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This article assesses current understanding of hysteresis in transport relations, and its impact on the field. The rapid changes of fluxes compared to slow changes of plasma parameters are overviewed for both core and edge plasmas. The modulation ECH experiment is explained, in which the heating power cycles on-and-off periodically, revealing hysteresis and fast changes in the gradient–flux relation. The key finding is that hystereses were observed simultaneously in both the the gradient–flux and gradient–fluctuation relations. Hysteresis with rapid timescale exists in the channels of energy, electron and impurity densities, and plausibly in momentum. Advanced methods of data analysis are explained. Transport hysteresis can be studied by observing the higher harmonics of temperature perturbation in heating modulation experiments. The hysteresis introduces the term , which depends on the harmonic number m in an algebraic manner (not exponential decay). Next, the causes of hysteresis and its fast timescale are discussed. The nonlocal-in-space coupling works here, but does not suffice. One mechanism for 'the heating heats turbulence' is that the external source S in phase space for heating has its fluctuation in turbulent plasma. This coupling can induce the direct input of heating power into fluctuations. The height of the jump in transport hysteresis is smaller for heavier hydrogen isotopes, and could be one of the origins of isotope effects on confinement. Finally, the impacts of transport hysteresis on the control system are assessed. Control systems must be designed so as to protect the system from sudden plasma loss.

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.

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.

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).

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.

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.