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This Letter reports the first observation of the onset of fully developed turbulence in the solar corona. Long time series of white-light coronal images, acquired by Metis aboard Solar Orbiter at 2 minutes cadence and spanning about 10 hr, were studied to gain insight into the statistical properties of fluctuations in the density of the coronal plasma in the time domain. From pixel-by-pixel spectral frequency analysis in the whole Metis field of view, the scaling exponents of plasma fluctuations were derived. The results show that, over timescales ranging from 1 to 10 hr and corresponding to the photospheric mesogranulation-driven dynamics, the density spectra become shallower moving away from the Sun, resembling a Kolmogorov-like spectrum at 3 R _⊙ . According to the latest observation and interpretive work, the observed 5/3 scaling law for density fluctuations is indicative of the onset of fully developed turbulence in the corona. Metis observation-based evidence for a Kolmogorov turbulent form of the fluctuating density spectrum casts light on the evolution of 2D turbulence in the early stages of its upward transport from the low corona.

We study the solar cycle dependence of various turbulence cascade rates based on the methodology developed by Adhikari et al. that utilizes Kolmogorov phenomenology. This approach is extended to derive the heating rates for an Iroshnikov–Kriachnan (IK) phenomenology. The observed turbulence cascade rates corresponding to the total turbulence energy, fluctuating magnetic energy density, fluctuating kinetic energy, and the normalized cross helicity are derived from WIND spacecraft plasma and magnetometer data from 1995 through 2020. We find that (i) the turbulence cascade rate derived from a Kolmogorov phenomenology and an IK phenomenology changes with solar cycle, such that the cascade rate is largest during solar maximum and smallest during solar minimum; (ii) the turbulence energy Kolmogorov cascade rate increases from θ _UB (angle between mean magnetic field and velocity) = 0° to 90° and peaks near θ _UB = 90°, and then decreases as θ _UB tends to 180°; (iii) the 2D turbulence heating rate is larger than the slab heating rate; (iv) the 2D and slab fluctuating magnetic energy density cascade rates are larger than the corresponding cascade rates of the fluctuating kinetic energy; and (v) the total turbulence energy cascade rate is positively correlated with the solar wind speed and temperature and the normalized cross-helicity cascade rate. Finally, we find that the total turbulent energy Kolmogorov cascade rate is larger than the IK cascade rate.

Analytical solutions for 2D and slab turbulence energies in the solar corona are presented, including a derivation of the corresponding correlation lengths, with implications for the proton and electron temperatures in the solar corona. These solutions are derived by solving the transport equations for 2D and slab turbulence energies and their correlation lengths, as well as proton and electron pressures. The solutions assume background profiles for the solar wind speed, solar wind mass density, and Alfvén velocity. Our analytical solutions can be related to those obtained from joint Parker Solar Probe and Solar Orbiter Metis coronagraph observations, as reported in Telloni et al. We find that the solution for 2D turbulence energy in the absence of nonlinear dissipation decreases more slowly compared to the dissipative solution. The solution for slab turbulence energy with no dissipation exhibits a more rapid increase compared to the dissipative solution. The proton heating rate is found to be about 82% of the total plasma heating rate at 6.3 R _⊙ , which gradually decreases with increasing distance, eventually becoming ∼80% of the total plasma heating rate at ∼13 R _⊙ , consistent with that found by Bandyopadhyay et al. (2023). These analytical solutions provide valuable insight for our understanding of turbulence, and its effect on proton and electron heating rates, in the solar corona. We compare the numerically solved turbulent transport equations for the 2D and slab turbulence energies, correlation lengths, and proton and electron pressures with the analytical solutions, finding good agreement between them.

We study solar wind turbulence anisotropy in the inertial and energy-containing ranges in the inbound and outbound directions during encounters 1–9 by the Parker Solar Probe (PSP) for distances between ∼21 and 65 R _⊙ . Using the Adhikari et al. approach, we derive theoretical equations to calculate the ratio between the 2D and slab fluctuating magnetic energy, fluctuating kinetic energy, and the outward/inward Elsässer energy in the inertial range. For this, in the energy-containing range, we assume a wavenumber k ^−1 power law. In the inertial range, for the magnetic field fluctuations and the outward/inward Elsässer energy, we consider that (i) both 2D and slab fluctuations follow a power law of k ^−5/3 , and (ii) the 2D and slab fluctuations follow the power laws with k ^−5/3 and k ^−3/2 , respectively. For the velocity fluctuations, we assume that both the 2D and slab components follow a k ^−3/2 power law. We compare the theoretical results of the variance anisotropy in the inertial range with the derived observational values measured by PSP, and find that the energy density of 2D fluctuations is larger than that of the slab fluctuations. The theoretical variance anisotropy in the inertial range relating to the k ^−5/3 and k ^−3/2 power laws between 2D and slab turbulence exhibits a smaller value in comparison to assuming the same power law k ^−5/3 between 2D and slab turbulence. Finally, the observed turbulence energy measured by PSP in the energy-containing range is found to be similar to the theoretical result of a nearly incompressible/slab turbulence description.

The nature and radial evolution of solar wind electrons in the suprathermal energy range are studied. A wave–particle interaction tensor and a Fokker–Planck Coulomb collision operator are introduced into the kinetic transport equation describing electron collisions and resonant interactions with whistler waves. The diffusion tensor includes diagonal and off-diagonal terms, and the Coulomb collision operator applies to arbitrary electron velocities describing collisions with both background protons and electrons. The background proton and electron densities and temperatures are based on previous turbulence models that mediate the supersonic solar wind. The electron velocity distribution functions and electron heat flux are calculated. Comparison and analysis of the numerical results with analytical solutions and observations in the near-Sun region are made. The numerical results reproduce well the creation of the sunward electron deficit observed in the near-Sun region. The deficit of the electron velocity distribution function below the core Maxwellian fit at low velocities results from Coulomb collisions, and the excess part above the core Maxwellian fit at high velocities is determined by strong wave–particle interactions.

Interplanetary (IP) shocks are believed to play a significant role in both amplifying the background level of turbulent fluctuations and in heating the bulk solar wind (SW). This study investigates the thermodynamic properties downstream of IP shocks. We examine the temperature, density, and specific entropy changes in the shocked plasma, taking into consideration the geometric aspects of IP shock propagation within the expanding SW. Specifically, in our analysis, we account for the fact that any particular temporal range of one-point measurement may correspond to vastly different physically relevant temporal and/or spatial dimensions, such as the age of the shocked plasma and/or radial distance to the place where the plasma encountered the shock. Thus, our approach resolves the contradictions in previously reported temperature and specific entropy profiles in downstream regions and suggests that downstream regions exhibit greater turbulent heating compared to the pristine SW. This may contribute to the overall heating of the SW plasma. The paper presents a phenomenological parameter to predict specific entropy profiles and demonstrates the consistency of the proposed model with observations. We discuss the implications of these results for the thermodynamics of the SW beyond 1 au.

This Letter reports the first observational estimate of the heating rate in the slowly expanding solar corona. The analysis exploits the simultaneous remote and local observations of the same coronal plasma volume, with the Solar Orbiter/Metis and the Parker Solar Probe instruments, respectively, and relies on the basic solar wind magnetohydrodynamic equations. As expected, energy losses are a minor fraction of the solar wind energy flux, since most of the energy dissipation that feeds the heating and acceleration of the coronal flow occurs much closer to the Sun than the heights probed in the present study, which range from 6.3 to 13.3 R _⊙ . The energy deposited to the supersonic wind is then used to explain the observed slight residual wind acceleration and to maintain the plasma in a nonadiabatic state. As derived in the Wentzel–Kramers–Brillouin limit, the present energy transfer rate estimates provide a lower limit, which can be very useful in refining the turbulence-based modeling of coronal heating and subsequent solar wind acceleration.

This paper addresses the first direct investigation of the energy budget in the solar corona. Exploiting joint observations of the same coronal plasma by Parker Solar Probe and the Metis coronagraph aboard Solar Orbiter and the conserved equations for mass, magnetic flux, and wave action, we estimate the values of all terms comprising the total energy flux of the proton component of the slow solar wind from 6.3 to 13.3 R _⊙ . For distances from the Sun to less than 7 R _⊙ , we find that the primary source of solar wind energy is magnetic fluctuations including Alfvén waves. As the plasma flows away from the low corona, magnetic energy is gradually converted into kinetic energy, which dominates the total energy flux at heights above 7 R _⊙ . It is found too that the electric potential energy flux plays an important role in accelerating the solar wind only at altitudes below 6 R _⊙ , while enthalpy and heat fluxes only become important at even lower heights. The results finally show that energy equipartition does not exist in the solar corona.

Nearly incompressible magnetohydrodynamic (NI MHD) theory for β ∼ 1 (or β ≪ 1) plasma has been developed and applied to the study of solar wind turbulence. The leading-order term in β ∼ 1 or β ≪ 1 plasma describes the majority of 2D turbulence, while the higher-order term describes the minority of slab turbulence. Here, we develop new NI MHD turbulence transport model equations in the high plasma beta regime. The leading-order term in a β ≫ 1 plasma is fully incompressible and admits both structures (flux ropes or magnetic islands) and slab (Alfvén waves) fluctuations. This paper couples the NI MHD turbulence transport equations with three fluid (proton, electron, and pickup ion) equations, and solves the 1D steady-state equations from 1–75 au. The model is tested against 27 yr of Voyager 2 data, and Ulysses and NH SWAP data. The results agree remarkably well, with some scatter, about the theoretical predictions.

Evidence for the presence of ion cyclotron waves (ICWs), driven by turbulence, at the boundaries of the current sheet is reported in this paper. By exploiting the full potential of the joint observations performed by Parker Solar Probe and the Metis coronagraph on board Solar Orbiter, local measurements of the solar wind can be linked with the large-scale structures of the solar corona. The results suggest that the dynamics of the current sheet layers generates turbulence, which in turn creates a sufficiently strong temperature anisotropy to make the solar-wind plasma unstable to anisotropy-driven instabilities such as the Alfvén ion cyclotron, mirror-mode, and firehose instabilities. The study of the polarization state of high-frequency magnetic fluctuations reveals that ICWs are indeed present along the current sheet, thus linking the magnetic topology of the remotely imaged coronal source regions with the wave bursts observed in situ. The present results may allow improvement of state-of-the-art models based on the ion cyclotron mechanism, providing new insights into the processes involved in coronal heating.

This paper addresses the first direct investigation of the energy budget in the solar corona. Exploiting joint observations of the same coronal plasma by Parker Solar Probe and the Metis coronagraph aboard Solar Orbiter and the conserved equations for mass, magnetic flux, and wave action, we estimate the values of all terms comprising the total energy flux of the proton component of the slow solar wind from 6.3 to 13.3 R ⊙. For distances from the Sun to less than 7 R ⊙, we find that the primary source of solar wind energy is magnetic fluctuations including Alfvén waves. As the plasma flows away from the low corona, magnetic energy is gradually converted into kinetic energy, which dominates the total energy flux at heights above 7 R ⊙. It is found too that the electric potential energy flux plays an important role in accelerating the solar wind only at altitudes below 6 R ⊙, while enthalpy and heat fluxes only become important at even lower heights. The results finally show that energy equipartition does not exist in the solar corona. [ABSTRACT FROM AUTHOR]

The properties of Alfvénic solar wind turbulence have been studied for decades using spacecraft measurements. In particular, the observation of spectral anisotropy of magnetic fluctuations has stimulated the development of several phenomenological models, one of the most popular being critical balance. However, the experimental validation of these models is intrinsically difficult because of the one-dimensional nature of the measurements provided by spacecraft instrumentation. In this work, a thorough search is performed in the Wind spacecraft database to extract samples of field-aligned fast solar wind, which allow the precise estimation of the parallel spectral properties of the magnetic fluctuations, and of their intermittency. Hilbert spectral analysis is used, in order to eliminate the possible role of nonstationarity and large-scale structures. Our results indicate that the spectral anisotropy predicted by the critical balance theory is not observed in the selected database, thus questioning the validity of the critical balance in the solar wind turbulence. A stochastic process characterized by a −5/3 spectral scaling, which is not necessarily attributed to usual turbulence, as indicated by the absence of intermittency, is indeed observed in the analyzed data samples. [ABSTRACT FROM AUTHOR]