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Abstract 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 6.3R_⊙, which gradually decreases with increasing distance, eventually becoming ∼80% of the total plasma heating rate at ∼13R_⊙, 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. 

Abstract 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 65R_⊙. 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 wavenumberk⁻¹power 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 ofk^−5/3, and (ii) the 2D and slab fluctuations follow the power laws withk^−5/3andk^−3/2, respectively. For the velocity fluctuations, we assume that both the 2D and slab components follow ak^−3/2power 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 thek^−5/3andk^−3/2power laws between 2D and slab turbulence exhibits a smaller value in comparison to assuming the same power lawk^−5/3between 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. 

Abstract 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. 

Abstract This paper reports the first possible evidence for the development of the Kelvin–Helmholtz (KH) instability at the border of coronal holes separating the associated fast wind from the slower wind originating from adjacent streamer regions. Based on a statistical data set of spectroscopic measurements of the UV corona acquired with the UltraViolet Coronagraph Spectrometer on board the SOlar and Heliospheric Observatory during the minimum activity of solar cycle 22, high temperature–velocity correlations are found along the fast/slow solar wind interface region and interpreted as manifestations of KH vortices formed by the roll-up of the shear flow, whose dissipation could lead to higher heating and, because of that, higher velocities. These observational results are supported by solving coupled solar wind and turbulence transport equations including a KH-driven source of turbulence along the tangential velocity discontinuity between faster and slower coronal flows: numerical analysis indicates that the correlation between the solar wind speed and temperature is large in the presence of the shear source of turbulence. These findings suggest that the KH instability may play an important role both in the plasma dynamics and in the energy deposition at the boundaries of coronal holes and equatorial streamers. 

Abstract 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 3R_⊙. 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. 

Abstract 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. 

The statistical properties of fast Alfvénic solar wind turbulence have been analyzed by means of empirical mode decomposition and the associated Hilbert spectral analysis. The stringent criteria employed for the data selection in the Wind spacecraft database, has made possible to sample multiple k‖ field-aligned intervals of the three magnetic field components. The results suggest that the spectral anisotropy predicted by the critical balance theory is not observed in the selected database, whereas a Kolmogorov-like scaling (E(k‖)∼k−5/3) and a weak or absent level of intermittency are robust characteristics of the Alfvénic slab component of solar wind turbulence. 

Abstract 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.