We consider the problem of spectra for acoustic type of turbulence generated by shocks being randomly distributed in space. We show that for turbulence with a weak anisotropy such spectra have the same dependence in $k$-space as the Kadomtsev-Petviashvili (KP) spectrum: $E(k)\sim k^{-2}$. However, the frequency spectrum has always the falling $\sim ω^{-2}$, independently on anisotropy. In the strong anisotropic case the energy distribution relative to wave vectors takes anisotropic dependence forming in the large $% k $ region the spectra of the jet type.
The theory of the nonmodal ion-acoustic instability in the skin layer of the inductively coupled plasma (ICP) is developed. This instability has time dependent growth rate and is driven by the current formed in the skin layer by the accelerated motion of electrons relative to ions under the action of the ponderomotive force. It is found that the development of the ion acoustic turbulence (IAT) in the skin layer and the scattering of electrons by IAT are basic nonlinear channels of the nonlinear absorption of the RF energy in the skin layer.
In this work the first demonstration of a high frequency branch of the geodesic acoustic mode (GAM) driven by electron temperature gradient (ETG) modes is presented. The work is based on a fluid description of the ETG mode retaining non-adiabatic ions and the dispersion relation for high frequency GAMs driven nonlinearly by ETG modes is derived. A new saturation mechanism for ETG turbulence through the interaction with high frequency GAMs is found, resulting in a significantly enhanced ETG turbulence saturation level compared to the mixing length estimate.
We study electron heating in collisionless current-driven turbulence due to the nonlinear interactions between electron- and ion-acoustic waves. PIC simulation results show that due to a large difference between the electron and ion mean velocities the Buneman instability excites large-amplitude ion-acoustic waves, which strongly modifies the electron velocity distribution function, leading to a secondary instability that generates fast electron-acoustic waves; and in this process, a giant electron hole is ultimately created. This giant electron hole is responsible for strong electron heating …
In this work the finite $β$-effects of an electron branch of the geodesic acoustic mode (el-GAM) driven by electron temperature gradient (ETG) modes is presented. The work is based on a fluid description of the ETG mode retaining non-adiabatic ions and the dispersion relation for el-GAMs driven non-linearly by ETG modes is derived. The ETG growth rate from the fluid model is compared to the results found from gyrokinetic simulations with good agreement. A new saturation mechanism for ETG turbulence through the interaction with el-GAMs is found, resulting in a significantly enhanced ETG turbule…
The problem of the occurrence of an energy cascade for Alfvénic turbulence in solar wind plasmas was hystorically addressed by using phenomenological arguments based to the weakness of nonlinear interactions and the anisotropy of the cascade in wave vectors space. Here, this paradox is reviewed through the formal derivation of a Yaglom relation from anisotropic Magnetohydrodynamic equation. The Yaglom relation involves a third-order moment calculated from velocity and magnetic fields and involving both Elsässer vector fields, and is particularly useful to be used as far as spacecraft observati…
We present a linear stability analysis of the perturbation modes in anisotropic MHD flows with velocity shear and strong magnetic field. Collisionless or weakly collisional plasma is described within the 16-momentum MHD fluid closure model, that takes into account not only the effect of pressure anisotropy, but also the effect of anisotropic heat fluxes. In this model the low frequency acoustic wave is revealed into a standard acoustic mode and higher frequency fast thermo-acoustic and lower frequency slow thermo-acoustic waves. It is shown that thermo-acoustic waves become unstable and grow e…
We present a quantitative estimate of the anisotropic power and scaling of magnetic field fluctuations in inertial range magnetohydrodynamic turbulence, using a novel wavelet technique applied to spacecraft measurements in the solar wind. We show for the first time that, when the local magnetic field direction is parallel to the flow, the spacecraft-frame spectrum has a spectral index near 2. This can be interpreted as the signature of a population of fluctuations in field-parallel wavenumbers with a $k_{\parallel}^{-2}$ spectrum but is also consistent with the presence of a "critical balance"…
We investigate the influence of a uniform magnetic field ${\bf B_0}=B_0 e//$ on energy decay laws in incompressible magnetohydrodynamic (MHD) turbulence. The nonlinear transfer reduction along $B_0$ is included in a model that distinguishes parallel and perpendicular directions, following a phenomenology {\it à la} Kraichnan. We predict a slowing down of the energy decay due to anisotropy in the limit of strong $B_0$, with distinct power laws for energy decay of shear- and pseudo-Alfvén waves. Numerical results from the kinetic equations of Alfvén wave turbulence recover these predictions, and…
For a Z-pinch geometry, we report on the nonlinear redistribution of free energy across scales perpendicular to the magnetic guide field, for a turbulent plasma described in the framework of gyrokinetics. The analysis is performed using a local flux-surface approximation, in a regime dominated by electrostatic fluctuations driven by the entropy mode, with both ion and electron species being treated kinetically. To explore the anisotropic nature of the free energy redistribution caused by the emergence of zonal flows, we use a polar coordinate representation for the field-perpendicular directio…
Effects of anisotropy on the geodesic acoustic mode (GAM) is analyzed by using gyro-kinetic equations applicable to low-frequency microinstabilities in a toroidally rotating tokamak plasma. Dispersion relation in the presence of arbitrary Mach number $M$, anisotropy strength $σ$, and the temperature ration $τ$ is analytically derived. It is shown that when $σ$ is less than $ 3 + 2 τ$, the increased electron temperature with fixed ion parallel temperature increases the normalized GAM frequency. When $σ$ is larger than $ 3 + 2 τ$, the increasing of electron temperature decreases the GAM frequenc…
A Two-dimensional Numerical Study of Ion-Acoustic Turbulence
Massachusetts Institute of Technology（麻省理工学院）；Department of Defense（国防部）；Princeton Plasma Physics Laboratory（普林斯顿等离子体物理实验室）；Proxima Fusion GmbH（Proxima Fusion有限公司）
A higher-order multiscale analysis of spatial anisotropy in inertial range magnetohydrodynamic turbulence is presented using measurements from the STEREO spacecraft in fast ambient solar wind. We show for the first time that, when measuring parallel to the local magnetic field direction, the full statistical signature of the magnetic and Elsässer field fluctuations is that of a non-Gaussian globally scale-invariant process. This is distinct from the classic multi-exponent statistics observed when the local magnetic field is perpendicular to the flow direction. These observations are interprete…
In an earlier paper (Wan et al. 2012), the authors showed that a similarity solution for anisotropic incompressible 3D magnetohydrodynamic (MHD) turbulence, in the presence of a uniform mean magnetic field $\vB_0$, exists if the ratio of parallel to perpendicular (with respect to $\vB_0$) similarity length scales remains constant in time. This conjecture appears to be a rather stringent constraint on the dynamics of decay of the energy-containing eddies in MHD turbulence. However, we show here, using direct numerical simulations, that this hypothesis is indeed satisfied in incompressible MHD t…
The energy input and frequency shift of geodesic acoustic modes (GAMs) due to turbulence in tokamak edge plasmas are investigated in numerical two-fluid turbulence studies. Surprisingly, the turbulent GAM dispersion relation is qualitatively equivalent to the linear GAM dispersion but can have drastically enhanced group velocities. In up-down asymmetric geometry the energy input due to turbulent transport may favor the excitation of GAMs with one particular sign of the radial phase velocity relative to the magnetic drifts and may lead to pulsed GAM activity.
A heuristic model is given for anisotropic magnetohydrodynamics (MHD) turbulence in the presence of a uniform external magnetic field $B_0 {\bf {\hat e}_{\pa}}$. The model is valid for both moderate and strong $B_0$ and is able to describe both the strong and weak wave turbulence regimes as well as the transition between them. The main ingredient of the model is the assumption of constant ratio at all scales between \add{the} linear wave period and \add{the} nonlinear turnover timescale. Contrary to the model of critical balance introduced by Goldreich and Sridhar [P. Goldreich and S. Sridhar,…
The anisotropy of magnetophydrodynamic turbulence is investigated by using solar wind data from the Helios 2 spacecraft. We investigate the behaviour of the complete high-order moment tensors of magnetic field increments and we compare the usual longitudinal structure functions which have both isotropic and anisotropic contributions, to the fully anisotropic contribution. Scaling exponents have been extracted by an interpolation scaling function. Unlike the usual turbulence in fluid flows, small-scale magnetic fluctuations remain anisotropic. We discuss the radial dependence of both anisotropy…
The solar wind and the interstellar medium are permeated by large-scale magnetic fields that render magnetohydrodynamic (MHD) turbulence anisotropic. In the weak-turbulence limit in which three-wave interactions dominate, analytical and high-resolution numerical results based on random scattering of shear-Alfvén waves propagating parallel to a large-scale magnetic field, as well as direct simulations demonstrate rigorously an anisotropic energy spectrum that scales as $k^{-2}_\perp$, instead of the famous Iroshnikov-Kraichnan (IK) spectrum of $k^{-3/2}$ for the isotropic case. Even in the abse…
We derive a first exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence. For a gyrotropic pressure tensor, we study the double-adiabatic case and show the presence of new flux and source terms in the exact law, reminiscent of the plasma instability conditions due to pressure anisotropy. The Hall term is shown to bring ion-scale corrections to the exact law without affecting explicitly the pressure terms. In the pressure isotropy limit we recover all known results obtained for isothermal and polytropic closures. The incompressible limit of the gyrotropic system leads to…
Solar wind turbulence is dominated by Alfvénic fluctuations but the power spectral exponents somewhat surprisingly evolve toward the Kolmogorov value of -5/3, that of hydrodynamic turbulence. We show that at 1AU the turbulence decomposes linearly into two coexistent components perpendicular and parallel to the local average magnetic field. The first of these is consistent with propagating Alfvén wavepackets and shows the scaling expected of Alfvénic turbulence, namely Irosnikov- Kraichnan. The second shows Kolmogorov scaling which we also find in the number and magnetic energy density, and Poy…
This chapter reviews the recent progress made mainly during the last two decades on wave turbulence in magnetized plasmas (MHD, Hall MHD and electron MHD) in the incompressible and compressible cases. The emphasis is made on homogeneous and anisotropic turbulence which usually provides the best theoretical framework to investigate space and laboratory plasmas. The interplanetary medium and the solar atmosphere are presented as two examples of media where anisotropic wave turbulence is relevant. The most important results of wave turbulence are reported and discussed in the context of space and…
It has been proposed recently by Loureiro & Boldyrev [Phys. Rev. Lett. 118, 245101 (2017)] and Mallet et al. [Mon. Not. R. Astron. Soc. 468, 4862 (2017)] that strongly anisotropic current sheets formed in the inertial range of magnetohydrodynamic turbulence become affected by the tearing instability at scales smaller than a critical scale $λ_\mathrm{c}$, and larger than the dissipation scale of turbulence. If true, this process can modify the nature of energy cascade at smaller scales, leading to a new, tearing-mediated regime of magnetohydrodynamic (MHD) turbulence. In this work we present a …
In a series of experiments on the Omega laser facility at LLE, we have demonstrated the suppression of SRS in prescribed spectral windows due to the presence of externally controlled levels of ion acoustic waves (IAW, by crossing two blue beams at the Mach -1 surface) and electron plasma waves (EPW, by crossing a blue and a green beam around a tenth critical density plasma) generated via optical mixing. We have further observed SRS backscattering of a green beam when crossed with a blue pump beam, in whose absence, that (green beam) backscattering signature was five times smaller. This is dire…
Large-scale magnetic fields thread through the electrically conducting matter of the interplanetary and interstellar medium, stellar interiors, and other astrophysical plasmas, producing anisotropic flows with regions of high-Reynolds-number turbulence. It is common to encounter turbulent flows structured by a magnetic field with a strength approximately equal to the root-mean-square magnetic fluctuations. In this work, direct numerical simulations of anisotropic magnetohydrodynamic (MHD) turbulence influenced by such a magnetic field are conducted for a series of cases that have identical res…
Context. The presence of a magnetic guide field induces several types of anisotropy in solar wind turbulence. The energy cascade rate between scales in the inertial range depends strongly on the direction of this magnetic guide field, splitting the energy cascade according to the parallel and perpendicular directions with respect to magnetic guide field. Aims. Using more than two years of Parker Solar Probe (PSP) observations, the isotropy and anisotropy energy cascade rates are investigated. The variance and normalized fluctuation ratios, the kinetic and magnetic energies, and the normalized …
In this paper we analyze the effect of dynamical three-dimensional MHD turbulence on test particle acceleration, and compare how this evolving system affects particle energization by current sheets interaction, against frozen-in-time fields. To do this we analize the ensamble particle acceleration for static electromagnetic fields extracted from direct numerical simulations of the MHD equations, and compare with the dynamical fields. We show that a reduction in particle acceleration in the dynamical model results from the particle trapping in the field lines, which forces the particles to rema…
Energy dissipation in collisionless plasmas is a longstanding fundamental physics problem. Although it is well known that magnetic reconnection and turbulence are coupled and transport energy from system-size scales to sub-proton scales, the details of the energy distribution and energy dissipation channels remain poorly understood. Especially, the energy transfer and transport associated with three dimensional (3D) small-scale reconnection that occurs as a consequence of a turbulent cascade is unknown. We use an explicit fully kinetic particle-in-cell code to simulate 3D small scale magnetic …
Weak turbulence of magnetohydrodynamic (MHD) waves in strongly magnetized plasma is studied when the thermal pressure is less than the magnetic field pressure. In this situation the main nonlinear mechanism is the resonance scattering of fast magneto-acoustic and Alfvenic waves on slow magneto-acoustic waves. As a result, the former waves serve as the high-frequency waves with respect to the latter ones so that the total number of HF waves - an adiabatic invariant - conserves additionally. In the weak turbulence regime this invariant is shown to generate the Kolmogorov type spectrum with a con…
We perform a high-resolution two-dimensional fully-kinetic numerical simulation of a turbulent plasma system with observation-driven conditions, in order to investigate the interplay between turbulence, magnetic reconnection, and particle heating from ion to sub-electron scales in the near-Sun solar wind. We find that the power spectra of the turbulent plasma and electromagnetic fluctuations show multiple power-law intervals down to scales smaller than the electron gyroradius. Magnetic reconnection is observed to occur in correspondence of current sheets with a thickness of the order of the el…
We present a theoretical framework for describing electromagnetic kinetic turbulence in a multi-species, magnetized, pressure-anisotropic plasma. Turbulent fluctuations are assumed to be small compared to the mean field, to be spatially anisotropic with respect to it, and to have frequencies small compared to the ion cyclotron frequency. At scales above the ion Larmor radius, the theory reduces to the pressure-anisotropic generalization of kinetic reduced magnetohydrodynamics (KRMHD) formulated by Kunz et al. (2015). At scales at and below the ion Larmor radius, three main objectives are achie…
In presence of an externally supported, mean magnetic field a turbulent, conducting medium, such as plasma, becomes anisotropic. This mean magnetic field, which is separate from the fluctuating, turbulent part of the magnetic field, has considerable effects on the dynamics of the system. In this paper, we examine the dissipation rates for decaying incompressible magnetohydrodynamic (MHD) turbulence with increasing Reynolds number, and in the presence of a mean magnetic field of varying strength. Proceeding numerically, we find that as the Reynolds number increases, the dissipation rate asympto…
We present results from three-dimensional hybrid-kinetic simulations of Alfvénic turbulence in a high-beta, collisionless plasma. The key feature of such turbulence is the interplay between local wave--wave interactions between the fluctuations in the cascade and the non-local wave-particle interactions associated with kinetic micro-instabilities driven by anisotropy in the thermal pressure (namely, firehose, mirror, and ion-cyclotron). We present theoretical estimates for, and calculate directly from the simulations, the effective collisionality and plasma viscosity in pressure-anisotropic hi…
We use 3D fully kinetic particle-in-cell simulations to study the occurrence of magnetic reconnection in a simulation of decaying turbulence created by anisotropic counter-propagating low-frequency Alfvén waves consistent with critical-balance theory. We observe the formation of small-scale current-density structures such as current filaments and current sheets as well as the formation of magnetic flux ropes as part of the turbulent cascade. The large magnetic structures present in the simulation domain retain the initial anisotropy while the small-scale structures produced by the turbulent ca…
A theoretical framework for low-frequency electromagnetic (drift-)kinetic turbulence in a collisionless, multi-species plasma is presented. The result generalises reduced magnetohydrodynamics (RMHD) and kinetic RMHD (Schekochihin et al. 2009) for pressure-anisotropic plasmas, allowing for species drifts---a situation routinely encountered in the solar wind and presumably ubiquitous in hot dilute astrophysical plasmas (e.g. intracluster medium). Two main objectives are achieved. First, in a non-Maxwellian plasma, the relationships between fluctuating fields (e.g., the Alfven ratio) are order-un…
