Showing papers by "Patrick Diamond published in 2015"

Finding the Elusive E×B Staircase in Magnetized Plasmas

Abstract: 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.

Towards an emerging understanding of non-locality phenomena and non-local transport

Abstract: 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

Zonal flows and pattern formation

Abstract: The general aspects of zonal flow physics, their formation, damping and interplay with quasi two dimensional turbulence are explained in the context of magnetized plasmas and quasi-geostrophic fluids with an emphasis on formation and selection of spatial patterns. General features of zonal flows as they appear in planetary atmospheres, rotating convection experiments and fusion plasmas are reviewed. Detailed mechanisms for excitation and damping of zonal flows, and their effect on turbulence via shear decorrelation is discussed. Recent results on nonlocality and staircase formation are outlined.

Towards an emerging understanding of non-locality phenomena and non-local transport

Abstract: 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

The negative triangularity tokamak: stability limits and prospects as a fusion energy system

Abstract: The paper discusses edge stability, beta limits and power handling issues for negative triangularity tokamaks. The edge magnetohydrodynamic stability is the most crucial item for power handling. For the case of negative triangularity the edge stability picture is quite different from that for conventional positive triangularity tokamaks: the second stability access is closed for localized Mercier/ballooning modes due to the absence of a magnetic well, and nearly internal kink modes set the pedestal height limit to be weakly sensitive to diamagnetic stabilization just above the margin of the localized mode Mercier criterion violation. While a negative triangularity tokamak is thought to have a low beta limit with its magnetic hill property, it is found that plasmas with reactor-relevant values of normalized beta beta(N) > 3 can be stable to global kink modes without wall stabilization with appropriate core pressure profile optimization against localized mode stability, and also with increased magnetic shear in the outer half-radius. The beta limit is set by the n = 1 mode for the resulting flat pressure profile. The wall stabilization is very inefficient due to strong coupling between external and internal modes. The n > 1 modes are increasingly internal when approaching the localized mode limit, and set a lower beta in the case of the peaked pressure profile leading to a Mercier unstable core. With the theoretical predictions supported by experiments, a negative triangularity tokamak would become a prospective fusion energy system with other advantages including a larger separatrix wetted area, more flexible divertor configuration design, wider trapped particle-free scrape-off layer, lower background magnetic field for internal poloidal field coils, and larger pumping conductance from the divertor room.

Overview of the recent research on the J-TEXT tokamak

Abstract: The experimental research over last two years on the J-TEXT tokamak is summarized and presented in the paper. The high-performance polarimeter-interferometer developed on J-TEXT, aiming to measure electron density and Faraday angle simultaneously, has time response up to 1 µs, phase resolution <0.1° and spatial resolution ~3 cm. Such high resolution permits investigations of fast equilibrium dynamics as well as magnetic and density perturbations associated with magnetohydrodynamic instabilities. Particle transport due to the sawtooth crashes is analysed. The sawteeth only partially flatten the core density profile and recovery between crashes implies an inward pinch velocity extending to the centre. The resonant magnetic perturbation (RMP) system on J-TEXT can generate a rotating helical field perturbation with a maximum rotation frequency up to 6 kHz, and dominant resonant modes of m/n = 2/1, 3/1 or 1/1. It is found that tearing modes can be easily locked and then rotate together with a rotating RMP. The effects of RMPs on plasma flows and fluctuations are studied with Langmuir probe arrays at the plasma edge. The toroidal velocity increases and the radial electric field decreases with RMP coil current when the RMP current is no more than 5 kA. When the RMP current reaches 6 kA, the toroidal velocity profile becomes flattened near the last closed flux surface. The geodesic acoustic mode is damped in most of the edge region, while the low frequency zonal flow is damped inside the islands, but increases at its boundary.

From phase locking to phase slips: a mechanism for a quiescent H mode.

Abstract: We demonstrate that E×B shear, V_{E×B}^{'}, governs the dynamics of the cross phase of the peeling-ballooning-(PB-)mode-driven heat flux, and so determines the evolution from the edge-localized (ELMy) H mode to the quiescent (Q) H mode. A physics-based scaling of the critical E×B shearing rate (V_{E×B,cr}^{'}) for accessing the QH mode is predicted. The ELMy H mode to the QH-mode evolution is shown to follow from the conversion from a phase locked state to a phase slip state. In the phase locked state, PB modes are pumped continuously, so bursts occur. In the slip state, the PB activity is a coherent oscillation. Stronger E×B shearing implies a higher phase slip frequency. This finding predicts a new state of cross phase dynamics and shows a new way to understand the physics mechanism for ELMy to the QH-mode evolution.

Plasma flows and fluctuations with magnetic islands in the edge plasmas of J-TEXT tokamak

Abstract: The first comprehensive measurements of plasma flows and fluctuations nearby static magnetic islands driven by resonant magnetic perturbations are presented. These experiments were performed using multiple Langmuir probe arrays on the edge plasmas of the J-TEXT tokamak. Controlled variations of the island size and location are explored. This study aims to understand the interaction between turbulence and magnetic islands, and to elucidate magnetic island effects on edge turbulence and flow intensity profiles, edge electric fields, and thus confinement regime transitions. Turbulence and low frequency flows (LFFs) all drop inside the magnetic island, but increase at its boundary, as island width increases. The geodesic acoustic mode is damped in most of the edge area with magnetic islands. The sign of the radial electric field changes from negative to positive within the islands. The gradient of turbulent stresses vanishes at the island center, and becomes steeper at the boundaries of the islands. The particle transport induced by the turbulence is reduced inside the magnetic islands. The magnetic island effects on flows and turbulence can lead to an increase in LFFs and enhance Reynolds stresses near the last closed flux surface (LCFS). A stronger radial electric field layer can be formed near the LCFS when magnetic islands are present. The results suggest that magnetic islands can be used as a tool to enhance edge turbulence and flows, edge electric fields, and thus to trigger confinement regime transitions.

Direct identification of predator-prey dynamics in gyrokinetic simulations

Abstract: The interaction between spontaneously formed zonal flows and small-scale turbulence in nonlinear gyrokinetic simulations is explored in a shearless closed field line geometry. It is found that when clear limit cycle oscillations prevail, the observed turbulent dynamics can be quantitatively captured by a simple Lotka-Volterra type predator-prey model. Fitting the time traces of full gyrokinetic simulations by such a reduced model allows extraction of the model coefficients. Scanning physical plasma parameters, such as collisionality and density gradient, it was observed that the effective growth rates of turbulence (i.e., the prey) remain roughly constant, in spite of the higher and varying level of primary mode linear growth rates. The effective growth rate that was extracted corresponds roughly to the zonal-flow-modified primary mode growth rate. It was also observed that the effective damping of zonal flows (i.e., the predator) in the parameter range, where clear predator-prey dynamics is observed, (i.e., near marginal stability) agrees with the collisional damping expected in these simulations. This implies that the Kelvin-Helmholtz-like instability may be negligible in this range. The results imply that when the tertiary instability plays a role, the dynamics becomes more complex than a simple Lotka-Volterra predator prey.

Flux-driven simulations of turbulence collapse

Abstract: Using three-dimensional nonlinear simulations of tokamak turbulence, we show that an edge transport barrier (ETB) forms naturally once input power exceeds a threshold value. Profiles, turbulence-driven flows, and neoclassical coefficients are evolved self-consistently. A slow power ramp-up simulation shows that ETB transition is triggered by the turbulence-driven flows via an intermediate phase which involves coherent oscillation of turbulence intensity and E×B flow shear. A novel observation of the evolution is that the turbulence collapses and the ETB transition begins when RT > 1 at t = tR (RT: normalized Reynolds power), while the conventional transition criterion ( ωE×B>γlin where ωE×B denotes mean flow shear) is satisfied only after t = tC ( >tR), when the mean flow shear grows due to positive feedback.

Linking the micro and macro: L-H transition dynamics and threshold physics

Abstract: The links between the microscopic dynamics and macroscopic threshold physics of the L → H transition are elucidated. Emphasis is placed on understanding the physics of power threshold scalings, and especially on understanding the minimum in the power threshold as a function of density Pthr (n). By extending a numerical 1D model to evolve both electron and ion temperatures, including collisional coupling, we find that the decrease in Pthr (n) along the low-density branch is due to the combination of an increase in collisional electron-to-ion energy transfer and an increase in the heating fraction coupled to the ions. Both processes strengthen the edge diamagnetic electric field needed to lock in the mean electric field shear for the L→H transition. The increase in Pthr (n) along the high-density branch is due to the increase with ion collisionality of damping of turbulence-driven shear flows. Turbulence driven shear flows are needed to trigger the transition by extracting energy from the turbulence. Thus, we identify the critical transition physics components of the separatrix ion heat flux and the zonal flow excitation. The model reveals a power threshold minimum in density scans as a crossover between the threshold decrease supported by an increase in heat fraction received by ions (directly or indirectly, from electrons) and a threshold increase, supported by the rise in shear flow damping. The electron/ion heating mix emerges as important to the transition, in that it, together with electron-ion coupling, regulates the edge diamagnetic electric field shear. The importance of possible collisionless electron-ion heat transfer processes is explained.

Particle transport in low-collisionality H-mode plasmas on DIII-D

Abstract: In this paper we show that changing from an ion temperature gradient (ITG) to a trapped electron mode (TEM) dominant turbulence regime (based on linear gyrokinetic simulations) results experimentally in a strong density pump-out (defined as a reduction in line-averaged density) in low collisionality, low power H-mode plasmas. We vary the turbulence drive by changing the heating from predominantly ion heated using neutral beam injection to electron heated using electron cyclotron heating, which changes the ratio and the temperature gradients. Perturbed gas puff experiments show an increase in transport outside , through a strong increase in the perturbed diffusion coefficient and a decrease in the inward pinch. Linear gyrokinetic simulations with TGLF show an increase in the particle flux outside the mid-radius. In conjunction an increase in intermediate-scale length density fluctuations is observed, which indicates an increase in turbulence intensity at typical TEM wavelengths. However, although the experimental changes in particle transport agree with a change from ITG to TEM turbulence regimes, we do not observe a reduction in the core rotation at mid-radius, nor a rotation reversal.

Nonlinear transfer in heated L-modes approaching the L–H transition threshold in Alcator C-Mod

Abstract: Nonlinear transfer processes between large-scale edge flows and the ambient broadband fluctuations have been shown to play a significant role in the dynamics of edge turbulence, including spreading power from coherent modes and suppressing turbulence at the formation of edge transport barriers. In order to predict thresholds of confinement regimes, both the transition dynamics and the parametric dependence of the nonlinear energy transfer must be studied. Since the expected flow damping terms depend on ion collision rates and local safety factors, recent experiments aimed also to explore the nonlinear drive at various values of the plasma current, density and amount of auxiliary heating. Nonlinear interactions between zonal flows and turbulence in L-mode are estimated using bispectral as well as time-resolved methods based on gas-puff-imaging in Alcator C-Mod [1].

Up-gradient particle flux in a drift wave-zonal flow system

Abstract: We report a net inward, up-gradient turbulent particle flux in a cylindrical plasma when collisional drift waves generate a sufficiently strong sheared azimuthal flow that drives positive (negative) density fluctuations up (down) the background density gradient, resulting in a steepening of the mean density gradient. The results show the existence of a saturation mechanism for drift-turbulence driven sheared flows that can cause up-gradient particle transport and density profile steepening.

Intrinsic torque reversals induced by magnetic shear effects on the turbulence spectrum in tokamak plasmasa)

Abstract: Intrinsic torque, which can be generated by turbulent stresses, can induce toroidal rotation in a tokamak plasma at rest without direct momentum injection. Reversals in intrinsic torque have been inferred from the observation of toroidal velocity changes in recent lower hybrid current drive (LHCD) experiments. This work focuses on understanding the cause of LHCD-induced intrinsic torque reversal using gyrokinetic simulations and theoretical analyses. A new mechanism for the intrinsic torque reversal linked to magnetic shear ( s) effects on the turbulence spectrum is identified. This reversal is a consequence of the ballooning structure at weak s. Based on realistic profiles from the Alcator C-Mod LHCD experiments, simulations demonstrate that the intrinsic torque reverses for weak s discharges and that the value of scrit is consistent with the experimental results scritexp≈0.2∼0.3 [Rice et al., Phys. Rev. Lett. 111, 125003 (2013)]. The consideration of this intrinsic torque feature in our work is imp...

Ion temperature and toroidal velocity edge transport barriers in KSTAR

Abstract: The structure and evolution of the ion temperature () and toroidal rotation () profile have been investigated in neutral beam injection (NBI)-heated KSTAR H-mode plasmas, both without and with resonant magnetic pertubations (RMPs). A clear disparity between the width of the -pedestal and that of the -pedestal was observed. Also, it was found that there exists a close correlation and weak relative hysteresis between the pedestal and during both L → H and H → L transitions. During the L → H transition, the -pedestal is observed to form ahead of the -pedestal, and build inward from the separatrix. Linear gyrokinetic stability analysis of these KSTAR profiles was performed. The results indicate that parallel velocity shear is a relevant drive for pedestal turbulence and transport. This was largely ignored in previous studies of the pedestal micro-stability. Pedestal ion temperature and rotation profiles were also measured during edge localized mode (ELM) suppression experiments on KSTAR using an n = 1 RMPs. It was found that the top values of the ion temperature and toroidal rotation pedestal drop with RMPs when ELMs are suppressed.

Effects of q-profile structures on intrinsic torque reversals

Abstract: Changes in rotation have been observed in LHCD experiments. From these observations, reversals in intrinsic torque have been inferred. This paper identifies the mechanism for intrinsic torque reversal linked to magnetic shear (). Gyrokinetic simulations demonstrate that as compared to the normal case, the intrinsic torque reverses, for . Analysis shows that the reversal occurs due to the dominance of the symmetry breaking mechanism in residual stress due to the synergy of toroidal coupling and the intensity gradient. This mechanism is a consequence of ballooning structure at weak . Gyrokinetic simulation gives for trapped electron modes (TEM) and for ion temperature gradient (ITG) modes. The value of is consistent with results from the Alcator C-Mod LHCD experiments, for which in the whole plasma column and (Rice et al Phys. Rev. Lett. 111 125003).

Turbulence spreading as a non-local mechanism of global confinement degradation and ion temperature profile stiffness

Abstract: A new non-local mechanism of the global confinement degradation and ion temperature profile stiffness is proposed based on the results of global gyrokinetic simulations. We find that turbulence spreading into a marginally stable zone can increase turbulent transport to a level exceeding the predictions of the local theories. Also, we present the first quantification of the parametric dependence of turbulence spreading and resulting confinement degradation on toroidal rotation shear and magnetic shear: turbulence spreading is significant for high magnetic shears s > 0.2, while it is slowed for low magnetic shears. The suppression of turbulence spreading by toroidal rotation shear is only effective for the low magnetic shears, which is in a good agreement with the experimental trends of core confinement improvement. Our findings suggest that the non-local mechanism is indispensable for accurate transport modeling in tokamak plasmas.

Nonlinear parallel momentum transport in strong electrostatic turbulence

Abstract: Most existing theoretical studies of momentum transport focus on calculating the Reynolds stress based on quasilinear theory, without considering the nonlinear momentum flux- ⟨vrnu∥⟩. However, a recent experiment on TORPEX found that the nonlinear toroidal momentum flux induced by blobs makes a significant contribution as compared to the Reynolds stress [Labit et al., Phys. Plasmas 18, 032308 (2011)]. In this work, the nonlinear parallel momentum flux in strong electrostatic turbulence is calculated by using a three dimensional Hasegawa-Mima equation, which is relevant for tokamak edge turbulence. It is shown that the nonlinear diffusivity is smaller than the quasilinear diffusivity from Reynolds stress. However, the leading order nonlinear residual stress can be comparable to the quasilinear residual stress, and so may be important to intrinsic rotation in tokamak edge plasmas. A key difference from the quasilinear residual stress is that parallel fluctuation spectrum asymmetry is not required for non...

Nonlinear parallel momentum transport in strong turbulence

Abstract: Most existing theoretical studies of momentum transport focus on calculating the Reynolds stress based on quasilinear theory, without considering the \emph{nonlinear} momentum flux-$ $. However, a recent experiment on TORPEX found that the nonlinear toroidal momentum flux induced by blobs makes a significant contribution as compared to the Reynolds stress [Labit et al., Phys. Plasmas {\bf 18}, 032308 (2011)]. In this work, the nonlinear parallel momentum flux in strong turbulence is calculated by using three dimensional Hasegawa-Mima equation. It is shown that nonlinear diffusivity is smaller than quasilinear diffusivity from Reynolds stress. However, the leading order nonlinear residual stress can be comparable to the quasilinear residual stress, and so could be important to intrinsic rotation in tokamak edge plasmas. A key difference from the quasilinear residual stress is that parallel fluctuation spectrum asymmetry is not required for nonlinear residual stress.

Small scale coherent vortex generation in drift wave-zonal flow turbulence

Abstract: We present a paradigm for the generation of small scale coherent vortex (SSCV) in drift wave-zonal flow (DW-ZF) turbulence. We demonstrate that phases of DWs can couple coherently, mediated by the ZF shearing. A SSCV is formed when the phases of the DWs are “attracted” to form a stable “phase cluster.” We show that the ZF shearing induces asymmetry between “attractive” and “repulsive” phase couplings, so that a net attractive phase coupling results. The turbulent DWs will (partially)synchronize into a stable SSCV at locations, where the attractive phase coupling induced by the ZF shearing exceeds the “detuning” effects by the DW dispersion and random phase scattering. We also discuss the “self-binding” effect of the newly formed SSCV.

Ion-acoustic Shocks with Self-Regulated Ion Reflection and Acceleration

Abstract: An analytic solution describing an ion-acoustic collisionless shock, self-consistently with the evolution of shock-reflected ions, is obtained. The solution extends the classic soliton solution beyond a critical Mach number, where the soliton ceases to exist because of the upstream ion reflection. The reflection transforms the soliton into a shock with a trailing wave and a foot populated by the reflected ions. The solution relates parameters of the entire shock structure, such as the maximum and minimum of the potential in the trailing wave, the height of the foot, as well as the shock Mach number, to the number of reflected ions. This relation is resolvable for any given distribution of the upstream ions. In this paper, we have resolved it for a simple "box" distribution. Two separate models of electron interaction with the shock are considered. The first model corresponds to the standard Boltzmannian electron distribution in which case the critical shock Mach number only insignificantly increases from M=1.6 (no ion reflection) to M=1.8 (substantial reflection). The second model corresponds to adiabatically trapped electrons. They produce a stronger increase, from M=3.1 to M=4.5. The shock foot that is supported by the reflected ions also accelerates them somewhat further. A self-similar foot expansion into the upstream medium is also described analytically.

Rotation and momentum transport in magnetized plasmas

Abstract: The Atmospheric Wave-Turbulence Jigsaw (Michael E McIntyre) A Review of the Possible Role of Constraints in MHD Turbulence (Annick Pouquet) Dynamics of Structures in Configuration Space and Phase Space: A Tutorial (P H Diamond, Y Kosuga and M Lesur) Fast Dynamos (D W Hughes) The Effect of Flow on Ideal Magnetohydrodynamic Balooning Instabilities (H R Wilson, P B Buxton and J W Connor) Color Figures Elements of Neoclassical Theory and Plasma Rotation in a Tokamak (A Smolyakov) The General Fishbone Like Dispersion Relation (Fulvio Zonca) What is a Reversed Field Pinch? (D F Escande)

Perspective of Negative Triangularity Tokamak as Fusion Energy System

Abstract: Keywords: nuclear fusion ; tokamak ; magnetic confinement Reference EPFL-CONF-217063 URL: http://www.ipfn.ist.utl.pt/EPS2015/ URL: https://crpplocal.epfl.ch/pinboard/papers/154812701.pdf Record created on 2016-03-02, modified on 2017-05-12

On calculating the potential vorticity flux

Abstract: We discuss and compare different approaches to calculating the dynamics of anisotropic flow structure formation in quasi two-dimensional turbulence based on potential vorticity (PV) transport in real space. The general structure of the PV flux in the relaxation processes is deduced non-perturbatively. The transport coefficients of the PV flux are then systematically calculated using perturbation theory. We develop two non-perturbative relaxation models: the first is a mean field theory for the dynamics of minimum enstrophy relaxation based on the requirement that the mean flux of PV dissipates total potential enstrophy but conserves total fluid kinetic energy. The results show that the structure of PV flux has the form of a sum of a positive definite hyper-viscous and a negative or positive viscous flux of PV. Turbulence spreading is shown to be related to PV mixing via the link of turbulence energy flux to PV flux. In the relaxed state, the ratio of the PV gradient to zonal flow velocity is homogenized. This homogenized quantity sets a constraint on the amplitudes of PV and zonal flow in the relaxed state. The second relaxation model is derived from symmetry principles alone. The form of PV flux contains a nonlinear convective term in addition to viscous and hyper-viscous terms. For both cases, the transport coefficients are calculated using perturbation theory. For a broad turbulence spectrum, a modulational calculation of the PV flux gives both a negative viscosity and a positive hyper-viscosity. For a narrow turbulence spectrum, the result of a parametric instability analysis shows that PV transport is also convective. In both relaxation and perturbative analyses, it is shown that turbulent PV transport is sensitive to flow structure, and the transport coefficients are nonlinear functions of flow shear.

Nonperturbative mean-field theory for minimum enstrophy relaxation

Abstract: The dual cascade of enstrophy and energy in quasi-two-dimensional turbulence strongly suggests that a viscous but otherwise potential vorticity (PV) conserving system decays selectively toward a state of minimum potential enstrophy. We derive a nonperturbative mean field theory for the dynamics of minimum enstrophy relaxation by constructing an expression for PV flux during the relaxation process. The theory is used to elucidate the structure of anisotropic flows emerging from the selective decay process. This structural analysis of PV flux is based on the requirements that the mean flux of PV dissipates total potential enstrophy but conserves total fluid kinetic energy. Our results show that the structure of PV flux has the form of a sum of a positive definite hyperviscous and a negative or positive viscous transport of PV. Transport parameters depend on zonal flow and turbulence intensity. Turbulence spreading is shown to be related to PV mixing via the link of turbulence energy flux to PV flux. In the relaxed state, the ratio of the PV gradient to zonal flow velocity is homogenized. This homogenized quantity sets a constraint on the amplitudes of PV and zonal flow in the relaxed state. A characteristic scale is defined by the homogenized quantity and is related to a variant of the Rhines scale. This relaxation model predicts a relaxed state with a structure which is consistent with PV staircases, namely, the proportionality between mean PV gradient and zonal flow strength.

Zonal flow formation in the presence of ambient mean shear

Abstract: The effect of mean shear flows on zonal flow formation is considered in the contexts of plasma drift wave turbulence and quasi-geostrophic turbulence models. The generation of zonal flows by modulational instability in the presence of large-scale mean shear flows is studied using the method of characteristics as applied to the wave kinetic equation. It is shown that mean shear flows reduce the modulational instability growth rate by shortening the coherency time of the wave spectrum with the zonal shear. The scalings of zonal flow growth rate and turbulent vorticity flux with mean shear are determined in the strong shear limit.

Turbulence elasticity: a key concept to a unified paradigm of L → I → H transition

Abstract: 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|/??k???1, with |?V??ZF| the ZF shearing rate and ??k 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 ??k? ??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.

The Plasma Staircase: Turbulence Self-Regulation through Spontaneous Flow Patterning

Abstract: The E × B staircase [1, 2] is a spontaneously formed, turbulence-driven self-organising pattern of quasi-regular, long-lived and localised shear flow [3] and stress layers. These layers coincide with long-lived pressure corrugations and are interspersed between regions of turbulent avalanching. The typical spacing between these layers is mesoscale, noted ∆ ∼ 25 − 30ρ i [1, 4] —in-between the turbulence auto-correlation length c ∼ 5ρ i at micro scales and the profile macroscale L 100ρ i , see e.g. Fig.2 in [1]— and sets the outer scale of the turbulent avalanching. Here ρ i is ion Larmor radius. Whilst arresting, statistically, to mesoscales the detrimental avalanching these layers, located at the " steps of the staircase " are beneficial to confinement. The E×B staircase is thus best understood as a self-organising and dynamical set of weak or permeable transport barriers. Strong mean zonal flows are generated and endure at the steps of the staircase, resulting in localised deviations of the poloidal flow from its oft-assumed neoclassical prediction [5].