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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.

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.

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.

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.

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.

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 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)

© 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 temporal-spatial structures of plasma flows and turbulence around tearing mode islands are presented. The experiments were performed using Langmuir probe arrays in the edge plasmas of J-TEXT tokamak. The correlation analyses clearly show that the flows have similar structures of m/n = 3/1 as the magnetic island does (m and n are the poloidal and toroidal mode numbers, respectively). The sign of the potential fluctuations for the flows inverses and the powers significantly reduce at q = 3 surface. Approaching to the last closed flux surface for the magnetic islands, the radially elongated flow structure forms. The flows are concentrated near separatrix and show quadrupole structures. The turbulence is concentrated near X-point and partly trapped inside the magnetic islands.

Author(s): Rice, JE; Hughes, JW; Diamond, PH; Cao, N; Chilenski, MA; Hubbard, AE; Irby, JH; Kosuga, Y; Lin, Y; Metcalf, IW; Reinke, ML; Tolman, EA; Victora, MM; Wolfe, SM; Wukitch, SJ

The abrupt and strong excitation of the geodesic acoustic mode (GAM) has been found in the large helical device (LHD), when the frequency of a chirping energetic particle-driven GAM (EGAM) approaches twice that of the GAM frequency. The temporal evolution of the phase relation between the abrupt GAM and the chirping EGAM is common in all events. The result indicates a coupling between the GAM and the EGAM. In addition, the nonlinear evolution of the growth rate of the GAM is observed, and there is a threshold in the amplitude of the GAM for the appearance of nonlinear behavior. A threshold in the amplitude of the EGAM for the abrupt excitation of the GAM is also observed. According to one theory (Lesur et al 2016 Phys. Rev. Lett. 116 015003, Itoh et al 2016 Plasma Phys. Rep. 42 418) the observed abrupt phenomenon can be interpreted as the excitation of the subcritical instability of the GAM. The excitation of a subcritical instability requires a trigger and a seed with sufficient amplitude. The observed threshold in the amplitude of the GAM seems to correspond with the threshold in the seed, and the threshold in the amplitude of the EGAM seems to correspond with the threshold in the magnitude of the trigger. Thus, the observed threshold supports the interpretation that the abrupt phenomenon is the excitation of a subcritical instability of the GAM.

In fusion plasmas, several mechanisms such as heating, wave-particle interaction etc can drive deviations of distribution function from Maxwelian to form phase space structures. This article discusses the impact of phase space structures in drift wave turbulence on dynamics and transport modeling. The two cases of (i) coherent holes and (ii) incoherent granulations (clusters of correlated resonant particles with finite life time) are treated. Their dynamical impact on driving subcritical instability is analyzed by explicitly calculating the nonlinear growth rate. The role of zonal flows is also addressed. It is explained how phase space structures can be related to transient events and non-diffusive transport, issues in current confinement research.

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

International audience; The nonlinear stability of current-driven ion-acoustic waves in collisionless electron-ion plasmas is analyzed. Seminal simulations from the 1980s are revisited. Accurate numerical treatment shows that subcritical instabilities do not grow from an ensemble of waves, except very close to marginal stability and for large initial amplitudes. Further from marginal stability, one isolated phase-space structure can drive subcritical instabilities by stirring the phase-space in its wake. Phase-space turbulence, which includes many structures, is much more efficient than an ensemble of waves or an isolated hole for driving subcritically particle redistribution, turbulent heating and anomalous resistivity. Phase-space jets are observed in subcritical simulations.

International audience; A novel theory to describe the formation of E x B flow patterns by radially propagating heat flux waves is presented. A model for heat avalanche dynamics is extended to include a finite delay time between the instantaneous heat flux and the mean flux, based on an analogy between heat avalanche dynamics and traffic flow dynamics. The response time introduced here is an analogue of the drivers' response time in traffic dynamics. The microscopic foundation for the time delay is the time for mixing of the phase space density. The inclusion of the finite response time changes the model equation for avalanche dynamics from Burgers equation to a nonlinear telegraph equation. Based on the telegraph equation, the formation of heat flux jams is predicted. The growth rate and typical interval of jams are calculated. The connection of the jam interval to the typical step size of the E x B staircase is discussed. (C) 2014 AIP Publishing LLC.

International audience; We present a new, unified model of transport barrier formation in ``elastic'' drift wave-zonal flow (DW-ZF) turbulence. A new physical quantity-the delay time (i.e., the mixing time for the DW turbulence)-is demonstrated to parameterize each stage of the transport barrier formation. Quantitative predictions for the onset of limit-cycle-oscillation (LCO) among DW and ZF intensities (also denoted as I-mode) and I-mode to high-confinement mode (H-mode) transition are also given. The LCO occurs when the ZF shearing rate (vertical bar < u >(ZF)'vertical bar) enters the regime Delta omega(k) < vertical bar < V >(ZF)'vertical bar < tau(-1)(cr), where Delta omega(k) is the local turbulence decorrelation rate and tau(cr) is the threshold delay time. In the basic predator-prey feedback system, tau(cr) is also derived. The I-H transition occurs when vertical bar < V >(ExB)'vertical bar > tau(-1)(cr), where the mean E x B shear flow driven by ion pressure ``locks'' the DW-ZF system to the H-mode by reducing the delay time below the threshold value. (C) 2014 AIP Publishing LLC.

Author(s): KOSUGA, Yusuke; ITOH, Sanae-I; DIAMOND, Patrick H; ITOH, Kimitaka; LESUR, Maxime

A theory to describe the conversion of poloidal momentum into toroidal momentum by phase space structures in trapped ion resonance driven turbulence is presented. In trapped ion resonance driven turbulence, phase space structures are expected to form and can contribute to transport by exerting dynamical friction. Toroidal momentum flux by dynamical friction is calculated. It is shown that dynamical friction exerted on trapped ion granulations can mediate momentum transfer between poloidal and toroidal flows. The conversion coefficient is calculated as measurable, which can be validated in current devices. © 2013 IOP Publishing Ltd.

We present a theory of turbulent elasticity, a property of drift-wave--zonal-flow (DW-ZF) turbulence, which follows from the time delay in the response of DWs to ZF shears. An emergent dimensionless parameter ${|\ensuremath{\langle}v\ensuremath{\rangle}}^{\ensuremath{'}}|/\ensuremath{\Delta}{\ensuremath{\omega}}_{k}$ is found to be a measure of the degree of Fickian flux-gradient relation breaking, where ${|\ensuremath{\langle}v\ensuremath{\rangle}}^{\ensuremath{'}}|$ is the ZF shearing rate and $\ensuremath{\Delta}{\ensuremath{\omega}}_{k}$ is the turbulence decorrelation rate. For ${|\ensuremath{\langle}v\ensuremath{\rangle}}^{\ensuremath{'}}|/\ensuremath{\Delta}{\ensuremath{\omega}}_{k}g1$, we show that the ZF evolution equation is converted from a diffusion equation, usually assumed, to a telegraph equation, i.e., the turbulent momentum transport changes from a diffusive process to wavelike propagation. This scenario corresponds to a state very close to the marginal instability of the DW-ZF system, e.g., the Dimits shift regime. The frequency of the ZF wave is ${\ensuremath{\Omega}}_{\mathrm{ZF}}=\ifmmode\pm\else\textpm\fi{}{\ensuremath{\gamma}}_{d}^{1/2}{\ensuremath{\gamma}}_{\mathrm{modu}}^{1/2}$, where ${\ensuremath{\gamma}}_{d}$ is the ZF friction coefficient and ${\ensuremath{\gamma}}_{\mathrm{modu}}$ is the net ZF growth rate for the case of the Fickian flux-gradient relation. This insight provides a natural framework for understanding temporally periodic ZF structures in the Dimits shift regime and in the transition from low confined mode to high confined mode in confined plasmas.

An overview of the physics of intrinsic torque is presented, with special emphasis on the phenomenology of intrinsic toroidal rotation in tokamaks, its theoretical understanding, and the variety of momentum transport bifurcation dynamics. Ohmic reversals and electron cyclotron heating-driven counter torque are discussed in some detail. Symmetry breaking by lower single null versus upper single null asymmetry is related to the origin of intrinsic torque at the separatrix. (Some figures may appear in colour only in the online journal)

International audience; Simple flux-gradient relations that involve time delay and radial coupling are discussed. Such a formulation leads to a rather simple description of avalanches and may explain breaking of gyroBohm transport scaling. The generalization of the flux-gradient relation (i.e., constitutive relation), which involve both time delay and spatial coupling, is derived from drift-kinetic equation, leading to kinetic definitions of constitutive elements such as the flux of radial heat flux. This allows numerical simulations to compute these cubic quantities directly. The formulation introduced here can be viewed as an extension of turbulence spreading to include the effect of spreading of cross-phase as well as turbulence intensity, combined in such a way to give the flux. The link between turbulence spreading and entropy production is highlighted. An extension of this formulation to general quasi-linear theory for the distribution function in the phase space of radial position and parallel velocity is also discussed.

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.

In collisionless plasma, it is known that linearly stable modes can be destabilized (subcritically) by the presence of structures in phase-space. The growth of such structures is a nonlinear, kinetic mechanism, which provides a channel for free-energy extraction, different from conventional inverse Landau damping. However, such nonlinear growth requires the presence of a seed structure with a relatively large threshold in amplitude. We demonstrate that, in the presence of another, linearly unstable (supercritical) mode, wave–wave coupling can provide a seed, which can lead to subcritical instability by either one of two mechanisms. Both mechanisms hinge on a collaboration between fluid nonlinearity and kinetic nonlinearity. If collisional velocity diffusion is low enough, the seed provided by the supercritical mode overcomes the threshold for nonlinear growth of phase-space structure. Then, the supercritical mode triggers the conventional subcritical instability. If collisional velocity diffusion is too large, the seed is significantly below the threshold, but can still grow by a sustained collaboration between fluid and kinetic nonlinearities. Both of these subcritical instabilities can be triggered, even when the frequency of the supercritical mode is rapidly sweeping. These results were obtained by modeling the subcritical mode kinetically, and the impact of the supercritical mode by simple wave–wave coupling equations. This model is applied to bursty onset of geodesic acoustic modes in an LHD experiment. The model recovers several key features such as relative amplitude, timescales, and phase relations. It suggests that the strongest bursts are subcritical instabilities, with sustained collaboration between fluid and kinetic nonlinearities.

The influence of relative displacement of Mach probe (which is placed near the top of magnetic surface) on the interference of signals is discussed. An error can arise in measured value of poloidal electric field. The Mach number perturbation at the GAM frequency has an interference from the density perturbation. The interference from the density perturbation can propagate to all of Mach number measurement. By observing the signals associated with GAM oscillations, the error in setting the probe arrays can be detected. This result can be applied to correct the positioning of probes.

International audience; We propose a novel mechanism to describe E×B flow pattern formation based upon the dynamics of propagation of heat-flux modulations. The E×B flows of interest are staircases, which are quasiregular patterns of strong, localized shear layers and profile corrugations interspersed between regions of avalanching. An analogy of staircase formation to jam formation in traffic flow is used to develop an extended model of heat avalanche dynamics. The extension includes a flux response time, during which the instantaneous heat flux relaxes to the mean heat flux, determined by symmetry constraints. The response time introduced here is the counterpart of the drivers’ response time in traffic, during which drivers adjust their speed to match the background traffic flow. The finite response time causes the growth of mesoscale temperature perturbations, which evolve to form profile corrugations. The length scale associated with the maximum growth rate scales as Δ2∼(vthi/λTi)ρi√χneoτ, where λTi is a typical heat pulse speed, χneo is the neoclassical thermal diffusivity, and τ is the response time of the heat flux. The connection between the scale length Δ2 and the staircase interstep scale is discussed.