Simulation of amplitude‐modulated circularly polarized Alfvén waves for beta less than one

Machida, Shigeru; Spangler, S. R.; Goertz, C. K.

doi:10.1029/ja092ia07p07413

Cited by 33 publications

(23 citation statements)

References 32 publications

(21 reference statements)

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“…The presence of the modes in the above process is consistent with previous theories and simulations of parametric decay instabilities. 30,32,33 It is found that such parametric decay occurs more easily for ␤Ӷ1 and B p р1, consistent with the theoretical results by Jayanti and Hollweg. 34 For ␤у1, the instabilities are very sensitive to B p .…”

Section: A Wave Evolution Through Four Phases and Formation Of The Asupporting

confidence: 90%

Generation of nonlinear Alfvén and magnetosonic waves by beam–plasma interaction

Wang

Lin

2003

Physics of Plasmas

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One-dimensional (1-D) and two-dimensional (2-D) hybrid simulations are carried out to study the interaction between a background plasma and an ion beam, whose velocity is parallel to the ambient magnetic field B0. It is found that the beam–plasma interaction and the associated wave evolution can be divided into four phases. The simulation results in phase 1 in the early stage of wave evolution are consistent with the linear theory. Right-hand nonresonant instabilities are present and dominant in cases with a relatively strong ion beam (e.g., the ratio of beam ion density to background ion density >0.06 for beam velocity =10VA, where VA is the Alfvén speed), while right-hand resonant instabilities are present in the weak beam cases. During phases 2 and 3, the waves grow to form nonlinear structure, and are then saturated. A detailed analysis shows that the wave evolution in these phases is through secondary instabilities associated with parametric decay or the wave modulation. In addition, it is shown for the first time from the self-consistent simulation that in the final phase, nonlinear shear Alfvén waves with right-hand polarization in the magnetic field are generated. The magnetohydrodynamic (MHD) wave conditions of the Alfvén mode are satisfied. These Alfvén waves propagate mainly with k⋅B0>0, and the dispersion relation ω=kVA cos α is satisfied, where α is the angle between the wave vector k and B0. On the other hand, fast magnetosonic/whistler waves and slow mode waves are formed in the final phase of weak beam cases. In the 2-D simulations, field-aligned filaments (with k∼k⊥) in the density and magnetic field can be present due to the 2-D effects, in addition to the Alfvén, fast, and slow modes. The heating rate of background ions and its dependence on the wave propagation direction are also examined.

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Section: A Wave Evolution Through Four Phases and Formation Of The Asupporting

confidence: 90%

Generation of nonlinear Alfvén and magnetosonic waves by beam–plasma interaction

Wang

Lin

2003

Physics of Plasmas

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“…Terasawa et al [1986] and Machida et al [1987] examined a number of interactions between particles and large-amplitude waves which are similar to ones which arise in our simulations. Machida et al [1987] also make a detailed study of wave-particle interactions when wave trains are modulationally unstable and compare results with calculations using the derivative nonlinear SchrSedinger (DNLS) equation. The wave trains undergo steepening, and in this sense, the results are applicable to our study.…”

Section: Introductionmentioning

confidence: 63%

“…This instability has some of the required features in that the cascade is sustained and has waves traveling in opposite directions (but along B0) [e.g., Terasawa et al, 1986;Machida et al, 1987;Inhester, 1990;Vasquez, 1995]. Terasawa et al [1986] and Machida et al [1987] examined a number of interactions between particles and large-amplitude waves which are similar to ones which arise in our simulations. Machida et al [1987] also make a detailed study of wave-particle interactions when wave trains are modulationally unstable and compare results with calculations using the derivative nonlinear SchrSedinger (DNLS) equation.…”

Section: Introductionmentioning

confidence: 76%

Evolution and dissipation of imbedded rotational discontinuities and Alfvén waves in nonuniform plasma and the resultant proton heating

Vasquez¹,

Hollweg²

2001

J. Geophys. Res.

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Abstract. We show that nonuniform Alfv6n speed gradients across field lines generally arise from the evolution of Alfv6n waves. The evolution of a group of nonlinear Alfv6n waves with the same sign of parallel wavenumber generate smallamplitude pressure-balanced structures (PBSs) which cause the speed variations.This always causes refraction. In most cases, the Alfv6n waves also couple to magnetosonic waves and acquire a weak compressional component and can undergo resonant absorption or transfer, wherein wave energy can propagate across field lines. At large amplitudes the waves also generate imbedded rotational discontinuities (RDs). Some of these RDs can be dissipated owing to resonant transfer. This process could partly contribute to the observed decrease of solar wind RDs with increasing distance from the Sun. Resonant transfer also triggers a cascade due to steepening, which leads to sustained proton heating. The cascade produces oblique and large wavenumber waves which travel in different directions and have associated compressions. Protons interact with these by pitch angle scattering. They gain energy from second-order Fermi acceleration and from Landau and transit time damping. Oblique waves are inferred to be present in the dissipation range of Alfv6nic fluctuations at i AU. We argue that the process of proton heating should proceed similarly to simulation results. We also propose a role for the wave imbedded RD in coronal heating through its formation in the chromosphere and its likely dissolution in the corona where wave amplitudes are very small.

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“…By performing hybrid (kinetic ions + an electron fluid) simulations, Machida et al (1987) argues that the system automatically adjusts itself to a state described by the static approximation when ion kinetic effects are included. However, as time elapses, longitudinal mode grows and the static approximation is soon violated.…”

Section: Nonlinear Relation Among Phase and Frequency: Hall-mhd Equatmentioning

confidence: 99%

Remarks on nonlinear relation among phases and frequencies in modulational instabilities of parallel propagating Alfvén waves

Nariyuki

Hada

2006

Nonlin. Processes Geophys.

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Abstract. 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 Correspondence to: Y. Nariyuki (nariyuki@esst.kyushu-u.ac.jp) 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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Simulation of amplitude‐modulated circularly polarized Alfvén waves for beta less than one

Cited by 33 publications

References 32 publications

Generation of nonlinear Alfvén and magnetosonic waves by beam–plasma interaction

Generation of nonlinear Alfvén and magnetosonic waves by beam–plasma interaction

Evolution and dissipation of imbedded rotational discontinuities and Alfvén waves in nonuniform plasma and the resultant proton heating

Remarks on nonlinear relation among phases and frequencies in modulational instabilities of parallel propagating Alfvén waves

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