Parametric instability in the solar wind: numerical study of the nonlinear evolution

2003 ◽  
Author(s):  
Leonardo Primavera
Keyword(s):  
Solar Wind ◽  
Nonlinear Evolution ◽  
Numerical Study ◽  
Parametric Instability

scholarly journals Parametric Instability of a Broad-band Alfvén Wave: Nonlinear Evolution and Saturation

2001 ◽  
Vol 203 ◽  
pp. 511-513 ◽  
Author(s):  
F. Malara ◽  
L. Primavera ◽  
P. Veltri
Keyword(s):  
Solar Wind ◽  
Numerical Simulations ◽  
Qualitative Agreement ◽  
Nonlinear Evolution ◽  
Broad Band ◽  
Parametric Instability ◽  
Alfven Wave ◽  
Wind Data ◽  
Linear Stage ◽  
Initial Mode

The nonlinear evolution of parametric instability of a non-monocrhomatic Alfvén wave is studied using numerical simulations. After a linear stage the instability saturates. For β ~ 1 the initial mode remains dominant, except at large scales, where an inverse cascade of backscattered Alfvénic modes is present. A comparison with solar wind data gives a qualitative agreement, indicating that parametric instability could play an important role in the evolution of solar wind turbulence.

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

2018 ◽  
Vol 84 (1) ◽  
Author(s):  
Benjamin D. G. Chandran
Keyword(s):  
Solar Wind ◽  
Nonlinear Evolution ◽  
Parametric Instability ◽  
Alfven Waves ◽  
Turbulence Theory ◽  
Alfven Wave ◽  
Alfvén Waves ◽  
Fast Solar Wind ◽  
Parametric Decay ◽  
Inverse Cascade

In this paper, weak-turbulence theory is used to investigate the nonlinear evolution of the parametric instability in three-dimensional low-$\unicode[STIX]{x1D6FD}$ 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 $e^{+}\gg e^{-}$, 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 $f\gtrsim 3\times 10^{-4}~\text{Hz}$. The results of this paper suggest that the $f^{-1}$ spectrum seen by Helios in the fast solar wind at $f\gtrsim 3\times 10^{-4}~\text{Hz}$ 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.

scholarly journals On the probability distribution function of small-scale interplanetary magnetic field fluctuations

2004 ◽  
Vol 22 (10) ◽  
pp. 3751-3769 ◽  
Author(s):  
R. Bruno ◽  
V. Carbone ◽  
L. Primavera ◽  
F. Malara ◽  
L. Sorriso-Valvo ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Robust Statistics ◽  
Interplanetary Space ◽  
Parametric Instability ◽  
Field Vector ◽  
Small Scale ◽  
Magnetic Fluctuations ◽  
Mhd Turbulence ◽  
The One

Abstract. In spite of a large number of papers dedicated to the study of MHD turbulence in the solar wind there are still some simple questions which have never been sufficiently addressed, such as: a) Do we really know how the magnetic field vector orientation fluctuates in space? b) What are the statistics followed by the orientation of the vector itself? c) Do the statistics change as the wind expands into the interplanetary space? A better understanding of these points can help us to better characterize the nature of interplanetary fluctuations and can provide useful hints to investigators who try to numerically simulate MHD turbulence. This work follows a recent paper presented by some of the authors which shows that these fluctuations might resemble a sort of random walk governed by Truncated Lévy Flight statistics. However, the limited statistics used in that paper did not allow for final conclusions but only speculative hypotheses. In this work we aim to address the same problem using more robust statistics which, on the one hand, forces us not to consider velocity fluctuations but, on the other hand, allows us to establish the nature of the governing statistics of magnetic fluctuations with more confidence. In addition, we show how features similar to those found in the present statistical analysis for the fast speed streams of solar wind are qualitatively recovered in numerical simulations of the parametric instability. This might offer an alternative viewpoint for interpreting the questions raised above.

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