Gyrokinetic simulations of solar wind turbulence from ion to electron scales

Monofractality in the Solar Wind at Electron Scales: Insights from Kinetic Alfvén Waves Turbulence

The breakdown of scale invariance in turbulent flows, known as multifractal scaling, is considered a cornerstone of turbulence. In solar wind turbulence, a monofractal behavior can be observed at electron scales, in contrast to larger scales where multifractality always prevails. Why scale invariance appears at electron scales is a challenging theoretical puzzle with important implications for understanding solar wind heating and acceleration. We investigate this long-standing problem using direct numerical simulations of three-dimensional electron reduced magnetohydrodynamics. Both weak and strong kinetic Alfvén waves turbulence regimes are studied in the balanced case. After recovering the expected theoretical predictions for the magnetic spectra, a higher-order multiscale statistical analysis is performed. This study reveals a striking difference between the two regimes, with the emergence of monofractality only in weak turbulence, whereas strong turbulence is multifractal. This result, combined with recent studies, shows the relevance of collisionless weak KAW turbulence to describe the solar wind at electron scales.

Mediation of collisionless turbulent dissipation through cyclotron resonance

The dissipation of turbulence in astrophysical systems is fundamental to energy transfer and heating in environments ranging from the solar wind and corona to accretion disks and the intracluster medium. Although turbulent dissipation is relatively well understood in fluid dynamics, astrophysical plasmas often exhibit exotic behaviour, arising from the lack of interparticle collisions, which complicates turbulent dissipation and heating in these systems. Recent observations by NASA's Parker Solar Probe mission in the inner heliosphere have shed new light on the role of ion cyclotron resonance as a potential candidate for turbulent dissipation and plasma heating. Here, using in situ observations of turbulence and wave populations, we show that ion cyclotron waves provide a major pathway for dissipation and plasma heating in the solar wind. Our results support recent theoretical predictions of turbulence in the inner heliosphere, known as the helicity barrier, that suggest a role of cyclotron resonance in ion-scale dissipation. Taken together, these results provide important constraints for turbulent dissipation and acceleration efficiency in astrophysical plasmas.

Extended Magnetic Reconnection in Kinetic Plasma Turbulence

Magnetic reconnection and plasma turbulence are ubiquitous processes important for laboratory, space, and astrophysical plasmas. Reconnection has been suggested to play an important role in the energetics and dynamics of turbulence by observations, simulations, and theory for two decades. The fundamental properties of reconnection at kinetic scales, essential to understanding the general problem of reconnection in magnetized turbulence, remain largely unknown at present. Here, we present an application of the magnetic flux transport method that can accurately identify reconnection in turbulence to a three-dimensional simulation. Contrary to ideas that reconnection in turbulence would be patchy and unpredictable, highly extended reconnection X lines, on the same order of magnitude as the system size, form at kinetic scales. Extended X lines develop through bidirectional reconnection spreading. They satisfy critical balance characteristic of turbulence, which predicts the X-line extent at a given scale. These results present a picture of fundamentally extended reconnection in kinetic-scale turbulence.

Subion-Scale Turbulence Driven by Magnetic Reconnection

The interplay between plasma turbulence and magnetic reconnection remains an unsettled question in astrophysical and laboratory plasmas. Here, we report the first observational evidence that magnetic reconnection drives subion-scale turbulence in magnetospheric plasmas by transferring energy to small scales. We employ a spatial "coarse-grained" model of Hall magnetohydrodynamics, enabling us to measure the nonlinear energy transfer rate across scale ℓ at position x. Its application to Magnetospheric Multiscale mission data shows that magnetic reconnection drives intense energy transfer to subion-scales. This observational evidence is remarkably supported by the results from Hybrid Vlasov-Maxwell simulations of turbulence to which the coarse-grained model is also applied. These results can potentially answer some open questions on plasma turbulence in planetary environments.

In Situ Signature of Cyclotron Resonant Heating in the Solar Wind

The dissipation of magnetized turbulence is an important paradigm for describing heating and energy transfer in astrophysical environments such as the solar corona and wind; however, the specific collisionless processes behind dissipation and heating remain relatively unconstrained by measurements. Remote sensing observations have suggested the presence of strong temperature anisotropy in the solar corona consistent with cyclotron resonant heating. In the solar wind, in situ magnetic field measurements reveal the presence of cyclotron waves, while measured ion velocity distribution functions have hinted at the active presence of cyclotron resonance. Here, we present Parker Solar Probe observations that connect the presence of ion-cyclotron waves directly to signatures of resonant damping in observed proton-velocity distributions using the framework of quasilinear theory. We show that the quasilinear evolution of the observed distribution functions should absorb the observed cyclotron wave population with a heating rate of 10^{-14}  W/m^{3}, indicating significant heating of the solar wind.

Kinetic Heating by Alfvén Waves in Magnetic Shears

With first-principles kinetic simulations, we show that a large-scale Alfvén wave (AW) propagating in an inhomogeneous background decays into kinetic Alfvén waves (KAWs), triggering ion and electron energization. We demonstrate that the two species can access unequal amounts of the initial AW energy, experiencing differential heating. During the decay process, the electric field carried by KAWs produces non-Maxwellian features in the particle velocity distribution functions, in accordance with space observations. The process we present solely requires the interaction of a large-scale AW with a magnetic shear and may be relevant for several astrophysical and laboratory plasmas.

Properties of Hall-MHD Turbulence at Sub-Ion Scales: Spectral Transfer Analysis

We present results of a multiscale study of Hall-magnetohydrodynamic (MHD) turbulence, carried out on a dataset of compressible nonlinear 2D Hall-MHD numerical simulations of decaying Alfvénic turbulence. For the first time, we identify two distinct regimes of fully developed turbulence. In the first one, the power spectrum of the turbulent magnetic fluctuations at sub-ion scales exhibits a power law with a slope of ∼−2.9, typically observed both in solar wind and in magnetosheath turbulence. The second regime, instead, shows a slope of −7/3, in agreement with classical theoretical models of Hall-MHD turbulence. A spectral-transfer analysis reveals that the latter regime occurs when the energy transfer rate at sub-ion scales is dominated by the Hall term, whereas in the former regime, the governing process is the dissipation (and the system exhibits large intermittency). Results of this work are relevant to the space plasma community, as they may potentially reconcile predictions from theoretical models with results from numerical simulations and spacecraft observations.

Constraining Ion-Scale Heating and Spectral Energy Transfer in Observations of Plasma Turbulence

We perform a statistical study of the turbulent power spectrum at inertial and kinetic scales observed during the first perihelion encounter of the Parker Solar Probe. We find that often there is an extremely steep scaling range of the power spectrum just above the ion-kinetic scales, similar to prior observations at 1 A.U., with a power-law index of around -4. Based on our measurements, we demonstrate that either a significant (>50%) fraction of the total turbulent energy flux is dissipated in this range of scales, or the characteristic nonlinear interaction time of the turbulence decreases dramatically from the expectation based solely on the dispersive nature of nonlinearly interacting kinetic Alfvén waves.

Hidden Cores of Active Galactic Nuclei as the Origin of Medium-Energy Neutrinos: Critical Tests with the MeV Gamma-Ray Connection

Mysteries about the origin of high-energy cosmic neutrinos have deepened by the recent IceCube measurement of a large diffuse flux in the 10-100 TeV range. Based on the standard disk-corona picture of active galactic nuclei (AGN), we present a phenomenological model enabling us to systematically calculate the spectral sequence of multimessenger emission from the AGN coronae. We show that protons in the coronal plasma can be stochastically accelerated up to PeV energies by plasma turbulence, and find that the model explains the large diffuse flux of medium-energy neutrinos if the cosmic rays carry only a few percent of the thermal energy. We find that the Bethe-Heitler process plays a crucial role in connecting these neutrinos and cascaded MeV gamma rays, and point out that the gamma-ray flux can even be enhanced by the reacceleration of secondary pairs. Critical tests of the model are given by its prediction that a significant fraction of the MeV gamma-ray background correlates with ∼10  TeV neutrinos, and nearby Seyfert galaxies including NGC 1068 are promising targets for IceCube, KM3Net, IceCube-Gen2, and future MeV gamma-ray telescopes.

Magnetic pumping model for energizing superthermal particles applied to observations of the Earth's bow shock

Energetic particle generation is an important component of a variety of astrophysical systems, from seed particle generation in shocks to the heating of the solar wind. It has been shown that magnetic pumping is an efficient mechanism for heating thermal particles, using the largest-scale magnetic fluctuations. Here we show that when magnetic pumping is extended to a spatially-varying magnetic flux tube, magnetic trapping of superthermal particles renders pumping an effective energization method for particles moving faster than the speed of the waves and naturally generates power-law distributions. We validated the theory by spacecraft observations of the strong, compressional magnetic fluctuations near the Earth’s bow shock from the Magnetospheric Multiscale mission. Given the ubiquity of magnetic fluctuations in different astrophysical systems, this mechanism has the potential to be transformative to our understanding of how the most energetic particles in the universe are generated.

Energetic particle generation is an important component of a variety of astrophysical systems. Here, the authors show when magnetic pumping is extended to a spatially-varying magnetic flux tube, magnetic trapping of superthermal particles renders pumping an effective energization method for particles moving faster than the speed of the waves.

Persistence of Ion Temperature Gradient Turbulent Transport at Finite Normalized Pressure

Plasma β dependence of electromagnetic turbulent transport is investigated by means of gyrokinetic simulations with self-consistent change of the equilibrium magnetic field. It is found that energy transport due to ion-temperature-gradient (ITG) driven turbulence does not decrease with increasing β; that is, the ion energy diffusivity does not decrease, and the electron energy diffusivity increases with β. This is because magnetic fluctuations are significantly influenced by the background magnetic field structure change with β by the Pfirsch-Schluter current. The magnetic field change weakens the suppression effect of magnetic perturbations on the growth of the ITG mode, and it also suppresses nonlinear zonal flow production. The influence of the magnetic field change is significant as the global magnetic shear increases.

Evidence for electron Landau damping in space plasma turbulence

How turbulent energy is dissipated in weakly collisional space and astrophysical plasmas is a major open question. Here, we present the application of a field-particle correlation technique to directly measure the transfer of energy between the turbulent electromagnetic field and electrons in the Earth's magnetosheath, the region of solar wind downstream of the Earth's bow shock. The measurement of the secular energy transfer from the parallel electric field as a function of electron velocity shows a signature consistent with Landau damping. This signature is coherent over time, close to the predicted resonant velocity, similar to that seen in kinetic Alfven turbulence simulations, and disappears under phase randomisation. This suggests that electron Landau damping could play a significant role in turbulent plasma heating, and that the technique is a valuable tool for determining the particle energisation processes operating in space and astrophysical plasmas.

Fluidization of collisionless plasma turbulence

In a collisionless, magnetized plasma, particles may stream freely along magnetic field lines, leading to "phase mixing" of their distribution function and consequently, to smoothing out of any "compressive" fluctuations (of density, pressure, etc.). This rapid mixing underlies Landau damping of these fluctuations in a quiescent plasma-one of the most fundamental physical phenomena that makes plasma different from a conventional fluid. Nevertheless, broad power law spectra of compressive fluctuations are observed in turbulent astrophysical plasmas (most vividly, in the solar wind) under conditions conducive to strong Landau damping. Elsewhere in nature, such spectra are normally associated with fluid turbulence, where energy cannot be dissipated in the inertial-scale range and is, therefore, cascaded from large scales to small. By direct numerical simulations and theoretical arguments, it is shown here that turbulence of compressive fluctuations in collisionless plasmas strongly resembles one in a collisional fluid and does have broad power law spectra. This "fluidization" of collisionless plasmas occurs, because phase mixing is strongly suppressed on average by "stochastic echoes," arising due to nonlinear advection of the particle distribution by turbulent motions. Other than resolving the long-standing puzzle of observed compressive fluctuations in the solar wind, our results suggest a conceptual shift for understanding kinetic plasma turbulence generally: rather than being a system where Landau damping plays the role of dissipation, a collisionless plasma is effectively dissipationless, except at very small scales. The universality of "fluid" turbulence physics is thus reaffirmed even for a kinetic, collisionless system.

Thermal disequilibration of ions and electrons by collisionless plasma turbulence

Does overall thermal equilibrium exist between ions and electrons in a weakly collisional, magnetized, turbulent plasma? And, if not, how is thermal energy partitioned between ions and electrons? This is a fundamental question in plasma physics, the answer to which is also crucial for predicting the properties of far-distant astronomical objects such as accretion disks around black holes. In the context of disks, this question was posed nearly two decades ago and has since generated a sizeable literature. Here we provide the answer for the case in which energy is injected into the plasma via Alfvénic turbulence: Collisionless turbulent heating typically acts to disequilibrate the ion and electron temperatures. Numerical simulations using a hybrid fluid-gyrokinetic model indicate that the ion-electron heating-rate ratio is an increasing function of the thermal-to-magnetic energy ratio, [Formula: see text]: It ranges from [Formula: see text] at [Formula: see text] to at least 30 for [Formula: see text] This energy partition is approximately insensitive to the ion-to-electron temperature ratio [Formula: see text] Thus, in the absence of other equilibrating mechanisms, a collisionless plasma system heated via Alfvénic turbulence will tend toward a nonequilibrium state in which one of the species is significantly hotter than the other, i.e., hotter ions at high [Formula: see text] and hotter electrons at low [Formula: see text] Spectra of electromagnetic fields and the ion distribution function in 5D phase space exhibit an interesting new magnetically dominated regime at high [Formula: see text] and a tendency for the ion heating to be mediated by nonlinear phase mixing ("entropy cascade") when [Formula: see text] and by linear phase mixing (Landau damping) when [Formula: see text].

Space-time structure and wavevector anisotropy in space plasma turbulence

Space and astrophysical plasmas often develop into a turbulent state and exhibit nearly random and stochastic motions. While earlier studies emphasize more on understanding the energy spectrum of turbulence in the one-dimensional context (either in the frequency or the wavenumber domain), recent achievements in plasma turbulence studies provide an increasing amount of evidence that plasma turbulence is essentially a spatially and temporally evolving phenomenon. This review presents various models for the space-time structure and anisotropy of the turbulent fields in space plasmas, or equivalently the energy spectra in the wavenumber-frequency domain for the space-time structures and that in the wavevector domain for the anisotropies. The turbulence energy spectra are evaluated in different one-dimensional spectral domains; one speaks of the frequency spectra in the spacecraft observations and the wavenumber spectra in the numerical simulation studies. The notion of the wavenumber-frequency spectrum offers a more comprehensive picture of the turbulent fields, and good models can explain the one-dimensional spectra in the both domains at the same time. To achieve this goal, the Doppler shift, the Doppler broadening, linear-mode dispersion relations, and sideband waves are reviewed. The energy spectra are then extended to the wavevector domain spanning the directions parallel and perpendicular to the large-scale magnetic field. By doing so, the change in the spectral index at different projections onto the one-dimensional spectral domain can be explained in a simpler way.

Magnetorotational Turbulence and Dynamo in a Collisionless Plasma

We present results from the first 3D kinetic numerical simulation of magnetorotational turbulence and dynamo, using the local shearing-box model of a collisionless accretion disk. The kinetic magnetorotational instability grows from a subthermal magnetic field having zero net flux over the computational domain to generate self-sustained turbulence and outward angular-momentum transport. Significant Maxwell and Reynolds stresses are accompanied by comparable viscous stresses produced by field-aligned ion pressure anisotropy, which is regulated primarily by the mirror and ion-cyclotron instabilities through particle trapping and pitch-angle scattering. The latter endow the plasma with an effective viscosity that is biased with respect to the magnetic-field direction and spatiotemporally variable. Energy spectra suggest an Alfvén-wave cascade at large scales and a kinetic-Alfvén-wave cascade at small scales, with strong small-scale density fluctuations and weak nonaxisymmetric density waves. Ions undergo nonthermal particle acceleration, their distribution accurately described by a κ distribution. These results have implications for the properties of low-collisionality accretion flows, such as that near the black hole at the Galactic center.

Small-scale behavior of Hall magnetohydrodynamic turbulence

Decaying Hall magnetohydrodynamic (HMHD) turbulence is studied using three-dimensional (3D) direct numerical simulations with grids up to 768(3) points and two different types of initial conditions. Results are compared to analogous magnetohydrodynamic (MHD) runs and both Laplacian and Laplacian-squared dissipative operators are examined. At scales below the ion inertial length, the ratio of magnetic to kinetic energy as a function of wave number transitions to a magnetically dominated state. The transition in behavior is associated with the advection term in the momentum equation becoming subdominant to dissipation. Examination of autocorrelation functions reveals that, while current and vorticity structures are similarly sized in MHD, HMHD current structures are narrower and vorticity structures are wider. The electric field autocorrelation function is significantly narrower in HMHD than in MHD and is similar to the HMHD current autocorrelation function at small separations. HMHD current structures are found to be significantly more intense than in MHD and appear to have an enhanced association with strong alignment between the current and magnetic field, which may be important in collisionless plasmas where field-aligned currents can be unstable. When hyperdiffusivity is used, a longer region consistent with a k(-7/3) scaling is present for right-polarized fluctuations when compared to Laplacian dissipation runs.

A dynamical model of plasma turbulence in the solar wind

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 Alfvén 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 first dynamical model of kinetic turbulence in the weakly collisional solar wind plasma that combines self-consistently the physics of Alfvén waves with the development of small-scale current sheets is presented and its physical implications are discussed. This model leads to a simplified perspective on the nature of turbulence in a weakly collisional plasma: the nonlinear interactions responsible for the turbulent cascade of energy and the formation of current sheets are essentially fluid in nature, while the collisionless damping of the turbulent fluctuations and the energy injection by kinetic instabilities are essentially kinetic in nature.

Short-wavelength plasma turbulence and temperature anisotropy instabilities: recent computational progress

Plasma turbulence consists of an ensemble of enhanced, broadband electromagnetic fluctuations, typically driven by multi-wave interactions which transfer energy in wavevector space via non- linear cascade processes. Temperature anisotropy instabilities in collisionless plasmas are driven by quasi-linear wave-particle interactions which transfer particle kinetic energy to field fluctuation energy; the resulting enhanced fluctuations are typically narrowband in wavevector magnitude and direction. Whatever their sources, short-wavelength fluctuations are those at which charged particle kinetic, that is, velocity-space, properties are important; these are generally wavelengths of the order of or shorter than the ion inertial length or the thermal ion gyroradius. The purpose of this review is to summarize and interpret recent computational results concerning short-wavelength plasma turbulence, short-wavelength temperature anisotropy instabilities and relationships between the two phenomena.

Kinetic scale turbulence and dissipation in the solar wind: key observational results and future outlook

Turbulence is ubiquitous in the solar wind. Turbulence causes kinetic and magnetic energy to cascade to small scales where they are eventually dissipated, adding heat to the plasma. The details of how this occurs are not well understood. This article reviews the evidence for turbulent dissipation and examines various diagnostics for identifying solar wind regions where dissipation is occurring. We also discuss how future missions will further enhance our understanding of the importance of turbulence to solar wind dynamics.

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.

Transition between saturation regimes of gyrokinetic turbulence

A gyrokinetic model of ion temperature gradient driven turbulence in magnetized plasmas is used to study the injection, nonlinear redistribution, and collisional dissipation of free energy in the saturated turbulent state over a broad range of driving gradients and collision frequencies. The dimensionless parameter L(T)/L(C), where L(T) is the ion temperature gradient scale length and L(C) is the collisional mean free path, is shown to parametrize a transition between a saturation regime dominated by nonlinear transfer of free energy to small perpendicular (to the magnetic field) scales and a regime dominated by dissipation at large scales in all phase space dimensions.

Nature of subproton scale turbulence in the solar wind

The nature of subproton scale fluctuations in the solar wind is an open question, partly because two similar types of electromagnetic turbulence can occur: kinetic Alfvén turbulence and whistler turbulence. These two possibilities, however, have one key qualitative difference: whistler turbulence, unlike kinetic Alfvén turbulence, has negligible power in density fluctuations. In this Letter, we present new observational data, as well as analytical and numerical results, to investigate this difference. These results show, for the first time, that the fluctuations well below the proton scale are predominantly kinetic Alfvén turbulence, and, if present at all, the whistler fluctuations make up only a small fraction of the total energy.

Detection of small-scale structures in the dissipation regime of solar-wind turbulence

Recent observations of the solar wind have pointed out the existence of a cascade of magnetic energy from the scale of the proton Larmor radius ρ(p) down to the electron Larmor radius ρ(e) scale. In this Letter we study the spatial properties of magnetic field fluctuations in the solar wind and find that at small scales the magnetic field does not resemble a sea of homogeneous fluctuations, but rather a two-dimensional plane containing thin current sheets and discontinuities with spatial sizes ranging from l >/~ ρ(p) down to ρ(e) and below. These isolated structures may be manifestations of intermittency that localize sites of turbulent dissipation. Studying the relationship between turbulent dissipation, reconnection, and intermittency is crucial for understanding the dynamics of laboratory and astrophysical plasmas.

Density fluctuation spectrum of solar wind turbulence between ion and electron scales

We present a measurement of the spectral index of density fluctuations between ion and electron scales in solar wind turbulence using the EFI instrument on the ARTEMIS spacecraft. The mean spectral index at 1 AU was found to be -2.75±0.06, steeper than predictions for pure whistler or kinetic Alfvén wave turbulence but consistent with previous magnetic field measurements. The steep spectra are also consistent with expectations of increased intermittency or damping of some of the turbulent energy over this range of scales. Neither the spectral index nor the flattening of the density spectra before ion scales were found to depend on the proximity to the pressure anisotropy instability thresholds, suggesting that they are features inherent to the turbulent cascade.