Nonlinear evolution of parametric instability of a large-amplitude nonmonochromatic Alfvén wave

2000 ◽  
Vol 7 (7) ◽  
pp. 2866-2877 ◽  
Author(s):  
F. Malara ◽  
L. Primavera ◽  
P. Veltri
Keyword(s):  
Large Amplitude ◽  
Nonlinear Evolution ◽  
Parametric Instability ◽  
Alfven Wave

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.

Geomagnetic response to large-amplitude interplanetary Alfvén wave trains

1995 ◽  
Vol T60 ◽  
pp. 140-143 ◽  
Author(s):  
W D Gonzalez ◽  
A L Clúa de Gonzalez ◽  
B T Tsurutani
Keyword(s):  
Large Amplitude ◽  
Alfven Wave ◽  
Wave Trains

Chaotic dynamics of large-amplitude alfvén-wave trains in the solar wind.

2001 ◽  
Vol 28 (5) ◽  
pp. 771-774 ◽  
Author(s):  
F.A. Borotto ◽  
A.C.-L. Chian ◽  
A.L.C. Gonzalez ◽  
W.D. Gonzalez ◽  
B.T. Tsurutani
Keyword(s):  
Solar Wind ◽  
Large Amplitude ◽  
Chaotic Dynamics ◽  
Alfven Wave ◽  
Wave Trains

scholarly journals Nonlinear evolution of the parametric instability: numerical predictions versus observations in the heliosphere

2001 ◽  
Vol 8 (3) ◽  
pp. 159-166 ◽  
Author(s):  
F. Malara ◽  
L. Primavera ◽  
P. Veltri
Keyword(s):  
Large Scale ◽  
Parametric Instability ◽  
Low Frequency ◽  
Heliospheric Current Sheet ◽  
Mhd Equations ◽  
Alfven Wave ◽  
The Sun ◽  
High Latitudes ◽  
Initial Correlation ◽  
Numerical Predictions

Abstract. Low-frequency turbulence in the solar wind is characterized by a high degree of Alfvénicity close to the Sun. Cross-helicity, which is a measure of Alfvénic correlation, tends to decrease with increasing distance from the Sun at high latitudes as well as in slow-speed streams at low latitudes. In the latter case, large scale inhomogeneities (velocity shears, the heliospheric current sheet) are present, which are sources of decorrelation; yet at high latitudes, the wind is much more homogeneous, and a possible evolution mechanism is represented by the parametric instability. The parametric decay of an circularly polarized broadband Alfvén wave is then investigated, as a source of decorrelation. The time evolution is followed by numerically integrating the full set of nonlinear MHD equations, up to instability saturation. We find that, for <beta>  ~ 1, the final cross-helicity is ~ 0.5, corresponding to a partial depletion of the initial correlation. Compressive fluctuations at a moderate level are also present. Most of the spectrum is dominated by forward propagating Alfvénic fluctuations, while backscattered fluctuations dominate large scales. With increasing time, the spectra of Elsässer variables tend to approach each other. Some results concerning quantities measured in the high-latitude wind are reviewed, and a qualitative agreement with the results of the numerical model is found.

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