eITB formed transiently and disappears at 195 and 235 ms. Figure 10 shows the trace of T e atr a 0.1 as a function ofn e . In this figure, we control n e from the red arrow to the blue arrow. When T e increase,´n 0.9 10 m ; e 19 3 however, when T e decrease,´n 1.0 10 m e 19 3 . Therefore, a hysteresis loop of the ECE signal for the n e change is formed during the eITB formation. Due to hysteresis, the core T e shows different values for the n e decrease and n e increase phases even at same n e . This hysteresis indicates that after its formation, the eITB remains in the higher n e plasma. In CHS, a bifurcation behavior is observed in the plasma potential measurement [33]. The hysteresis loop is ascribed to the local bifurcation nature predicted in the NC theory. It is suggested that the behavior of the ECE signal in Heliotron J is caused by the bifurcated E r and that the thermal transport has the hysteresis feature.

Summary
The peaked T e profile of Heliotron J has the following four features: (1) heat transport analysis shows the significant improvement of c e eff in the plasma, with the eITB relative to that without the eITB. (2) Numerical calculations using the moment method predicts that a large positive E r is formed in the core region. (3) When the value ofP n ECH e exceeds the threshold of´-250 10 kW m 19 3 , both central T e and the core T e gradient increase transiently. (4) The large gap between c e eff and c e NC suggests that the suppression of anomalous thermal transport contributes to the core improved confinement of the eITB plasma. These features provide the evidence for the formation of an eITB in Heliotron J. Furthermore, the time evolution of the core T e obtained by the ECE measurement shows the transient increase and hysteresis phenomena during the formation of the eITB.
Heliotron J is a suitable device for studying eITB physics with both various diagnostics and plasma control systems. We plan to measure E r and a plasma flow via the CXRS. The ECH system of Heliotron J shows several advantages for the study of dynamics such as the hysteresis phenomena obtained by utilizing the continuous control of P ECH during a single shot. The heat pulse thermal diffusivity will be evaluated by measuring the propagation of the heat pulses for eITB plasmas using a modulation ECH technique. In addition, we also plan to investigate the effect of the magnetic field configurations, such as a helical ripple and a magnetic island, on the mechanism of the eITB formation. This research is the first report of the eITB formation in the helical-axis heliotron configuration. The research of eITB physics in Heliotron J contributes to expand the variety of configuration research in stellarator/heliotron devices.