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| Titel |
Remarks on nonlinear relation among phases and frequencies in modulational instabilities of parallel propagating Alfvén waves |
| VerfasserIn |
Y. Nariyuki, T. Hada |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 13, no. 4 ; Nr. 13, no. 4 (2006-08-24), S.425-441 |
| Datensatznummer |
250011812
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| Publikation (Nr.) |
 copernicus.org/npg-13-425-2006.pdf |
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| Zusammenfassung |
| Nonlinear relations among frequencies and phases
in modulational instability of circularly polarized Alfvén waves
are discussed, within the context of one dimensional, dissipation-less,
unforced fluid system.
We show that generation of phase coherence is a natural consequence of
the modulational instability of Alfvén waves.
Furthermore, we quantitatively evaluate intensity of wave-wave interaction
by using bi-coherence, and also by computing energy flow among wave modes,
and demonstrate that the energy flow is directly related to the phase coherence generation.
We first discuss the modulational instability within the derivative
nonlinear Schrödinger (DNLS) equation, which is a subset of the Hall-MHD
system including the right- and left-hand polarized,
nearly degenerate quasi-parallel Alfvén waves.
The dominant nonlinear process within this model is the four wave interaction,
in which a quartet of waves in resonance can exchange energy.
By numerically time integrating the DNLS equation with periodic boundary
conditions, and by evaluating relative
phase among the quartet of waves, we show that the phase coherence
is generated when the waves exchange energy among the quartet of waves.
As a result, coherent structures (solitons) appear in the real space,
while in the phase space of the wave frequency and the wave number,
the wave power is seen to be distributed around a straight line.
The slope of the line corresponds to the propagation speed of the coherent
structures.
Numerical time integration of the Hall-MHD system with periodic boundary
conditions reveals that, wave power of
transverse modes and that of longitudinal modes are aligned with
a single straight line in the dispersion relation phase space, suggesting that
efficient exchange of energy among transverse and longitudinal wave modes
is realized in the Hall-MHD.
Generation of the longitudinal wave modes violates the assumptions employed in
deriving the DNLS such as the quasi-static approximation, and thus
long time evolution of the Alfvén modulational instability
in the DNLS and in the Hall-MHD models differs significantly, even though the
initial plasma and parent wave parameters are chosen in such a way that the
modulational instability is the most dominant instability among various
parametric instabilities.
One of the most important features which only appears in the Hall-MHD model
is the generation of sound waves driven by ponderomotive density fluctuations.
We discuss relationship between the dispersion relation,
energy exchange among wave modes, and coherence of phases in the waveforms
in the real space.
Some relevant future issues are discussed as well. |
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