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1. Linear Mode Decomposition in Magnetohydrodynamics Revisited

   https://doi.org/10.3847/1538-4365/acdf5d  

   Zank, G. P.; Zhao, L. -L.; Adhikari, L.; Nakanotani, M.; Pitňa, A.; Telloni, D.; Che, H. (August 2023, The Astrophysical Journal Supplement Series)

   Abstract Small-amplitude fluctuations in the magnetized solar wind are measured typically by a single spacecraft. In the magnetohydrodynamics (MHD) description, fluctuations are typically expressed in terms of the fundamental modes admitted by the system. An important question is how to resolve an observed set of fluctuations, typically plasma moments such as the density, velocity, pressure, and magnetic field fluctuations, into their constituent fundamental MHD modal components. Despite its importance in understanding the basic elements of waves and turbulence in the solar wind, this problem has not yet been fully resolved. Here, we introduce a new method that identifies between wave modes and advected structures such as magnetic islands or entropy modes and computes the phase information associated with the eligible MHD modes. The mode-decomposition method developed here identifies the admissible modes in an MHD plasma from a set of plasma and magnetic field fluctuations measured by a single spacecraft at a specific frequency and an inferred wavenumberk_m. We present data from three typical intervals measured by the Wind and Solar Orbiter spacecraft at ∼1 au and show how the new method identifies both propagating (wave) and nonpropagating (structures) modes, including entropy and magnetic island modes. This allows us to identify and characterize the separate MHD modes in an observed plasma parcel and to derive wavenumber spectra of entropic density, fast and slow magnetosonic, Alfvénic, and magnetic island fluctuations for the first time. These results help identify the fundamental building blocks of turbulence in the magnetized solar wind. 

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2. 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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3. Characterization of Turbulent Fluctuations in the Sub-Alfvénic Solar Wind

   https://doi.org/10.3847/1538-4357/ad34ab  

   Zank, G. P.; Zhao, L. -L.; Adhikari, L.; Telloni, D.; Baruwal, Prashant; Baruwal, Prashrit; Zhu, Xingyu; Nakanotani, M.; Pitňa, A.; Kasper, J. C.; et al (April 2024, The Astrophysical Journal)

   Abstract Parker Solar Probe (PSP) observed sub-Alfvénic solar wind intervals during encounters 8–14, and low-frequency magnetohydrodynamic (MHD) turbulence in these regions may differ from that in super-Alfvénic wind. We apply a new mode decomposition analysis to the sub-Alfvénic flow observed by PSP on 2021 April 28, identifying and characterizing entropy, magnetic islands, forward and backward Alfvén waves, including weakly/nonpropagating Alfvén vortices, forward and backward fast and slow magnetosonic (MS) modes. Density fluctuations are primarily and almost equally entropy- and backward-propagating slow MS modes. The mode decomposition provides phase information (frequency and wavenumberk) for each mode. Entropy density fluctuations have a wavenumber anisotropy ofk_∥≫k_⊥, whereas slow-mode density fluctuations havek_⊥>k_∥. Magnetic field fluctuations are primarily magnetic island modes (δBⁱ) with anO(1) smaller contribution from unidirectionally propagating Alfvén waves (δB^A+) giving a variance anisotropy of $〈{\delta B^i}^2〉/〈{\delta B^A}^2〉=4.1$. Incompressible magnetic fluctuations dominate compressible contributions from fast and slow MS modes. The magnetic island spectrum is Kolmogorov-like $k_{\perp }^{-1.6}$in perpendicular wavenumber, and the unidirectional Alfvén wave spectra are $k_{\parallel }^{-1.6}$and $k_{\perp }^{-1.5}$. Fast MS modes propagate at essentially the Alfvén speed with anticorrelated transverse velocity and magnetic field fluctuations and are almost exclusively magnetic due toβ_p≪ 1. Transverse velocity fluctuations are the dominant velocity component in fast MS modes, and longitudinal fluctuations dominate in slow modes. Mode decomposition is an effective tool in identifying the basic building blocks of MHD turbulence and provides detailed phase information about each of the modes. 

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4. Observations of Waves and Structures by Frequency–Wavenumber Spectrum in Solar Wind Turbulence

   https://doi.org/10.3847/1538-4357/acb33b  

   Zhao, L.-L.; Zank, G. P.; Nakanotani, M.; Adhikari, L. (February 2023, The Astrophysical Journal)

   Abstract A well-known shortcoming of single-spacecraft spectral analysis is that only the 1D wavenumber spectrum can be observed, assuming the characteristic wave propagation speed is much smaller than the solar wind flow speed. This limitation has motivated an extended debate about whether fluctuations observed in the solar wind are waves or structures. Multispacecraft analysis techniques can be used to calculate the wavevector independent of the observed frequency, thus allowing one to study the frequency–wavenumber spectrum of turbulence directly. The dispersion relation for waves can be identified, which distinguishes them from nonpropagating structures. We use magnetic field data from the four Magnetospheric Multiscale (MMS) spacecraft to measure the frequency–wavenumber spectrum of solar wind turbulence based on the k -filtering and phase differencing techniques. Both techniques have been used successfully in the past for the Earth’s magnetosphere, although applications to solar wind turbulence have been limited. We conclude that the solar wind turbulence intervals observed by MMS show features of nonpropagating structures that are associated with frequencies close to zero in the plasma rest frame. However, there is no clear evidence of propagating Alfvén waves that have a nonzero rest-frame frequency. The lack of waves may be due to instrument noise and spacecraft separation. Our results support the idea of turbulence dominated by quasi-2D structures. 

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5. Turbulence in the Sub-Alfvénic Solar Wind

   https://doi.org/10.3847/2041-8213/ac51da  

   Zank, G. P.; Zhao, L. -L.; Adhikari, L.; Telloni, D.; Kasper, J. C.; Stevens, M.; Rahmati, A.; Bale, S. D. (February 2022, The Astrophysical Journal Letters)

   Abstract The Parker Solar Probe (PSP) entered a region of sub-Alfvénic solar wind during encounter 8, and we present the first detailed analysis of low-frequency turbulence properties in this novel region. The magnetic field and flow velocity vectors were highly aligned during this interval. By constructing spectrograms of the normalized magnetic helicity, cross-helicity, and residual energy, we find that PSP observed primarily Alfvénic fluctuations, a consequence of the highly field-aligned flow that renders quasi-2D fluctuations unobservable to PSP. We extend Taylor’s hypothesis to sub- and super-Alfvénic flows. Spectra for the fluctuating forward and backward Elsässer variables (z^±, respectively) are presented, showing thatz⁺modes dominatez⁻by an order of magnitude or more, and thez⁺spectrum is a power law in frequency (parallel wavenumber)f^−3/2( $k_{\parallel }^{-3/2}$) compared to the convexz⁻spectrum withf^−3/2( $k_{\parallel }^{-3/2}$) at low frequencies, flattening around a transition frequency (at which the nonlinear and Alfvén timescales are balanced) tof^−1.25at higher frequencies. The observed spectra are well fitted using a spectral theory for nearly incompressible magnetohydrodynamics assuming a wavenumber anisotropy $k_{\perp }\sim k_{\parallel }^{3/4}$, that thez⁺fluctuations experience primarily nonlinear interactions, and that the minorityz⁻fluctuations experience both nonlinear and Alfvénic interactions withz⁺fluctuations. The density spectrum is a power law that resembles neither thez^±spectra nor the compressible magnetic field spectrum, suggesting that these are advected entropic rather than magnetosonic modes and not due to the parametric decay instability. Spectra in the neighboring modestly super-Alfvénic intervals are similar. 

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