An instability of finite amplitude circularly polarized Alfven waves

Goldstein, M. L.

doi:10.1086/155829

Cited by 303 publications

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“…This calculation was initiated at a heliocentric radial position r = 2 R s, which is well beyond the region where This discovery, that cyclotron dissipation of outward propagating ion cyclotron waves in the solar wind necessarily leads to the generation of inward propagating waves, has important implications for wave-particle interactions and turbulence theory. We emphasize that this process is quasi-linear, in contrast to nonlinear processes such as parametric decay [Derby, 1978;Goldstein, 1978;Hollweg, 1994;Del Zanna et al, 2001] which are otherwise assumed to be necessary to reverse the wave propagation. It is the purpose of this paper to extend the kinetic shell calculation of paper 1 to include the interaction with inward propagating waves.…”

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confidence: 99%

The kinetic shell model of coronal heating and acceleration by ion cyclotron waves: 2. Inward and outward propagating waves

Isenberg¹

2001

J. Geophys. Res.

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Abstract. We extend the kinetic shell model of the cyclotron resonant interaction between coronal hole protons and outward propagating ion cyclotron waves presented in the first paper of this series . That work showed that the resonant dissipation of outward propagating waves produced proton distributions that were unstable to the generation of inward propagating waves. Here we include the kinetic shell interaction with the inward waves, assuming that both the wave generation and wave dissipation proceed much faster than all other processes in the collisionless coronal hole. In this case, the entire proton distribution will be resonant with one set of waves or the other and is thus composed of constant-energy shells in both the sunward and antisunward regions of velocity space. The evolution of the distribution as the plasma flows away from the Sun is then described by following the motion of these shells under the action of the nonresonant forces in the coronal hole. We find that the distribution consists of a core population which circulates through velocity space and a halo which continually expands to higher energy. The halo population is shown to be essential to obtain acceleration of the bulk proton plasma through its response to the mirror force. We present an illustrative calculation of this system which assumes the waves to be dispersionless. We find for this case that the halo particles soon reach extremely high energies, leading to a continuous, rather than declining, acceleration of the plasma. We suggest that these properties are due to the dispersionless assumption and that an improved model incorporating wave dispersion may give more reasonable quantitative results.

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confidence: 99%

The kinetic shell model of coronal heating and acceleration by ion cyclotron waves: 2. Inward and outward propagating waves

Isenberg¹

2001

J. Geophys. Res.

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“…The y and z-components of the velocity and the magnetic field are proportional to exp͓i͑k 0 x − 0 t͔͒, and their magnitudes are constant. The stability of this wave is determined by the following dispersion equation 3,4,31 …”

Section: Formulation and Methods Descriptionmentioning

confidence: 99%

“…This implies that k 4 − gives rise to a spatially amplifying wave as x → ϱ when U Ͻ −1, and k 4 + gives rise to a spatially amplifying wave as x → −ϱ when U Ͼ b.…”

Section: ͑40͒mentioning

confidence: 99%

“…After that the stability analysis was extended in a few different directions. Derby 3 and Goldstein 4 studied the stability of Alfvén waves with an arbitrary amplitude in a finite ␤ plasma. Mio et al, 5,6 Mjølhus, 7 Ovenden, 8 and Spangler and Sheerin 9,10 used the derivative nonlinear Schrödinger equation to study the stability of a small amplitude circularly polarized Alfvén wave in a dispersive plasma.…”

Section: Introductionmentioning

confidence: 99%

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Absolute and convective instabilities of parallel propagating circularly polarized Alfvén waves: Decay instability

Simpson

2004

Physics of Plasmas

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The absolute and convective instabilities of circularly polarized Alfvén waves propagating along an ambient magnetic field are studied. The approximation of ideal magnetohydrodynamics is used. The analysis is restricted to the decay instability that occurs when the sound speed is smaller than the Alfvén speed. In addition, it is assumed that the amplitude a of an unstable Alfvén wave (pump wave) is small. This assumption allows us to study the problem analytically using expansions in power series with respect to a. It is shown that there are quantities, U l Ͻ 0 and U r Ͼ 0, such that the pump wave is absolutely unstable in a reference frame moving with velocity U with respect to the rest plasma if U l Ͻ U Ͻ U r . If either U Ͻ U l or U Ͼ U r , then the pump wave is convectively unstable. The expressions for U l and U r are found. The signaling problem is studied in a reference frame where the pump wave is convectively unstable. It is shown that spatially amplifying waves exist only when the signaling frequency is in two narrow symmetric frequency bands with the widths of the order of a. The implication of the obtained results on the interpretation of observational data obtained in space missions is discussed. It is shown that circularly polarized Alfvén waves propagating in the solar wind are convectively unstable in a reference frame of any spacecraft moving with the velocity not exceeding a few tens of km/s in the solar reference frame. The spatial amplification scale of these waves is very large, of the order of 1 / 6 a.u. In view of these results it is not surprising at all that evidence of the decay instability of Alfvén waves in the solar wind is sparse.

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“…The parametric instability of a finite-amplitude circularly polarized Alfvén wave has been studied for the last several decades (Derby 1978;Goldstein 1978;Hollweg 1994). Recently, this problem has been studied in the single fluid MHD framework for a self-gravitating molecular cloud (Fukuda & Hanawa 1999).…”

Section: Introductionmentioning

confidence: 99%

Parametric Instability in Dark Molecular Clouds

Pandey

Владимиров

2007

ApJ

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The present work investigates the parametric instability of parallel propagating circularly polarized Alfvén ( pump) waves in a weakly ionized molecular cloud. It is shown that the relative drift between the plasma particles gives rise to the Hall effect, resulting in the modified pump wave characteristics. Although the linearized fluid equations with periodic coefficients are difficult to solve analytically, it is shown that a linear transformation can remove the periodic dependence. The resulting linearized equations with constant coefficients are used to derive an algebraic dispersion relation. The growth rate of the parametric instability is a sensitive function to the amplitude of the pump wave as well as to the ratio of the pump and the modified dust-cyclotron frequencies. The instability is insensitive to the plasma . The results are applied to the molecular clouds.

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An instability of finite amplitude circularly polarized Alfven waves

Cited by 303 publications

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The kinetic shell model of coronal heating and acceleration by ion cyclotron waves: 2. Inward and outward propagating waves

The kinetic shell model of coronal heating and acceleration by ion cyclotron waves: 2. Inward and outward propagating waves

Absolute and convective instabilities of parallel propagating circularly polarized Alfvén waves: Decay instability

Parametric Instability in Dark Molecular Clouds

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