Turbulence In Magnetized Plasma Research Articles

Role of nonlinear localized structures and turbulence in magnetized plasma

In the present study, we have analyzed the field localization of kinetic Alfven wave (KAW) due to the presence of background density perturbation, which are assumed to be originated by the three dimensionally propagating low frequency KAW. These localized structures play an important role for energy transportation at smaller scales in the dispersion range of magnetic power spectrum. For the present model, governing dynamic equations of high frequency pump KAW and low frequency KAW has been derived by considering ponderomotive nonlinearity. Further, these coupled equations have been numerically solved to analyze the resulting localized structures of pump KAW and magnetic power spectrum in the magnetopause regime. Numerically calculated spectrum exhibits inertial range having spectral index of \(-3/2\) followed by steeper scaling; this steepening in the turbulent spectrum is a signature of energy transportation from larger to smaller scales. In this way, the proposed mechanism, which is based on nonlinear wave-wave interaction, may be useful for understanding the particle acceleration and turbulence in magnetopause.

Viriato: A Fourier–Hermite spectral code for strongly magnetized fluid–kinetic plasma dynamics

We report on the algorithms and numerical methods used in Viriato, a novel fluid–kinetic code that solves two distinct sets of equations: (i) the Kinetic Reduced Electron Heating Model (KREHM) equations (Zocco and Schekochihin, 2011) (which reduce to the standard Reduced-MHD equations in the appropriate limit) and (ii) the kinetic reduced MHD (KRMHD) equations (Schekochihin et al., 2009). Two main applications of these equations are magnetized (Alfvénic) plasma turbulence and magnetic reconnection. Viriato uses operator splitting (Strang or Godunov) to separate the dynamics parallel and perpendicular to the ambient magnetic field (assumed strong). Along the magnetic field, Viriato allows for either a second-order accurate MacCormack method or, for higher accuracy, a spectral-like scheme composed of the combination of a total variation diminishing (TVD) third order Runge–Kutta method for the time derivative with a 7th order upwind scheme for the fluxes. Perpendicular to the field Viriato is pseudo-spectral, and the time integration is performed by means of an iterative predictor–corrector scheme. In addition, a distinctive feature of Viriato is its spectral representation of the parallel velocity-space dependence, achieved by means of a Hermite representation of the perturbed distribution function. A series of linear and nonlinear benchmarks and tests are presented, including a detailed analysis of 2D and 3D Orszag–Tang-type decaying turbulence, both in fluid and kinetic regimes.

Fundamental form of the electrostatic δf-PIC algorithm and discovery of a converged numerical instability

The δf particle-in-cell algorithm has been a useful tool in studying the physics of plasmas, particularly turbulent magnetized plasmas in the context of gyrokinetics. The reduction in noise due to not having to resolve the full distribution function indicates an efficiency advantage over the standard (“full-f”) particle-in-cell. Despite its successes, the algorithm behaves strangely in some circumstances. In this work, we document a fully resolved numerical instability that occurs in the simplest of multiple-species test cases: the electrostatic ΩH mode. There is also a poorly understood numerical instability that occurs when one is under-resolved in particle number, which may require a prohibitively large number of particles to stabilize. Both of these are independent of the time-stepping scheme, and we conclude that they exist if the time advancement were exact. The exact analytic form of the algorithm is presented, and several schemes for mitigating these instabilities are also presented.

Wavelet characterization of 2D turbulence and intermittency in magnetized electron plasmas

A study of the free relaxation of turbulence in a two-dimensional (2D) flow is presented, with a focus on the role of the initial vorticity conditions. Exploiting a well-known analogy with 2D inviscid incompressible fluids, the system investigated here is a magnetized pure electron plasma. The dynamics of this system are simulated by means of a 2D particle-in-cell code, starting from different spiral density (vorticity) distributions.A wavelet multiresolution analysis is adopted, which allows the coherent and incoherent parts of the flow to be separated. Comparison of the turbulent evolution in the different cases is based on the investigation of the time evolution of statistical properties, including the probability distribution functions and structure functions of the vorticity increments. It is also based on an analysis of the enstrophy evolution and its spectrum for the two components.In particular, while the statistical features assess the degree of flow intermittency, spectral analysis allows us not only to estimate the time required to reach a state of fully developed turbulence, but also estimate its dependence on the thickness of the initial spiral density distribution, accurately tracking the dynamics of both the coherent structures and the turbulent background. The results are compared with those relevant to annular initial vorticity distributions (Chen et al 2015 J. Plasma Phys. 81 495810511).

''DOUBLE-HUMPED EFFECT'' IN THE TURBULENT COLLISION MAGNETIZED PLASMA

Statistical moments of the spatial power spectrum of multiple scattered ordinary and extraordinary waves in the turbulent collision magnetized plasma with aligned anisotropic electron density irregularities are investigated using modify smooth perturbation method taking into account diffraction effects. Correlation function and variances of the phase fluctuations are obtained for arbitrary correlation function of the electron density fluctuations. Double-humped Effect is investigated analytically and numerically using the anisotropic Gaussian spectral function of electron density irregularities for the polar ionospheric F-region applying the experimental data. Investigation of the anisotropy of the F layer irregularities is of great interest in ionospheric physics. It is well known that the irregularities are elongated in the direction of the geomagnetic field of lines, but especially at high latitudes they are also found to be anisotropic in the plane perpendicular to the external magnetic field vector. The anisotropy is usually investigated by correlation analysis of radio signals from satellites, observed by space receiver on the ground. The fluctuations in amplitude and phase (scintillations) of radio waves passing through the ionosphere are caused by spatial irregularities in the electron density. The spatial fluctuations in phase cause fluctuations of the angle of arrival at the observation points. Broadening of the spatial power spectrum (SPS) of scattered electromagnetic (EM) waves in the turbulent collision magnetized plasma for both power-law and anisotropic Gaussian correlation functions of electron density fluctuations was analyzed in (1) using the complex ray (-optics) approximation. Double-humped Effect, the features of the SPS, spectral width and shift of its maximum of multiple scattered EM waves in the turbulent collisionless magnetized plasma were considered in (2, 3). The influence of the collision frequency between plasma particles on the statistical characteristics of scattered EM waves in the turbulent magnetized plasma with both electron density and external magnetic field fluctuations was investigated in (4). The present paper reports the results of an analysis of the SPS, which is related to fluctuations of the radio refractive index in the F region. Analytical expressions of the correlation function of phase fluctuations of scattered both ordinary and extraordinary waves are obtained for the arbitrary correlation functions of electron density fluctuation using modify smooth perturbation method taking into account the diffraction effects. The Double-humped Effect in the collision magnetized plasma with elongated electron density irregularities is considered for the first time. Formation of a gap in the SPS of scattered radiation is analyzed numerically for the polar ionospheric F -region using the anisotropic Gaussian spectral function of electron density fluctuations. This spectrum contains angle of aligned plasma irregularities to the direction of an external magnetic field and anisotropy factor. The numerical calculation is computed based on experimental data. Finally, paper concludes the obtained results and their significance.

MULTI-SPACECRAFT MEASUREMENT OF TURBULENCE WITHIN A MAGNETIC RECONNECTION JET

The relationship between magnetic reconnection and plasma turbulence is investigated using multipoint in-situ measurements from the Cluster spacecraft within a high-speed reconnection jet in the terrestrial magnetotail. We show explicitly that work done by electromagnetic fields on the particles, $\mathbf{J}\cdot\mathbf{E}$, has a non-Gaussian distribution and is concentrated in regions of high electric current density. Hence, magnetic energy is converted to kinetic energy in an intermittent manner. Furthermore, we find the higher-order statistics of magnetic field fluctuations generated by reconnection are characterized by multifractal scaling on magnetofluid scales and non-Gaussian global scale invariance on kinetic scales. These observations suggest $\mathbf{J}\cdot\mathbf{E}$ within the reconnection jet has an analogue in fluid-like turbulence theory in that it proceeds via coherent structures generated by an intermittent cascade. This supports the hypothesis that turbulent dissipation is highly nonuniform, and thus these results could have far reaching implications for space and astrophysical plasmas.

Optimising Performance through Unbalanced Decompositions

GS2 is an initial value gyrokinetic simulation code developed to study low-frequency turbulence in magnetized plasma. It is parallelised using MPI with the simulation domain decomposed across tasks. The optimal domain decomposition is non-trivial, and complicated by the different requirements of the linear and non-linear parts of the calculations. GS2 users currently choose a data layout, and are guided towards processor count that are efficient for linear calculations. These choices can, however, lead to data decompositions that are relatively inefficient for the non-linear calculations. We have analysed the performance impact of the data decompositions on the non-linear calculation and associated communications. This has helped us to optimise the decomposition algorithm by using unbalanced data layouts for the non-linear calculations whilst maintaining the existing decompositions for the linear calculations, which has completely eliminated communications for parts of the non-linear simulation and improved performance by up to 15% for a representative simulation.

Kinetic theory of weak turbulence in magnetized plasmas: Perpendicular propagation

The present paper formulates a weak turbulence theory in which electromagnetic perturbations are assumed to propagate in directions perpendicular to the ambient magnetic field. By assuming that all wave vectors lie in one direction transverse to the ambient magnetic field, the linear solution and second-order nonlinear solutions to the equation for the perturbed distribution function are obtained. Nonlinear perturbed current from the second-order nonlinearity is derived in general form, but the limiting situation of cold plasma temperature is taken in order to derive an explicit nonlinear wave kinetic equation that describes three-wave decay/coalescence interactions among X and Z modes. A potential application of the present formalism is also discussed.

Lattice Boltzmann model for collisionless electrostatic drift wave turbulence obeying Charney–Hasegawa–Mima dynamics

A lattice Boltzmann method (LBM) approach to the Charney–Hasegawa–Mima (CHM) model for adiabatic drift wave turbulence in magnetised plasmas is implemented. The CHM-LBM model contains a barotropic equation of state for the potential, a force term including a cross-product analogous to the Coriolis force in quasigeostrophic models, and a density gradient source term. Expansion of the resulting lattice Boltzmann model equations leads to cold-ion fluid continuity and momentum equations, which resemble CHM dynamics under drift ordering. The resulting numerical solutions of standard test cases (monopole propagation, stable drift modes and decaying turbulence) are compared to results obtained by a conventional finite difference scheme that directly discretizes the CHM equation. The LB scheme resembles characteristic CHM dynamics apart from an additional shear in the density gradient direction. The occurring shear reduces with the drift ratio and is ascribed to the compressible limit of the underlying LBM.

Understanding nonlinear saturation in zonal-flow-dominated ion temperature gradient turbulence

We propose a quantitative model of ion temperature gradient driven turbulence in toroidal magnetized plasmas. In this model, the turbulence is regulated by zonal flows, i.e. mode saturation occurs by a zonal-flow-mediated energy cascade (‘shearing’), and zonal flow amplitude is controlled by nonlinear decay. Our model is tested in detail against numerical simulations to confirm that both its assumptions and predictions are satisfied. Key results include (1) a sensitivity of the nonlinear zonal flow response to the energy content of the linear instability, (2) a persistence of zonal-flow-regulated saturation at high temperature gradients, (3) a physical explanation of the nonlinear saturation process in terms of secondary and tertiary instabilities, and (4) dependence of heat flux in terms of dimensionless parameters.

Finding the elusive E×B staircase in magnetized plasmas.

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.

The inherently three-dimensional nature of magnetized plasma turbulence

It is often asserted or implicitly assumed, without justification, that the results of two-dimensional investigations of plasma turbulence are applicable to the three-dimensional plasma environments of interest. A projection method is applied to derive two scalar equations that govern the nonlinear evolution of the Alfvénic and pseudo-Alfvénic components of ideal incompressible magnetohydrodynamic (MHD) plasma turbulence. The mathematical form of these equations makes clear the inherently three-dimensional nature of plasma turbulence, enabling an analysis of the nonlinear properties of two-dimensional limits often used to study plasma turbulence. In the anisotropic limit, k⊥ ≫ k∥, that naturally arises in magnetized plasma systems, the perpendicular 2D limit retains the dominant nonlinearities that are mediated only by the Alfvénic fluctuations but lacks the wave physics associated with the linear term that is necessary to capture the anisotropic cascade of turbulent energy. In the in-plane 2D limit, the nonlinear energy transfer is controlled instead by the pseudo-Alfvén waves, with the Alfvén waves relegated to a passive role. In the oblique 2D limit, an unavoidable azimuthal dependence connecting the wavevector components will likely cause artificial azimuthal asymmetries in the resulting turbulent dynamics. Therefore, none of these 2D limits is sufficient to capture fully the rich three-dimensional nonlinear dynamics critical to the evolution of plasma turbulence.

The multifractal nature of solar magnetism and the solar dynamo problem

Based on observation data with a high spatial resolution, the multifractal properties of turbulent magnetized plasma in a nonperturbed solar atmosphere are revealed. It is shown that magnetic fluxes in elements of the magnetic field, as well as the size of elements, are distributed lognormally, which is indicative of multifractality. In coronal holes (CHs), the multifractality of magnetic fields is observed on scales of 10000-400 km; at the same time, it is observed on smaller scales as the resolution improves, and its degree increases. It is shown that two subsets of granules exist: the usual granules, with a characteristic size of 1000–1300 km and Gaussian size distribution, and mini-granules, which do not have a well-pronounced characteristic size and are mostly less than 600 km in diameter. The size distribution function of the mini-granules obeys lognormal law and their multifractal character is seen on small scales down to 50 km, which allows one to make a conclusion about the presence of multifractality of photospheric plasma flows in CHs and in a nonperturbed photosphere. A conclusion is made that multifractality takes place for small-scale magnetic fields of quiet regions, as well as for large-scale fields of active regions. This makes it possible to suppose that solar magnetic fields are generated by a common nonlinear dynamical process.

Stochastic modeling of MHD turbulence in magnetized plasma

This paper concerns the magneto-fluid dynamics modeled by the stochastic flow where the turbulent term is driven by the random forcing. Magnetohydrodynamic (MHD) turbulence can be interpreted in terms of a standard map (SM), modeling perturbed Hamiltonian systems, to explain some of the features of the problem. The dynamics generated by SM, although being chaotic, are influenced by periodic islands embedded in the chaotic sea due to stickiness effect and also to the behavior of the diffusion coefficient. Anomalous diffusion exists only up to some crossover time, beyond which the diffusion is Gaussian consistent with quasi-linear predictions. The results can be applicable to systems where there exist intensive interaction between a stochastic turbulent system and waves.

Nonlinear competition of turbulent structures and improved confinement in magnetized cylindrical plasmas

Nonlinear competition of turbulent structures and their roles in transport are investigated by using three-dimensional simulation code of resistive drift wave turbulence in magnetized cylindrical plasmas. Selective formation of zonal flows and streamers has been obtained by controlling the strength of damping of the zonal flow. In addition, there is an energy path from the drift waves to a flute type structure, which is linearly stable, and it becomes effective just below the stability boundary of the zonal flow. The flute structure directly induces transport effectively, and affects the drift waves and the zonal flow. A large amplitude zonal flow is formed selectively even with existence of the flute structure. The property of the particle confinement is investigated by changing the particle source intensity, which controls the strength of driving of the drift waves. The characteristic of the particle confinement changes according to turbulent states, and an improved confinement regime is obtained in the zonal flow dominant state. Study on cylindrical plasmas reveals the fundamental mechanism of improved confinement in the magnetized plasma with influence of turbulent structural formation.

The statistics of a passive scalar in field-guided magnetohydrodynamic turbulence

A variety of studies of magnetised plasma turbulence invoke theories for the advection of a passive scalar by turbulent fluctuations. Examples include modelling the electron density fluctuations in the interstellar medium, understanding the chemical composition of galaxy clusters and the intergalactic medium, and testing the prevailing phenomenological theories of magnetohydrodynamic turbulence. While passive scalar turbulence has been extensively studied in the hydrodynamic case, its counterpart in MHD turbulence is significantly less well understood. Herein we conduct a series of high-resolution direct numerical simulations of incompressible, field-guided, MHD turbulence in order to establish the fundamental properties of passive scalar evolution. We study the scalar anisotropy, establish the scaling relation analogous to Yaglom’s law, and measure the intermittency of the passive scalar statistics. We also assess to what extent the pseudo Alfvén fluctuations in strong MHD turbulence can be modelled as a passive scalar. The results suggest that the dynamics of a passive scalar in MHD turbulence is considerably more complicated than in the hydrodynamic case.

Landau fluid closures with nonlinear large-scale finite Larmor radius corrections for collisionless plasmas

With the aim to develop a tool for simulating turbulence in collisionless magnetized plasmas, fluid models retaining low-frequency kinetic effects such as Landau damping and finite Larmor radius (FLR) corrections are discussed. It turns out that, in the absence of ion-cyclotron resonance, the dispersion and damping of kinetic Alfvén waves at scales as small as a fraction of the ion Larmor radius are accurately reproduced when using fluid estimates of the non-gyrotropic moments, at leading-order within a large-scale asymptotics. Differently, evaluations based on the low-frequency linear kinetic theory are necessary in regimes of large temperature anisotropies, and in particular in the presence of the mirror instability. Combining both descriptions leads to a new Landau fluid model retaining large-scale FLR nonlinearities, while reproducing the linear dynamics of low-frequency modes at the sub-ionic scales.

The energetic coupling of scales in gyrokinetic plasma turbulence

In magnetized plasma turbulence, the couplings of perpendicular spatial scales that arise due to the nonlinear interactions are analyzed from the perspective of the free-energy exchanges. The plasmas considered here, with appropriate ion or electron adiabatic electro-neutrality responses, are described by the gyrokinetic formalism in a toroidal magnetic geometry. Turbulence develops due to the electrostatic fluctuations driven by temperature gradient instabilities, either ion temperature gradient (ITG) or electron temperature gradient (ETG). The analysis consists in decomposing the system into a series of scale structures, while accounting separately for contributions made by modes possessing special symmetries (e.g., the zonal flow modes). The interaction of these scales is analyzed using the energy transfer functions, including a forward and backward decomposition, scale fluxes, and locality functions. The comparison between the ITG and ETG cases shows that ETG turbulence has a more pronounced classical turbulent behavior, exhibiting a stronger energy cascade, with implications for gyrokinetic turbulence modeling.

KINETIC TURBULENCE IN THE TERRESTRIAL MAGNETOSHEATH: CLUSTER OBSERVATIONS

We present a first statistical study of subproton- and electron-scale turbulence in the terrestrial magnetosheath using waveform data measured by the Cluster/STAFF search coil magnetometer in the frequency range [1, 180] Hz. It is found that clear spectral breaks exist near the electron scale, which separate two power-law-like frequency bands referred to as the dispersive and the electron dissipation ranges. The frequencies of the breaks fb are shown to be well correlated with the electron gyroscale ρ e rather than with the electron inertial length de . The distribution of the slopes below fb is found to be narrow and peaks near –2.9, while that of the slopes above fb is found to be broader, peaking near –5.2, with values as low as –7.5. This is the first time that such steep power-law spectra are reported in space plasma turbulence. These observations provide new constraints on theoretical modeling of kinetic turbulence and dissipation in collisionless magnetized plasmas.

Study of wave propagation in various kinds of plasmas using adapted simulation methods, with illustrations on possible future applications

Abstract The understanding of wave propagation in turbulent magnetized plasmas can be rather complex, particularly if they are inhomogeneous and time-dependent. Simulation can be a useful tool for wave propagation studies, provided that the “model” equations take into account the characteristics of the medium relevant for the studied problem and that the numerical scheme including boundary conditions is stable and accurate enough. The choices for the model equations and the corresponding schemes are analyzed and discussed as a function of various parameters, such as the order of the numerical scheme and the number of grid points per wavelength. A quick review of the up-to-date numerical developments is given on the sheath boundary conditions and on the perfect matching layer in anisotropic media. Possible developments of plasma diagnostics conclude this state-of-the-art of simulations of electromagnetic waves in plasmas.