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

<p>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 Alfv\ en wave quanta, and several exact solutions to the wave kinetic equations are presented. The main results of the paper concern the parametric decay of Alfv\ en waves that initially satisfy e<sup>+</sup> >> e<sup>-</sup>, where e<sup>+</sup> and e<sup>-</sup> are the frequency (f) spectra of Alfv\ en waves propagating in opposite directions along the magnetic field lines. If e<sup>+</sup> initially has a peak frequency f<sub>0</sub> (at which fe<sup>+</sup> is maximized) and an \textquoterightinfrared\textquoteright scaling f<sup>p</sup> at smaller f with $-1, then e<sup>+</sup> acquires an f<sup>1</sup> scaling throughout a range of frequencies that spreads out in both directions from f<sub>0</sub>. At the same time, e<sup>0-</sup> acquires an f<sup>-2</sup> scaling within this same frequency range. If the plasma parameters and infrared e<sup>+</sup> 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<sup>+</sup> spectrum that matches fast-wind measurements from the Helios spacecraft at 0.3 AU, including the observed f<sup>-1</sup> scaling at f ≳ 3\texttimes10<sup>-4</sup> Hz. The results of this paper suggest that the f<sup>-1</sup> spectrum seen by Helios in the fast solar wind at f ≳ 3\texttimes10<sup>-4</sup> Hz is produced in situ by parametric decay and that the f<sup>-1</sup> range of e<sup>+</sup> 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.\&nbsp;\&nbsp;\&nbsp;\&nbsp;</p>
Year of Publication
Journal of Plasma Physics
Number of Pages
Date Published
ISSN Number