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1. 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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2. 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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3. 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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4. The Transport and Evolution of MHD Turbulence throughout the Heliosphere: Models and Observations

   https://doi.org/10.3390/fluids6100368  

   Adhikari, Laxman ; Zank, Gary P. ; Zhao, Lingling ( October 2021 , Fluids)

   null (Ed.)

   A detailed study of solar wind turbulence throughout the heliosphere in both the upwind and downwind directions is presented. We use an incompressible magnetohydrodynamic (MHD) turbulence model that includes the effects of electrons, the separation of turbulence energy into proton and electron heating, the electron heat flux, and Coulomb collisions between protons and electrons. We derive expressions for the turbulence cascade rate corresponding to the energy in forward and backward propagating modes, the fluctuating kinetic and magnetic energy, the normalized cross-helicity, and the normalized residual energy, and calculate the turbulence cascade rate from 0.17 to 75 au in the upwind and downwind directions. Finally, we use the turbulence transport models to derive cosmic ray (CR) parallel and perpendicular mean free paths (mfps) in the upwind and downwind heliocentric directions. We find that turbulence in the upwind and downwind directions is different, in part because of the asymmetric distribution of new born pickup ions in the two directions, which results in the CR mfps being different in the two directions. This is important for models that describe the modulation of cosmic rays by the solar wind. 

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5. Turbulence and Waves in the Sub-Alfvénic Solar Wind Observed by the Parker Solar Probe during Encounter 10

   https://doi.org/10.3847/2041-8213/ac8353  

   Zhao, L.-L. ; Zank, G. P. ; Adhikari, L. ; Telloni, D. ; Stevens, M. ; Kasper, J. C. ; Bale, S. D. ; Raouafi, N. E. ( August 2022 , The Astrophysical Journal Letters)

   Abstract During its 10th orbit around the Sun, the Parker Solar Probe sampled two intervals where the local Alfvén speed exceeded the solar wind speed, lasting more than 10 hours in total. In this paper, we analyze the turbulence and wave properties during these periods. The turbulence is observed to be Alfvénic and unbalanced, dominated by outward-propagating modes. The power spectrum of the outward-propagating Elsässer z + mode steepens at high frequencies while that of the inward-propagating z − mode flattens. The observed Elsässer spectra can be explained by the nearly incompressible (NI) MHD turbulence model with both 2D and Alfvénic components. The modeling results show that the z + spectra are dominated by the NI/slab component, and the 2D component mainly affects the z − spectra at low frequencies. An MHD wave decomposition based on an isothermal closure suggests that outward-propagating Alfvén and fast magnetosonic wave modes are prevalent in the two sub-Alfvénic intervals, while the slow magnetosonic modes dominate the super-Alfvénic interval in between. The slow modes occur where the wavevector is nearly perpendicular to the local mean magnetic field, corresponding to nonpropagating pressure-balanced structures. The alternating forward and backward slow modes may also be features of magnetic reconnection in the near-Sun heliospheric current sheet. 

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