Parametric instability, inverse cascade and the  range of solar-wind turbulence

Abstract

In this paper, weak-turbulence theory is used to investigate the nonlinear evolution of the parametric instability in three-dimensional low-β plasmas at wavelengths much greater than the ion inertial length under the assumption that slow magnetosonic waves are strongly damped. It is shown analytically that the parametric instability leads to an inverse cascade of Alfvén wave quanta, and several exact solutions to the wave kinetic equations are presented. The main results of the paper concern the parametric decay of Alfvén waves that initially satisfy e + e − , where e + and e − are the frequency ( f ) spectra of Alfvén waves propagating in opposite directions along the magnetic field lines. If e + initially has a peak frequency f 0 (at which fe + is maximized) and an 'infrared' scaling f p at smaller f with −1 < p < 1, then e + acquires an f −1 scaling throughout a range of frequencies that spreads out in both directions from f 0 . At the same time, e − acquires an f −2 scaling within this same frequency range. If the plasma parameters and infrared e + spectrum are chosen to match conditions in the fast solar wind at a heliocentric distance of 0.3 astronomical units (AU), then the nonlinear evolution of the parametric instability leads to an e + spectrum that matches fast-wind measurements from the Helios spacecraft at 0.3 AU, including the observed f −1 scaling at f 3 × 10 −4 Hz. The results of this paper suggest that the f −1 spectrum seen by Helios in the fast solar wind at f 3 × 10 −4 Hz is produced in situ by parametric decay and that the f −1 range of e + extends over an increasingly narrow range of frequencies as r decreases below 0.3 AU. This prediction will be tested by measurements from the Parker Solar Probe.

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

“…This indicates that the fluctuations in the large-scale flat scaling range have had significant time for nonlinear processing, and increasingly so closer to the Sun. This would suggest that this range might not be a simple spectrum of non-interacting waves, but could be undergoing nonlinear interactions, as in more recent models of the 1/f range (Velli et al 1989;Verdini et al 2012;Perez & Chandran 2013;Chandran 2018;Matteini et al 2018;Matteini 2019).…”

The multi-scale nature of the solar wind

“…Malara and Velli (1996) show that, even in the large-amplitude limit and when the pump mode is nonmonochromatic, the PDI continues to operate without a significant reduction in its growth rate. Theoretical work suggests that the PDI may develop an inverse cascade near the Sun and, therefore, be essential in driving solar-wind turbulence (Chandran, 2018).…”

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

“…For example, the plasma density varies by a factor of ∼ 6 over a distance of a few thousand km perpendicular to the background magnetic field B 0 in the low corona (Raymond et al 2014), which suggests that phase mixing (Heyvaerts & Priest 1983) is an efficient mechanism for cascading AW energy to small scales measured perpendicular to B 0 near the Sun. † We also neglect the parametric decay of AWs into slow magnetosonic waves and counter-propagating AWs (e.g., Galeev & Oraevskii 1963;Sagdeev & Galeev 1969;Cohen & Dewar 1974;Tenerani et al 2017), which may cause outward-propagating AWs in the fast solar wind to acquire a k −1 spectrum by the time these fluctuations reach r = 0.3 au (Chandran 2018), where k is the wave-vector component parallel to the background magnetic field, and 1 au is the mean Earth-Sun distance. Nevertheless, the simulations that we report in Section 3 describe an important subset of the full turbulent dynamics.…”