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The conditional average is a technique to extract a typical waveform from bursty or quasi-periodic phenomena regarded as a combination of deterministic trend and residual fluctuations (or probabilistic part). The article proposes a new conditional average technique that is an extension from what is called the template method that allows automatic selection, using the correlation analysis, of the identical events of the phenomena. The proposed method is applied on a quasi-periodic oscillation observed in a linear magnetized plasma, and successfully divides the phenomenon into the deterministic trend and residual fluctuations. Moreover, the statistical error analysis on the power of the residual fluctuations discloses the presence of mutual interactions between the deterministic trend and the residual fluctuations.

In this paper, we evaluated electron temperature fluctuations by using a conditional sampling and a statistical phase detection method. These methods allow us to reconstruct probe I − V characteristics at each time delay; that is, we can extract electron temperature and ion saturation current fluctuations in high temporal resolution without complex electronic circuits. Our method was applied to two quasi-coherent fluctuations observed in a linear magnetized plasma device, PANTA. We observed spatiotemporal structures of electron temperature and ion saturation current fluctuations. The results revealed the amplitudes and phase relation between electron temperature and density fluctuations.

The novel technique of dynamical mode decomposition (DMD) is applied to the outputs of a numerical simulation of Kelvin–Helmholtz turbulence in a cylindical plasma, so as to capture and quantify the time evolution of the dominant nonlinear structures. Empirically, these structures comprise rotationally symmetric deformations together with spiral patterns, and they are found to be identified as the main modes of the DMD. A new method to calculate the time evolution of DMD mode amplitudes is proposed, based on convolution-type correlation integrals, and then applied to the simulation outputs in a limit cycle regime. The resulting time traces capture the essential physics far better than Fourier techniques applied to the same data.\ud \ud

A numerical measurement module simulating a heavy ion beam probe was developed, and numerical measurements of electrostatic potential and density fluctuations are carried out for 3-D turbulent data generated by a global simulation of drift-interchange mode turbulence in helical plasmas. The deviation between measured and local values is estimated. It is found that the characteristic structures can be detected in spite of the screening effect due to the finite spatial resolution.

Selection rule of the radial propagation direction of geodesic acoustic modes (GAMs) is investigated. Here, we study the influence of nonlinear coupling with drift wave turbulence on the propagation direction of GAMs. Based on wave-kinetic equation for the turbulence, the phase-space dynamics is numerically solved and the nonlinear saturated states are obtained, where the phase-space consists of the real space and the wavenumber space. A wave pattern of the GAM in a nonlinear saturated state varies to form a standing wave, outward and inward propagating waves, depending on the peak radial wavenumber of the turbulence. The impact of nonlinear coupling with turbulence is discussed by deriving the GAM dispersion relation that includes the effect of the turbulence.

Numerical diagnostics using 3-D simulation data are carried out to capture fluctuation properties in helical plasmas. Here Ion-Temperature-Gradient (ITG) turbulence data are used, obtained by the gyrokinetic code GKV-X with realistic magnetic configuration. Fluctuations are calculated in the field aligned coordinates, which have long wave lengths in the magnetic field direction and are anisotropic in the radial and poloidal directions, and their features are represented in the experimental frame. For the validation, the density fluctuation spectrum is calculated, which is integrated along the line of sight as in the phase contrast imaging signals. From that integrated signal its vertical profile is reconstructed by utilizing the variation of the direction of the magnetic field, as the operation carried out in experimental data. Usually in experiments, there exists limitation on the observation region and spatial resolution, so difference between the deteriorated and real spectra is confirmed by numerical simulations with variations related to the spatial limitations. ITG modes have a characteristic wavelength and frequency, and are identified with the sufficient spatial resolution even from the integrated signal by comparing the wavenumber spectra at different radial positions. Combination of multiple flux-tube data is also tested for calculation to give fluctuations spreading in wider radial ranges of plasma. These fluctuation spectra are compared with the experimental one for comprehensive understanding of experimental observations.

In the edge transport barrier of H-mode plasmas, a large poloidal flow exists and the electrostatic potential and density can have steep gradients both in the radial and poloidal directions. The accessibility to a two-dimensionally steep structure is demonstrated by solving the model equation including the poloidal structure, combined with the equation giving the time evolution of the radial electric field. The analysis is carried out with the parameter set of the electrode biasing experiment and shows the existence of the convective particle flux arising from poloidal inhomogeneity. This study provides an essential explanation for improving the transport analyses in H-modes by taking account of the two-dimensional effect in toroidal plasmas.

The 'fishbone' fast wave travelling wave antenna was developed for LHD to provide a capability for rotational transform profile control by current drive. The fishbone antenna is equivalent to two combline antennae stacked vertically. The antenna operates around 75 MHz and excites a wavenumber of 14 m−1 when the phase difference between adjacent current straps is 90°. A test of a combline antenna with plasma load on the TST-2 spherical tokamak suggested the possibility that this type of antenna does not need to be installed in the immediate vicinity of the last closed flux surface. Optimization of the design was performed based on measurements on mock-up antennas and model calculations. In the fishbone antenna, controlled excitation of the even mode (with currents in the top and bottom halves of a current strap in the same direction) is necessary. A predominant excitation of the even mode was realized in the LHD fishbone antenna with simulated loading by selecting an appropriate operating frequency.

The mechanism for formation of a steep structure in the radial electric field is a key issue in plasma confinement. Properties of the radial electric field bifurcation are studied taking into account the effect of electrode biasing. The radial electric field structure is determined by the charge conservation equation. From the nonlinear mechanism associated with local current due to ion bulk viscosity, a transition can take place. Various types of radial electric field structures with multiple peaks are allowed for the same boundary condition. The ion orbit loss term breaks the symmetry of the radial current similarly to the ambipolar radial electric field. A radial current driven by the electrode plays the role of a control parameter in a transition similarly to the pressure gradient. A phase diagram is given in the spontaneous drive vs external drive space. Differences in the radial shape of solitary electric field structures are demonstrated in the presence of spatial varying components. This study clarifies the mechanisms of nonlinear structure formation in transport barriers.

Radial electric field bifurcation induced by electrode biasing near the tokamak edge is considered in this paper. The radial electric field structure is analysed including two non-linear terms in the radial current, namely the neoclassical term and the orbit loss term. Their competition gives various radial electric field structures, and biasing transition is compared with spontaneous transition. Bifurcation has different features for positive and negative biasing, with a larger number of structures available for the negative biasing case. Effectiveness of the solitary radial electric field structures induced by biasing for confinement improvement is discussed.

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.

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).

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.

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.

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.

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.

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.

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.

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.

A transition of the fluctuation spectrum of ion saturation current is observed in linear magnetized plasmas. A power spectrum with regular peaks and a broadband spectrum appear alternately during a discharge. The temporal order of changes in the modes is investigated at the transition. The low poloidal mode number components change before the higher modes begin to change. The delay times of change between modes are determined.

The three-field reduced fluid model was extended to describe the resistive drift wave turbulence in magnetized cylindrical plasmas. There include multiple energy exchange paths, and two kinds of nonlinear steady states were obtained in simulations with a fixed particle source: one with a zonal flow generated by modulational coupling of various unstable modes, which suppress transport, and the other with a streamer, which is a azimuthally-localized vortex structure and induces convective transport, formed by parametric coupling. These structures are formed selectively, depending on the ion-neutral collision frequency, which is a damping force of a zonal flow and has a stabilizing effect of linear instability in this model. This is a minimal model for analyzing the turbulent structural formation mechanism by mode coupling in cylindrical plasmas, and competitive nature of structural formation was revealed.

The formation of a poloidal shock structure is predicted in H-mode transport barriers, which must be taken into account for transport analyses to clarify the rapid formation mechanism of the H-mode pedestal. The analyses are carried out with edge plasmas in tokamak H-modes, which are induced either spontaneously or by electrode biasing. Two-dimensional structures of the potential, density and flow velocity are calculated with the momentum conservation equation. The validity of one-dimensional L/H transition theory and the iterative process to obtain the two-dimensional structure are confirmed by our analysis. A steep electric field structure both in the radial and poloidal directions induces radial ion fluxes, which increase in the H-mode transport barrier. If the Boltzmann relation is violated, radial electron fluxes are induced. A transport model is constructed, including generation of particle fluxes associated with the two-dimensional structure and reduction of anomalous transport by the steep gradient of the radial electric field. A self-consistent evolution of the density profile is calculated in the L/H transition, which clarifies that the generation of particle fluxes accelerates the density pedestal formation.