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Abstract The Parker Solar Probe (PSP) and Wind spacecraft observed the same plasma flow during PSP encounter 15. The solar wind evolves from a sub-Alfvénic flow at 0.08 au to become modestly super-Alfvénic at 1 au. We study the radial evolution of the turbulence properties and deduce the spectral anisotropy based on the nearly incompressible (NI) MHD theory. We find that the spectral index of thez⁺spectrum remains unchanged (∼−1.53), while thez⁻spectrum steepens, the index of which changes from −1.35 to −1.47. The fluctuating kinetic energy is on average greater than the fluctuating magnetic field energy in the sub-Alfvénic flow while smaller in the modestly super-Alfvénic flow. The NI MHD theory well interprets the observed Elsässer spectra. The contribution of 2D fluctuations is nonnegligible for the observedz⁻frequency spectra for both intervals. Particularly, the magnitudes of 2D and NI/slab fluctuations are comparable in the frequency domain for the modestly super-Alfvénic flow, resulting in a slightly concave shape ofz⁻spectrum at 1 au. We show that, in the wavenumber domain, the power ratio of the observed forward NI/slab and 2D fluctuations is  ∼15 at 0.08 au, while it decreases to  ∼3 at 1 au, suggesting the growing significance of the 2D fluctuations as the turbulence evolves in low Mach number solar wind. 

Abstract A multispecies energetic particle intensity enhancement event at 1 au is analyzed. We identify this event as a corotating interaction region (CIR) structure that includes a stream interface (SI), a forward-reverse shock pair, and an embedded heliospheric current sheet (HCS). The distinct feature of this CIR event is that (1) the high-energy (>1 MeV) ions show significant flux enhancement at the reverse wave (RW)/shock of the CIR structure, following their passage through the SI and HCS. The flux amplification appears to depend on the energy per nucleon. (2) Electrons in the energy range of 40.5–520 keV are accelerated immediately after passing through the SI and HCS regions, and the flux quickly reaches a peak for low-energy electrons. At the RW, only high-energy electrons (∼520 keV) show significant local flux enhancement. The CIR structure is followed by a fast-forward perpendicular shock driven by a coronal mass ejection (CME), and we observed a significant flux enhancement of low-energy protons and high-energy electrons. Specifically, the 210–330 keV proton and 180–520 keV electron fluxes are enhanced by approximately 2 orders of magnitude. This suggests that the later ICME-driven shock may accelerate particles out of the suprathermal pool. In this paper, we further present that for CIR-accelerated particles, the increase in turbulence power at SI and RWs may be an important factor for the observed flux enhancement in different species. The presence of ion-scale waves near the RW, as indicated by the spectral bump near the proton gyrofrequency, suggests that the resonant wave–particle interaction may act as an efficient energy transferrer between energetic protons and ion-scale waves. 

Abstract 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 fromθ_UB(angle between mean magnetic field and velocity) = 0° to 90° and peaks nearθ_UB= 90°, and then decreases asθ_UBtends 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. 

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. 

The distribution of turbulence in the heliosphere remains a mystery, due to the complexity in not only modeling the turbulence transport equations but also identifying the drivers of turbulence that vary with time and spatial location. Beyond the ionization cavity (a few astronomical units (AU) from the Sun), the turbulence is driven predominantly by freshly created pickup ions (PUIs), in contrast to the driving by stream shear and compression. Understanding the source characteristics is necessary to refine turbulence transport models and interpret measurements of turbulence and solar wind temperature in the outer heliosphere. Using a recent latitude-dependent solar wind speed model and the ionization rate of neutral interstellar hydrogen (H), we investigate the temporal and spatial variation in the strength of low-frequency turbulence driven by PUIs from 1998 to 2020. We find that the driving rate is stronger during periods of high solar activity and at lower latitudes in the outer heliosphere. The driving rates for parallel and anti-parallel propagating (relative to the background magnetic field) slab turbulence have different spatial and latitude dependences. The calculated generation rate of turbulence by PUIs is an essential ingredient to investigate the latitude dependence of turbulence in the outer heliosphere, which is important to understand the heating of the distant solar wind and the modulation of cosmic rays. 

The transport of energetic particles in response to solar wind turbulence is important for space weather. To understand charged particle transport, it is usually assumed that the phase of the turbulence is randomly distributed (the random phase approximation) in quasi-linear theory and simulations. In this paper, we calculate the coherence index, C ϕ , of solar wind turbulence observed by the Helios 2 and Parker Solar Probe spacecraft using the surrogate data technique to check if the assumption is valid. Here, values of C ϕ = 0 and 1 indicate that the phase coherence is random and correlated, respectively. We estimate that the coherence index at the resonant scale of energetic ions (10 MeV protons) is 0.1 at 0.87 and 0.65 au, 0.18 at 0.29 au, and 0.3 (0.35) at 0.09 au for super (sub)-Alfvénic intervals, respectively. Since the random phase approximation corresponds to C ϕ = 0, this may indicate that the random phase approximation is not valid for the transport of energetic particles in the inner heliosphere, especially very close to the Sun ( ∼ 0.09  au). 

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. 

We investigate particle acceleration in an MHD-scale system of multiple current sheets by performing 2D and 3D MHD simulations combined with a test particle simulation. The system is unstable for the tearing-mode instability, and magnetic islands are produced by magnetic reconnection. Due to the interaction of magnetic islands, the system relaxes to a turbulent state. The 2D (3D) case both yield −5/3 (− 11/3 and −7/3) power-law spectra for magnetic and velocity fluctuations. Particles are efficiently energized by the generated turbulence, and form a power-law tail with an index of −2.2 and −4.2 in the energy distribution function for the 2D and 3D case, respectively. We find more energetic particles outside magnetic islands than inside. We observe super-diffusion in the 2D (∼ t 2.27 ) and 3D (∼ t 1.2 ) case in the energy space of energetic particles. 

Turbulence is ubiquitous in space plasmas. It is one of the most important subjects in heliospheric physics, as it plays a fundamental role in the solar wind—local interstellar medium interaction and in controlling energetic particle transport and acceleration processes. Understanding the properties of turbulence in various regions of the heliosphere with vastly different conditions can lead to answers to many unsolved questions opened up by observations of the magnetic field, plasma, pickup ions, energetic particles, radio and UV emissions, and so on. Several space missions have helped us gain preliminary knowledge on turbulence in the outer heliosphere and the very local interstellar medium. Among the past few missions, the Voyagers have paved the way for such investigations. This paper summarizes the open challenges and voices our support for the development of future missions dedicated to the study of turbulence throughout the heliosphere and beyond.