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A combination of the Fourier transform and the maximum entropy method for estimating the frequency-wavenumber resolved power spectrum density is proposed. After illustrating the physical insight of the maximum entropy method by using synthetic test data, capability of the proposed method is tested using numerical simulation data. The method is also applied to experimental data obtained by the beam emission spectroscopy in the Large Helical Device. All of those examinations show that the proposed method provides more plausible results than conventional methods when the available spatial points are limited.

A new beam emission spectroscopy system that has improved lines of sight is installed in the Large Helical Device (LHD), and routine measurement has been started in the 21st LHD experiment campaign in 2019–2020. The new system is optimized for hydrogen isotope experiments by equipping a rotatable large-diameter interference filter to be compatible with either the hydrogen or the deuterium beam emission component. An avalanche photo diode detector array having 8 × 8 pixels is used for obtaining a radial–vertical image of electron density fluctuation covering the mid-radius to the plasma periphery. Spatial resolution and wavenumber cutoff are derived from equilibrium reconstruction and plasma kinetic profiles. Obtained fluctuation data is presented for a low field high beta discharge. The spatiotemporal structure of the fluctuations is clearly shown by Fourier correlation analyses.

In this paper, a new criterion for the internal transport barrier (ITB) formation is proposed by defining a unique scalar parameter, the profile gain factor. The profile gain factor shows degree of the confinement improvement with respect to an arbitrary reference temperature profile in the L-mode. As the reference L-mode profile for the large helical device (LHD), the edge ion temperature profile data is extrapolated to the core by the L-mode profile function, which is characterized by the thermal diffusion coefficient being proportional to the local ion temperature. The profile gain factor is defined as the ratio of the ion stored energy experimentally measured to that evaluated from the reference L-mode profile. The proposed method is applied to the LHD experimental data, and its capability for quantification of the ITB strength is demonstrated.

The behavior of carbon impurities in deuterium plasmas and its impact on thermal confinement were investigated in comparison with hydrogen plasmas in the Large Helical Device (LHD). Deuterium plasma experiments have been started in the LHD and high-ion-temperature plasmas with central ion temperature (T i) of 10 keV were successfully obtained. The thermal confinement improvement could be sustained for a longer time compared with hydrogen plasmas. An isotope effect was observed in the time evolution of the carbon density profiles. A transiently peaked profile was observed in the deuterium plasmas due to the smaller carbon convection velocity and diffusivity in the deuterium plasmas compared with the hydrogen plasmas. The peaked carbon density profile was strongly correlated to the ion thermal confinement improvement. The peaking of the carbon density profile will be one of the clues to clarify the unexplained mechanisms for the formations of ion internal transport barrier and impurity hole on LHD. These results could also lead to a better understanding of the isotope effect in the thermal confinement in torus plasma.

"A high density regime with an internal diffusion barrier (IDB) has been extended to the helical divertor (HD) configuration in the Large Helical Device (LHD). Avoidance of the local enhancement of neutral pressure is necessary to enable IDB formation, which is consistent with earlier works by using the Local Island Divertor (LID) with efficient active pumping. The central pressure reached 1.3 times atmospheric pressure, where ne(0) = 6 × 1020 m?3 and Te(0) = 660 eV. The plasmas with an IDB are located in the plateau collisionality regime. The significant impurity effect has not been observed throughout the discharges in spite of the existence of a negative radial electric field. A central pressure limiting event is observed in the plasmas with an IDB using the HD. During this event which is referred to as the core density collapse (CDC), particles are flushed out from the core on the time scale of a few hundreds of microseconds. The suppression of the Shafranov shift by vertical elongation (κ) is effective to mitigate CDC. At κ = 1.2, the central β value is increased up to 6.6% at 1 T."

One of the main objectives of the LHD is to extend the plasma confinement database for helical systems and to demonstrate such extended plasma confinement properties to be sustained in steady state. Among the various plasma parameter regimes, the study of confinement properties in the collisionless regime is of particular importance. Electron cyclotron resonance heating (ECRH) has been extensively used for these confinement studies of the LHD plasma from the initial operation. The system optimizations including the modification of the transmission and antenna system are performed with the special emphasis on the local heating properties. As the result, central electron temperature of more than 10 keV with the electron density of 0.6 x 10$^{19}$ m$^{-3}$ is achieved near the magnetic axis. The electron temperature profile is characterized by a steep gradient similar to those of an internal transport barrier observed in tokamaks and stellarators. 168 GHz ECRH system demonstrated efficient heating at over the density more than 1.0 x 10$^{20}$ m$^{-3}$. CW ECRH system is successfully operated to sustain 756 s discharge.

The mitigation of a tracer impurity accumulation in the core region of high-temperature helical plasma was clearly observed by applying electron cyclotron heating (ECH) in the large helical device (LHD). In the LHD, the accumulation of impurities toward the centre of the plasma has been observed in a high-density regime. In this study, for observing clearly the behaviour of impurity ions in the plasma core, the extrinsic 'tracer' impurity was injected into that region by means of a tracer-encapsulated solid pellet (TESPEL). The high-density LHD plasma without ECH definitely shows the strong impurity accumulation, and then it causes the reduction in electron and ion temperatures in the core region. When ECH was applied just after the TESPEL injection, the accumulation of the tracer impurity ions was mitigated. Even after ECH was switched-off, the intensities of the line emissions from the highly-ionized tracer impurity were increased very slightly. The micro-turbulence measurement with a 2-dimensional phase contrast imaging diagnostic during ECH does not support the view that the change in the micro-turbulence would enhance the outward flow (an increase in a diffusive flux, a decrease in an inward convective flux and/or a change the direction of the convective flux from inward to outward) of the impurity ions. Moreover, at this moment, there is no conclusive data regarding a radial electric field measured with a charge exchange spectroscopy diagnostic to support the view that the change in the radial electric field would be attributed to the increment in the outward flow of the impurity ions from the core region of the LHD plasma.

An integrated transport simulation code, TASK3D, is developed and applied to the high ion temperature plasma of LHD. The particle and heat transport equations are solved and compared with LHD experimental results. The heat and particle transports are assumed to be the sum of the neoclassical transport and the turbulent transport. The neoclassical transport is evaluated by the LHD/DGN neoclassical transport database, and the gyro-Bohm and the gyro-Bohm + gradT turbulent transport models are applied to the heat transport analysis. On the other hand we assume a constant turbulent transport model for particle transport. Relatively good agreements are obtained between the simulated and experimental profiles of the density and temperature in the steady state plasma of LHD. Next the high ion temperature plasma with the carbon pellet injection is simulated. It is found that the reduction of turbulence transport is the most significant contribution to achieving the high ion temperature and that the reduction of the turbulent transport compared to the L-mode plasma (normal hydrogen plasma) is evaluated to be a factor of about five.

Effects of carbon impurities on the thermal confinement properties were discussed for carbon-pellet-injected high-Ti discharges in the Large Helical Device (LHD). To clarify their role, the amounts of carbon impurities introduced into plasmas were scanned by varying the number of injections in a discharge or the size of the pellet, and the changes of thermal confinement properties with these variations were examined. In all cases, strong correlations between the densities of carbon impurities and the thermal diffusivities of plasmas were found. Thermal diffusivities were small when the carbon densities were greater than a certain value, e.g. ~1.5 × 1017 m3 at r/a ≈ 0.72, and the thermal diffusivity degraded drastically below this density. This indicates the existence of a threshold density of carbon impurity for an improved confinement in plasmas. Combined with the formation of the impurity hole, the variation of confinement property with carbon density can explain the degradation of ion temperature in high-Ti discharges with carbon pellet injection in the LHD.

Impurity behavior has so far been investigated in steady state hydrogen plasmas in the Large Helical Device, which is a heliotron-type device and excellent for steady state operation. There was always found to be an impurity accumulation window, as observed before (Nakamura et al 2002 Plasma Phys. Control. Fusion 44 2121, Nakamura et al 2003 Nucl. Fusion 43 219). To clarify the boundary conditions, the dependences of impurity transport on edge plasma parameters are investigated with a database of steady state hydrogen discharges, and the boundary conditions for the impurity accumulation window are discussed. It is found that two different types of impurity screening effects are essential for preventing intrinsic impurities from entering the core plasma. One of them is due to positive radial electric field at the plasma edge on the low collisionality side and the other is impurity retention caused by friction force in the ergodic layer on the high collisionality side. The classification of steady state discharges on n–T space shows that the impurity behavior can be predicted by the impurity shielding criteria based on each empirical scaling.

In the Large Helical Device experiments, a significant pressure gradient is observed in the edge region where the three-dimensional magnetohydrodynamics equilibrium analysis predicts the stochastization of magnetic field lines. Therefore, experimental investigation of this edge plasma behavior is attracting much interest to identify either the plasma response to stochastic magnetic fields or the topological change of magnetic fields due to the plasma. In this study, we have investigated the relation of the stochastization of magnetic field lines to the radial electric field, Er. When magnetic field lines become stochastic or open and connected to the vessel, electrons are lost along these field lines while ions are trapped. Then, a strong Er shear from negative to positive appears at the boundary. Two magnetic configurations with different widths of the stochastic layer in the vacuum are studied for low-? discharges. It has been found that the position of a strong Er shear appears outside of the last closed flux surface. When comparing the vacuum magnetic field, the positions of strong Er shear are observed in the edge of the stochastic layer. In the stochastic region, the scatter of stochastic field lines is studied. The position of a strong Er shear appears in the region where the outward scatter of the field lines increases. In that region, stochastic field lines intersect the regions with long and short connection lengths. Although the connection length is longer than the electron mean free path, the scatter of stochastic field lines with short connection lengths appear in the regions with positive Er. These results are compared with moderate-? discharges, where a large plasma response is expected. The prediction of the vacuum magnetic field qualitatively agree with the experimental observations but quantitative differences are found.

The effect of resonant magnetic perturbation (RMP) on MHD characteristics is investigated in high-beta plasmas of the Large Helical Device. The ramp-up and static m/n = 1/1 RMP field are applied in medium- (~2%) and high- (~4%) beta plasmas in order to find beta dependences of mode penetration, MHD activities and confinement. The results show that the threshold of mode penetration linearly increases with the beta value and/or plasma collisionality. The threshold of mode penetration in the RMP ramp-up experiments is roughly consistent with the static RMP case. The beta value gradually decreases with the RMP field strength before mode penetration, which is caused by a reduction in the pressure inside the ι/2π = 1 resonance. The width of the magnetic island after the penetration becomes larger than the given RMP field, and it is further enhanced by the increment of the beta value.

Dynamic transport study taking account of the slowing-down effect on the neutral beam injection heating is applied to a high ion temperature plasma with an ion internal transport barrier (ITB) obtained by carbon pellet injection, which records the highest ion temperature of around ~7 keV in the Large Helical Device. The transient increase in ion heating is clarified during the density decay phase just after the carbon pellet injection by considering the slowing-down effect. The dynamic transport analysis also includes the change in heat flux due to the change in kinetic energy inside the plasma with the time scale of the global energy confinement time, which is required to investigate the heat and momentum transport during the transient phase more exactly. The characteristics of the ion heat and momentum transport improvement during the ion ITB formation phase are clarified by the dynamic transport study.

A heavy ion beam probe was installed on the Large Helical Device (LHD) to investigate the roles of radial electric fields (Er) in magnetically confined high-temperature plasmas. Two new observations are presented. One is the observation of electrostatic potential profiles during the formation of extremely hollow density profiles of impurities, called the impurity hole (Ida K et al 2009 Phys. Plasmas 16 056111), in the LHD plasmas. The measured Er is negative, and the Er determined by the ambipolarity condition of neoclassical particle fluxes is consistent with this observation. However, the transport analysis indicates that the formation of the extremely hollow profile is not attributable to the impurity fluxes driven by Er and the density and temperature gradients of the impurity. The other new observation is on the geodesic acoustic mode (GAM). The electrostatic potential fluctuation associated with the GAM, which is probably induced by energetic particles, in plasmas with the reversed or weak magnetic shear is identified. The GAM is localized in the core region of the plasma.