Reflection-driven magnetohydrodynamic turbulence in the solar atmosphere and solar wind

Abstract

We present three-dimensional direct numerical simulations and an analytic model of reflection-driven magnetohydrodynamic (MHD) turbulence in the solar wind. Our simulations describe transverse, non-compressive MHD fluctuations within a narrow magnetic flux tube that extends from the photosphere, through the chromosphere and corona, and out to a heliocentric distance r of 21 solar radii (R ⊙ ). We launch outward-propagating "z + fluctuations" into the simulation domain by imposing a randomly evolving photospheric velocity field. As these fluctuations propagate away from the Sun, they undergo partial reflection, producing inward-propagating "z − fluctuations." Counter-propagating fluctuations subsequently interact, causing fluctuation energy to cascade to small scales and dissipate. Our analytic model incorporates dynamic alignment, allows for strongly or weakly turbulent nonlinear interactions, and divides the z + fluctuations into two populations with different characteristic radial correlation lengths. The inertial-range power spectra of z + and z − fluctuations in our simulations evolve toward a k −3/2 ⊥ scaling at r > 10R ⊙ , where k ⊥ is the wave-vector component perpendicular to the background magnetic field. In two of our simulations, the z + power spectra are much flatter between the coronal base and r ≃ 4R ⊙ . We argue that these spectral scalings are caused by: (1) high-pass filtering in the upper chromosphere; (2) the anomalous coherence of inertial-range z − fluctuations in a reference frame propagating outwards with the z + fluctuations; and (3) the change in the sign of the radial derivative of the Alfvén speed at r = r m ≃ 1.7R ⊙ , which disrupts this anomalous coherence between r = r m and r ≃ 2r m . At r > 1.3R ⊙ , the turbulent-heating rate in our simulations is comparable to the turbulent-heating rate in a previously developed solar-wind model that agreed with a number of observational constraints, consistent with the hypothesis that MHD turbulence accounts for much of the heating of the fast solar wind. Key words: solar wind -Sun: corona -turbulence -waves † In contrast, Helios radio occultation observations show that the fractional density variations drop to 0.1 − 0.2 at r ∈ (5R⊙, 20R⊙) (Hollweg et al. 2010).

The Evolution and Role of Solar Wind Turbulence in the Inner Heliosphere

“…The power law fit to the pre- dicted amplitudes, taking L ⊥⊙ = 1.4 × 10 4 km as the correlation length and B ⊙ = 1.18 mT as the magnetic field at the base of the corona, is marked in Figure 7 as the green line, and has a variation ∝ r −0.58 . This power law is a good match to that observed, and the values of L ⊥⊙ and B ⊙ are within a reasonable expected range (Chandran et al 2011;Chandran & Perez 2019), indicating that the inwardpropagating fluctuations are consistent with being generated by reflection past the Alfvén point. However, it remains possible that other mechanisms such as local driving or parametric decay may also contribute, and further analysis will be needed to test these.…”

“…Regarding the cause of the −3/2 spectra at 0.17 au, this scaling is consistent 5 with models of both balanced (Boldyrev 2006;Chandran et al 2015;Mallet & Schekochihin 2017) and imbalanced (Perez & Boldyrev 2009;Podesta & Bhattacharjee 2010) Alfvénic turbulence in homogeneous plasmas (e.g., without wave reflection) that involve scale-dependent alignment. In addition, recent simulations (Chandran & Perez 2019) of inhomogeneous reflection-driven MHD turbulence from the photosphere to 21 R ⊙ found that both E + and E − also tend towards α = −3/2 past the Alfvén point for a range of values of the correlation time and perpendicular correlation length at the photosphere. Chandran & Perez (2019) considered this in partial agreement with a reflection-driven version of the Lithwick et al (2007) model of strong imbalanced MHD turbulence, which predicts the same spectral index (α = −5/3) for both E + and E − , with the −3/2 scaling possibly resulting from additional phenomena such as intermittency and scale-dependent alignment (e.g., Boldyrev 2006;Chandran et al 2015).…”

“…In addition, recent simulations (Chandran & Perez 2019) of inhomogeneous reflection-driven MHD turbulence from the photosphere to 21 R ⊙ found that both E + and E − also tend towards α = −3/2 past the Alfvén point for a range of values of the correlation time and perpendicular correlation length at the photosphere. Chandran & Perez (2019) considered this in partial agreement with a reflection-driven version of the Lithwick et al (2007) model of strong imbalanced MHD turbulence, which predicts the same spectral index (α = −5/3) for both E + and E − , with the −3/2 scaling possibly resulting from additional phenomena such as intermittency and scale-dependent alignment (e.g., Boldyrev 2006;Chandran et al 2015). However, it is also possible that the trend seen in Figure 2 is part way through a transition from an even shallower spectrum closer to the Sun or an effect of the driving on the cascade; these possibilities are discussed further in Section 4.…”

The Enhancement of Proton Stochastic Heating in the Near-Sun Solar Wind

“…We expect an increased level of turbulence below the Alfvén point, predicted by theoretical models (Matthaeus et al 1999) and MHD simulations (Perez & Chandran 2013;Chhiber et al 2018;Chandran & Perez 2019), to effectively drive SH. Resent results (Kasper & Klein 2019) indicate that the region of preferential minor ion heating (Kasper et al 2017) terminates at the Alfvén surface.…”

Constraining Ion-Scale Heating and Spectral Energy Transfer in Observations of Plasma Turbulence

“…Using continuity of turbulent energy flux, assuming local wavenumber spectral transfer [12,13,49,50], we demonstrate that the observed steepening has drastic implications for turbulent heating and/or nonlinear cascade rates. Statistical analysis shows that transition-range steepening is consistent with levels of dissipation sufficient for required bulk in situ heating of the solar wind [14,[51][52][53][54][55][56]. As our model cannot identify heating as the unique cause of the steepening, we consider an alternative framework, in which steepening is the result of increased spectral transfer rates.…”