Imbalanced Turbulence Research Articles

On the Heating of the Slow Solar Wind by Imbalanced Alfvén-wave Turbulence from 0.06 to 1 au: Parker Solar Probe and Solar Orbiter Observations

In this work we analyze plasma and magnetic field data provided by the Parker Solar Probe and Solar Orbiter missions to investigate the radial evolution of the heating of Alfvénic slow wind by imbalanced Alfvén-wave (AW) turbulent fluctuations from 0.06 to 1 au. in our analysis we focus on slow solar-wind intervals with highly imbalanced and incompressible turbulence (i.e., magnetic compressibility C B = δ B/B ≤ 0.25, plasma compressibility C n = δ n/n ≤ 0.25, and normalized cross helicity σ c ≥ 0.65). First, we estimate the AW turbulent dissipation rate from the wave energy equation and find that the radial profile trend is similar to the proton heating rate. Second, we find that the scaling of the empirical AW turbulent dissipation rate Q W obtained from the wave energy equation matches the scaling from the phenomenological AW turbulent dissipation rate Q CH09 (with Q CH09 ≃ 1.55Q W ) derived by Chandran & Hollweg based on the model of reflection-driven turbulence. Our results suggest that, as in the fast solar wind, AW turbulence plays a major role in the ion heating that occurs in incompressible slow-wind streams.

Gyrofluid simulations of turbulence and reconnection in space plasmas

A Hamiltonian two-field gyrofluid model is used to investigate the dynamics of an electron-ion collisionless plasma subject to a strong ambient magnetic field, within a spectral range extending from the magnetohydrodynamic (MHD) scales to the electron skin depth. This model isolates Alfvén, Kinetic Alfvén and Inertial Kinetic Alfvén waves that play a central role in space plasmas, and extends standard reduced fluid models to broader ranges of the plasma parameters. Recent numerical results are reviewed, including (i) the reconnection-mediated MHD turbulence developing from the collision of counter-propagating Alfvén wave packets, (ii) the specific features of the cascade dynamics in strongly imbalanced turbulence, including a possible link between the existence of a spectral transition range and the presence of co-propagating wave interactions at sub-ion scales, for which new simulations are reported, (iii) the influence of the ion-to-electron temperature ratio in two-dimensional collisionless magnetic reconnection. The role of electron finite Larmor radius corrections is pointed out and the extension of the present model to a four-field gyrofluid model is discussed. Such an extended model accurately describes electron finite Larmor radius effects at small or moderate values of the electron beta parameter, and also retains the coupling to slow magnetosonic waves.

Electron–Ion Heating Partition in Imbalanced Solar-wind Turbulence

A likely candidate mechanism to heat the solar corona and solar wind is low-frequency “Alfvénic” turbulence sourced by magnetic fluctuations near the solar surface. Depending on its properties, such turbulence can heat different species via different mechanisms, and the comparison of theoretical predictions to observed temperatures, wind speeds, anisotropies, and their variation with heliocentric radius provides a sensitive test of this physics. Here we explore the importance of normalized cross helicity, or imbalance, for controlling solar-wind heating, since it is a key parameter of magnetized turbulence and varies systematically with wind speed and radius. Based on a hybrid-kinetic simulation in which the forcing’s imbalance decreases with time—a crude model for a plasma parcel entrained in the outflowing wind—we demonstrate how significant changes to the turbulence and heating result from the “helicity barrier” effect. Its dissolution at low imbalance causes its characteristic features—strong perpendicular ion heating with a steep “transition-range” drop in electromagnetic fluctuation spectra—to disappear, driving a larger fraction of the energy into electrons and parallel ion heat, and halting the emission of ion-scale waves. These predictions seem to agree with a diverse array of solar-wind observations, offering to explain a variety of complex correlations and features within a single theoretical framework.

Imbalanced Turbulence Modified by Large-scale Velocity Shears in the Solar Wind

We have investigated how the degree of imbalance in solar wind turbulence is modified by large-scale velocity shears in the solar wind plasma. The balance between counterpropagating Alfvénic fluctuations, which interact nonlinearly to generate the turbulence, has been quantified by the cross helicity and Elsasser ratio. Velocity shears at a 30 minute timescale were identified, with the shear amplitude defined in terms of the linear Kelvin–Helmholtz (KH) instability threshold. The shears were associated with 74 interplanetary coronal mass ejection (ICME) sheaths observed by the Wind spacecraft at 1 au between 1997 and 2018. Typically weaker shears upstream of the sheaths and downstream in the ICME ejecta were also analyzed. In shears below the KH threshold, imbalance was approximately invariant or weakly rising with shear amplitude. Above the KH threshold, fluctuations tended toward a balanced state with increasing shear amplitude. Magnetic compressibility was also found to increase above the KH threshold. These findings are consistent with velocity shears being local sources of sunward fluctuations that act to reduce net imbalances in the antisunward direction, and suggest that the KH instability plays a role in this process.

MHD turbulence: a biased review

This review of scaling theories of magnetohydrodynamic (MHD) turbulence aims to put the developments of the last few years in the context of the canonical time line (from Kolmogorov to Iroshnikov–Kraichnan to Goldreich–Sridhar to Boldyrev). It is argued that Beresnyak's (valid) objection that Boldyrev's alignment theory, at least in its original form, violates the Reduced-MHD rescaling symmetry can be reconciled with alignment if the latter is understood as an intermittency effect. Boldyrev's scalings, a version of which is recovered in this interpretation, and the concept of dynamic alignment (equivalently, local 3D anisotropy) are thus an example of a physical theory of intermittency in a turbulent system. The emergence of aligned structures naturally brings into play reconnection physics and thus the theory of MHD turbulence becomes intertwined with the physics of tearing, current-sheet disruption and plasmoid formation. Recent work on these subjects by Loureiro, Malletet al.is reviewed and it is argued that we may, as a result, finally have a reasonably complete picture of the MHD turbulent cascade (forced, balanced, and in the presence of a strong mean field) all the way to the dissipation scale. This picture appears to reconcile Beresnyak's advocacy of the Kolmogorov scaling of the dissipation cutoff (as$\mathrm {Re}^{3/4}$) with Boldyrev's aligned cascade. It turns out also that these ideas open the door to some progress in understanding MHD turbulence without a mean field – MHD dynamo – whose saturated state is argued to be controlled by reconnection and to contain, at small scales, a tearing-mediated cascade similar to its strong-mean-field counterpart (this is a new result). On the margins of this core narrative, standard weak-MHD-turbulence theory is argued to require some adjustment – and a new scheme for such an adjustment is proposed – to take account of the determining part that a spontaneously emergent 2D condensate plays in mediating the Alfvén-wave cascade from a weakly interacting state to a strongly turbulent (critically balanced) one. This completes the picture of the MHD cascade at large scales. A number of outstanding issues are surveyed: imbalanced turbulence (for which a new, tentative theory is proposed), residual energy, MHD turbulence at subviscous scales, and decaying MHD turbulence (where there has been dramatic progress recently, and reconnection again turned out to feature prominently). Finally, it is argued that the natural direction of research is now away from the fluid MHD theory and into kinetic territory – and then, possibly, back again. The review lays no claim to objectivity or completeness, focusing on topics and views that the author finds most appealing at the present moment.

Structure and fluctuations of a slow ICME sheath observed at 0.5 au by the Parker Solar Probe

Context.Sheath regions ahead of interplanetary coronal mass ejections (ICMEs) are compressed and turbulent global heliospheric structures. Their global and fine-scale structure are outstanding research problems, and only a few studies have been conducted on this topic closer to the Sun than 1 au. Comprehensive knowledge of the sheath structure and embedded fluctuations and of their evolution in interplanetary space is important for understanding their geoeffectiveness, their role in accelerating charged particles to high energies, the interaction of ICMEs with the ambient wind, and the transport of energy between boundaries.Aims.Our key aims are to investigate in detail the overall structure, as well as nature (stochastic, chaotic, or periodic) and origin, of magnetic fluctuations within a sheath ahead of a slow ICME in the inner heliosphere.Methods.We used magnetic field and plasma observations from the Parker Solar Probe (PSP) during a sheath region observed at ∼0.5 au on March 15, 2019, ahead of a slow and slowly expanding streamer blow-out CME bracketed between a slower and faster stream. To examine the magnetohydrodynamic-scale turbulent properties, we present an analysis of the fluctuation amplitudes, magnetic compressibility of fluctuations, partial variance of increments (PVI), normalised cross helicity (σc), and normalised residual energy (σr). We also conducted a Jensen-Shannon permutation entropy and complexity analysis.Results.The investigated sheath consisted of slower and faster flows that were separated by a brief (∼15 min) change in the magnetic sector bounded by current sheet crossings and a velocity shear zone. The fluctuation amplitudes and frequency of high PVI values were larger and higher throughout the sheath than in the upstream wind and had dominantly negativeσrand strongly positiveσc. The velocity shear region marked a strong increase in temperature and specific entropy, and the following faster flow had large local patches of positiveσras well as larger fluctuation amplitudes and higher PVI values, in particular at smaller timescales. Fluctuations in the preceding wind and in the sheath were found to be stochastic. However, sheath fluctuations showed lower entropy and higher complexity, with entropy showing a reducing and complexity an increasing trend with increasing time lag.Conclusions.The two-part sheath structure was likely a result of a warp in the heliospheric current sheet (HCS) that was swept up and compressed into the sheath. The driving ejecta accelerated and heated the wind at the back of the sheath, which then interacted with the slower wind ahead of the HCS warp. This also caused some distinct differences in fluctuation properties across the sheath. Sheaths of slow ICMEs originating as streamer blow-outs can thus have complex structure where fluctuation properties are not just downstream shock properties, but are generated within the sheath. At short timescales, fluctuations feature fully developed and imbalanced MHD turbulence, while at longer scales, fluctuations are increasingly dominated by intermittent coherent and ordered structures.

Analysis of Magnetohydrodynamic Perturbations in the Radial-field Solar Wind from Parker Solar Probe Observations

Abstract We report analysis of sub-Alfvénic magnetohydrodynamic (MHD) perturbations in the low-β radial-field solar wind employing the Parker Solar Probe spacecraft data from 2018 October 31 to November 12. We calculate wavevectors using the singular value decomposition method and separate MHD perturbations into three eigenmodes (Alfvén, fast, and slow modes) to explore the properties of sub-Alfvénic perturbations and the role of compressible perturbations in solar wind heating. The MHD perturbations show a high degree of Alfvénicity in the radial-field solar wind, with the energy fraction of Alfvén modes dominating (∼45%–83%) over those of fast modes (∼16%–43%) and slow modes (∼1%–19%). We present a detailed analysis of a representative event on 2018 November 10. Observations show that fast modes dominate magnetic compressibility, whereas slow modes dominate density compressibility. The energy damping rate of compressible modes is comparable to the heating rate, suggesting the collisionless damping of compressible modes could be significant for solar wind heating. These results are valuable for further studies of the imbalanced turbulence near the Sun and possible heating effects of compressible modes at MHD scales in low-β plasma.

Kinetic simulations of imbalanced turbulence in a relativistic plasma: Net flow and particle acceleration

ABSTRACT Turbulent high-energy astrophysical systems often feature asymmetric energy injection: for instance, Alfvén waves propagating from an accretion disc into its corona. Such systems are ‘imbalanced’: the energy fluxes parallel and antiparallel to the large-scale magnetic field are unequal. In the past, numerical studies of imbalanced turbulence have focused on the magnetohydrodynamic regime. In this study, we investigate externally driven imbalanced turbulence in a collision-less, ultrarelativistically hot, magnetized pair plasma using 3D particle-in-cell (PIC) simulations. We find that the injected electromagnetic momentum efficiently converts into plasma momentum, resulting in net motion along the background magnetic field with speeds up to a significant fraction of lightspeed. This discovery has important implications for the launching of accretion disc winds. We also find that although particle acceleration in imbalanced turbulence operates on a slower time-scale than in balanced turbulence, it ultimately produces a power-law energy distribution similar to balanced turbulence. Our results have ramifications for black hole accretion disc coronae, winds, and jets.

Threaded-field-line Model for the Low Solar Corona Powered by the Alfvén Wave Turbulence

Abstract We present an updated global model of the solar corona, including the transition region. We simulate the realistic three-dimensional (3D) magnetic field using the data from the photospheric magnetic field measurements and assume the magnetohydrodynamic (MHD) Alfvén wave turbulence and its nonlinear dissipation to be the only source for heating the coronal plasma and driving the solar wind. In closed-field regions, the dissipation efficiency in a balanced turbulence is enhanced. In the coronal holes, we account for a reflection of the outward-propagating waves, which is accompanied by the generation of weaker counterpropagating waves. The nonlinear cascade rate degrades in strongly imbalanced turbulence, thus resulting in colder coronal holes. The distinctive feature of the presented model is the description of the low corona as almost-steady-state low-beta plasma motion and heat flux transfer along the magnetic field lines. We trace the magnetic field lines through each grid point of the lower boundary of the global corona model, chosen at some heliocentric distance, R = R b ∼ 1.1R ⊙, well above the transition region. One can readily solve the plasma parameters along the magnetic field line from 1D equations for the plasma motion and heat transport together with the Alfvén wave propagation, which adequately describe the physics within the heliocentric distance range R ⊙ < R < R b , in the low solar corona. By interfacing this threaded-field-line model with the full MHD global corona model at r = R b , we find the global solution and achieve a faster-than-real-time performance of the model on ∼200 cores.

Spectrum of imbalanced Alfvénic turbulence at ion-kinetic scales in the solar wind

Using a semi-phenomenological model of the imbalanced Alfvenic turbulence, we study the turbulence transition from magnetohydrodynamic to sub-ion kinetic scales in the conditions typical for the fast solar wind. We show that the transition takes place in a wide wave number interval where the energy spectrum does not follow any power law. For larger turbulence imbalances, both boundaries of the transition wave number interval shift to larger scales. The energy exchange between dominant and subdominant components of the turbulence is essential in the model reducing the imbalance at kinetic scales; however, the total balance is never reached. Our results are compatible with recent solar wind observations at ion scales and numerical simulations of imbalanced turbulence.

Spectral Anisotropy in 2D plus Slab Magnetohydrodynamic Turbulence in the Solar Wind and Upper Corona

Abstract The 2D + slab superposition model of solar wind turbulence has its theoretical foundations in nearly incompressible magnetohydrodynamics (NI MHD) in the plasma beta ∼1 or ≪1 regimes. Solar wind turbulence measurements show that turbulence in the inertial range is anisotropic, for which the superposition model offers a plausible explanation. We provide a detailed theoretical analysis of the spectral characteristics of the Elsässer variables in the 2D + NI/slab model. We find that (1) the majority 2D component has a power spectrum in perpendicular wavenumber k ⊥; (2) the strongly imbalanced minority NI/slab turbulence has power spectra and , where k z is aligned with the mean magnetic field; (3) NI/slab turbulence can exhibit a double-power-law spectrum, with the steeper part being G*(k) ∼ k −5/3 and corresponding to strong turbulence and the flatter spectrum satisfying G*(k) ∼ k −3/2 and corresponding to weak turbulence; (4) there is a critical balance regime for NI/slab turbulence that satisfies and ; and (5) the forward and backward Elsässer power spectra can have different spectral forms provided that the triple-correlation times for each are different. We use the spectral analysis to compute the total power spectra in frequency parallel to the solar wind flow for the superposition model, showing that strongly imbalanced turbulence yields an f −5/3 spectrum for all angles between the mean flow and magnetic field, and that double power laws are possible when the nonlinear and Alfvén timescales are both finite.

Eulerian space-time correlation of strong magnetohydrodynamic turbulence

In this work the scale-dependent temporal decorrelation of incompressible MHD turbulence is investigated by means of high-resolution numerical simulations and phenomenological modeling. The simulations show that counterpropagating Alfv\'enic fluctuations at each scale decorrelate at the same rate in both balanced and imbalanced turbulence, and consistent with random advection of small-scale eddies by the velocity of the energy containing scales.

A Nearly Incompressible Turbulence-Driven Solar Wind Model

We develop a 1D steady-state turbulence driven-solar wind model by coupling recently developed nearly incompressible magnetohydrodynamic turbulence transport model equations and 1D hydrodynamic solar wind equations. The dissipation of majority component quasi-2D turbulence and minority slab turbulence generated by the emergence of the “magnetic carpet” from the photosphere is responsible for heating the coronal plasma. We solve the coupled quasi-2D and slab turbulence transport equations and the solar wind equations from the base of the solar corona until 20 solar radii. We find that i) the coronal temperature increases to ~ 2.5 × 106 K near the base of the solar corona; ii) the solar wind accelerates rapidly within a few solar radii; iii) turbulence energy densities decrease and correlation lengths increase with distance; iv) balanced quasi-2D turbulence at the coronal base becomes imbalanced, and imbalanced slab turbulence becomes more imbalanced with distance, and v) the normalized quasi-2D and slab residual energy becomes positive near the coronal base, and both energies become negative with increasing distance.

Solar Plasma Radio Emission in the Presence of Imbalanced Turbulence of Kinetic-Scale Alfvén Waves

We study the influence of kinetic-scale Alfv\'enic turbulence on the generation of plasma radio emission in the solar coronal regions where the plasma/magnetic pressure ratio $\beta $ is smaller than the electron/ion mass ratio $m_{e}/m_{i}$. The present study is motivated by the phenomenon of solar type I radio storms associated with the strong magnetic field of active regions. The measured brightness temperature of the type I storms can be up to $10^{10}$ K for continuum emission, and can exceed $10^{11}$ K for type I bursts. At present, there is no generally accepted theory explaining such high brightness temperatures and some other properties of the type I storms. We propose the model with the imbalanced turbulence of kinetic-scale Alfv\'en waves producing an asymmetric quasilinear plateau on the upward half of the electron velocity distribution. The Landau damping of resonant Langmuir waves is suppressed and their amplitudes grow spontaneously above the thermal level. The estimated saturation level of Langmuir waves is high enough to generate observed type I radio emission at the fundamental plasma frequency. Harmonic emission does not appear in our model because the backward-propagating Langmuir waves undergo a strong Landau damping. Our model predicts $100\%$ polarization in the sense of the ordinary (o-) mode of type I emission.

Imbalanced magnetohydrodynamic turbulence modified by velocity shear in the solar wind

We study incompressible imbalanced magnetohydrodynamic turbulence in the presence of background velocity shears. Using scaling arguments, we show that the turbulent cascade is significantly accelerated when the background velocity shear is stronger than the velocity shears in the subdominant Alfven waves at the injection scale. The spectral transport is then controlled by the background shear rather than the turbulent shears and the Tchen spectrum with spectral index −1 is formed. This spectrum extends from the injection scale to the scale of the spectral break where the subdominant wave shear becomes equal to the background shear. The estimated spectral breaks and power spectra are in good agreement with those observed in the fast solar wind. The proposed mechanism can contribute to enhanced turbulent cascades and modified −1 spectra observed in the fast solar wind with strong velocity shears. This mechanism can also operate in many other astrophysical environments where turbulence develops on top of non-uniform plasma flows.

Spectral evolution of helical electron magnetohydrodynamic turbulence

AbstractProperties of turbulence in space plasmas above and below the proton gyroscale are very different and different descriptions should be used for the large and the small scales. On scales larger than the proton gyroscale, we can treat the plasmas as conducting fluids and use magnetohydrodynamics (MHD). However, on scales smaller than the proton gyroscale, we cannot use MHD due to various kinetic effects. Electron magnetohydrodynamics (EMHD) is a simple fluid‐like model for small‐scale plasmas. In this paper, we discuss properties of EMHD waves and turbulence. In particular, we focus on inverse cascade in EMHD turbulence. Since EMHD waves are helical and magnetic helicity is a conserved quantity, inverse cascade is expected to be a common phenomenon in EMHD. We first focus on inverse cascade and spectral evolution of completely imbalanced EMHD wave packets, in which all waves are moving in the same direction. Then, we discuss inverse cascade and spectral evolution of driven imbalanced EMHD turbulence. We also discuss “pinning” of energy spectra in imbalanced EMHD turbulence.

COSMIC-RAY PITCH-ANGLE SCATTERING IN IMBALANCED MHD TURBULENCE SIMULATIONS

Pitch-angle scattering rates for cosmic-ray particles in magnetohydrodynamic (MHD) simulations with imbalanced turbulence are calculated for fully evolving electromagnetic turbulence. We compare with theoretical predictions derived from the quasilinear theory of cosmic-ray diffusion for an idealized slab spectrum and demonstrate how cross helicity affects the shape of the pitch-angle diffusion coefficient. Additional simulations in evolving magnetic fields or static field configurations provide evidence that the scattering anisotropy in imbalanced turbulence is not primarily due to coherence with propagating Alfven waves, but an effect of the spatial structure of electric fields in cross-helical MHD turbulence.

INVERSE CASCADE IN IMBALANCED ELECTRON MAGNETOHYDRODYNAMIC TURBULENCE

Electron magnetohydrodynamics (EMHD) provides a fluid-like description of small-scale magnetized plasmas. Balanced EMHD turbulence has been studied for a long time. However, driven imbalanced EMHD turbulence, in which waves moving in one direction (dominant waves) have higher amplitudes than waves moving in the other direction (sub-dominant waves), has not been well studied. In this paper, we numerically study driven three-dimensional imbalanced weak EMHD turbulence. We find the following results. First, in driven imbalanced EMHD turbulence, we clearly observe inverse cascade of magnetic helicity, as well as magnetic energy. This is because magnetic helicity is a conserved quantity and non-zero magnetic helicity is injected into the system in driven imbalanced EMHD turbulence. Second, the magnetic energy spectrum of the dominant waves on scales larger than the energy injection scale does not show a single power-law spectrum, which indicates that the inverse cascade is not a self-similar process. The peak of the spectrum roughly follows a k –3/2 spectrum, which can be explained by a Kolmogorov-type argument for weak turbulence. Third, a small amount of sub-dominant waves is induced by the dominant waves on large scales and the ratio of helicity densities of the dominant and the sub-dominant waves on large scales seems to converge to a certain value.

Acceleration of particles in imbalanced magnetohydrodynamic turbulence

The present work investigates the acceleration of test particles, relevant to the solar-wind problem, in balanced and imbalanced magnetohydrodynamic turbulence (terms referring here to turbulent states possessing zero and nonzero cross helicity, respectively). 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 nonresonant particle accelerations are automatically considered and the correct turbulent phases are taken into account. For imbalanced turbulence, it is found that the acceleration rate of charged particles is reduced and the heating rate diminished. This behavior is independent of the particle gyroradius, although particles that have a stronger adiabatic motion (smaller gyroradius) tend to experience a larger heating.

IMBALANCED RELATIVISTIC FORCE-FREE MAGNETOHYDRODYNAMIC TURBULENCE

When magnetic energy density is much larger than that of matter, as in pulsar/black hole magnetospheres, the medium becomes force-free and we need relativity to describe it. As in non-relativistic magnetohydrodynamics (MHD), Alfv\'enic MHD turbulence in the relativistic limit can be described by interactions of counter-traveling wave packets. In this paper we numerically study strong imbalanced MHD turbulence in such environments. Here, imbalanced turbulence means the waves traveling in one direction (dominant waves) have higher amplitudes than the opposite-traveling waves (sub-dominant waves). We find that (1) spectrum of the dominant waves is steeper than that of sub-dominant waves, (2) the anisotropy of the dominant waves is weaker than that of sub-dominant waves, and (3) the dependence of the ratio of magnetic energy densities of dominant and sub-dominant waves on the ratio of energy injection rates is steeper than quadratic (i.e., \$b_+^2/b_-^2 \propto (\epsilon_+/\epsilon_-)^n \$ with n>2). These results are consistent with those obtained for imbalanced non-relativistic Alfv\'enic turbulence. This corresponds well to the earlier reported similarity of the relativistic and non-relativistic balanced magnetic turbulence.