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1. Coronal Loop Heating by Nearly Incompressible Magnetohydrodynamic and Reduced Magnetohydrodynamic Turbulence Models

   https://doi.org/10.3847/1538-4357/acb151  

   Yalim, M. S. ; Zank, G. P. ; Asgari-Targhi, M. ( February 2023 , The Astrophysical Journal)

   The transport of waves and turbulence beyond the photosphere is central to the coronal heating problem. Turbulence in the quiet solar corona has been modeled on the basis of the nearly incompressible magnetohydrodynamic (NI MHD) theory to describe the transport of low-frequency turbulence in open magnetic field regions. It describes the evolution of the coupled majority quasi-2D and minority slab component, driven by the magnetic carpet and advected by a subsonic, sub-Alfvénic flow from the lower corona. In this paper, we couple the NI MHD turbulence transport model with an MHD model of the solar corona to study the heating problem in a coronal loop. In a realistic benchmark coronal loop problem, we find that a loop can be heated to ∼1.5 million K by transport and dissipation of MHD turbulence described by the NI MHD model. We also find that the majority 2D component is as important as the minority slab component in the heating of the coronal loop. We compare our coupled MHD/NI MHD model results with a reduced MHD (RMHD) model. An important distinction between these models is that RMHD solves for small-scale velocity and magnetic field fluctuations and obtains the actual viscous/resistive dissipation associated with their evolution whereas NI MHD evolves scalar moments of the fluctuating velocity and magnetic fields and approximates dissipation using an MHD turbulence phenomenology. Despite the basic differences between the models, their simulation results match remarkably well, yielding almost identical heating rates inside the corona.

    

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2. Modeling proton and electron heating in the fast solar wind

   https://doi.org/10.1051/0004-6361/202039297  

   Adhikari, L. ; Zank, G. P. ; Zhao, L.-L. ; Nakanotani, M. ; Tasnim, S. ( June 2021 , Astronomy & Astrophysics)

   null (Ed.)

   Context. The Parker Solar Probe (PSP) measures solar wind protons and electrons near the Sun. To study the thermodynamic properties of electrons and protons, we include electron effects, such as distributed turbulent heating between protons and electrons, Coulomb collisions between protons and electrons, and heat conduction of electrons. Aims. We develop a general theoretical model of nearly incompressible magnetohydrodynamic (NI MHD) turbulence coupled with a solar wind model that includes electron pressure and heat flux. Methods. It is important to note that 60% of the turbulence energy is assigned to proton heating and 40% to electron heating. We use an empirical expression for the electron heat flux. We derived a nonlinear dissipation term for the residual energy that includes both the Alfvén effect and the turbulent small-scale dynamo effect. Similarly, we obtained the NI/slab time-scale in an NI MHD phenomenology to use in the derivation of the nonlinear term that incorporates the Alfvén effect. Results. A detailed comparison between the theoretical model solutions and the fast solar wind measured by PSP and Helios 2 shows that they are consistent. The results show that the nearly incompressible NI/slab turbulence component describes observations of the fast solar wind periods when the solar wind flow is aligned or antialigned with the magnetic field. 

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3. On the Conservation of Turbulence Energy in Turbulence Transport Models

   https://doi.org/10.3847/1538-4357/ac596e  

   Wang, B.-B. ; Zank, G. P. ; Adhikari, L. ; Zhao, L.-L. ( April 2022 , The Astrophysical Journal)

   Abstract Zank et al. developed models describing the transport of low-frequency incompressible and nearly incompressible turbulence in inhomogeneous flows. The formalism was based on expressing the fluctuating variables in terms of the Elsässar variables and then taking “moments” subject to various closure hypotheses. The turbulence transport models are different according to whether the plasma beta regime is large, of order unity, or small. Here, we show explicitly that the three sets of turbulence transport models admit a conservation representation that resembles the well-known WKB transport equation for Alfvén wave energy density after introducing appropriate definitions of the “pressure” associated with the turbulent fluctuations. This includes introducing a distinct turbulent pressure tensor for 3D incompressible turbulence (the large plasma beta limit) and pressure tensors for quasi-2D and slab turbulence (the plasma beta order-unity or small regimes) that generalize the form of the WKB pressure tensor. Various limits of the different turbulent pressure tensors are discussed. However, the analogy between the conservation form of the turbulence transport models and the WKB model is not close for multiple reasons, including that the turbulence models express fully nonlinear physical processes unlike the strictly linear WKB description. The analysis presented here both serves as a check on the validity and correctness of the turbulence transport models and also provides greater transparency of the energy dissipation term and the “turbulent pressure” in our models, which is important for many practical applications. 

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4. 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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5. Alternative formulation of weak magnetohydrodynamic turbulence theory

   https://doi.org/10.1063/5.0097084  

   Yoon, Peter H. ; Ziebell, Luiz F. ; Choe, Gwangson ( November 2022 , Physics of Plasmas)

   In a recent paper [P. H. Yoon and G. Choe, Phys. Plasmas 28, 082306 (2021)], the weak turbulence theory for incompressible magnetohydrodynamics is formulated by employing the method customarily applied in the context of kinetic weak plasma turbulence theory. Such an approach simplified certain mathematical procedures including achieving the closure relationship. The formulation in the above-cited paper starts from the equations of incompressible magnetohydrodynamic (MHD) theory expressed via Elsasser variables. The derivation of nonlinear wave kinetic equation therein is obtained via a truncated solution at the second-order of iteration following the standard practice. In the present paper, the weak MHD turbulence theory is alternatively formulated by employing the pristine form of incompressible MHD equation rather than that expressed in terms of Elsasser fields. The perturbative expansion of the nonlinear momentum equation is carried out up to the third-order iteration rather than imposing the truncation at the second order. It is found that while the resulting wave kinetic equation is identical to that obtained in the previous paper cited above, the third-order nonlinear correction plays an essential role for properly calculating derived quantities such as the total and residual energies.

    

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