Probing the energetic particle environment near the Sun.

NASA's Parker Solar Probe mission1 recently plunged through the inner heliosphere of the Sun to its perihelia, about 24 million kilometres from the Sun. Previous studies farther from the Sun (performed mostly at a distance of 1 astronomical unit) indicate that solar energetic particles are accelerated from a few kiloelectronvolts up to near-relativistic energies via at least two processes: 'impulsive' events, which are usually associated with magnetic reconnection in solar flares and are typically enriched in electrons, helium-3 and heavier ions2, and 'gradual' events3,4, which are typically associated with large coronal-mass-ejection-driven shocks and compressions moving through the corona and inner solar wind and are the dominant source of protons with energies between 1 and 10 megaelectronvolts. However, some events show aspects of both processes and the electron-proton ratio is not bimodally distributed, as would be expected if there were only two possible processes5. These processes have been very difficult to resolve from prior observations, owing to the various transport effects that affect the energetic particle population en route to more distant spacecraft6. Here we report observations of the near-Sun energetic particle radiation environment over the first two orbits of the probe. We find a variety of energetic particle events accelerated both locally and remotely including by corotating interaction regions, impulsive events driven by acceleration near the Sun, and an event related to a coronal mass ejection. We provide direct observations of the energetic particle radiation environment in the region just above the corona of the Sun and directly explore the physics of particle acceleration and transport.

Kinetic Range Spectral Features of Cross Helicity Using the Magnetospheric Multiscale Spacecraft.

We study spectral features of ion velocity and magnetic field correlations in the magnetosheath and in the solar wind using data from the Magnetospheric Multiscale (MMS) spacecraft. High-resolution MMS observations enable the study of the transition of these correlations between their magnetofluid character at larger scales into the subproton kinetic range, previously unstudied in spacecraft data. Cross-helicity, angular alignment, and energy partitioning is examined over a suitable range of scales, employing measurements based on the Taylor frozen-in approximation as well as direct two-spacecraft correlation measurements. The results demonstrate signatures of alignment at large scales. As kinetic scales are approached, the alignment between v and b is destroyed by demagnetization of protons.

Magnetospheric Multiscale Observation of Plasma Velocity-Space Cascade: Hermite Representation and Theory.

Plasma turbulence is investigated using unprecedented high-resolution ion velocity distribution measurements by the Magnetospheric Multiscale mission (MMS) in the Earth's magnetosheath. This novel observation of a highly structured particle distribution suggests a cascadelike process in velocity space. Complex velocity space structure is investigated using a three-dimensional Hermite transform, revealing, for the first time in observational data, a power-law distribution of moments. In analogy to hydrodynamics, a Kolmogorov approach leads directly to a range of predictions for this phase-space transport. The scaling theory is found to be in agreement with observations. The combined use of state-of-the-art MMS data sets, novel implementation of a Hermite transform method, and scaling theory of the velocity cascade opens new pathways to the understanding of plasma turbulence and the crucial velocity space features that lead to dissipation in plasmas.

Ensemble Space-Time Correlation of Plasma Turbulence in the Solar Wind.

Single point measurement turbulence cannot distinguish variations in space and time. We employ an ensemble of one- and two-point measurements in the solar wind to estimate the space-time correlation function in the comoving plasma frame. The method is illustrated using near Earth spacecraft observations, employing ACE, Geotail, IMP-8, and Wind data sets. New results include an evaluation of both correlation time and correlation length from a single method, and a new assessment of the accuracy of the familiar frozen-in flow approximation. This novel view of the space-time structure of turbulence may prove essential in exploratory space missions such as Solar Probe Plus and Solar Orbiter for which the frozen-in flow hypothesis may not be a useful approximation.

Explosive Particle Dispersion in Plasma Turbulence.

Particle dynamics are investigated in plasma turbulence, using self-consistent kinetic simulations, in two dimensions. In the steady state, the trajectories of single protons and proton pairs are studied, at different values of plasma ß (ratio between kinetic and magnetic pressure). For single-particle displacements, results are consistent with fluids and magnetic field line dynamics, where particles undergo normal diffusion for very long times, with higher ß's being more diffusive. In an intermediate time range, with separations lying in the inertial range, particles experience an explosive dispersion in time, consistent with the Richardson prediction. These results, obtained for the first time with a self-consistent kinetic model, are relevant for astrophysical and laboratory plasmas, where turbulence is crucial for heating, mixing, and acceleration processes.

Intermittent Dissipation and Heating in 3D Kinetic Plasma Turbulence.

High resolution, fully kinetic, three dimensional (3D) simulation of collisionless plasma turbulence shows the development of turbulence characterized by sheetlike current density structures spanning a range of scales. The nonlinear evolution is initialized with a long wavelength isotropic spectrum of fluctuations having polarizations transverse to an imposed mean magnetic field. We present evidence that these current sheet structures are sites for heating and dissipation, and that stronger currents signify higher dissipation rates. The analyses focus on quantities such as J·E, electron, and proton temperatures, and conditional averages of these quantities based on local electric current density. Evidently, kinetic scale plasma, like magnetohydrodynamics, becomes intermittent due to current sheet formation, leading to the expectation that heating and dissipation in astrophysical and space plasmas may be highly nonuniform. Comparison with previous results from 2D kinetic simulations, as well as high frequency solar wind observational data, are discussed.

Anisotropy in solar wind plasma turbulence.

A review of spectral anisotropy and variance anisotropy for solar wind fluctuations is given, with the discussion covering inertial range and dissipation range scales. For the inertial range, theory, simulations and observations are more or less in accord, in that fluctuation energy is found to be primarily in modes with quasi-perpendicular wavevectors (relative to a suitably defined mean magnetic field), and also that most of the fluctuation energy is in the vector components transverse to the mean field. Energy transfer in the parallel direction and the energy levels in the parallel components are both relatively weak. In the dissipation range, observations indicate that variance anisotropy tends to decrease towards isotropic levels as the electron gyroradius is approached; spectral anisotropy results are mixed. Evidence for and against wave interpretations and turbulence interpretations of these features will be discussed. We also present new simulation results concerning evolution of variance anisotropy for different classes of initial conditions, each with typical background solar wind parameters.

Intermittency, nonlinear dynamics and dissipation in the solar wind and astrophysical plasmas.

An overview is given of important properties of spatial and temporal intermittency, including evidence of its appearance in fluids, magnetofluids and plasmas, and its implications for understanding of heliospheric plasmas. Spatial intermittency is generally associated with formation of sharp gradients and coherent structures. The basic physics of structure generation is ideal, but when dissipation is present it is usually concentrated in regions of strong gradients. This essential feature of spatial intermittency in fluids has been shown recently to carry over to the realm of kinetic plasma, where the dissipation function is not known from first principles. Spatial structures produced in intermittent plasma influence dissipation, heating, and transport and acceleration of charged particles. Temporal intermittency can give rise to very long time correlations or a delayed approach to steady-state conditions, and has been associated with inverse cascade or quasi-inverse cascade systems, with possible implications for heliospheric prediction.

Von Kármán energy decay and heating of protons and electrons in a kinetic turbulent plasma.

Decay in time of undriven weakly collisional kinetic plasma turbulence in systems large compared to the ion kinetic scales is investigated using fully electromagnetic particle-in-cell simulations initiated with transverse flow and magnetic disturbances, constant density, and a strong guide field. The observed energy decay is consistent with the von Kármán hypothesis of similarity decay, in a formulation adapted to magnetohydrodyamics. Kinetic dissipation occurs at small scales, but the overall rate is apparently controlled by large scale dynamics. At small turbulence amplitudes the electrons are preferentially heated. At larger amplitudes proton heating is the dominant effect. In the solar wind and corona the protons are typically hotter, suggesting that these natural systems are in the large amplitude turbulence regime.

Proton kinetic effects and turbulent energy cascade rate in the solar wind.

The first observed connection between kinetic instabilities driven by proton temperature anisotropy and estimated energy cascade rates in the turbulent solar wind is reported using measurements from the Wind spacecraft at 1 AU. We find enhanced cascade rates are concentrated along the boundaries of the (ß∥, T⊥/T∥) plane, which includes regions theoretically unstable to the mirror and firehose instabilities. A strong correlation is observed between the estimated cascade rate and kinetic effects such as temperature anisotropy and plasma heating, resulting in protons 5-6 times hotter and 70%-90% more anisotropic than under typical isotropic plasma conditions. These results offer new insights into kinetic processes in a turbulent regime.

Intermittency and local heating in the solar wind.

Evidence for nonuniform heating in the solar wind plasma near current sheets dynamically generated by magnetohydrodynamic (MHD) turbulence is obtained using measurements from the ACE spacecraft. These coherent structures only constitute 19% of the data, but contribute 50% of the total plasma internal energy. Intermittent heating manifests as elevations in proton temperature near current sheets, resulting in regional heating and temperature enhancements extending over several hours. The number density of non-Gaussian structures is found to be proportional to the mean proton temperature and solar wind speed. These results suggest magnetofluid turbulence drives intermittent dissipation through a hierarchy of coherent structures, which collectively could be a significant source of coronal and solar wind heating.

Kinetic signatures and intermittent turbulence in the solar wind plasma.

A connection between kinetic processes and intermittent turbulence is observed in the solar wind plasma using measurements from the Wind spacecraft at 1 A.U. In particular, kinetic effects such as temperature anisotropy and plasma heating are concentrated near coherent structures, such as current sheets, which are nonuniformly distributed in space. Furthermore, these coherent structures are preferentially found in plasma unstable to the mirror and firehose instabilities. The inhomogeneous heating in these regions, which is present in both the magnetic field parallel and perpendicular temperature components, results in protons at least 3-4 times hotter than under typical stable plasma conditions. These results offer a new understanding of kinetic processes in a turbulent regime, where linear Vlasov theory is not sufficient to explain the inhomogeneous plasma dynamics operating near non-Gaussian structures.

Intermittent dissipation at kinetic scales in collisionless plasma turbulence.

High resolution kinetic simulations of collisionless plasma driven by shear show the development of turbulence characterized by dynamic coherent sheetlike current density structures spanning a range of scales down to electron scales. We present evidence that these structures are sites for heating and dissipation, and that stronger current structures signify higher dissipation rates. Evidently, kinetic scale plasma, like magnetohydrodynamics, becomes intermittent due to current sheet formation, leading to the expectation that heating and dissipation in astrophysical and space plasmas may be highly nonuniform and patchy.

von Karman correlation similarity in solar wind magnetohydrodynamic turbulence.

A major development underlying hydrodynamic turbulence theory is the similarity decay hypothesis due to von Karman and Howarth, here extended empirically to plasma turbulence in the solar wind. In similarity decay the second-order correlation experiences a continuous transformation based on a universal functional form and a rescaling of energy and characteristic length. Solar wind turbulence follows many principles adapted from classical fluid turbulence, but previously this similarity property has not been examined explicitly. Here, we analyze an ensemble of Elsässer autocorrelation functions computed from Advanced Composition Explorer data at 1 astronomical unit (AU), and demonstrate explicitly that the two-point correlation functions undergo a collapse to a similarity form of the type anticipated from von Karman's hypothesis applied to weakly compressive magnetohydrodynamic turbulence. This provides a firm empirical basis for employing the similarity decay hypothesis to the Elsässer correlations that represent the incompressive turbulence cascade. This approach is of substantial utility in space turbulence data analysis, and for adopting von Karman-type heating rates in global and subgrid-scale dynamical modeling.

Anisotropic third-moment estimates of the energy cascade in solar wind turbulence using multispacecraft data.

The first direct determination of the inertial range energy cascade rate, using an anisotropic form of Yaglom's law for magnetohydrodynamic turbulence, is obtained in the solar wind with multispacecraft measurements. The two-point mixed third-order structure functions of Elsässer fluctuations are integrated over a sphere in magnetic field-aligned coordinates, and the result is consistent with a linear scaling. Therefore, volume integrated heating and cascade rates are obtained that, unlike previous studies, make only limited assumptions about the underlying spectral geometry of solar wind turbulence. These results confirm the turbulent nature of magnetic and velocity field fluctuations in the low frequency limit, and could supply the energy necessary to account for the nonadiabatic heating of the solar wind.

Energy transfer in reconnection and turbulence.

Reconnection and turbulence are two of the most commonly observed dynamical processes in plasmas, but their relationship is still not fully understood. Using 2.5D kinetic particle-in-cell simulations of both strong turbulence and reconnection, we compare the cross-scale transfer of energy in the two systems by analyzing the generalization of the von Kármán Howarth equations for Hall magnetohydrodynamics, a formulation that subsumes the third-order law for steady energy transfer rates. Even though the large scale features are quite different, the finding is that the decomposition of the energy transfer is structurally very similar in the two cases. In the reconnection case, the time evolution of the energy transfer also exhibits a correlation with the reconnection rate. These results provide explicit evidence that reconnection dynamics fundamentally involves turbulence-like energy transfer.

Similarity decay of enstrophy in an electron fluid.

A similarity decay law is proposed for enstrophy of a one-signed-vorticity fluid in a circular free-slip domain. It excludes the metastable equilibrium enstrophy which cannot drive turbulence, and approaches Batchelor's t(-2) law for strong turbulence. Measurements of the decay of a turbulent electron fluid agree well with the predictions of the decay law for a variety of initial conditions.

Anisotropic magnetohydrodynamic spectral transfer in the diffusion approximation.

A theoretical model of spectral transfer for anisotropic magnetohydrodynamic (MHD) turbulence is introduced, approximating energy transport in wave vector (k) space as a nonlinear diffusion process, extending previous isotropic k -space diffusion theories for hydrodynamics and MHD. This formal closure at the spectral equation level may be useful in space and astrophysical applications.

Ergodicity of ideal Galerkin three-dimensional magnetohydrodynamics and Hall magnetohydrodynamics models.

We explore the problem of the ergodicity of magnetohydrodynamics and Hall magnetohydrodynamics in three-dimensional, ideal Galerkin systems that are truncated to a finite number of Fourier modes. We show how single Fourier modes follow the Gibbs ensemble prediction, and how the ergodicity of the phase space is restored for long-time Galerkin solutions. Running time averages and two-time correlation functions show, at long times, a convergence towards zero of time averaged single Fourier modes. This suggests a delayed approach to, rather than a breaking of, ergodicity. Finally, we present some preliminary ideas concerning the origin of the associated time scales.

Low-frequency 1/f fluctuations in hydrodynamic and magnetohydrodynamic turbulence.

We investigate the occurrence of 1/f spectra of low-frequency fluctuations in numerical simulations of three-dimensional hydrodynamic and magnetohydrodynamic turbulence driven by a random forcing with a controlled correlation time. A range of one decade of 1/f spectrum is observed when a strong background magnetic field is present. The frequency spectra of individual Fourier modes is also analyzed and it is observed that the 1/f range is present in the largest available wavelength mode for the magnetohydrodynamic simulations with and without a background magnetic field and it is not observed (or is less clear) for the hydrodynamic case. The presence of 1/f spectra of low-frequency fluctuations is also analyzed for two-dimensional magnetohydrodynamic and hydrodynamic turbulence simulations and it is observed in both cases. The origin of these long period fluctuations is discussed.