Turbulent transport reduction by zonal flows: massively parallel simulations

Reversal of the Parallel Drift Frequency in Anomalous Transport of Impurity Ions

It is found that, in the studies of heavy ion transport with gyrokinetic simulations, the ion parallel drift frequency can reverse sign in velocity space when the amplitude variation of the electrostatic potential fluctuation is strong along the magnetic field line. As a result, the particle transport related to the parallel dynamics is strongly enhanced. It is noted that, while parallel gradient of the fluctuation amplitude can be instigated by a large magnetic shear or safety factor in a tokamak, the generic mechanism is independent of its cause, which suggests broader applications to kinetic plasma problems. Some relevant topics are briefly addressed in the end.

Saturation of Fishbone Instability by Self-Generated Zonal Flows in Tokamak Plasmas

Gyrokinetic simulations of the fishbone instability in DIII-D tokamak plasmas find that self-generated zonal flows can dominate the nonlinear saturation by preventing coherent structures from persisting or drifting in the energetic particle phase space when the mode frequency down-chirps. Results from the simulation with zonal flows agree quantitatively, for the first time, with experimental measurements of the fishbone saturation amplitude and energetic particle transport. Moreover, the fishbone-induced zonal flows are likely responsible for the formation of an internal transport barrier that was observed after fishbone bursts in this DIII-D experiment. Finally, gyrokinetic simulations of a related ITER baseline scenario show that the fishbone induces insignificant energetic particle redistribution and may enable high performance scenarios in ITER burning plasma experiments.

Self-Organized Evolution of the Internal Transport Barrier in Ion-Temperature-Gradient Driven Gyrokinetic Turbulence

Understanding the self-organization of the most promising internal transport barrier in fusion plasmas needs a long-time nonlinear gyrokinetic global simulation. The neighboring equilibrium update method is proposed, which solves the secularity problem in a perturbative simulation and speeds up the numerical computation by more than 10 times. It is found that the internal transport barrier emerges at the magnetic axis due to inward propagated turbulence avalanche, and its outward expansion is the catastrophe of self-organized structure induced by outward propagated avalanche.

Impact of impurities on drift wave instabilities in reversed-field pinch plasmas

The drift wave in the presence of impurity ions was investigated numerically in reversed-field pinch plasmas, using the gyrokinetic integral eigenmode equation. By comparing the results of regular and hollow plasma density profiles, it was found that the ion temperature gradient mode for the hollow density profile case is much harder to excite. For the impurity effects, when the impurity density gradient is opposite to the electrons, namely when L_{ez} (L_{ez}=L_{ne}/L_{nz} with 1/L_{n} being the density gradient scale length, and the subscript "e" and "z" indicates electrons and impurity ions, respectively) is negative, the impurities can enhance the instability. On the contrary, when L_{ez} is positive, the instability is stabilized. Regarding the trapped electron mode (TEM), the growth rate for plasmas with a hollow density profile remains smaller than that of the standard density gradient. There exists a threshold in L_{ez}. When L_{ez} is less than this value, the impurities destabilize the TEMs, while when L_{ez} is greater than this value, the impurities stabilize the TEMs. In addition, the influence of the collisionality on the TEMs was also studied.

Nonlinear excitation of zonal flows by turbulent energy flux

The nonlinear excitation of zonal flows (ZFs) generated by the ion-temperature-gradient turbulence in a tokamak plasma is investigated by using the global gyrokinetic code nlt. It is found that ZFs are initially driven by the nonlinear self-interaction of the eigenmode. In the nonlinear saturation, the modulational instability becomes important, and its contribution to ZFs can finally be comparable to that of the self-interaction mechanism. More importantly, both types of nonlinear wave-wave interactions can be well described by the turbulent energy flux model.

Gyrokinetic electrostatic turbulence close to marginality in the Wendelstein 7-X stellarator

The transition from strong (fluidlike) to nearly marginal (Floquet-type) regimes of ion-temperature-gradient (ITG) driven turbulence is studied in the stellarator Wendelstein 7-X by means of numerical simulations. Close to marginality, extended (along magnetic field lines) linearly unstable modes are dominant, even in the presence of kinetic electrons, and provide a drive that results in finite turbulent transport. A total suppression of turbulence above the linear stability threshold of the ITG modes, commonly present in tokamaks and known as the "Dimits shift," is not observed. We show that this is mostly due to the peculiar radial structure of marginal turbulence, which is more localized than in the fluid case and therefore less likely to be stabilized by shearing flows.

Long Term Vortex Flow Evolution around a Magnetic Island in Tokamaks

We present a gyrokinetic analysis of the vortex flow evolution in a magnetic island in collisionless tokamak plasmas. In a short term ω[over ¯]_{D}t<1, where ω[over ¯]_{D} is the secular magnetic drift of the orbit center, initial monopolar vortex flow approaches to its residual level determined by the neoclassical enhancement of polarization shielding after collisionless relaxation. The residual level depends on the location inside an island and is higher than the Rosenbluth-Hinton level [M.N. Rosenbluth and F.L. Hinton, Phys. Rev. Lett. 80, 724 (1998)PRLTAO0031-900710.1103/PhysRevLett.80.724] due to finite island width. In a long term ω[over ¯]_{D}t>1, the residual vortex flow evolves to a dipolar zonal-vortex flow mixture due to toroidicity-induced breaking of a helical symmetry. The mixture forms localized flow shear layers near the island separatrix away from X points. The deviation of the streamlines of the mixture flows from magnetic surfaces allows turbulence advection across the island. We expect a small island w≲qρ_{Ti}/s[over ^] provides a favorable condition for this mixture flow formation, while the monopolar vortex flow persists for a larger island.

Regulation of Alfvén Eigenmodes by Microturbulence in Fusion Plasmas

Global gyrokinetic simulations of mesoscale reversed shear Alfven eigenmodes (RSAE) excited by energetic particles (EP) in fusion plasmas find that RSAE amplitude and EP transport are much higher than experimental levels at nonlinear saturation, but quickly diminish to very low levels after the saturation if background microturbulence is artificially suppressed. In contrast, in simulations coupling micro-meso scales, the RSAE amplitude and EP transport decrease drastically at the initial saturation but later increases to the experimental levels in the quasisteady state with bursty dynamics due to regulation by thermal ion temperature gradient (ITG) microturbulence. The quasisteady state EP transport is larger for a stronger microturbulence. The RSAE amplitude in the quasisteady state ITG-RSAE turbulence from gyrokinetic simulations, for the first time, agrees very well with experimental measurements.

Applications and Techniques for Fast Machine Learning in Science

In this community review report, we discuss applications and techniques for fast machine learning (ML) in science-the concept of integrating powerful ML methods into the real-time experimental data processing loop to accelerate scientific discovery. The material for the report builds on two workshops held by the Fast ML for Science community and covers three main areas: applications for fast ML across a number of scientific domains; techniques for training and implementing performant and resource-efficient ML algorithms; and computing architectures, platforms, and technologies for deploying these algorithms. We also present overlapping challenges across the multiple scientific domains where common solutions can be found. This community report is intended to give plenty of examples and inspiration for scientific discovery through integrated and accelerated ML solutions. This is followed by a high-level overview and organization of technical advances, including an abundance of pointers to source material, which can enable these breakthroughs.

Analysis of the polarization effects in the gyrokinetic theory of magnetized plasmas

By adopting the hybrid coordinates, in which the nonlinearity of polarization displacement is included in the configuration space variables compared to the conventional gyrocenter coordinates, the polarization effects are analyzed by using the modern gyrokinetic (GK) theory of magnetized plasmas. Based on the invariant property, the velocity transformation between the gyrocenter and hybrid coordinates is calculated, and the phase-space velocity in terms of the hybrid coordinates is obtained. The linear and nonlinear polarization distribution functions are defined, and the evolutions for the polarization distribution functions are derived. It is well known that the polarization density is important in the GK calculation of particle density. Analogously, it is shown that the polarization current should be considered in the GK calculation of current density. In the case with electrostatic fluctuations, the roles of the polarization current are illustrated in the derivations of the Hasegawa-Mima equation and the dispersion relation for geodesic acoustic mode. In the case with magnetic fluctuations, the procedure for the GK calculation of perpendicular current is clarified, the dispersion relation for compressional Alfvén wave is derived, in which the effect of polarization current is discussed.

The first observation of 4D tomography measurement of plasma structures and fluctuations

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.

Theory of the Tertiary Instability and the Dimits Shift from Reduced Drift-Wave Models

Tertiary modes in electrostatic drift-wave turbulence are localized near extrema of the zonal velocity U(x) with respect to the radial coordinate x. We argue that these modes can be described as quantum harmonic oscillators with complex frequencies, so their spectrum can be readily calculated. The corresponding growth rate γ_{TI} is derived within the modified Hasegawa-Wakatani model. We show that γ_{TI} equals the primary-instability growth rate plus a term that depends on the local U^{''}; hence, the instability threshold is shifted compared to that in homogeneous turbulence. This provides a generic explanation of the well-known yet elusive Dimits shift, which we find explicitly in the Terry-Horton limit. Linearly unstable tertiary modes either saturate due to the evolution of the zonal density or generate radially propagating structures when the shear |U^{'}| is sufficiently weakened by viscosity. The Dimits regime ends when such structures are generated continuously.

Amplitude Modulation And Nonlinear Self-Interactions of the Geodesic Acoustic Mode at the Edge of MAST

We studied the amplitude modulation of the radial electric field constructed from the Langmuir probe plasma potential measurements at the edge of the mega-ampere spherical tokamak (MAST). The Empirical Mode Decomposition (EMD) technique was applied, which allowed us to extract fluctuations on temporal scales of plasma turbulence, the Geodesic Acoustic Mode (GAM), and those associated with the residual poloidal flows. This decomposition preserved the nonlinear character of the signal. Hilbert transform (HT) was then used to obtain the amplitude modulation envelope of fluctuations associated with turbulence and with the GAM. We found significant spectral coherence at frequencies between 1–5 kHz, in the turbulence and the GAM envelopes and for the signal representing the low frequency zonal flows (LFZFs). We present the evidence of local and nonlocal, in frequency space, three wave interactions leading to coupling between the GAM and the low frequency (LF) part of the spectrum.

Computing the Double-Gyroaverage Term Incorporating Short-Scale Perturbation and Steep Equilibrium Profile by the Interpolation Algorithm

In the gyrokinetic model and simulations, when the double-gyroaverage term incorporates the combining effect contributed by the finite Larmor radius, short scales of the perturbation, and steep gradient of the equilibrium profile, the low-order approximation of this term could generate unignorable error. This paper implements an interpolation algorithm to compute the double-gyroaverage term without low-order approximation to avoid this error. For a steep equilibrium density, the obvious difference between the density on the gyrocenter coordinate frame and the one on the particle coordinate frame should be accounted for in the quasi-neutrality equation. A Euler–Maclaurin-based quadrature integrating algorithm is developed to compute the quadrature integral for the distribution of the magnetic moment. The application of the interpolation algorithm to computing the double-gyroaverage term and to solving the quasi-neutrality equation is benchmarked by comparing the numerical results with the known analytical solutions. Finally, to take advantage of the interpolation solver clearer, the numerical comparison between the interpolation solver and a classical second order solver is carried out in a constant theta-pinch magnetic field configuration using SELALIB code. When the equilibrium profile is not steep and the perturbation only has the non-zero mode number along the parallel spatial dimension, the results computed by the two solvers match each other well. When the gradient of the equilibrium profile is steep, the interpolation solver provides a bigger driving effect for the ion-temperature-gradient modes, which possess large polar mode numbers.

Fully Kinetic Simulation of Ion-Temperature-Gradient Instabilities in Tokamaks

The feasibility of using full ion kinetics, instead of gyrokinetics, in simulating low-frequency Ion-Temperature-Gradient (ITG) instabilities in tokamaks has recently been demonstrated. The present work extends the full ion kinetics to the nonlinear regime and investigates the nonlinear saturation of a single-n ITG instability due to the E × B trapping mechanism (n is the toroidal mode number). The saturation amplitude predicted by the E × B trapping theory is found to agree with the saturation level observed in the simulation. In extending to the nonlinear regime, we developed a toroidal Boris full orbit integrator, which proved to be accurate in capturing both the short-time scale cyclotron motion and long time scale drift motion, with good kinetic energy conservation and toroidal angular momentum conservation in tokamak equilibrium magnetic fields. This work also extends the previous work from analytic circular magnetic equilibria to general numerical magnetic equilibria, enabling simulation of realistic equilibria reconstructed from tokamak experiments.

A proposal of Fourier-Bessel expansion with optimized ensembles of bases to analyse two dimensional image

It is a critical issue to find the best set of fitting function bases in mode structural analysis of two dimensional images like plasma emission profiles. The paper proposes a method to optimize a set of the bases in the case of Fourier-Bessel function series, using their orthonormal property, for more efficient and precise analysis. The method is applied on a tomography image of plasma emission obtained with the Maximum-likelihood expectation maximization method in a linear cylindrical device. The result demonstrates the excellency of the method that realizes the smaller residual error and minimum Akaike information criterion using smaller number of fitting function bases.

Isotope Effects on Trapped-Electron-Mode Driven Turbulence and Zonal Flows in Helical and Tokamak Plasmas

Impacts of isotope ion mass on trapped-electron-mode (TEM)-driven turbulence and zonal flows in magnetically confined fusion plasmas are investigated. Gyrokinetic simulations of TEM-driven turbulence in three-dimensional magnetic configuration of helical plasmas with hydrogen isotope ions and real-mass kinetic electrons are realized for the first time, and the linear and the nonlinear nature of the isotope and collisional effects on the turbulent transport and zonal-flow generation are clarified. It is newly found that combined effects of the collisional TEM stabilization by the isotope ions and the associated increase in the impacts of the steady zonal flows at the near-marginal linear stability lead to the significant transport reduction with the opposite ion mass dependence in comparison to the conventional gyro-Bohm scaling. The universal nature of the isotope effects on the TEM-driven turbulence and zonal flows is verified for a wide variety of toroidal plasmas, e.g., axisymmetric tokamak and non-axisymmetric helical or stellarator systems.

New Paradigm for Turbulent Transport Across a Steep Gradient in Toroidal Plasmas

First principles gyrokinetic simulation of the edge turbulent transport in toroidal plasmas finds a reverse trend in the turbulent transport coefficients under strong gradients. It is found that there exist both linear and nonlinear critical gradients for the nonmonotonicity of transport characteristics. The discontinuity of the transport flux slope around the turning gradient shows features of a second order phase transition. Under a strong gradient the most unstable modes are in nonground eigenstates with unconventional mode structures, which significantly reduces the effective correlation length and thus reverse the transport trend. Our results suggest a completely new mechanism for the low to high confinement mode transition without invoking shear flow or zonal flow.

Suppressed ion-scale turbulence in a hot high-β plasma

An economic magnetic fusion reactor favours a high ratio of plasma kinetic pressure to magnetic pressure in a well-confined, hot plasma with low thermal losses across the confining magnetic field. Field-reversed configuration (FRC) plasmas are potentially attractive as a reactor concept, achieving high plasma pressure in a simple axisymmetric geometry. Here, we show that FRC plasmas have unique, beneficial microstability properties that differ from typical regimes in toroidal confinement devices. Ion-scale fluctuations are found to be absent or strongly suppressed in the plasma core, mainly due to the large FRC ion orbits, resulting in near-classical thermal ion confinement. In the surrounding boundary layer plasma, ion- and electron-scale turbulence is observed once a critical pressure gradient is exceeded. The critical gradient increases in the presence of sheared plasma flow induced via electrostatic biasing, opening the prospect of active boundary and transport control in view of reactor requirements.

How mesoscopic staircases condense to macroscopic barriers in confined plasma turbulence

This Rapid Communication sets forth the mechanism by which mesoscale staircase structures condense to form macroscopic states of enhanced confinement. Density, vorticity, and turbulent potential enstrophy are the variables for this model. Formation of the staircase structures is due to inhomogeneous mixing of (generalized) potential vorticity (PV). Such mixing results in the local sharpening of density and vorticity gradients. When PV gradients steepen, the density staircase structure develops into a lattice of mesoscale "jumps" and "steps," which are, respectively, regions of local gradient steepening and flattening. The jumps then merge and migrate in radius, leading to the emergence of a new macroscale profile structure, so indicating that profile self-organization is a global process, which may be described by a local, but nonlinear model. This work predicts and demonstrates how mesoscale condensation of staircases leads to global states of enhanced confinement.

Subdominant modes in zonal-flow-regulated turbulence

From numerical solutions of a gyrokinetic model for ion temperature gradient turbulence it is shown that nonlinear coupling is dominated by three-wave interactions that include spectral components of the zonal flow and damped subdominant modes. Zonal flows dissipate very little energy injected by the instability, but facilitate its transfer from the unstable mode to dissipative subdominant modes, in part due to the small frequency sum of such triplets. Although energy is transferred to higher wave numbers, consistent with shearing, a large fraction is transferred to damped subdominant modes within the instability range. This is a new aspect of regulation of turbulence by zonal flows.

Multiscale gyrokinetics for rotating tokamak plasmas: fluctuations, transport and energy flows

This paper presents a complete theoretical framework for studying turbulence and transport in rapidly rotating tokamak plasmas. The fundamental scale separations present in plasma turbulence are codified as an asymptotic expansion in the ratio ε = ρi/α of the gyroradius to the equilibrium scale length. Proceeding order by order in this expansion, a set of coupled multiscale equations is developed. They describe an instantaneous equilibrium, the fluctuations driven by gradients in the equilibrium quantities, and the transport-timescale evolution of mean profiles of these quantities driven by the interplay between the equilibrium and the fluctuations. The equilibrium distribution functions are local Maxwellians with each flux surface rotating toroidally as a rigid body. The magnetic equilibrium is obtained from the generalized Grad-Shafranov equation for a rotating plasma, determining the magnetic flux function from the mean pressure and velocity profiles of the plasma. The slow (resistive-timescale) evolution of the magnetic field is given by an evolution equation for the safety factor q. Large-scale deviations of the distribution function from a Maxwellian are given by neoclassical theory. The fluctuations are determined by the 'high-flow' gyrokinetic equation, from which we derive the governing principle for gyrokinetic turbulence in tokamaks: the conservation and local (in space) cascade of the free energy of the fluctuations (i.e. there is no turbulence spreading). Transport equations for the evolution of the mean density, temperature and flow velocity profiles are derived. These transport equations show how the neoclassical and fluctuating corrections to the equilibrium Maxwellian act back upon the mean profiles through fluxes and heating. The energy and entropy conservation laws for the mean profiles are derived from the transport equations. Total energy, thermal, kinetic and magnetic, is conserved and there is no net turbulent heating. Entropy is produced by the action of fluxes flattening gradients, Ohmic heating and the equilibration of interspecies temperature differences. This equilibration is found to include both turbulent and collisional contributions. Finally, this framework is condensed, in the low-Mach-number limit, to a more concise set of equations suitable for numerical implementation.

Radial localization of toroidicity-induced Alfvén eigenmodes

Linear gyrokinetic simulation of fusion plasmas finds a radial localization of the toroidal Alfvén eigenmodes (TAEs) due to the nonperturbative energetic particle (EP) contribution. The EP-driven TAE has a radial mode width much smaller than that predicted by the magnetohydrodynamic theory. The TAE radial position stays around the strongest EP pressure gradients when the EP profile evolves. The nonperturbative EP contribution is also the main cause for the breaking of the radial symmetry of the ballooning mode structure and for the dependence of the TAE frequency on the toroidal mode number. These phenomena are beyond the picture of the conventional magnetohydrodynamic theory.

Kinetic theory of weak turbulence in plasmas

From the nonlinear Vlasov equation, a nonlinear turbulence scattering term is found to describe stochastic dissipation on a time scale longer than the turbulence correlation time. The evolution of the plasma distribution is determined by the well-understood unperturbed motion of charged particles, with the effects of the fluctuating part of fields described by the turbulence scattering term. In the present framework, one can identify various important physics, from the linear and quasilinear regimes to the nonlinear regime, in particular, the connections between the widely used Kadomtsev-Pogutse equation [B. B. Kadomtsev and O. P. Pogutse, in Reviews of Plasma Physics, edited by M. A. Leontovich (Consultants Bureau, New York, 1970), pp. 368-387] and the Frieman-Chen equation [Frieman and Chen, Phys. Fluids 25, 502 (1982)]. The nonlinear scattering term indicates the Onsager symmetry relation of turbulent transport and a nonlinear frequency or k spectrum shift of a resonantly excited wave.

Experimental signatures of critically balanced turbulence in MAST

Beam emission spectroscopy (BES) measurements of ion-scale density fluctuations in the MAST tokamak are used to show that the turbulence correlation time, the drift time associated with ion temperature or density gradients, the particle (ion) streaming time along the magnetic field, and the magnetic drift time are consistently comparable, suggesting a "critically balanced" turbulence determined by the local equilibrium. The resulting scalings of the poloidal and radial correlation lengths are derived and tested. The nonlinear time inferred from the density fluctuations is longer than the other times; its ratio to the correlation time scales as ν(*i)(-0.8 ± 0.1), where ν(*i) = ion  collision rate/streaming rate. This is consistent with turbulent decorrelation being controlled by a zonal component, invisible to the BES, with an amplitude exceeding those of the drift waves by ∼ ν(*i)(-0.8).

Numerical simulations of Hall-effect plasma accelerators on a magnetic-field-aligned mesh

The ionized gas in Hall-effect plasma accelerators spans a wide range of spatial and temporal scales, and exhibits diverse physics some of which remain elusive even after decades of research. Inside the acceleration channel a quasiradial applied magnetic field impedes the current of electrons perpendicular to it in favor of a significant component in the E×B direction. Ions are unmagnetized and, arguably, of wide collisional mean free paths. Collisions between the atomic species are rare. This paper reports on a computational approach that solves numerically the 2D axisymmetric vector form of Ohm's law with no assumptions regarding the resistance to classical electron transport in the parallel relative to the perpendicular direction. The numerical challenges related to the large disparity of the transport coefficients in the two directions are met by solving the equations on a computational mesh that is aligned with the applied magnetic field. This approach allows for a large physical domain that extends more than five times the thruster channel length in the axial direction and encompasses the cathode boundary where the lines of force can become nonisothermal. It also allows for the self-consistent solution of the plasma conservation laws near the anode boundary, and for simulations in accelerators with complex magnetic field topologies. Ions are treated as an isothermal, cold (relative to the electrons) fluid, accounting for the ion drag in the momentum equation due to ion-neutral (charge-exchange) and ion-ion collisions. The density of the atomic species is determined using an algorithm that eliminates the statistical noise associated with discrete-particle methods. Numerical simulations are presented that illustrate the impact of the above-mentioned features on our understanding of the plasma in these accelerators.

Three-dimensional mode conversion associated with kinetic Alfvén waves

We report the first three-dimensional (3D) ion particle simulation of mode conversion from a fast mode compressional wave to kinetic Alfvén waves (KAWs) that occurs when a compressional mode propagates across a plasma boundary into a region of increasing Alfvén velocity. The magnetic field is oriented in the z direction perpendicular to the gradients in the background density and magnetic field (x direction). Following a stage dominated by linear physics in which KAWs with large wave numbers k(x)ρ(i)∼1 (with ρ(i) being the ion Larmor radius) are generated near the Alfvén resonance surface, the growth of KAW modes with k(y)ρ(i)∼1 is observed in the nonlinear stage when the amplitude of KAWs generated by linear mode conversion becomes large enough to drive a nonlinear parametric decay process. The simulation provides a comprehensive picture of mode conversion and shows the fundamental importance of the 3D nonlinear physics in transferring energy to large perpendicular k(y) modes, which can provide large transport across plasma boundaries in space and laboratory plasmas.

Nonlinear frequency oscillation of Alfvén eigenmodes in fusion plasmas

A nonlinear oscillation of frequency and amplitude is found by massively parallel gyrokinetic simulations of Alfvén eigenmodes excited by energetic particles in toroidal plasmas. The fast and repetitive frequency chirping is induced by the evolution of coherent structures in the phase space. The dynamics of the coherent structures is controlled by the competition between the phase-space island formation due to the nonlinear particle trapping and the island destruction due to the free streaming. The chirping dynamics provides a conceptual framework for understanding nonlinear wave-particle interactions underlying the transport process in collisionless plasmas.

Coherent vortices in strongly coupled liquids

Strongly coupled liquids are ubiquitous in both nature and laboratory plasma experiments. They are unique in the sense that their average potential energy per particle dominates over the average kinetic energy. Using "first principles" molecular dynamics (MD) simulations, we report for the first time the emergence of isolated coherent tripolar vortices from the evolution of axisymmetric flows in a prototype two-dimensional (2D) strongly coupled liquid, namely, the Yukawa liquid. Linear growth rates directly obtained from MD simulations are compared with a generalized hydrodynamic model. Our MD simulations reveal that the tripolar vortices persist over several turn over times and hence may be observed in strongly coupled liquids such as complex plasma, liquid metals and astrophysical systems such as white dwarfs and giant planetary interiors, thereby making the phenomenon universal.

Characterizations of low-frequency zonal flow in the edge plasma of the HL-2A tokamak

A low-frequency (<4 kHz), poloidally and toroidally symmetrical potential structure that peaks near zero frequency is observed in the edge plasma of the HL-2A tokamak. The axisymmetry structure exhibits a radial coherence length less than 1 cm. These characteristics are consistent with the theoretically predicted low-frequency zonal flows (LFZF). The radial wave-number frequency spectra of the LFZF show that the LFZF packets propagate both outwards and inwards. The geodesic acoustic mode (GAM) is found to coexist with the LFZF, and the LFZF is found to modulate the GAM and ambient turbulence with in-phase and antiphase relations, respectively, through an envelope analysis.

Turbulent transport of trapped-electron modes in collisionless plasmas

Global gyrokinetic particle simulations of collisionless trapped-electron mode turbulence in toroidal plasmas find that electron heat transport exhibits a device size scaling with a gradual transition from Bohm to gyro-Bohm scaling. A comprehensive analysis of spatial and temporal scales shows that the turbulence eddies are predominantly microscopic because of zonal flow shearing, but the presence of mesoscale structures drives a nondiffusive component in the electron heat flux due to the weak nonlinear detuning of the precessional resonance that excites the linear instability.

Generic mechanism of microturbulence suppression by vortex flows

The interaction between two-dimensional vortex flows and microturbulence is studied numerically using gyrofluid simulations. It is shown that, qualitatively different from usual mean flows, vortex flows can dramatically suppress microturbulence even with weak flow shear. A generic suppression mechanism is identified as the multiplied effect of both radial and poloidal mode couplings, which induce the formation of a new global mode. Furthermore, an oscillatory zonal flow is found to form through interaction between the vortex flows and microturbulence.

Sheared plasma rotation in partially stochastic magnetic fields

It is shown that resonant magnetic perturbations generate sheared flow velocities in magnetized plasmas. Stochastic magnetic fields in incomplete chaos influence the drift motion of electrons and ions differently. Using a fast mapping technique, it is demonstrated that a radial electric field is generated due to the different behavior of passing particles (electrons and ions) in tokamak geometry; magnetic trapping of ions is neglected. Radial profiles of the polodial velocity resulting from the force balance in the presence of a strong toroidal magnetic field are obtained. Scaling laws for plasma losses and the forms of sheared plasma rotation profiles are discussed.

Nature of transport across sheared zonal flows in electrostatic ion-temperature-gradient gyrokinetic plasma turbulence

It is shown that the usual picture for the suppression of turbulent transport across a stable sheared flow based on a reduction of diffusive transport coefficients is, by itself, incomplete. By means of toroidal gyrokinetic simulations of electrostatic, collisionless ion-temperature-gradient turbulence, it is found that the nature of the transport is altered fundamentally, changing from diffusive to anticorrelated and subdiffusive. Additionally, whenever the flows are self-consistently driven by turbulence, the transport gains an additional non-Gaussian character. These results suggest that a description of transport across sheared flows using effective diffusivities is oversimplified.

Transport of energetic particles by microturbulence in magnetized plasmas

Transport of energetic particles by the microturbulence in magnetized plasmas is studied in gyrokinetic simulations of the ion temperature gradient turbulence. The probability density function of the ion radial excursion is found to be very close to a Gaussian, indicating a diffusive transport process. The particle diffusivity can thus be calculated from a random walk model. The diffusivity is found to decrease drastically for high energy particles due to the averaging effects of the large gyroradius and orbit width, and the fast decorrelation of the energetic particles with the waves.

Reduction of turbulent transport with zonal flows enhanced in helical systems

Gyrokinetic Vlasov simulations of the ion temperature gradient turbulence are performed in order to investigate effects of helical magnetic configurations on turbulent transport and zonal flows. The obtained results confirm the theoretical prediction that helical configurations optimized for reducing neoclassical ripple transport can simultaneously reduce the turbulent transport with enhancing zonal-flow generation. Stationary zonal-flow structures accompanied with transport reduction are clearly identified by the simulation for the neoclassically optimized helical geometry. The generation of the stationary zonal flow explains a physical mechanism for causing the confinement improvement observed in the inward-shifted plasma in the Large Helical Device [O. Motojima, Nucl. Fusion 43, 1674 (2003)].

Wave-particle decorrelation and transport of anisotropic turbulence in collisionless plasmas

Comprehensive analysis of the largest first-principles simulations to date shows that stochastic wave-particle decorrelation is the dominant mechanism responsible for electron heat transport driven by electron temperature gradient turbulence with extended radial streamers. The transport is proportional to the local fluctuation intensity, and phase-space island overlap leads to a diffusive process with a time scale comparable to the wave-particle decorrelation time, determined by the fluctuation spectral width. This kinetic time scale is much shorter than the fluid time scale of eddy mixing.