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Enhancements of edge zonal flows, radial electric fields, and turbulence are observed in electron cyclotron resonance heating-heated plasmas (Zhao et al 2013 Nucl. Fusion 53 083011). In this paper, the effects of sawtooth heat pulses on flows and turbulence are presented. These experiments are performed using multiple Langmuir probe arrays in the edge plasmas of the HL-2A tokamak. The edge zonal flows, radial electric fields, and turbulence are all enhanced by sawteeth. Propagation of the zonal flow and turbulence intensities is also observed. The delay time of the maximal intensity of the electric fields, zonal flows, and turbulence with respect to the sawtooth crashes is estimated as ∼1 ms and comparable to that of the sawtooth-triggered intermediate phases. Not only the zonal flows but also the radial electric fields lag behind the turbulence. Furthermore, the intensities of both the zonal flows and electric fields nearly linearly increase/decrease with the increase/decrease of the turbulence intensity. A double-source predator–prey model analysis suggests that a relatively strong turbulence source may contribute to the dominant zonal flow formation during sawtooth cycles.

A tomography system is installed as one of the diagnostics of new age to examine the three-dimensional characteristics of structure and dynamics including fluctuations of a linear magnetized helicon plasma. The system is composed of three sets of tomography components located at different axial positions. Each tomography component can measure the two-dimensional emission profile over the entire cross-section of plasma at different axial positions in a sufficient temporal scale to detect the fluctuations. The four-dimensional measurement including time and space successfully obtains the following three results that have never been found without three-dimensional measurement: (1) in the production phase, the plasma front propagates from the antenna toward the end plate with an ion acoustic velocity. (2) In the steady state, the plasma emission profile is inhomogeneous, and decreases along the axial direction in the presence of the azimuthal asymmetry. Furthermore, (3) in the steady state, the fluctuations should originate from a particular axial position located downward from the helicon antenna.

This paper presents the experimental identification of the dynamic interaction between three fluctuations excited by different thermodynamical forces in a linear plasma. The observed fluctuations are characterized as an axial symmetric mode, a drift wave, and an azimuthally symmetric potential fluctuation from the spatiotemporal structures measured with Langmuir probe arrays. The intermittent burst of the axial symmetric mode is observed by the instantaneous wave number spectrum. The energy transfer analysis revealed that the axially symmetric mode gains energy from the other mode during the burst while the drift wave loses energy. The intermittent burst synchronizes with the azimuthal symmetric potential fluctuation.

Computational results are presented to describe the development of the staircase pattern as a result of the jam of heat flux avalanches. The nonlinear stage of the heat flux avalanche jam formation is analyzed based on the numerical simulations. Both hyperdiffusivity and shearing feedback provide a relevant saturation effect on the jam growth. The role of forcing is also discussed. Drawing analogy from the multiple jam formation in traffic dynamics, the formation of multiple corrugated layers of the temperature is demonstrated. It is shown that the staircase structure may be controlled by changing the strength of heating power.

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.

A method is discussed to evaluate the localized radial heat flux, which is associated with the streamer, based on the observed temperature perturbation at the onset of Type-III ELMs in HL-2A tokama...

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.

An analytic model is developed for understanding the abrupt onset of geodesic acoustic mode (GAM) in the presence of chirping energetic-particle-driven GAM (EGAM). This abrupt excitation phenomenon has been observed on LHD plasma. Threshold conditions for the onset of abrupt growth of GAM are derived, and the period doubling phenomenon is explained. The phase relation between the mother mode (EGAM) and the daughter mode (GAM) is also discussed. This result contributes to the understanding of “trigger problems” of laboratory and nature plasmas.

Emission intensity \(\epsilon \) from plasmas is a complicated function of electron temperature Te and electron density ne. To understand the dependence of \(\epsilon \) on Te and ne, an experiment...

The neutral drag effect on the parallel velocity gradient driven instability (PVG) in the presence of density inhomogeneity is theoretically investigated. The dispersion relation of PVG mode with the effect of the density gradient and neutral particle drag is derived, and its solution is analytically obtained. The neutral particle drag gives rise to the phase shift between parallel flow and electrostatic potential fluctuations and modifies the parallel compression. As a result, the stability of the PVG mode changes. It is found that the neutral particle drag does not only reduce but also enhances the instability. Specifically, near the marginal condition, the neutral particle effect suppresses the density gradient effect, and the parameter region where the PVG mode is linearly unstable significantly expands.

A dramatic increase of density gradient and a slight decrease of electron temperature gradient were observed in the pedestal just prior to each onset in a series of ELM bursts. An inward particle flux induced by a quasi-coherent mode was found to be responsible for such changes. The characteristics of the quasi-coherent mode, including frequency, wave vector, propagation direction and velocity were identified. The nonlinear three-wave coupling is a plausible mechanism for the generation of the mode. Decoupling of the mode induced density transport from energy transport was discovered. The gradient of density was observed always much higher than that of temperature for electrons at the starting point of the ELM burst and, therefore, the dominant role of density gradient over electron temperature gradient for ELM onset is demonstrated. Consistence and contrast of the results with confinement and transport in I-mode discharges are discussed.

The propagation direction of parallel velocity gradient driven mode in the edge of H-mode plasmas is investigated. We study the possibility to observe a preferential propagation (either up-ward or ...

In order to explore the impact of the neutrals on the plasma turbulence, a new gas puff system is developed for a linear magnetized plasma column PANTA. Helium gas is injected into the argon plasma without changing the electron density profile. After the helium gas puff, the dominant fluctuation mode changes from the broadband m = 2 drift wave to the coherent m = 1 mode, where m is the azimuthal mode number. Accordingly, the property of the nonlinear coupling with other fluctuating modes changes from broadband couplings to coherent couplings.

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 helicity of flow field is an important quantity for describing the topological feature of turbulent fluids and plasmas. In this work, we discuss how helicity is determined in turbulent plasmas, by considering the drift wave turbulence and the parallel velocity gradient driven turbulence as concrete examples. Helicity evolution for each turbulence is derived and compared against the simulation data. Links between the plasma helicity and the transport channels, such as particle transport and momentum transport, are demonstrated. Several applications including the excitation of the 3D flow patterns in fusion plasmas and dynamo action in astrophysical plasmas are discussed.

Helical flow structure is ubiquitous in nature. In this short contribution, possible origins of these flow structures are presented. One is due to the parallel flow shear driven turbulence, where perpendicular zonal flows are nonlinearly excited. The other is conversion of perpendicular flows into parallel flows via phase space. Both processes highlight a fundamental process of helical flow generation in turbulent plasmas.

We propose a novel mechanism of enhancement of turbulence by energetic-particle-driven geodesic acoustic modes (EGAMs). The dynamics of drift-wave-type turbulence in the phase space is investigated by wave-kinetic equation. Spatially inhomogeneous turbulence in the presence of a transport barrier is considered. We discovered that trapping of turbulence clumps by the EGAMs is the key parameter that determines either suppress or enhance turbulence. In regions where turbulence is unstable, EGAM suppresses the turbulence. In contrast, in the stable region, EGAM traps clumps of turbulence and carries them across the transport barrier, so that the turbulence can be enhanced. The turbulence trapped by EGAMs can propagate independent of the gradients of density and temperature, which leads to non-Fickian transport. Hence, there appear a new global characteristic velocity, the phase velocity of GAMs, for turbulence dynamics, in addition to the local group velocity and that of the turbulence spreading. With these effect, EGAMs can deteriorate transport barriers and affect turbulence substantially. This manuscript provides a basis to consider whether a coherent wave breaks or strengthen transport barriers.

New mesoscale electric fluctuations (MSEFs) are identified in the edge plasmas of the HL-2A tokamak using multiple Langmuir probe arrays. The MSEFs, resulting from the synchronization and having components of dominant geodesic acoustic mode (GAM) and m/n = 6/2 potential fluctuations, are found at the same frequency as that of the magnetic fluctuations of m/n = 6/2 (m and n are poloidal and toroidal mode numbers, respectively). The temporal evolutions of the MSEFs and the magnetic fluctuations clearly show the frequency entrainment and the phase lock between the GAM and the m/n = 6/2 magnetic fluctuations. The results indicate that GAMs and magnetic fluctuations can transfer energy through nonlinear synchronization. The nonlinear coupling analyses show that the MSEFs couple to turbulence and low frequency zonal flows (LFZFs). This suggests that the MSEFs may contribute to the LFZF formation, reduction of turbulence level, and thus confinement regime transitions. The analysis of the envelope modulation demonstrates that both the MSEFs and the LFZFs modulate the turbulence while the MSEFs are modulated by the LFZFs.

It is demonstrated that the zonal flow is controlled by the parallel flow in the cylindrical plasmas. A three-dimensional turbulence simulation is performed, based on the reduced fluid model. The background parallel flow is applied by introducing the time independent parallel momentum source. Changing the magnitude of the momentum source, the behavior of the zonal flow is investigated. The drift wave turbulence is affected by the parallel flow, and it shows the spatial competition between turbulence modes. The spatial competition appears/disappears abruptly, depending on the intensity of the parallel momentum source. As a consequence of the transition between the turbulence state, the radial profile of the turbulence drastically changes, which leads to the change of the turbulence force to drive the zonal flow. In this way, the parallel flow indirectly affects the zonal flow through the deformation of the turbulence.

An analysis method is developed for imaging measurement systems, such as the tomography system or fast camera imaging, in order to extract the spatial structure properties of fluctuation. In this analysis method, rectangular functions and Fourier series are adopted for the basis functions of the radial and azimuthal coordinates, respectively. The examples of this analysis method show that this method is useful for quantifying the spatial structure of the 2D image such as the radial profile of the power and the rotation angle of each azimuthal mode. The method proposed in this article allows us to elucidate the features of the 2D spatial structure of phenomena in magnetized plasma.An analysis method is developed for imaging measurement systems, such as the tomography system or fast camera imaging, in order to extract the spatial structure properties of fluctuation. In this analysis method, rectangular functions and Fourier series are adopted for the basis functions of the radial and azimuthal coordinates, respectively. The examples of this analysis method show that this method is useful for quantifying the spatial structure of the 2D image such as the radial profile of the power and the rotation angle of each azimuthal mode. The method proposed in this article allows us to elucidate the features of the 2D spatial structure of phenomena in magnetized plasma.

We theoretically investigate turbulence in high-confinement mode (H-mode) plasmas with the pressure gradient and the mean flow. The toroidal flow, which is induced by the poloidal mean flow so as to satisfy the divergence free condition, exists in the H-mode, thus the effect of the toroidal return flow on instabilities is considered. The proposed model self-consistently includes not only the destabilization of the drift wave and the parallel flow shear instability, called the D'Angelo mode, but also the stabilization due to the poloidal flow shear. Depending on the strength of the flow shear or on the magnetic geometrical parameter, we obtain the stabilization of the drift wave and the destabilization of the D'Angelo mode. The competition between different instabilities through coupling of the poloidal flow with the toroidal return flow could be a key concept for understanding the turbulence in the H-mode. The characteristics of the instabilities are similar to the observations of the precursor of the type-III edge-localized mode.

We experimentally investigate the roles of drift wave type fluctuations interacting with zonal flow. The drift wave type fluctuations examined in this paper are characterized by nonlinear solitary wave, splash, and solitary eddy [Arakawa et al., Sci. Rep. 6, 33371 (2016)]. Compared to the nonlinear solitary wave, splash has a short lifetime, while solitary eddy has a long lifetime. Excitation/damping of the splash and the solitary eddy are synchronized with zonal perturbation. The roles of the splash and the solitary eddy in transport processes are also discussed. Solitary eddy contributes to momentum transport and accelerates zonal flow. The particle flux driven by the solitary eddy and the splash is in the inward and outward directions, respectively, with similar magnitudes.

The streamer-driven particle flux is evaluated experimentally in a linear cylindrical plasma. The streamers, a radially elongated and azimuthally localized structure created in turbulent plasma, really induce ballistic transport, and directly connect the plasma core to the edge within one order faster time scale than that of turbulence. The occurrence of large transport deviates from a Gaussian distribution and is likely to obey a power law. The fundamental plasma experiment clearly shows the significant and essential contributions of streamers to cross-field transport and structural formation of turbulent plasmas.The streamer-driven particle flux is evaluated experimentally in a linear cylindrical plasma. The streamers, a radially elongated and azimuthally localized structure created in turbulent plasma, really induce ballistic transport, and directly connect the plasma core to the edge within one order faster time scale than that of turbulence. The occurrence of large transport deviates from a Gaussian distribution and is likely to obey a power law. The fundamental plasma experiment clearly shows the significant and essential contributions of streamers to cross-field transport and structural formation of turbulent plasmas.

Turbulence and its structure formation are universal in neutral fluids and in plasmas. Turbulence annihilates global structures but can organize flows and eddies. The mutual-interactions between flow and the eddy give basic insights into the understanding of non-equilibrium and nonlinear interaction by turbulence. In fusion plasma, clarifying structure formation by Drift-wave turbulence, driven by density gradients in magnetized plasma, is an important issue. Here, a new mutual-interaction among eddy, drift wave and flow in magnetized plasma is discovered. A two-dimensional solitary eddy, which is a perturbation with circumnavigating motion localized radially and azimuthally, is transiently organized in a drift wave – zonal flow (azimuthally symmetric band-like shear flows) system. The excitation of the eddy is synchronized with zonal perturbation. The organization of the eddy has substantial impact on the acceleration of zonal flow.

A calculation which describes the spin-up of toroidal plasmas by the radial propagation of turbulence fronts with broken parallel symmetry is presented. The associated flux of parallel momentum is calculated by using a two-scale direct-interaction approximation in the weak turbulence limit. We show that fluctuation momentum spreads faster than mean flow momentum. Specifically, the turbulent flux of wave momentum is stronger than the momentum pinch. The scattering of fluctuation momentum can induce edge-core coupling of toroidal flows, as observed in experiments.

The synchronization of geodesic acoustic modes (GAMs) and magnetic fluctuations is identified in the edge plasmas of the HL-2A tokamak. Mesoscale electric fluctuations (MSEFs) having components of a dominant GAM, and m/n=6/2 potential fluctuations are found at the same frequency as that of the magnetic fluctuations of m/n=6/2 (m and n are poloidal and toroidal mode numbers, respectively). The temporal evolutions of the MSEFs and the magnetic fluctuations clearly show the frequency entrainment and the phase lock between the GAM and the m/n=6/2 magnetic fluctuations. The results indicate that GAMs and magnetic fluctuations can transfer energy through nonlinear synchronization. Such nonlinear synchronization may also contribute to low-frequency zonal flow formation, reduction of turbulence level, and thus confinement regime transitions.

The variety of scalar and vector fields in laboratory and nature plasmas is formed by plasma turbulence. Drift-wave fluctuations, driven by density gradients in magnetized plasmas, are known to relax the density gradient while they can generate flows. On the other hand, the sheared flow in the direction of magnetic fields causes Kelvin-Helmholtz type instabilities, which mix particle and momentum. These different types of fluctuations coexist in laboratory and nature, so that the multiple mechanisms for structural formation exist in extremely non-equilibrium plasmas. Here we report the discovery of a new order in plasma turbulence, in which chained structure formation is realized by cross-interaction between inhomogeneities of scalar and vector fields. The concept of cross-ferroic turbulence is developed and the causal relation in the multiple mechanisms behind structural formation is identified, by measuring the relaxation rate and dissipation power caused by the complex turbulence-driven flux.

The role of density modulation in driving streamer flows in drift wave turbulence is discussed. In contrast to the conventional shearing mechanism, we emphasize the impact of frequency modulation by meso-scale density perturbation. This mechanism is more effective for streamers than for zonal flows. The Reynolds stress and nonlinear growth rate are calculated. The result indicates that the streamer growth is enhanced due to the density modulation. Implications on the selection of streamers and zonal flows are discussed as well.

Streamers and their mediator have been known to exist in linear cylindrical plasmas [Yamada et al., Nat. Phys. 4, 721 (2008)]. Conditional averaging is applied to extract the nonlinear characteristics of a mediator, which has been simply treated as a linear wave. This paper reports that a mediator should have higher harmonic components generated by self-couplings, and the envelope of a streamer should be generated with not only fundamental but also higher harmonic components of the mediator. Moreover, both the mediator and the envelope of the streamer have common features with solitary waves, i.e., the height should increase inversely as the square of their localization width.

The three-dimensional structures of the streamer and its carrier waves and mediator were observed in a linear plasma device for the first time. Not only the cross-sectional structure but also the a...

The spatio-temporal dynamics of turbulence with the interaction of geodesic acoustic modes (GAMs) are investigated, focusing on the phase-space structure of turbulence, where the phase-space consists of real-space and wavenumber-space. Based on the wave-kinetic framework, the coupling equation between the GAM and the turbulence is numerically solved. The turbulence trapped by the GAM velocity field is obtained. Due to the trapping effect, the turbulence intensity increases where the second derivative of the GAM velocity (curvature of the GAM) is negative. While, in the positive-curvature region, the turbulence is suppressed. Since the trapped turbulence propagates with the GAMs, this relationship is sustained spatially and temporally. The dynamics of the turbulence in the wavenumber spectrum are converted in the evolution of the frequency spectrum, and the simulation result is compared with the experimental observation in JFT-2M tokamak, where the similar patterns are obtained. The turbulence trapping effect is a key to understand the spatial structure of the turbulence in the presence of sheared flows.

International audience; We present a theory of turbulence elasticity, which follows from delayed response of drift waves (DWs) to zonal flow (ZF) shears. It is shown that when |〈V〉'ZF|/Δωk ≥ 1, with |〈V〉'ZF| the ZF shearing rate and Δωk the local turbulence decorrelation rate, the ZF evolution equation is converted from a diffusion equation to a telegraph equation. This insight provides a natural framework for understanding temporally periodic ZF structures, e.g., propagation of the ZF/turbulence intensity fronts. Furthermore, by incorporating the elastic property of the DW–ZF turbulence, we propose a unified paradigm of low-confinement-mode to intermediate-confinement-mode to high-confinement-mode (L → I → H) transitions. In particular, we predict the onset and termination conditions of the limit cycle oscillations, i.e. the I-mode. The transition from an unstable L-mode to I-mode is predicted to occur when Δωk < |〈V〉'ZF| 〈V〉'cr(〈V〉E×B is mean E × B shear flow driven by edge radial electrostatic field), the I-mode will terminate and spiral into the H-mode.

In this paper, recent progress on experimental analysis and theoretical models for non-local transport (non-Fickian fluxes in real space) is reviewed. The non-locality in the heat and momentum transport observed in the plasma, the departures from linear flux-gradient proportionality, and externally triggered non-local transport phenomena are described in both L-mode and improved-mode plasmas. Ongoing evaluation of 'fast front' and 'intrinsically non-local' models, and their success in comparisons with experimental data, are discussed, United States. Department of Energy (Contract DE-FC02-99ER54512)

Équipe 107 : Physique des plasmas chauds; International audience; To understand turbulent transport in magnetized plasmas, an end-plate biasing experiment was performed in a linear magnetized plasma device, PANTA. Here we report the change of bi-coherence among fluctuations during biasing. During biasing, coupling with drift waves is decrease, and that with the mediator is increase.

© 2015 American Physical Society. Turbulence in hot magnetized plasmas is shown to generate permeable localized transport barriers that globally organize into the so-called "ExB staircase" [G. Dif-Pradalier et al., Phys. Rev. E, 82, 025401(R) (2010)]. Its domain of existence and dependence with key plasma parameters is discussed theoretically. Based on these predictions, staircases are observed experimentally in the Tore Supra tokamak by means of high-resolution fast-sweeping X-mode reflectometry. This observation strongly emphasizes the critical role of mesoscale self-organization in plasma turbulence and may have far-reaching consequences for turbulent transport models and their validation.

The role of parallel shear flow in the pattern selection problem in drift wave turbulence is discussed. Patterns of interest here are E × B convective cells, which include poloidally symmetric zonal flows and radially elongated streamers. The competition between zonal flow formation and streamer formation is analyzed in the context of modulational instability analysis, with the parallel flow shear as a parameter. For drift wave turbulence with k⊥ρs ≲ O(1) and without parallel flow coupling, zonal flows are preferred structures. While increasing the magnitude of parallel flow shear, streamer growth overcomes zonal flow growth. This is because the self-focusing effect of the modulational instability becomes more effective for streamers through density and parallel velocity modulation. As a consequence, the bursty release of free energy may result as the parallel flow shear increases.

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.