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The mission of HL-2A is to explore the key physical topics relevant to ITER and to the advanced tokamak operation (e.g. the operation of future HL-2M), such as the access of H-mode, energetic particle physics, edge-localized mode (ELM) mitigation/suppression and disruption mitigation. Since the 2016 Fusion Energy Conference, the HL-2A team has focused on the investigations on the following areas: (i) pedestal dynamics and L-H transition, (ii) techniques of ELM control, (iii) turbulence and transport, (iv) energetic particle physics. The HL-2A results demonstrated that the increase of mean shear flow plays a key role in triggering L-I and I-H transitions, while the change of flow is mainly induced by the ion pressure gradient. Both mitigation and suppression of ELMs were realized by laser blow-off seeded impurity (Al, Fe, W). The 30% Ne mixture supersonic molecular beam injection seeding also robustly induced ELM mitigation. The ELMs were mitigated by low-hybrid current drive. The stabilization of m/n = 1/1 ion fishbone activities by electron cyclotron resonance heating was found on the HL-2A. A new m/n = 2/1 ion fishbone activity was observed recently, and the modelling indicated that passing fast ions dominantly contribute to the driving of 2/1 fishbone. The non-linear coupling between the toroidal Alfven eigenmode and tearing mode (TM) led to the generation of a high frequency mode with the toroidal mode number n = 0. The turbulence was modulated by TM when the island width exceeds a threshold and the modulation is localized merely in the inner area of the islands. Meanwhile, turbulence radial spread took place across the island region.

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.

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.

Trapped ion resonance-driven turbulence is investigated in the presence of electron dissipation in a simplified tokamak geometry. A reduced gyrokinetic bounce-averaged model for trapped ions is adopted. Electron dissipation is modeled by a simple phase-shift δ between density and electric potential perturbations. The linear eigenfunction features a peak at the resonant energy, which becomes stronger with increasing electron dissipation. Accurately resolving this narrow peak in numerical simulation of the initial-value problem yields a stringent lower bound on the number of grid points in the energy space. Further, the radial particle flux is investigated in the presence of electron dissipation, including kinetic effects. When the density gradient is higher than the temperature gradient, and the phase-shift is finite but moderate (δ≈0.02), the particle flux peaks at an order-of-magnitude above the gyro-Bohm estimate. Slight particle pinch is observed for δ

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.

A theory to describe basic characterization of ion temperature gradient driven turbulence with strong trapped ion resonance is presented. The role of trapped ion granulations, clusters of trapped ions correlated by precession resonance, is the focus. Microscopically, the presence of trapped ion granulations leads to a sharp (logarithmic) divergence of two point phase space density correlation at small scales. Macroscopically, trapped ion granulations excite potential fluctuations that do not satisfy dispersion relation and so broaden frequency spectrum. The line width from emission due only to trapped ion granulations is calculated. The result shows that the line width depends on ion free energy and electron dissipation, which implies that non-adiabatic electrons are essential to recover non-trivial dynamics of trapped ion granulations. Relevant testable predictions are summarized.

Transitions between low (L-mode) and intermediate (I-phase) confinement regimes triggered by sawteeth are investigated using multiple Langmuir probe arrays in the edge plasmas of the HL-2A tokamak. The I-phase is characterized by limit-cycle oscillations (LCOs). Repeated L-I-L transitions induced by sawtooth heat pulses are also observed. Statistical analyses show that the delay time of the L-I transition relative to sawtooth crashes is less than ∼1 ms. The intensity of turbulence bursts in the I-phase is stronger than those observed in L-mode plasmas. Measurements are consistent with zonal flow reducing turbulence intensity in the frequency band ∼20-100 kHz, while the LCO turbulence of frequency higher than 100 kHz has more power than that in the L-mode. The analyses of time-resolved power transfers between turbulence and zonal flows suggest that power transfers exist between turbulence and zonal flows. The direction of the power transfers is from turbulence into geodesic acoustic modes in ohmic plasmas. © 2013 IAEA, Vienna.

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.

The radial structures of multiple sheared flow populations and fluctuations are simultaneously measured using combinations of Langmuir probe arrays in the edge plasmas of the HL-2A tokamak with ohmic and electron cyclotron resonance heating (ECRH). The maximum of geodesic acoustic mode (GAM) amplitude locates at ∼2-3 cm inside the last close flux surface (LCFS). The low-frequency zonal flow (LFZF) and GAM tend to coexist in the inner region. The dependences of the amplitudes of the multiple sheared flows and turbulence on ECRH heating power are also investigated. The measured turbulent Reynolds stresses are shown to be strongly correlated with the sheared flows, as predicted by theory. The turbulence is modulated at the each frequency of the multiple sheared flows simultaneously, and the particle fluxes induced by the turbulence are significantly reduced near the LCFS and in the GAM peaking region. The analyses also show that the spatial structures of the turbulent envelopes at the LFZF and GAM frequencies are similar to those observed in LFZF and GAM. © 2013 IAEA, Vienna.

The experimental studies on zonal flows and turbulence have been carried out in Compact Helical System [K. Matsuoka, S. Kubo, M. Hosokawa, in Plasma Physics and Controlled Nuclear Fusion Research, Proc. 12th Int. Conf., Nice, 1988 (International Atomic Energy Agency, Vienna, 1989, Vol. 2, p. 411] using twin heavy ion beam probes. The paper presents the experimental observations of stationary zonal flow, nonlinear couplings between zonal flow and turbulence, and the role of zonal flow in the improved confinement, together with the recent discovery of zonal magnetic field. The presented experimental results strongly support the new paradigm that the plasma transport should be considered as a system of drift wave and zonal flows, and provides the first direct evidence for turbulence dynamo that the structured magnetic field can be really generated by turbulence. © 2008 American Institute of Physics.

The present status of experiments on zonal flows in magnetic confinement experiments is examined. The innovative use of traditional and modern diagnostics has revealed unambiguously the existence of zonal flows, their spatio-temporal characteristics, their relationship to turbulence and their effects on confinement. In particular, a number of observations have been accumulated on the oscillatory branch of zonal flows, named geodesic acoustic modes, suggesting the necessity for theories to give their proper description. In addition to these basic properties of zonal flows, several new methods have elucidated the processes of zonal flow generation from turbulence. Further investigation of the relationship between zonal flows and confinement is strongly encouraged as cross-device activity including low temperature, toroidal and linear devices. © 2007 IAEA.

A zonal magnetic field is found in a toroidal plasma. The magnetic field has a symmetric bandlike structure, which is uniform in the toroidal and poloidal directions and varies radially with a finite wavelength of mesoscale, which is analogous to zonal flows. A time-dependent bicoherence analysis reveals that the magnetic field should be generated by the background plasma turbulence. The discovery is classified as a new kind of phenomenon of structured magnetic field generation, giving insight into phenomena such as dipole field generation in rotational planets.

The role of zonal flows (ZFs) in the formation of an internal transport barrier in a toroidal helical plasma is analyzed. The turbulent transport coefficient is shown to be suppressed when the plasma state changes from the branch of a weak negative radial electric field to the strong positive one. This new transition of turbulent transport is caused by the change of the damping rate of the ZFs. It is clearly demonstrated, theoretically and experimentally, that the damping rate of the ZFs governs the global confinement of toroidal plasmas. © 2007 American Institute of Physics.

Zonal flows, which means azimuthally symmetric band-like shear flows, are ubiquitous phenomena in nature and the laboratory. It is now widely recognized that zonal flows are a key constituent in virtually all cases and regimes of drift wave turbulence, indeed, so much so that this classic problem is now frequently referred to as "drift wave-zonal flow turbulence." In this review, new viewpoints and unifying concepts are presented, which facilitate understanding of zonal flow physics, via theory, computation and their confrontation with the results of laboratory experiment. Special emphasis is placed on identifying avenues for further progress. © 2006 American Institute of Physics.

This is a report on fluctuation measurements using twin heavy ion beam probes in CHS. The observation shows that dozens of coherent modes with intermittent nature co-exist in an electron cyclotron heated plasma. The modes are found to have a long-distance correlation in the toroidal direction. The radial structure of the modes is evaluated in potential fluctuation. The characteristics are consistent with those of the geodesic acoustic modes. © 2006 IOP Publishing Ltd.

The bicoherence of fluctuations in a system of drift waves and zonal flows is discussed. In strong drift-wave turbulence, where broadband fluctuations are excited, the bicoherence is examined. A Langevin equation formalism of turbulent interactions allows us to relate the bicoherence coefficient to the projection of nonlinear force onto the test mode. The dependence of the summed bicoherence on the amplitude of zonal flows is clarified. The importance of observing biphase is also stressed. The results provide a basis for measurement of nonlinear interaction in a system of drift waves and zonal flow. © 2005 American Institute of Physics.

The influence of the turbulence spreading is studied on the self-sustained turbulence which is induced by the subcritical instability. It is found that there is a minimum system size that can sustain the self-sustained turbulence, and an analytic formula is derived. The generalization of the Maxwell's construction rule is also derived. ©2005 The Physical Society of Japan.

Excitation of the turbulence in the range of drift wave frequency and zonal flow in magnetized plasmas is analyzed. Nonlinear stabilization effect on zonal flow drive is introduced, and the steady state solution is obtained. The condition for the onset of turbulent transport is obtained and partition ratio of fluctuation energy into turbulence and zonal flows is derived. The turbulent transport coefficient, which includes the effect of zonal flow, is also obtained. Analytic result and direct numerical simulation show a good agreement. © 2005 American Institute of Physics.

A comprehensive review of zonal flow phenomena in plasmas is presented. While the emphasis is on zonal flows in laboratory plasmas, planetary zonal flows are discussed as well. The review presents the status of theory, numerical simulation and experiments relevant to zonal flows. The emphasis is on developing an integrated understanding of the dynamics of drift wave-zonal flow turbulence by combining detailed studies of the generation of zonal flows by drift waves, the back-interaction of zonal flows on the drift waves, and the various feedback loops by which the system regulates and organizes itself. The implications of zonal flow phenomena for confinement in, and the phenomena of fusion devices are discussed. Special attention is given to the comparison of experiment with theory and to identifying directions for progress in future research. © 2005 IOP Publishing Ltd.

This Letter presents experimental confirmation of the presence of zonal flows in magnetically confined toroidal plasma using an advanced diagnostic system--dual heavy ion beam probes. The simultaneous observation of an electric field at two distant toroidal locations (approximately 1.5 m apart) in the high temperature (approximately 1 keV) plasma provides a fluctuation spectrum of electric field (or flow), a spatiotemporal structure of the zonal flows (characteristic radial length of approximately 1.5 cm and lifetime of approximately 1.5 ms), their long-range correlation with toroidal symmetry (n=0), and the difference in the zonal flow amplitude with and without a transport barrier. These constitute essential elements of turbulence-zonal flow systems, and illustrate one of the fundamental processes of structure formation in nature.

We study the simplest problem of turbulence spreading corresponding to the spatio-temporal propagation of a patch of turbulence from a region where it is locally excited to a region of weaker excitation or even local damping. A single model equation for the local turbulence intensity, I(x, t), includes the effects of local linear growth and damping, spatially local nonlinear coupling to dissipation and spatial scattering of turbulence energy induced by nonlinear coupling. In the absence of dissipation, front propagation into the linearly stable zone occurs with the property of rapid progression at small t, followed by slower sub-diffusive progression at late times. The turbulence radial spreading into the linearly stable zone reduces the turbulent intensity in the linearly unstable zone and introduces an additional dependence on the ρ* ≡ ρi/a to the turbulent intensity and the transport scaling. These are in broad, semi-quantitative agreement with a number of global gyrokinetic simulation results with zonal flows and without zonal flows. Front propagation stops when the radial flux of fluctuation energy from the linearly unstable region is balanced by local dissipation in the linearly stable region.

Two examples of non-perturbative models of intermittency in drift-wave (DW) turbulence are presented. The first is a calculation of the probability distribution function (PDF) of ion heat flux due to structures in ion temperature gradient turbulence. The instanton calculus predicts the PDF to be a stretched exponential. The second is a derivation of a bi-variate Burgers equation for the evolution of the DW population density in the presence of radially extended streamer flows. The PDF of fluctuation intensity avalanches is determined. The relation of this to turbulence spreading, observed in simulations, is discussed.