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.
more »
« less
Modeling proton and electron heating in the fast solar wind
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.
more »
« less
- Award ID(s):
- 1655280
- NSF-PAR ID:
- 10300902
- Date Published:
- Journal Name:
- Astronomy & Astrophysics
- Volume:
- 650
- ISSN:
- 0004-6361
- Page Range / eLocation ID:
- A16
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
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.more » « less
-
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.more » « less
-
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.more » « less
-
Aims. Solar Orbiter (SolO) was launched on February 9, 2020, allowing us to study the nature of turbulence in the inner heliopshere. We investigate the evolution of anisotropic turbulence in the fast and slow solar wind in the inner heliosphere using the nearly incompressible magnetohydrodynamic (NI MHD) turbulence model and SolO measurements. Methods. We calculated the two dimensional (2D) and the slab variances of the energy in forward and backward propagating modes, the fluctuating magnetic energy, the fluctuating kinetic energy, the normalized residual energy, and the normalized cross-helicity as a function of the angle between the mean solar wind speed and the mean magnetic field ( θ UB ), and as a function of the heliocentric distance using SolO measurements. We compared the observed results and the theoretical results of the NI MHD turbulence model as a function of the heliocentric distance. Results. The results show that the ratio of 2D energy and slab energy of forward and backward propagating modes, magnetic field fluctuations, and kinetic energy fluctuations increases as the angle between the mean solar wind flow and the mean magnetic field increases from θ UB = 0° to approximately θ UB = 90° and then decreases as θ UB → 180°. We find that solar wind turbulence is a superposition of the dominant 2D component and a minority slab component as a function of the heliocentric distance. We find excellent agreement between the theoretical results and observed results as a function of the heliocentric distance.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1051/0004-6361/202039297
