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An improved confinement state can be attained by imposing a radial electric field at the plasma edge. This is characterized by a change of the Er structure. A charge conservation equation with a diffusion term has been solved to explain this mechanism. Various types of Er structures with multiple peaks are allowed for the same boundary condition. The relationship between the voltage and the current is obtained by numerical calculation. Both stable and unstable regions exist in the stationary solutions and their boundary points are critical points for transition from one state to another. Multiple transitions and hysteresis are predicted. The magnitude of the collision frequency affects the existence of solutions with multiple peaks.

The topological bifurcation of the flow in non-equilibrium magnetized plasmas is demonstrated by a turbulence simulation. A system with two generic sources of turbulence, the gradients of density and parallel flow, is considered. Topological index of the flow is introduced, in order to indicate the chirality of flow pattern. We here report that the turbulence-driven flow forms the structure of co-axial helixes with opposite chirality. By changing the source of plasma particles, which modifies the density gradient, the transition between three turbulent states is obtained. In addition to the two turbulent states, which are dominated by the drift wave and the D'Angelo mode, respectively, the new state is found. In this third state, fluctuations are driven by both of the free energy sources simultaneously, and compete with the others. The result illustrates the generic feature of turbulence flow generation in non-equilibrium magnetized plasmas.

Various types of peaked structure in the radial electric field are predicted theoretically in edge biasing experiments using electrodes. A nonlinear diffusion equation is employed to describe the radial electric field, and is solved in the region bounded by electrodes. Structures with multiple peaks are allowed when the distance between electrodes is finite. The minimum value for the distance between electrodes is obtained. The distance between electrodes, the externally driven current and the applied voltage determine the number of solutions. Multiple transitions and hysteresis are predicted from the relationship between the voltage and the current.

Changing the experimental conditions such as the neutral pressure and the magnetic field strength provides a drastic change in the turbulence states in linear magnetized helicon plasmas. In order to define the turbulence states and their occurrence region a throughout parameter scan in the two-dimensional parameter space was performed. The classification of the turbulence states is carried out phenomenologically based on the turbulence spectrum and the waveform.

Experimental plasma discharges in linear PANTA device are studied by Mach probe measurements, providing floating potential, ion saturation current, and parallel flow velocity time evolution, at different radii of the device. Spectral analysis indicates that drift waves and D'Angelo modes exist simultaneously in the plasma. A discrimination study shows they are located at different positions in radius and frequency. (C) 2017 The Japan Society of Plasma Science and Nuclear Fusion Research

Dynamical response of the streamer near a critical condition where the streamer disappears is investigated by using a three dimensional fluid simulation. The gradual change of the global control parameter is given to the plasma. When the control parameter approaches the critical condition, the phase mismatch between the drift waves (which form the streamer) and the mediator mode increases abruptly, finally loosing the nonlinear matching condition. The eigenmode is also modified after the transition from streamer to the other state occurs. The phase relation is much sensitive compared to the change of amplitude, and could be observed even by a one-point measurement.

Several innovative applications of a travelling wave (combline) antenna designed for fast wave current drive have been demonstrated for the first time in the JFT-2M tokamak. High energy electrons of at least 10 keV were produced in the plasma core by highly directional fast waves in electron cyclotron heated plasmas. The ponderomotive potential of the beat wave, produced by fast waves at two different frequencies, was directly measured for the first time by a heavy ion beam probe. Plasma production was demonstrated using the wave fields excited by the combline antenna over a wide range of toroidal magnetic fields (0.5-2.2 T).

In this paper, we show the direct observation of the parallel flow structure and the parallel Reynolds stress in a linear magnetized plasma, in which a cross-ferroic turbulence system is formed [Inagaki et al., Sci. Rep. 6, 22189 (2016)]. It is shown that the parallel Reynolds stress induced by the density gradient driven drift wave is the source of the parallel flow structure. Moreover, the generated parallel flow shear by the parallel Reynolds stress is found to drive the parallel flow shear driven instability D'Angelo mode, which coexists with the original drift wave. The excited D'Angelo mode induces the inward particle flux, which seems to help in maintaining the peaked density profile.

Eigenmode analysis of geodesic acoustic modes (GAMs) driven by fast ions is performed, based on a set of gyrokinetic equations. Resonance to the magnetic drift of the fast ions can destabilize GAMs. A new branch is found in the family of GAMs, whose frequency is close to the magnetic drift frequency of the fast ions. The poloidal eigenfunction of this branch has bump structures in the poloidal direction where the resonance of the magnetic drift with the mode is strong. The ion heating rate by the GAMs is evaluated in the framework of quasi-linear theory. The heating is localized poloidally around the resonance locations. Owing to the bumps in the eigenfunction, the magnitude of the heating is much larger than that estimated without the magnetic drift resonance.

Here we report changes in the turbulence spectrum and turbulence-driven particle flux during end-plate biasing experiments in a linear plasma. Outward radial flux driven by drift waves is decreased as the amplitude of the drift waves is reduced. During biasing, the cross-phase between potential and density fluctuations of mediator, which plays a key role in nonlinear interactions of turbulence, changed from negative to positive. Then the radial flux is induced reversal from inward to outward.

We have upgraded the multi-channel microwave reflectometer system which uses a frequency comb as a source and measure the distribution of the density fluctuation caused by magneto-hydro dynamics instability. The previous multi-channel system was composed of the Ka-band, and the U-band system has been developed. Currently, the U-band system has eight frequency channels, which are 43.0, 45.0, 47.0, 49.0, 51.0, 53.0, 55.0, and 57.0 GHz, in U-band. Before the installation to the Large Helical Device (LHD), several tests for understanding the system characteristics, which are the phase responsibility, the linearity of output signal, and others, have been carried out. The in situ calibration in LHD has been done for the cross reference. In the neutral beam injected plasma experiments, we can observe the density fluctuation of the interchange mode and obtain the radial distribution of fluctuation amplitude.

Fluctuation component in the turbulence regime is found to be azimuthally localized at a phase of the global coherent modes in a linear magnetized plasma PANTA. Spatial distribution of squared bicoherence is given in the azimuthal cross section as an indicator of nonlinear energy transfer function from the global coherent mode to the turbulence. Squared bicoherence is strong at a phase where the turbulence amplitude is large. As a result of the turbulence localization, time evolution of radial particle flux becomes bursty. Statistical features such as skewness and kurtosis are strongly modified by the localized turbulence component, although contribution to mean particle flux profile is small.

The solitary radial electric field in the edge of toroidal plasma is studied based on the electric field bifurcation model. Results are applied to tokamak and helical plasmas, and the dependence of the electric field structure on the plasma parameters and geometrical factors is analyzed. The order of magnitude estimate for tokamak plasma is not far from experimental observations. It is shown that, in helical plasmas, the height of electric field structure is reduced substantially owing to the ripple particle transport, while the width is influenced less. The implications of the results for the limit of achievable gradient in the H-mode pedestal are also discussed.

Global nonlinear simulations with heat modulation are carried out to understand the turbulent transport mechanism in toroidal plasmas. Rapid propagation of the heat modulation and a hysteresis in the gradient-flux relation are found in the turbulent simulation of drift-interchange modes. A global mode is excited nonlinearly, and the nonlinear couplings with Reynolds stress take a finite temporal duration for self-consistent redistribution of the energy. The mode also has a seesaw effect: increase of the amplitude of the global mode at one position affects the turbulence at the other radial position not by inducing the radial flux by itself, but by absorbing the energy from microscopic modes. Successive excitations of microscopic modes cause the accelerated propagation of the flux change like turbulence spreading after the onset of modulation. Owing to these non-diffusive processes, the hysteresis appears in the gradient-flux relation, which is compared with experiments.

Bifurcation from a streamer to a solitary drift wave is obtained in three dimensional simulation of resistive drift waves in cylindrical plasmas. The solitary drift wave is observed in the regime where the collisional transport is important as well as fluctuation induced transport. The solitary drift wave forms a steep wave front in the azimuthal direction. The phase of higher harmonic modes are locked to that of the fundamental mode, so that the steep wave front is sustained for a long time compared to the typical time scale of the drift wave oscillation. The phase entrainment between the fundamental and second harmonic modes is studied, and the azimuthal structure of the stationary solution is found to be characterized by a parameter which is determined by the deviation of the fluctuations from the Boltzmann relation. There are two solutions of the azimuthal structures, which have steep wave front facing forward and backward in the wave propagation direction, respectively. The selection criterion of these solutions is derived theoretically from the stability of the phase entrainment. The simulation result and experimental observations are found to be consistent with the theoretical prediction.

Meso-scale streamer has a radially elongated structure and is believed to enhance the radial transport. In order to study the control of the streamer, we demonstrated an end plate biasing to the streamer state in the PANTA linear plasma. During the end plate biasing, the electron density profile became more peaked, fluctuation was suppressed, the streamer structure was deconstructed, and the waveform became a periodic solitary state. The radial electric field only induced at around the end plate was found to play an important role for the streamer suppression.

Nonlinear competition of turbulent structures and their roles in transport are investigated by using three-dimensional simulation code of resistive drift wave turbulence in magnetized cylindrical plasmas. Selective formation of zonal flows and streamers has been obtained by controlling the strength of damping of the zonal flow. In addition, there is an energy path from the drift waves to a flute type structure, which is linearly stable, and it becomes effective just below the stability boundary of the zonal flow. The flute structure directly induces transport effectively, and affects the drift waves and the zonal flow. A large amplitude zonal flow is formed selectively even with existence of the flute structure. The property of the particle confinement is investigated by changing the particle source intensity, which controls the strength of driving of the drift waves. The characteristic of the particle confinement changes according to turbulent states, and an improved confinement regime is obtained in the zonal flow dominant state. Study on cylindrical plasmas reveals the fundamental mechanism of improved confinement in the magnetized plasma with influence of turbulent structural formation.

Rapid propagation of heat modulation and a hysteresis in the gradient-flux relation are found in a global nonlinear simulation of drift-interchange mode turbulence in toroidal helical plasmas. A global mode is excited nonlinearly and induces the turbulence flux in a limited radial region. The nonlinear couplings take a finite temporal duration for redistributing the energy. The mode also has a seesaw effect: increase of the amplitude of the global mode, at the other radii, works to absorb the energy form microscopic modes to suppress the turbulence. Successive excitations of microscopic modes cause the accelerated propagation of change of the heat flux like turbulence spreading after the onset of modulation. Owing to these processes, the hysteresis appears in the gradient-flux relation, which is compared with experiments.

Non-linear coupling between fluctuations at different radial locations is observed on the Large Helical Device (LHD) plasma. The summed bi-coherence between the low frequency macro-scale fluctuation (frequency is f = 2.75 kHz) at ρ = reff/a99 = 0.63 (where a99 is averaged plasma radius) and the high-frequency micro-scale fluctuations (frequency range of f > 150 kHz) at ρ = 0.88 is found to converge to a non-zero and finite value. The bi-phase analysis provides another basis for the non-linear interaction across the long distance. These results are associated with the violation local closure for transport relation.

In the JFT-2M tokamak (JFT standing for JAERI Fusion Torus), the limit cycle oscillation (LCO), together with several variables, i.e., the electrostatic potential, radial electric field, electron density, turbulence intensity, and Dα emission from the divertor region, is observed before the L-to-H transition. The spatiotemporal dynamics of the LCO is analysed in detail. Zonal flows are not seen, while modulation is observed in the edge-localized poloidal flow and density gradient. Modulation is also seen in the Reynolds stress, caused by that in the turbulence intensity and turbulence wavenumber. However, flow acceleration cannot be explained by the modulation in the Reynolds stress. Rapid inward propagation is also observed for the density gradient and turbulence packet. The characteristics of the propagation are verified by means of turbulence spreading theory and diffusion theory.

A new method is presented for identifying waveforms of fluctuations in turbulent plasmas. The method is based on heartbeat analysis in which the convolution of a waveform is obtained by employing the phase tracking method. Phase tracking is performed by correlating raw time-series data with a template waveform; the template is evaluated through iteration procedure. The method is applied to fluctuations in a PANTA plasma, and the nonlinear waveform and its distribution of periods are obtained. c

We analyzed the higher harmonics of temperature perturbation in the modulated electron cyclotron heating experiment on TJ-II plasma. The higher harmonics (e.g., 5th harmonic) exhibited significantly weaker decay in amplitude as they propagated in radius as compared with the prediction by diffusive model. The change in the time derivative of temperature at the onset (and turning-off) of the heating power propagates in radius with very little temporal smoothening.

We propose the use of a microwave comb for measuring the density profile as a continuous function of radius with high temporal resolution. The analysis focuses on phase-sensitive convolution of the reflected waves: convolution of pulses can eliminate statistical noise. The time resolution for constructing the density profile is also discussed.

Shigeru INAGAKI1,2), Sanae-I. ITOH1,2), Kimitaka ITOH2,3), Naohiro KASUYA1,2), Tatsuya KOBAYASHI4), Akihide FUJISAWA1,2), Tokihiko TOKUZAWA3), Katsumi IDA2,3), Shin KUBO3), Takashi SHIMOZUMA3), Naoki TAMURA3), Hayato TSUCHIYA3), Yoshio NAGAYAMA3), Kazuo KAWAHATA3), Hiroshi YAMADA3), Akio KOMORI3) and LHD Experiment Group 1)Research Institute for Applied Mechanics, Kyushu University, Kasuga, Fukuoka 816-8580, Japan 2)Itoh Research Center for Plasma Turbulence, Kyushu University, Kasuga, Fukuoka 816-8580, Japan 3)National Institute for Fusion Science, Toki, Gifu 509-5292, Japan 4)Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan

By employing a new method for studying dynamical transport, hysteresis in the flux-gradient relation was recently discovered for modulated heating. In this paper, the new method is compared to the conventional heat-pulse propagation method. We also demonstrate integration of results from the new method with the power balance thermal conductivity.

A nonlinear simulation of resistive drift wave turbulence in a cylindrical plasma is carried out. Long time evolution of turbulence with formation of a zonal flow is obtained for more than 1000 times of the typical drift wave period, which is sufficient for statistical analyses. Dynamical particle and momentum balance for the formation of the mean reveals that the radial turbulent fluxes are dominant contributors for the evolution of fluctuations. The particle flux is found to precede the momentum flux for 0.4 times of the typical drift wave period with large temporal variance. The analyses of the time series data of 3-D fields give the understanding of the dynamical structural formation mechanism. c

The progress of physical understanding as well as parameter improvement of net-current-free helical plasma is reported for the Large Helical Device since the last Fusion Energy Conference in Daejeon in 2010. The second low-energy neutral beam line was installed, and the central ion temperature has exceeded 7 keV, which was obtained by carbon pellet injection. Transport analysis of the high-T-i plasmas shows that the ion-thermal conductivity and viscosity decreased after the pellet injection although the improvement does not last long. The effort has been focused on the optimization of plasma edge conditions to extend the operation regime towards higher ion temperature and more stable high density and high beta. For this purpose a portion of the open helical divertors are being modified to the baffle-structured closed ones aimed at active control of the edge plasma. It is compared with the open case that the neutral pressure in the closed helical divertor increased by ten times as predicted by modelling. Studies of physics in a three-dimensional geometry are highlighted in the topics related to the response to a resonant magnetic perturbation at the plasma periphery such as edge-localized-mode mitigation and divertor detachment. Novel approaches of non-local and non-diffusive transport have also been advanced.

We report observations of the dynamic response of micro-fluctuations and turbulent flux to a low-frequency heating power modulation in the Large Helical Device. The responses of heat flux and micro-fluctuation intensity differ from that of the change in temperature gradient. This result violates the local transport model, where turbulence is determined by the local temperature gradient. A new relationship between flux, gradient and turbulence is found. In addition to the temperature gradient, the heating rate is proposed as a new, direct controlling parameter of turbulence to explain the fast response of turbulence against periodic modulation of heating power.

Turbulence Diagnostic Simulator is an assembly of simulation codes to clarify the formation mechanism of turbulent structures by numerical diagnostics in magnetically confined plasmas. Global simulations are carried out using a reduced MHD model of drift-interchange mode in helical plasmas, and time series data of 3-D fluctuation fields are produced. It includes localized modes in their rational surfaces, and broad modes spread in the radial direction. Magnitudes of nonlinear couplings from the convective derivative are evaluated in the nonlinear saturated states. The radial profile shows that there exist strong mode excitation near the center, various modes and nonlinear couplings with higher m modes in the middle radius, small number of propagating modes near the edge, which contribute to the pressure profile modification. For the detection of the different features, combination of several diagnostics is necessary.

Validation of modeling in meso-scale structure formation is undergoing by using multi-channel probe measurements and advanced analyzing techniques such as bispectrum. Study of meso-scale structures including streamers is important for understanding anomalous transports in magnetized plasmas. A streamer structure and its mediator mode were observed in the Large Mirror Device-Upgrade linear plasma. The mediator mode nonlinearly coupled with many other drift wave modes and generated a streamer structure by phase locking. The radial biphase profiles indicating the phase locking showed the radial elongation of the streamer structure. Modes having similar characteristics to the mediator were also found in a theoretical work based on the Hasegawa-Mima model and a numerical simulation code. c

(Received 7 December 2012 /Accepted 10 May 2013)To study the nonlinear saturation mechanism in turbulent plasmas, we plan to obseve ion temperature gra-dient (ITG) modes in the Plasma Assembly for Nonlinear Turbulence Analysis (PANTA). Linear growth ratesof ITG modes in the linear device are analyzed to determine their excitation conditions using a three-field fluidmodel to describe the ion motion. Parameter scans of the linear growth rate show the threshold for ITG modeexcitation, and the typical plasma parameters of the PANTA are found in the unstable domain.

The nonlinear dynamics of zonal flows (ZFs) is investigated when geodesic acoustic modes (GAMs) have substantial influence on plasma states. Simultaneous existence of multiple GAMs with different radial phase velocities gives additional nonlinear mode couplings, and asymmetry of the turbulence spectrum induces energy exchanges between GAMs and a ZF. A set of model equations is derived to describe the nonlinear dynamics of a ZF, GAMs and ambient turbulence. The model includes the mechanism of ZF generation by a pair of GAMs, and the back interaction from the turbulence is solved self-consistently. Two stationary solutions are obtained; one is the known solution that the GAM propagates as a travelling wave with no ZF excitation, and the other is a new solution that a pair of GAMs forms a standing wave, which induces a ZF. The accessibility to the steady states, and the threshold for the transition between them are obtained. The GAM and ZF formation in the new state affects the background plasmas. The effects on the turbulent heat diffusivity and the ion heating rate are discussed.

Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, 6-1 Kasuga-koen, Kasuga, Fukuoka 816-8580, Japan 1)Research Institute for Applied Mechanics, Kyushu University, 6-1 Kasuga-koen, Kasuga, Fukuoka 816-8580, Japan 2)Itoh Research Center for Plasma Turbulence, Kyushu University, 6-1 Kasuga-koen, Kasuga, Fukuoka 816-8580, Japan 3)Japan Atomic Energy Agency, 801-1 Mukoyama, Naka, Ibaraki 311-0193, Japan 4)Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Tokyo 277-8561, Japan 5)Japan Atomic Energy Agency, 2-166 Oaza-obuchi-aza-omotedate, Rokkasho, Kamikita, Aomori 039-3212, Japan 6)National Institute for Fusion Science, 322-6 Oroshi-cho, Toki, Gifu 509-5292, Japan

Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, 6-1 Kasuga-Koen, Kasuga 816-8580, Japan 1)Itoh Research Center for Plasma Turbulence, Kyushu University, 6-1 Kasuga-Koen, Kasuga 816-8580, Japan 2)Research Institute for Applied Mechanices, Kyushu University, 6-1 Kasuga-Koen, Kasuga 816-8580, Japan 3)Japan Atomic Energy Agency, Tokai-mura, Naka-gun 319-1195, Japan 4)Graduate School of Flontier Sciences, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa 277-8561, Japan 5)National Institute for Fusion Science, 322-6 Oroshi-cho, Toki 509-5292, Japan

Preliminary observation results are reported for a new discharge regime in the Plasma Assembly for Nonlinear Turbulent Analysis (PANTA), where spontaneous transitions in the equilibrium profile and fluctuation spectra occur. Two different states are defined by using the mean density value. Axial and radial profiles are observed for the two states, and large profile changes are found. The spatiotemporal evolution of the transition front is measured. Changes in the fluctuation spectrum are evaluated using conditional average and lock-in average. c

Non-Gaussian statistical properties of the azimuthally averaged momentum and particle fluxes driven by turbulence have been simultaneously observed in inhomogeneous magnetized plasmas for the first time. We identified the stretched Gaussian distribution of the both fluxes and the transition from the point-wise distribution to averaged ones was confirmed. The change of the particle flux precedes that of the momentum flux, demonstrating that the momentum flux is induced by the relaxation of density gradient.

Development of experimental diagnostics in fusion plasmas has made possible to measure plasma fluctuations with high spatial and temporal resolution. To detect a global mode, which contributes to global transport phenomena, it is helpful to use simulation data as a test field for the measurements. The turbulence diagnostic simulator is an assembly of codes for turbulence simulations and numerical diagnostics. Using the turbulence diagnostic simulator, a time series of turbulence data is obtained, on which numerical diagnostics are carried out to demonstrate how global modes to be observed. There exist modes, which are broad in the radial direction, and correlation analyses reveal the characteristic structures with a finite number of local observations in the radial direction, as in experiments.

A new method for estimating the wavenumber of a standing wave system by using three Langmuir probes is proposed. Analytical formulae are derived from a simple model in which two waves of the same frequency and the same wavenumber propagate in opposite directions. The proposed method can estimate the wavenumber correctly even if the two waves have equal amplitude.

Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Fukuoka 816-8580, Japan 1)Research Institute for Applied Mechanics, Kyushu University, Fukuoka 816-8580, Japan 2)Itoh Research Center for Plasma Turbulence, Kyushu University, Fukuoka 816-8580, Japan 3)Graduate School of Frontier Sciences, The University of Tokyo, Tokyo 277-8561, Japan 4)National Institute for Fusion Science, Toki 509-5292, Japan (Received 7 December 2010 / Accepted 10 May 2011)

Electron temperature fluctuations are measured with a rotatable triple probe in PANTA. Effects of fluctuation phase are cancelled by aligning the probe pins in the propagation direction of fluctuations. Evaluated electron temperature fluctuations normalized by average electron temperature are much smaller than normalized density fluctuations and normalized floating potential fluctuations in low electron temperature PANTA plasma. Additionally conditional sampling technique is applied to a single probe measurement.

We report a detailed correlation technique to identify the long-range temperature fluctuation in the Large Helical Device. Correlation hunting has successfully realized the observation of electron temperature fluctuations, which are characterized by their correlation length comparable to the plasma minor radius, with low frequency of ∼ 1-3 kHz, ballistic radial propagation (at a speed of ∼1 km/s, of the order of diamagnetic drift velocity), spatial mode number of m/n = 1/1 (or 2/1), and amplitude of ∼2% at the maximum. Bicoherence analysis confirmed their nonlinear coupling with local microscopic turbulent fluctuations. This long-range temperature fluctuation is a possible carrier of fast propagation in transport processes observed so far. We also comment on the theoretical interpretation.

Turbulent plasmas form a variety of mesoscale structures, which affect the level of anomalous transport in fusion plasmas. A streamer is a poloidally localized, radially elongated vortex, which increases convective transport. We have carried out numerical simulations of resistive drift wave turbulence in a linear configuration, as a minimal model for analysing the structural formation mechanism in magnetized plasmas by mode coupling. A three-field reduced MHD model is extended to describe the resistive drift wave turbulence in cylindrical plasmas. A poloidally localized turbulent structure, which has the typical temporal scale of the streamer, is formed by the self-bunching of a couple of unstable modes in nonlinear saturation states. The formed structure depends on the magnitude of the ion–neutral collision frequency, which is the damping parameter of the zonal flow, and the streamer is formed when the damping of the zonal flow is stronger than that of the intermediate mode for the streamer formation. We found that the streamer is selectively formed to keep the particle balance as long as the drift wave is unstable.

The turbulence fluctuation spectra of linear magnetized plasmas are measured under various neutral pressure conditions. Strong turbulent waves and symmetric waves are observed in low and high neutral pressure conditions. In this study, we compare the radial structure of the probability density function (PDF) of these fluctuations. The characteristics of the PDFs are related to those of the radial and poloidal turbulent structures.