We propose a new reduced fluid model for the study of the drift wave -- zonal flow dynamics in magnetically confined plasmas. Our model can be viewed as an extension of the classic Hasegawa-Wakatani (HW) model, and is based on an improved treatment of the electron dynamics parallel to the field lines, to guarantee a balanced electron flux on the magnetic surfaces. Our flux-balanced HW (bHW) model contains the same drift-wave instability as previous HW models, but unlike these models, it converges exactly to the modified Hasegawa-Mima model in the collisionless limit. We rely on direct numerical simulations to illustrate some of the key features of the bHW model, such as the enhanced variability in the turbulent fluctuations, and the existence of stronger and more turbulent zonal jets than the jets observed in other HW models, especially for high plasma resistivity. Our simulations also highlight the crucial role of the feedback of the third-order statistical moments in achieving a statistical equilibrium with strong zonal structures. Finally, we investigate the changes in the observed dynamics when more general dissipation effects are included, and in particular when we include the reduced model for ion Landau damping originally proposed by Wakatani and Hasegawa.
In electrostatic simulations of MAST plasma at electron-gyroradius scales, using the local flux-tube gyrokinetic code GS2 with adiabatic ions, we find that the long-time saturated electron heat flux (the level most relevant to energy transport) decreases as the electron collisionality decreases. At early simulation times, the heat flux "quasi-saturates" without any strong dependence on collisionality, and with the turbulence dominated by streamer-like radially elongated structures. However, the zonal fluctuation component continues to grow slowly until much later times, eventually leading to a…
High energy particles' behavior including fusion born alpha particles in an ITER like tokamak in the presence of background driftwave turbulence is investigated by an orbit following calculation. The background turbulence is given by the toroidal driftwave eigenmode combined with a random number generator. The transport level is reduced as the particle energy increase; the widths of the guiding center islands produced by the passing particles are inverse proportional to the square root of parallel velocities. On the other hand, the trapped particles are sensitive to $E \times B$ drift at the b…
We investigate the drift wave -- zonal flow dynamics in a shearless slab geometry with the new flux-balanced Hasegawa-Wakatani model. As in previous Hasegawa-Wakatani models, we observe a sharp transition from a turbulence dominated regime to a zonal jet dominated regime as we decrease the plasma resistivity. However, unlike previous models, zonal structures are always present in the flux-balanced model, even for high resistivity, and strongly reduce the level of particle and vorticity flux. The more robust zonal jets also have a higher variability than in previous models, which is further enh…
Drift ordered fluid models are widely applied in studies of low-frequency turbulence in the edge and scrape-off layer regions of magnetically confined plasmas. Here, we show how collisional transport across the magnetic field is self-consistently incorporated into drift-fluid models without altering the drift-fluid energy integral. We demonstrate that the inclusion of collisional transport in drift-fluid models gives rise to diffusion of particle density, momentum and pressures in drift-fluid turbulence models and thereby obviate the customary use of artificial diffusion in turbulence simulati…
We propose that pressure anisotropy causes weakly collisional turbulent plasmas to self-organize so as to resist changes in magnetic-field strength. We term this effect "magneto-immutability" by analogy with incompressibility (resistance to changes in pressure). The effect is important when the pressure anisotropy becomes comparable to the magnetic pressure, suggesting that in collisionless, weakly magnetized (high-$β$) plasmas its dynamical relevance is similar to that of incompressibility. Simulations of magnetized turbulence using the weakly collisional Braginskii model show that magneto-im…
A semiclassical nonlinear collisional drift wave model for dense magnetized plasmas is developed and solved numerically. The effects of fluid electron density fluctuations associated with quantum statistical pressure and quantum Bohm force are included, and their influences on the collisional drift wave instability and the resulting fully developed nanoscale drift wave turbulence are discussed. It is found that the quantum effects increase the growth rate of the collisional drift wave instability, and introduce a finite de Broglie length screening on the drift wave turbulent density perturbati…
We present turbulent properties of electrostatic drift waves in a nonuniform collisional plasma composed of magnetised electrons and ions in the presence of immobile dust particles. For this purpose, we derive a pair of nonlinear quasi-two-dimensional equations exhibiting the coupling between the generalized ion vorticity and density fluctuations associated with collisional drift waves. The effect of a dust density gradient on the initial drift instability and fully developed turbulence is examined numerically.
Scaling laws for ion temperature gradient driven turbulence in magnetized toroidal plasmas are derived and compared with direct numerical simulations. Predicted dependences of turbulence fluctuation amplitudes, spatial scales, and resulting heat fluxes on temperature gradient and magnetic field line pitch are found to agree with numerical results in both the driving and inertial ranges. Evidence is provided to support the critical balance conjecture that parallel streaming and nonlinear perpendicular decorrelation times are comparable at all spatial scales, leading to a scaling relationship be…
Statistical analysis of Faraday Rotation Measure (RM) maps of the intracluster medium (ICM) of galaxy clusters provides a unique tool to evaluate some spatial features of the magnetic fields there. Its combination with numerical simulations of magnetohydrodynamic (MHD) turbulence allows the diagnosis of the ICM turbulence. Being the ICM plasma weakly collisional, the thermal velocity distribution of the particles naturally develops anisotropies as a consequence of the large scale motions and the conservation of the magnetic moment of the charged particles. A previous study (Paper I) analyzed t…
The competition between drift wave and interchange physics in general E-cross-B drift turbulence is studied with computations in three dimensional tokamak flux tube geometry. For a given set of background scales, the parameter space can be covered by the plasma beta and drift wave collisionality. At large enough plasma beta the turbulence breaks out into ideal ballooning modes and saturates only by depleting the free energy in the background pressure gradient. At high collisionality it finds a more gradual transition to resistive ballooning. At moderate beta and collisionality it retains drift…
Observations of Transition from Imbalanced to Balanced Kinetic Alfvénic Turbulence
Purple Mountain Observatory, Chinese Academy of Sciences（中国科学院紫金山天文台）；Space Sciences Laboratory, University of California, Berkeley（加州大学伯克利分校空间科学实验室）；Physics Department, University of California, Berkeley（加州大学伯克利分校物理系）；School of Physics and Electronic Sciences, Changsha University of Science and Technology（长沙理工大学物理与电子科学学院）；LPC2E, CNRS, CNES, University of Orléans（奥尔良大学CNRS/CNES LPC2E研究中心）；International Space Science Institute (ISSI)（国际空间科学研究所）；University of California, Berkeley（加州大学伯克利分校）
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 …
In collisionless and weakly collisional plasmas, such as hot accretion flows onto compact objects, the magnetorotational instability (MRI) can differ significantly from the standard (collisional) MRI. In particular, pressure anisotropy with respect to the local magnetic-field direction can both change the linear MRI dispersion relation and cause nonlinear modifications to the mode structure and growth rate, even when the field and flow perturbations are small. This work studies these pressure-anisotropy-induced nonlinearities in the weakly nonlinear, high-ion-beta regime, before the MRI satura…
In magnetized plasmas, a turbulent cascade occurs in phase space at scales smaller than the thermal Larmor radius ("sub-Larmor scales") [Phys. Rev. Lett. 103, 015003 (2009)]. When the turbulence is restricted to two spatial dimensions perpendicular to the background magnetic field, two independent cascades may take place simultaneously because of the presence of two collisionless invariants. In the present work, freely decaying turbulence of two-dimensional electrostatic gyrokinetics is investigated by means of phenomenological theory and direct numerical simulations. A dual cascade (forward a…
Gyrokinetic turbulence is subject to the constraint that the turbulent charge flux vanishes. This is interpreted, in detail, as arising from momentum conservation at the fluctuation scale. There are beautiful and deep analogies with the classical transport from Coulomb collisions.
We present the first study of the formation and dissipation of current sheets at electron scales in a wave-driven, weakly collisional, 3D kinetic turbulence simulation. We investigate the relative importance of dissipation associated with collisionless damping via resonant wave-particle interactions versus dissipation in small-scale current sheets in weakly collisional plasma turbulence. Current sheets form self-consistently from the wave-driven turbulence, and their filling fraction is well correlated to the electron heating rate. However, the weakly collisional nature of the simulation neces…
The Lagrangian velocity statistics of dissipative drift-wave turbulence are investigated. For large values of the adiabaticity (or small collisionality), the probability density function of the Lagrangian acceleration shows exponential tails, as opposed to the stretched exponential or algebraic tails, generally observed for the highly intermittent acceleration of Navier-Stokes turbulence. This exponential distribution is shown to be a robust feature independent of the Reynolds number. For small adiabaticity, algebraic tails are observed, suggesting the strong influence of point-vortex-like dyn…
Chaotic electromagnetic fields are common in many relativistic plasma environments, where they can be excited by instabilities on kinetic spatial scales. When strong electric fluctuations exist on sub-electron scales, they may lead to small-angle, stochastic deflections of the electrons' pitch-angles. Under certain conditions, this closely resembles the effect of Coulomb collisions in collisional plasmas. The electric pitch-angle diffusion coefficient acts as an effective collision -- or "quasi-collision" -- frequency. We show that quasi-collisions may radically alter the expected radiative tr…
A closed-form analytical solution is found for the nonlinear dynamics of isolated, near-threshold waves in the presence of strong scattering. The proposed solution can be useful in verifying codes across several disciplines, including Alfvénic instabilities and thermal plasma turbulence in fusion plasmas and studies of viscous shear flows in fluid dynamics, as well as a rapid means for predicting and analyzing experimental outcome.
Turbulence at kinetic scales is an unresolved and ubiquitous phenomenon that characterizes both space and laboratory plasmas. Recently, new theories, {\it in-situ} spacecraft observations and numerical simulations suggest a novel scenario for turbulence, characterized by a so-called phase space cascade -- the formation of fine structures, both in physical and velocity space. This new concept is here extended by directly taking into account the role of inter-particle collisions, modeled through the nonlinear Landau operator or the simplified Dougherty operator. The characteristic times, associa…
The interpretation of single-point spacecraft measurements of solar wind turbulence is complicated by the fact that the measurements are made in a frame of reference in relative motion with respect to the turbulent plasma. The Taylor hypothesis---that temporal fluctuations measured by a stationary probe in a rapidly flowing fluid are dominated by the advection of spatial structures in the fluid rest frame---is often assumed to simplify the analysis. But measurements of turbulence in upcoming missions, such as Solar Probe Plus, threaten to violate the Taylor hypothesis, either due to slow flow …
The question of how nonlinear interactions redistribute the energy of fluctuations across available degrees of freedom is of fundamental importance in the study of turbulence and transport in magnetized weakly collisional plasmas, ranging from space settings to fusion devices. In this letter, we present a theory for the dual cascade found in such plasmas, which predicts a range of new behavior that distinguishes this cascade from that of neutral fluid turbulence. These phenomena are explained in terms of the constrained nature of spectral transfer in nonlinear gyrokinetics. Accompanying this t…
The present work investigates the acceleration of test particles in balanced and imbalanced Alfvénic turbulence, relevant to the solar-wind problem. These turbulent states, obtained numerically by prescribing the injection rates for the ideal invariants, are evolved dynamically with the particles. While the energy spectrum for balanced and imbalanced states is known, the impact made on particle heating is a matter of debate, with different considerations giving different results. By performing direct numerical simulations, resonant and non-resonant particle accelerations are automatically cons…
Isotope Effects on TEM-driven Turbulence and Zonal Flows in Helical and Tokamak Plasmas
National Institute for Fusion Science, National Institutes of Natural Sciences（国立研究開発法人 国立統合物理学研究所 核融合科学研究所）；The Graduate University for Advanced Studies（総合研究大学院大学）；Faculty of Arts and Sciences, Komazawa University（駒澤大学 文学部・理学部）；Nagoya University（名古屋大学）
We show that the recently introduced two-field flux-balanced Hasegawa-Wakatani (BHW) model captures the key features of drift-wave turbulent transport mediated by zonal flows observed in more complete and accurate gyrokinetic simulations, such as the existence of a nonlinear upshift of the threshold for drift wave turbulence driven transport, often called the Dimits shift, as well as non-local transport with avalanche bursts and solitary propagating structures. Because of the approximations made in the BHW model, these observations are made for the particle flux instead of the heat flux more c…
The collisional drift wave instability in a straight magnetic field configuration is studied within a full-F gyro-fluid model, which relaxes the Oberbeck-Boussinesq (OB) approximation. Accordingly, we focus our study on steep background density gradients. In this regime we report on corrections by factors of order one to the eigenvalue analysis of former OB approximated approaches as well as on spatially localised eigenfunctions, that contrast strongly with their OB approximated equivalent. Remarkably, non-modal phenomena arise for large density inhomogeneities and for all collisionalities. As…
The effect of changes in plasma parameters, that are characteristic near or at an L-H transition in fusion edge plasmas, on fluctuation correlation lengths are analysed by means of drift-Alfven turbulence computations. Scalings by density gradient length, collisionality, plasma beta, and by an imposed shear flow are considered. It is found that strongly sheared flows lead to the appearence of long-range correlations in electrostatic potential fluctuations parallel and perpendicular to the magnetic field.
A dynamical approach, rather than the usual statistical approach, is taken to explore the physical mechanisms underlying the nonlinear transfer of energy, the damping of the turbulent fluctuations, and the development of coherent structures in kinetic plasma turbulence. It is argued that the linear and nonlinear dynamics of Alfven waves are responsible, at a very fundamental level, for some of the key qualitative features of plasma turbulence that distinguish it from hydrodynamic turbulence, including the anisotropic cascade of energy and the development of current sheets at small scales. The …
Turbulence of magnetohydrodynamic waves in nature and in the laboratory is generally cross-helical or non-balanced, in that the energies of Afvén waves moving in opposite directions along the guide magnetic field are unequal. Based on high-resolution numerical simulations it is proposed that such turbulence spontaneously generates a condensate of the residual energy $E_v-E_b$ at small field-parallel wave numbers. As a result, the energy spectra of counter-propagating Alfvén waves are not scale-invariant. In the limit of infinite Reynolds number, the universality is asymptotically restored at l…
Characterization of compressible fluctuations in solar wind streams dominated by balanced and imbalanced turbulence: Parker Solar Probe, Solar Orbiter and Wind observations
The University of Texas at Austin（德克萨斯大学奥斯汀分校）
研究通过分析Wind、Solar Orbiter和Parker Solar Probe的数据，探讨太阳风中压缩性波动的尺度依赖性和与等离子体β值及径向距离的关系，揭示压缩性波动在太阳风加速和加热中的作用。
Astronomical Institute of the Czech Academy of Sciences（捷克科学院天文研究所）；Institute of Atmospheric Physics of the Czech Academy of Sciences（捷克科学院大气物理研究所）；Department of Electromagnetism and Electronics, University of Murcia（穆尔西亚大学电磁与电子系）
To faithfully simulate ITER and other modern fusion devices, one must resolve electron and ion fluctuation scales in a five-dimensional phase space and time. Simultaneously, one must account for the interaction of this turbulence with the slow evolution of the large-scale plasma profiles. Because of the enormous range of scales involved and the high dimensionality of the problem, resolved first-principles global simulations are very challenging using conventional (brute force) techniques. In this thesis, the problem of resolving turbulence is addressed by developing velocity space resolution d…
A numerically efficient framework that takes into account the effect of the Coulomb collision operator at arbitrary collisionalities is introduced. Such model is based on the expansion of the distribution function on a Hermite-Laguerre polynomial basis, to study the effects of collisions on magnetized plasma instabilities at arbitrary mean-free path. Focusing on the drift-wave instability, we show that our framework allows retrieving established collisional and collisionless limits. At the intermediate collisionalities relevant for present and future magnetic nuclear fusion devices, deviations…
This paper describes a conceptual framework for understanding kinetic plasma turbulence as a generalized form of energy cascade in phase space. It is emphasized that conversion of turbulent energy into thermodynamic heat is only achievable in the presence of some (however small) degree of collisionality. The smallness of the collision rate is compensated by the emergence of small-scale structure in the velocity space. For gyrokinetic turbulence, a nonlinear perpendicular phase mixing mechanism is identified and described as a turbulent cascade of entropy fluctuations simultaneously occurring a…
This paper presents the numerical verification of an asymptotic analytical solution for the nonlinear interaction between counterpropagating Alfven waves, the fundamental building block of astrophysical plasma turbulence. The analytical solution, derived in the weak turbulence limit using the equations of incompressible MHD, is compared to a nonlinear gyrokinetic simulation of an Alfven wave collision. The agreement between these methods signifies that the incompressible solution satisfactorily describes the essential dynamics of the nonlinear energy transfer, even under the weakly collisional…
Effects of Turbulent Energy Exchange between Electrons and Ions on Global Temperature Profiles
Graduate School of Frontier Science, The University of Tokyo（东京大学前沿科学研究生院）；National Institute for Fusion Science（国立研究开发法人核融合科学研究所）；Graduate School of Engineering, Kyoto University（京都大学工学研究科）
Kinetic Alfvén waves (KAWs) are the short-wavelength extension of the MHD Alfvén-wave branch in the case of highly-oblique propagation with respect to the background magnetic field. Observations of space plasma show that small-scale turbulence is mainly KAW-like. We apply two theoretical approaches, collisional two-fluid theory and collisionless kinetic theory, to obtain predictions for the KAW polarizations depending on $β_\mathrm{p}$ (the ratio of the proton thermal pressure to the magnetic pressure) at the ion gyroscale in terms of fluctuations in density, bulk velocity, and pressure. We pe…
Leveling of MHD turbulence imbalance in shear flows
Abastumani Astrophysical Observatory（阿巴斯图马尼天体物理观测站）；Department of Physics, Faculty of Exact and Natural Sciences, Tbilisi State University（第比利斯国立大学精确与自然科学学院物理系）；Helmholtz-Zentrum Dresden-Rossendorf（德累斯顿-罗斯多夫亥姆霍兹中心）；M. Nodia Institute of Geophysics（M.诺迪亚地球物理研究所）
Electrostatic turbulence in weakly collisional, magnetized plasma can be interpreted as a cascade of entropy in phase space, which is proposed as a universal mechanism for dissipation of energy in magnetized plasma turbulence. When the nonlinear decorrelation time at the scale of the thermal Larmor radius is shorter than the collision time, a broad spectrum of fluctuations at sub-Larmor scales is numerically found in velocity and position space, with theoretically predicted scalings. The results are important because they identify what is probably a universal Kolmogorov-like regime for kinetic…
Transfer of free energy from large to small velocity-space scales by phase mixing leads to Landau damping in a linear plasma. In a turbulent drift-kinetic plasma, this transfer is statistically nearly canceled by an inverse transfer from small to large velocity-space scales due to "anti-phase-mixing" modes excited by a stochastic form of plasma echo. Fluid moments (density, velocity, temperature) are thus approximately energetically isolated from the higher moments of the distribution function, so phase mixing is ineffective as a dissipation mechanism when the plasma collisionality is small.
The spontaneous pedestal formation above a power threshold at the edge of magnetically confined plasma is modelled for the first time in flux driven three-dimensional fluid simulations of electromagnetic turbulence with the code EMEDGE3D. The role of the collisional friction between trapped and passing particles is shown to be the key ingredient for shearing the radial electric field, hence stabilizing the turbulence, rather than the Maxwell and Reynolds stresses. The isotope effect, observed in many tokamaks worldwide, is recovered in EMEDGE3D simulations: the power threshold for pedestal for…
This study traces the emergence of sheared axial flow from collisional drift wave turbulence with broken symmetry in a linear plasma device---CSDX. As the density profile steepens, the axial Reynolds stress develops and drives a radially sheared axial flow that is parallel to the magnetic field. Results show that the non-diffusive piece of the Reynolds stress is driven by the density gradient and results from the spectral asymmetry of the turbulence and thus is dynamical in origin. Taken together, these findings constitute the first simultaneous demonstration of the causal link between the den…
The saturated state of turbulence driven by the ion-temperature-gradient instability is investigated using a two-dimensional long-wavelength fluid model that describes the perturbed electrostatic potential and perturbed ion temperature in a magnetic field with constant curvature (a $Z$-pinch) and an equilibrium temperature gradient. Numerical simulations reveal a well-defined transition between a finite-amplitude saturated state dominated by strong zonal-flow and zonal-temperature perturbations, and a blow-up state that fails to saturate on a box-independent scale. We argue that this transitio…
Turbulent high-energy astrophysical systems often feature asymmetric energy injection: for instance, Alfven waves propagating from an accretion disk into its corona. Such systems are "imbalanced": the energy fluxes parallel and anti-parallel to the large-scale magnetic field are unequal. In the past, numerical studies of imbalanced turbulence have focused on the magnetohydrodynamic regime. In the present study, we investigate externally-driven imbalanced turbulence in a collisionless, ultrarelativistically hot, magnetized pair plasma using three-dimensional particle-in-cell (PIC) simulations. …
The transport of heat and particles in the relatively collisional edge regions of magnetically confined plasmas is a scientifically challenging and technologically important problem. Understanding and predicting this transport requires the self-consistent evolution of plasma fluctuations, global profiles and flows, but the numerical tools capable of doing this in realistic (diverted) geometry are only now being developed. Here a 5-field reduced 2-fluid plasma model for the study of instabilities and turbulence in magnetised plasmas is presented, built on the BOUT++ framework. This cold ion mod…
This work, which extends Squire et al. [ApJL, 830 L25 (2016)], explores the effect of self-generated pressure anisotropy on linearly polarized shear-Alfvén fluctuations in low-collisionality plasmas. Such anisotropies lead to stringent limits on the amplitude of magnetic perturbations in high-beta plasmas, above which a fluctuation can destabilize itself through the parallel firehose instability. This causes the wave frequency to approach zero, "interrupting" the wave and stopping its oscillation. These effects are explored in detail in the collisionless and weakly collisional "Braginskii" reg…
A refined cascade model for kinetic turbulence in weakly collisional astrophysical plasmas is presented that includes both the transition between weak and strong turbulence and the effect of nonlocal interactions on the nonlinear transfer of energy. The model describes the transition between weak and strong MHD turbulence and the complementary transition from strong kinetic Alfven wave (KAW) turbulence to weak dissipating KAW turbulence, a new regime of weak turbulence in which the effects of shearing by large scale motions and kinetic dissipation play an important role. The inclusion of the e…
