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1. Modeling of Joint Parker Solar Probe–Metis/Solar Orbiter Observations

   https://doi.org/10.3847/2041-8213/ac91c6  

   Adhikari, L.; Zank, G. P.; Telloni, D.; Zhao, L.-L. (September 2022, The Astrophysical Journal Letters)

   Abstract We present the first theoretical modeling of joint Parker Solar Probe (PSP)–Metis/Solar Orbiter (SolO) quadrature observations. The combined observations describe the evolution of a slow solar wind plasma parcel from the extended solar corona (3.5–6.3 R ⊙ ) to the very inner heliosphere (23.2 R ⊙ ). The Metis/SolO instrument remotely measures the solar wind speed finding a range from 96 to 201 km s −1 , and PSP measures the solar wind plasma in situ, observing a radial speed of 219.34 km s −1 . We find theoretically and observationally that the solar wind speed accelerates rapidly within 3.3–4 R ⊙ and then increases more gradually with distance. Similarly, we find that the theoretical solar wind density is consistent with the remotely and in-situ observed solar wind density. The normalized cross helicity and normalized residual energy observed by PSP are 0.96 and −0.07, respectively, indicating that the slow solar wind is very Alfvénic. The theoretical NI/slab results are very similar to PSP measurements, which is a consequence of the highly magnetic field-aligned radial flow ensuring that PSP can measure slab fluctuations and not 2D ones. Finally, we calculate the theoretical 2D and slab turbulence pressure, finding that the theoretical slab pressure is very similar to that observed by PSP. 

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2. 2D and Slab Turbulent Cascade Rates in the Inner Heliosphere

   https://doi.org/10.3847/1538-4357/ac9234  

   Adhikari, L.; Zank, G. P.; Zhao, L.-L.; Telloni, D. (October 2022, The Astrophysical Journal)

   Abstract We present a theoretical and observational study of 2D and slab turbulence cascade (or heating) rates of transverse total turbulence energies, transverse cross helicity, transverse outward and inward Elsässer energy, transverse fluctuating magnetic energy density, and transverse fluctuating kinetic energy from the perihelion of the first Parker Solar Probe (PSP) orbit at ∼36.6 R ⊙ to Solar Orbiter (SolO) at ∼177 R ⊙ . We use the Adhikari et al. (2021a) approach to calculate the observed transverse turbulence heating rate, and the nearly incompressible magnetohydrodynamic (NI MHD) turbulence transport theory to calculate the theoretical turbulence cascade rate. We find from the 1 day long PSP measurements at 66.5 R ⊙ , and the SolO measurements at 176.3 R ⊙ that various transverse turbulent cascade rates increase with increasing angle, from 10° to 98°, between the mean solar wind speed and mean magnetic field ( θ UB ), indicating that the 2D heating rate is largest in the inner heliosphere. Similarly, we find from the theoretical and observed results that the 2D heating rate is larger than the slab heating rate as a function of heliocentric distance. We present a comparison between the theoretical and observed 2D and slab turbulence cascade rates as a function of heliocentric distance. 

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3. Turbulence, and Proton and Electron Heating Rates in the Solar Corona: Analytical Approach

   https://doi.org/10.3847/1538-4357/ad3109  

   Adhikari, Laxman; Zank, Gary P; Telloni, Daniele; Zhao, Lingling; Wang, Bingbing; Webb, Gary; Tang, Bofeng; Nykyri, Katariina (April 2024, The Astrophysical Journal)

   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. 

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4. MHD Turbulent Power Anisotropy in the Inner Heliosphere

   https://doi.org/10.3847/1538-4357/ac70cb  

   Adhikari, L.; Zank, G. P.; Zhao, L.-L.; Telloni, D. (July 2022, The Astrophysical Journal)

   Abstract We study anisotropic magnetohydrodynamic (MHD) turbulence in the slow solar wind measured by Parker Solar Probe (PSP) and Solar Orbiter (SolO) during its first orbit from the perspective of variance anisotropy and correlation anisotropy. We use the Belcher & Davis approach (M1) and a new method (M2) that decomposes a fluctuating vector into parallel and perpendicular fluctuating vectors. M1 and M2 calculate the transverse and parallel turbulence components relative to the mean magnetic field direction. The parallel turbulence component is regarded as compressible turbulence, and the transverse turbulence component as incompressible turbulence, which can be either Alfvénic or 2D. The transverse turbulence energy is calculated from M1 and M2, and the transverse correlation length from M2. We obtain the 2D and slab turbulence energy and the corresponding correlation lengths from those transverse turbulence components that satisfy an angle between the mean solar wind flow speed and mean magnetic field θ UB of either (i) 65° < θ UB < 115° or (ii) 0° < θ UB < 25° (155° < θ UB < 180°), respectively. We find that the 2D turbulence component is not typically observed by PSP near perihelion, but the 2D component dominates turbulence in the inner heliosphere. We compare the detailed theoretical results of a nearly incompressible MHD turbulence transport model with the observed results of PSP and SolO measurements, finding good agreement between them. 

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5. Solar Cycle Dependence of the Turbulence Cascade Rate at 1 au

   https://doi.org/10.3847/1538-4357/ad4797  

   Gautam, Sujan Prasad; Adhikari, Laxman; Zank, Gary P; Silwal, Ashok; Zhao, Lingling (June 2024, The Astrophysical Journal)

   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. 

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