Previous formulations of heating and transport associated with strong magnetohydrodynamic (MHD) turbulence are generalized to incorporate separate internal energy equations for electrons and protons. Electron heat conduction is included. Energy is supplied by turbulent heating that affects both electrons and protons, and is exchanged between them via collisions. Comparison to available Ulysses data shows that a reasonable accounting for the data is provided when (i) the energy exchange timescale is very long and (ii) the deposition of heat due to turbulence is divided, with 60% going to proton heating and 40% into electron heating. Heat conduction, determined here by an empirical fit, plays a major role in describing the electron data.
One proposed mechanism for heating the solar wind, from close to the sun to beyond 10 AU, invokes low-frequency, oblique, Alfven-wave turbulence. Because small-scale oblique Alfven waves (kinetic Alfven waves) are compressive, the measured density fluctuations in the solar wind place an upper limit on the amplitude of kinetic Alfven waves and hence an upper limit on the rate at which the solar wind can be heated by low-frequency, Alfvenic turbulence. We evaluate this upper limit for both coronal holes at 5 solar radii and in the near-Earth solar wind. At both radii, the upper limit we find is …
In solar wind, magnetohydrodynamic (MHD) discontinuities are ubiquitous and often found to be at the origin of turbulence intermittency. They may also play a key role in the turbulence dissipation and heating of the solar wind. The tangential (TD) and rotational (RD) discontinuities are the two most important types of discontinuities. Recently, the connection between turbulence intermittency and proton thermodynamics has been being investigated observationally. Here we present numerical results from three-dimensional MHD simulation with pressure anisotropy and define new methods to identify an…
The magnetorotational instability (MRI) drives vigorous turbulence in a region of protoplanetary disks where the ionization fraction is sufficiently high. It has recently been shown that the electric field induced by the MRI can heat up electrons and thereby affect the ionization balance in the gas. In particular, in a disk where abundant dust grains are present, the electron heating causes a reduction of the electron abundance, thereby preventing further growth of the MRI. By using the nonlinear Ohm's law that takes into account electron heating, we investigate where in protoplanetary disks t…
Recent theoretical studies argue that the rate of stochastic ion heating in low-frequency Alfvén-wave turbulence is given by $Q_\perp = c_1 [(δu)^3 /ρ] \exp(-c_2/ε)$, where $δu$ is the rms turbulent velocity at the scale of the ion gyroradius $ρ$, $ε= δu/v_{\perp \rm i}$, $v_{\perp \rm i}$ is the perpendicular ion thermal speed, and $c_1$ and $c_2$ are dimensionless constants. We test this theoretical result by numerically simulating test particles interacting with strong reduced magnetohydrodynamic (RMHD) turbulence. The heating rates in our simulations are well fit by this formula. The best-…
The fast solar wind's high speeds and nonthermal features require that significant heating occurs well above the Sun's surface. Two leading theories seem incompatible: low-frequency "Alfvénic" turbulence, which transports energy outwards and is observed ubiquitously by spacecraft but struggles to explain the observed dominance of ion over electron heating; and high-frequency ion-cyclotron waves (ICWs), which explain the nonthermal heating of ions but lack an obvious source. Here, we argue that the recently proposed "helicity barrier" effect, which limits electron heating by inhibiting the turb…
We study the heating of charged test particles in three-dimensional numerical simulations of weakly compressible magnetohydrodynamic (MHD) turbulence (``Alfvenic turbulence''); these results are relevant to particle heating and acceleration in the solar wind, solar flares, accretion disks onto black holes, and other astrophysics and heliospheric environments. The physics of particle heating depends on whether the gyrofrequency of a particle is comparable to the frequency of a turbulent fluctuation that is resolved on the computational domain. Particles with these frequencies nearly equal under…
Magnetohydronamic turbulence is believed to play a crucial role in heating the laboratorial, space, and astrophysical plasmas. However, the precise connection between the turbulent fluctuations and the particle kinetics has not yet been established. Here we present clear evidence of plasma turbulence heating based on diagnosed wave features and proton velocity distributions from solar wind measurements by the Wind spacecraft. For the first time, we can report the simultaneous observation of counter-propagating magnetohydrodynamic waves in the solar wind turbulence. Different from the tradition…
We develop a 1D solar-wind model that includes separate energy equations for the electrons and protons, proton temperature anisotropy, collisional and collisionless heat flux, and an analytical treatment of low-frequency, reflection-driven, Alfven-wave turbulence. To partition the turbulent heating between electron heating, parallel proton heating, and perpendicular proton heating, we employ results from the theories of linear wave damping and nonlinear stochastic heating. We account for mirror and oblique firehose instabilities by increasing the proton pitch-angle scattering rate when the pro…
Based on in-situ measurements by Wind spacecraft from 2005 to 2015, this letter reports for the first time a clearly scale-dependent connection between proton temperatures and the turbulence in the solar wind. A statistical analysis of proton-scale turbulence shows that increasing helicity magnitudes correspond to steeper magnetic energy spectra. In particular, there exists a positive power-law correlation (with a slope $\sim 0.4$) between the proton perpendicular temperature and the turbulent magnetic energy at scales $0.3 \lesssim kρ_p \lesssim 1$, with $k$ being the wavenumber and $ρ_p$ bei…
To simulate the energy balance of coronal plasmas on macroscopic scales, we often require the specification of the coronal heating mechanism in some functional form. To go beyond empirical formulations and to build a more physically motivated heating function, we investigate the wave-turbulence-driven (WTD) phenomenology for the heating of closed coronal loops. Our implementation is designed to capture the large-scale propagation, reflection, and dissipation of wave turbulence along a loop. The parameter space of this model is explored by solving the coupled WTD and hydrodynamic evolution in 1…
We propose a novel one-dimensional model that includes both shock and turbulence heating and qualify how these processes contribute to heating the corona and driving the solar wind. Compressible MHD simulations allow us to automatically consider shock formation and dissipation, while turbulent dissipation is modeled via a one-point closure based on Alfvén wave turbulence. Numerical simulations were conducted with different photospheric perpendicular correlation lengths $λ_0$, which is a critical parameter of Alfvén wave turbulence, and different root-mean-square photospheric transverse-wave am…
A model is presented for generation of fast solar wind in coronal holes, relying on heating that is dominated by turbulent dissipation of MHD fluctuations transported upwards in the solar atmosphere. Scale-separated transport equations include large-scale fields, transverse Alfvenic fluctuations, and a small compressive dissipation due to parallel shears near the transition region. The model accounts for proton temperature, density, wind speed, and fluctuation amplitude as observed in remote sensing and in situ satellite data.
We revisit the theory of stochastic heating of ions and investigate its phase-space signatures in kinetic turbulence of relevance to low-$β$ portions of the solar wind. We retain a full scale-dependent approach in our treatment, and consider the case in which electric-field fluctuations can be described by a generalized Ohm's law that includes Hall and thermo-electric effects. These two electric-field terms provide the dominant contributions to stochastic ion heating when the ion-Larmor scale is much smaller than the ion skin depth, $ρ_{\mathrm{i}}\ll d_{\mathrm{i}}$, which is the case at $β{\…
Enhancement of minor ions such as $^3$He and heavy ions in flare-associated solar energetic particle (SEP) events remains one of the major puzzles in heliophysics. In this work, we use 3D hybrid simulations (kinetic protons and fluid electrons) to investigate particle energization in a turbulent low-beta environment similar to solar flares. It is shown that in this regime the injected large-amplitude Alfvén waves develop into compressible and anisotropic turbulence, which efficiently heats thermal ions of different species. We find that temperature increase of heavy ions is inversely proportio…
To understand the nonlinear dynamics of the Parker scenario for coronal heating, long-time high-resolution simulations of the dynamics of a coronal loop in cartesian geometry are carried out. A loop is modeled as a box extended along the direction of the strong magnetic field $B_0$ in which the system is embedded. At the top and bottom plates, which represent the photosphere, velocity fields mimicking photospheric motions are imposed. We show that the nonlinear dynamics is described by different regimes of MHD anisotropic turbulence, with spectra characterized by intertial range power laws who…
The Parker or field line tangling model of coronal heating is investigated through long-time high-resolution simulations of the dynamics of a coronal loop in cartesian geometry within the framework of reduced magnetohydrodynamics (RMHD). Slow photospheric motions induce a Poynting flux which saturates by driving an anisotropic turbulent cascade dominated by magnetic energy and characterized by current sheets elongated along the axial magnetic field. Increasing the value of the axial magnetic field different regimes of MHD turbulence develop with a bearing on coronal heating rates. In physical …
The transport of waves and turbulence beyond the photosphere is central to the coronal heating problem. Turbulence in the quiet solar corona has been modeled on the basis of the nearly incompressible magnetohydrodynamic (NI MHD) theory to describe the transport of low-frequency turbulence in open magnetic field regions. It describes the evolution of the coupled majority quasi-2D and minority slab component, driven by the magnetic carpet and advected by a subsonic, sub-Alfvenic flow from the lower corona. In this paper, we couple the NI MHD turbulence transport model with an MHD model of the so…
The measured spectrum of kinetic Alfven wave fluctuations in the turbulent solar wind plasma is used to calculate the electron and ion distribution functions resulting from quasi-linear diffusion. The modified ion distribution function is found to be unstable to long wavelength electromagnetic ion cyclotron waves. These waves pitch angle scatter the parallel ion velocity into perpendicular velocity which effectively increases the perpendicular ion temperature.
The solar wind undergoes significant heating as it propagates away from the Sun; the exact mechanisms responsible for this heating are not yet fully understood. We present for the first time a statistical test for one of the proposed mechanisms, stochastic ion heating. We use the amplitude of magnetic field fluctuations near the proton gyroscale as a proxy for the ratio of gyroscale velocity fluctuations to perpendicular (with respect to the magnetic field) proton thermal speed, defined as $ε_p$. Enhanced proton temperatures are observed when $ε_p$ is larger than a critical value ($\sim 0.019 …
We present a new global model of the solar corona, including the low corona, the transition region and the top of chromosphere. The realistic 3D magnetic field is simulated using the data from the photospheric magnetic field measurements. The distinctive feature of the new model is incorporating the MHD Alfven wave turbulence. We assume this turbulence and its non-linear dissipation to be the only momentum and energy source for heating the coronal plasma and driving the solar wind. The difference between the turbulence dissipation efficiency in coronal holes and that in closed field regions is…
How ions are energized and heated is a fundamental problem in the study of energy dissipation in magnetized plasmas. In particular, the heating of heavy ions (including ${}^{4}\mathrm{He}^{2+}$, ${}^{3}\mathrm{He}^{2+}$ and others) has been a constant concern for understanding the microphysics of impulsive solar flares. In this article, via two-dimensional hybrid-kinetic Particle-in-Cell simulations, we study the heating of Helium ions (${}^{4}\mathrm{He}^{2+}$) by turbulence driven by cascading waves launched at large scales from the left-handed polarized Helium ion cyclotron wave branch of a…
Stochastic heating refers to an increase in the average magnetic moment of charged particles interacting with electromagnetic fluctuations whose frequencies are smaller than the particles' cyclotron frequencies. This type of heating arises when the amplitude of the gyroscale fluctuations exceeds a certain threshold, causing particle orbits in the plane perpendicular to the magnetic field to become stochastic rather than nearly periodic. We consider the stochastic heating of protons by Alfvén-wave (AW) and kinetic-Alfvén-wave (KAW) turbulence, which may make an important contribution to the hea…
In the present work, we test the predictions of the AWSoM model, a global extended-MHD model capable of calculating the propagation and turbulent dissipation of Alfvén waves in any magnetic topology, against high resolution spectra of the quiescent off-disk solar corona. Wave dissipation is the only heating mechanism assumed in this model. Combining 3D model results with the CHIANTI atomic database, we were able to create synthetic line-of-sight spectra which include the effects of emission line broadening due to both thermal and wave-related non-thermal motions. To the best of our knowledge t…
Some differences between theoretical, numerical and observational determinations of spectral slopes of solar wind turbulence are interpreted in the thermodynamical sense. Confirmations of turbulent Kolmogorov slopes in solar wind magnetic turbulence and magnetohydrodynamic simulations exhibit tiny differences. These are used to infer about entropy generation in the turbulent cascade and to infer about the anomalous turbulent collision frequency in the dissipative range as well as the average energy input in solar wind turbulence. Anomalous turbulent collision frequencies are obtained of the or…
The heating, acceleration, and pitch-angle scattering of charged particles by MHD turbulence are important in a wide range of astrophysical environments, including the solar wind, accreting black holes, and galaxy clusters. We simulate the interaction of high-gyrofrequency test particles with fully dynamical simulations of subsonic MHD turbulence, focusing on the parameter regime with beta ~ 1, where beta is the ratio of gas to magnetic pressure. We use the simulation results to calibrate analytical expressions for test particle velocity-space diffusion coefficients and provide simple fits tha…
MHD turbulence has long been proposed as a mechanism for the heating of coronal loops in the framework of the Parker scenario for coronal heating. So far most of the studies have focused on its dynamical properties without considering its thermodynamical and radiative features, because of the very demanding computational requirements. In this paper we extend this previous research to the compressible regime, including an energy equation, by using HYPERION, a new parallelized, viscoresistive, three-dimensional compressible MHD code. HYPERION employs a Fourier collocation -- finite difference sp…
A three-dimensional MHD model for the propagation and dissipation of Alfven waves in a coronal loop is developed. The model includes the lower atmospheres at the two ends of the loop. The waves originate on small spatial scales (less than 100 km) inside the kilogauss flux elements in the photosphere. The model describes the nonlinear interactions between Alfven waves using the reduced MHD approximation. The increase of Alfven speed with height in the chromosphere and transition region (TR) causes strong wave reflection, which leads to counter-propagating waves and turbulence in the photospheri…
Using particle-in-cell simulations and kinetic theory, we explore the current-driven turbulence and associated electron heating in the dissipation region during 3D magnetic reconnection with a guide field. At late time the turbulence is dominated by the Buneman and lower hybrid instabilities. Both produce electron holes that co-exist but have very different propagation speeds. The associated scattering of electrons by the holes enhances electron heating in the dissipation region.
The fourth orbit of Parker Solar Probe (PSP) reached heliocentric distances down to 27.9 Rs, allowing solar wind turbulence and acceleration mechanisms to be studied in situ closer to the Sun than previously possible. The turbulence properties were found to be significantly different in the inbound and outbound portions of PSP's fourth solar encounter, likely due to the proximity to the heliospheric current sheet (HCS) in the outbound period. Near the HCS, in the streamer belt wind, the turbulence was found to have lower amplitudes, higher magnetic compressibility, a steeper magnetic field spe…
Magnetorotational instability (MRI) has a potential to generate the vigorous turbulence in protoplanetary disks, although its turbulence strength and accretion stress remains debatable because of the uncertainty of MRI with low ionization fraction. We focus on the heating of electrons by strong electric fields which amplifies nonideal magnetohydrodynamic effects. The heated electrons frequently collide with and stick to dust grains, which in turn decreases the ionization fraction and is expected to weaken the turbulent motion driven by MRI. In order to quantitatively investigate the nonlinear …
The observed sub-proton scale turbulence spectrum in the solar wind raises the question of how that turbulence originates. Observations of keV energetic electrons during solar quite-time suggest them as possible source of free energy to drive the turbulence. Using particle-in-cell simulations, we explore how free energy in energetic electrons, released by an electron two-stream instability drives Weibel-like electromagnetic waves that excite wave-wave interactions. Consequently, both kinetic Alfvénic and whistler waves are excited that evolve through inverse and forward magnetic energy cascade…
We present the first study of the formation and dissipation of current sheets at electron scales in a wave-driven, weakly collisional, 3D kinetic turbulence simulation. We investigate the relative importance of dissipation associated with collisionless damping via resonant wave-particle interactions versus dissipation in small-scale current sheets in weakly collisional plasma turbulence. Current sheets form self-consistently from the wave-driven turbulence, and their filling fraction is well correlated to the electron heating rate. However, the weakly collisional nature of the simulation neces…
Plasma in the Sun's hot corona expands into the heliosphere as a supersonic and highly magnetized solar wind. This paper provides an overview of our current understanding of how the corona is heated and how the solar wind is accelerated. Recent models of magnetohydrodynamic turbulence have progressed to the point of successfully predicting many observed properties of this complex, multi-scale system. However, it is not clear whether the heating in open-field regions comes mainly from the dissipation of turbulent fluctuations that are launched from the solar surface, or whether the chaotic "mag…
Chromospheric turbulence as a regulator of stellar wind mass flux
The University of Tokyo（东京大学）；KU Leuven（荷语鲁汶大学）；Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM（巴黎萨克雷大学、巴黎西岱大学、法国原子能和替代能源委员会、法国国家科学研究中心、天体物理学和分子相互作用实验室）；Nagoya University（名古屋大学）
In this paper we further develop a model for the heating of coronal loops by Alfven wave turbulence (AWT). The Alfven waves are assumed to be launched from a collection of kilogauss flux tubes in the photosphere at the two ends of the loop. Using a three-dimensional magneto-hydrodynamic (MHD) model for an active-region loop, we investigate how the waves from neighboring flux tubes interact in the chromosphere and corona. For a particular combination of model parameters we find that AWT can produce enough heat to maintain a peak temperature of about 2.5 MK, somewhat lower than the temperatures …
Evidence for inhomogeneous heating in the interplanetary 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 a…
We summarize our recent studies on the origin of solar wind kinetic scale turbulence and electron halo in the electron velocity distribution function. Increasing observations of nanoflares and microscopic type III radio bursts strongly suggest that nanoflares and accelerated electron beams are common in the corona. Based on particle-in-cell simulations, we show that both the core-halo feature and kinetic scale turbulence observed in the solar wind can be produced by the nonlinear evolution of electron two-stream instability driven by nanoflare accelerated electron beams. The energy exchange be…
Low-frequency Alfven-wave turbulence causes ion trajectories to become chaotic, or "stochastic," when the turbulence amplitude is sufficiently large. Stochastic orbits enable ions to absorb energy from the turbulence, increasing the perpendicular ion temperature even when the fluctuation frequencies are too small for a cyclotron resonance to occur. In this paper, an analytic expression for the stochastic heating rate is used in conjunction with an observationally constrained turbulence model to obtain an analytic formula for the perpendicular ion temperature as a function of heliocentric dista…
In recent years, a phenomenological solar wind heating model based on a turbulent energy cascade prescribed by the Kolmogorov theory has produced reasonably good agreement with observations on proton temperatures out to distances around 70 AU, provided the effect of turbulence generation due to pickup ions is included in the model. In a recent study [Ng et al., J. Geophys. Res., 115, A02101 (2010)], we have incorporated in the heating model the energy cascade rate based on Iroshnikov-Kraichnan (IK) scaling. We showed that the IK cascade rate can also produce good agreement with observations, w…
We consider the radial evolution of perpendicular ion heating due to the violation of magnetic moment conservation caused by Alfven and kinetic Alfven wave turbulence. This process, referred to as stochastic heating, can be quantified by the ratio between the average velocity fluctuations at the ion gyroradius and the perpendicular ion thermal speed $ε\equiv δv / v_{t\perp}$. Using 17 years of Helios observations, we constrain how much energy could be dissipated by this mechanism between 0.29 and 0.98 au. We find that stochastic heating likely operates throughout the entire inner heliosphere, …
We consider ion heating by turbulent Alfven waves (AWs) and kinetic Alfven waves (KAWs) with perpendicular wavelengths comparable to the ion gyroradius and frequencies smaller than the ion cyclotron frequency. When the turbulence amplitude exceeds a certain threshold, an ion's orbit becomes chaotic. The ion then interacts stochastically with the time-varying electrostatic potential, and the ion's energy undergoes a random walk. Using phenomenological arguments, we derive an analytic expression for the rates at which different ion species are heated, which we test by simulating test particles i…
Estimation of the energy cascade rate in the inertial range of solar wind turbulence has been done so far mostly within the incompressible magnetohydrodynamics (MHD) theory. Here, we go beyond that approximation to include plasma compressibility using a reduced form of a recently derived exact law for compressible, isothermal MHD turbulence. Using in-situ data from the THEMIS/ARTEMIS spacecraft in the fast and slow solar wind, we investigate in detail the role of the compressible fluctuations in modifying the energy cascade rate with respect to the prediction of the incompressible MHD model. I…
We investigate the formation of hot coronae and vertical outflows in accretion disks by magneto-rotational turbulence. We perform local three-dimensional (3D) MHD simulations with the vertical stratification by explicitly solving an energy equation with various effective ratios of specific heats, gamma. Initially imposed weak vertical magnetic fields are effectively amplified by magnetorotational instability (MRI) and winding due to the differential rotation. In the isothermal case (gamma=1), the disk winds are mainly driven by the Poynting flux associated with the MHD turbulence and show quas…
A robust empirical relationship between speed and turbulence energy in the near-Earth solar wind
University of Delaware（特拉华大学）；NASA Goddard Space Flight Center（美国国家航空航天局戈达德太空飞行中心）；University of Maryland（马里兰大学）；Princeton University（普林斯顿大学）；Space Research Institute, Austrian Academy of Sciences（奥地利科学院空间研究所）
Measurements of small-scale turbulent fluctuations in the solar wind find a non-zero right-handed magnetic helicity. This has been interpreted as evidence for ion cyclotron damping. However, theoretical and empirical evidence suggests that the majority of the energy in solar wind turbulence resides in low frequency anisotropic kinetic Alfven wave fluctuations that are not subject to ion cyclotron damping. We demonstrate that a dissipation range comprised of kinetic Alfven waves also produces a net right-handed fluctuating magnetic helicity signature consistent with observations. Thus, the obse…
Turbulence is a chaotic flow regime filled by irregular flows. The dissipation of turbulence is a fundamental problem in the realm of physics. Theoretically, dissipation cannot be ultimately achieved without collisions, and so how turbulent kinetic energy is dissipated in the nearly collisionless solar wind is a challenging problem. Wave particle interactions and magnetic reconnection are two possible dissipation mechanisms, but which mechanism dominates is still a controversial topic. Here we analyze the dissipation region scaling around a solar wind magnetic reconnection region. We find that…
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 Alfven turbulence and whistler turbulence. These two possibilities, however, have one key qualitative difference: whistler turbulence, unlike kinetic Alfven 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. The results show, for the first time, that the fluctuations well below the proton scale are p…
We extend previous theories of stochastic ion heating to account for the motion of ions along the magnetic field. We derive an analytic expression for the ion-to-proton perpendicular temperature ratio in the solar wind for any ion species, assuming that stochastic heating is the dominant ion heating mechanism. This expression describes how this temperature ratio depends upon the average velocity of the ions along the magnetic field direction and the ratio of the parallel proton pressure to the magnetic pressure. We compare our model with previously published measurements of alpha particles and…
Coronal loops act as resonant cavities for low frequency fluctuations that are transmitted from the deeper layers of the solar atmosphere and are amplified in the corona, triggering nonlinear interactions. However trapping is not perfect, some energy leaks down to the chromosphere, thus limiting the turbulence development and the associated heating. We consider the combined effects of turbulence and leakage in determining the energy level and associated heating rate in models of coronal loops which include the chromosphere and transition region. We use a piece-wise constant model for the Alfve…
We revisit the question of how the unstable scattering of interstellar pickup ions (PUIs) may drive turbulence in the outer solar wind, and why the energy released into fluctuations by this scattering appears to be significantly less than the standard bispherical prediction. We suggest that energization of the newly picked-up ions by the ambient turbulence during the scattering process can result in a more spherical distribution of PUIs, and reduce the generated fluctuation energy to a level consistent with the observations of turbulent intensities and core solar wind heating. This scenario im…
Coronal flare emission is commonly observed to decay on timescales longer than those predicted by impulsively-driven, one-dimensional flare loop models. This discrepancy is most apparent during the gradual phase, where emission from these models decays over minutes, in contrast to the hour or more often observed. Magnetic reconnection is invoked as the energy source of a flare, but should deposit energy into a given loop within a matter of seconds. Models which supplement this impulsive energization with a long, persistent ad hoc heating have successfully reproduced long-duration emission, but…
