Wavevector spectral signature of decay instability in space plasmas

Abstract. Identification of a large-amplitude Alfvén wave decaying into a pair of ion-acoustic and daughter Alfvén waves is one of the major goals in the observational studies of space plasma nonlinearity. In this study, the decay instability is analytically evaluated in the 2-D wavenumber domain spanning the parallel and perpendicular directions to the mean magnetic field. The growth-rate determination of the density perturbations is based on the Hall MHD (magnetohydrodynamic) wave–wave coupling theory for circularly polarized Alfvén waves. The diagrams of the growth rates versus the wavenumber and propagation angle derived in analytical studies are replaced by 2-D wavenumber distributions and compared with the corresponding wavevector spectrum of density and magnetic field fluctuations. The actual study reveals a perpendicular spectral pattern consistent with the result of a previous study based on 3-D hybrid numerical simulations. The wavevector signature of the decay instability observed in the two-dimensional wavenumber domain ceases at values of plasma beta larger than β=0.1. Growth-rate maps serve as a useful tool for predictions of the wavevector spectrum of density or magnetic field fluctuations in various scenarios for the wave–wave coupling processes developing at different stages in space plasma turbulence.

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Wavevector spectral signature of decay instability in space plasmas

10.5194/angeo-2020-25 ◽

2020 ◽

Author(s):

Horia Comisel ◽

Yasuhito Narita ◽

Uwe Motschmann

Keyword(s):

Magnetic Field ◽

Growth Rate ◽

Space Plasma ◽

Alfven Waves ◽

Alfven Wave ◽

Alfvén Waves ◽

Wave Coupling ◽

Decay Instability ◽

Wavenumber Domain ◽

Field Fluctuations

Abstract. Identification of a large-amplitude Alfven wave decaying into a pair of ion-acoustic and daughter Alfven waves is one of the major goals in the observational studies of space plasma nonlinearity. In this study, the decay instability is analytically evaluated in the 2-D wavenumber domain spanning the parallel and perpendicular directions to the mean magnetic field. The growth-rate determination of the density perturbations is based on the Hall-MHD wave-wave coupling theory for circularly-polarized Alfven waves. The diagrams of the growth rates versus the wavenumber and propagation angle derived in analytical studies are replaced by 2-D wavenumber distributions and compared with the corresponding wavevector spectrum of density and magnetic field fluctuations. The actual study reveals a perpendicular-shape spectral pattern consistent with the result of a previous study based on 3-D hybrid numerical simulations. The wavevector signature of the decay instability observed in the two-dimensional wavenumber domain ceases at values of plasma beta larger than beta = 0.1. Growth-rate maps serve as a useful tool for predictions of the wavevector spectrum of density or magnetic field fluctuations in various scenarios for the wave-wave coupling processes developing at different stages in space plasma turbulence.

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Growth rate evaluation for the decay instability in space plasmas

10.5194/egusphere-egu2020-13622 ◽

2020 ◽

Author(s):

Horia Comisel ◽

Yasuhito Narita ◽

Uwe Motschmann

Keyword(s):

Magnetic Field ◽

Growth Rate ◽

Alfven Wave ◽

Wave Coupling ◽

Decay Instability ◽

Field Fluctuations ◽

Density Perturbations ◽

Rate Evaluation ◽

First Time ◽

Hall Mhd

<p><tt class="letterText">Here we evaluate for the first time the growth rate of the decay instability in the 2-D wavevector domain spanning the parallel and perpendicular directions to the mean magnetic field. The growth rate is computed for the density perturbations based on the Hall MHD wave-wave coupling theory, which serves as a proxy for the energy spectrum of the compressive magnetic field fluctuations. The growth rate is then also determined for the daughter waves by considering the conservation of the frequencies and the wavevectors for the wave transmission (additive wave-wave coupling) and the wave reflection (subtractive wave-wave coupling). The visualized growth rate is helpful in evaluating the maximum propagation angle to which the decay instability (of the parallel propagating pump Alfven wave) operates.</tt></p>

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Concerning the Dynamics of Energetic Protons in Coronal Magnetic Loops: Dispersion Effects of Alfven Waves

Symposium - International Astronomical Union ◽

10.1017/s007418090007618x ◽

1985 ◽

Vol 107 ◽

pp. 559-559

Author(s):

V. A. Mazur ◽

A. V. Stepanov

Keyword(s):

Magnetic Field ◽

Wave Dispersion ◽

Alfven Waves ◽

Alfven Wave ◽

Wave Number ◽

Alfvén Waves ◽

Coronal Loops ◽

Coronal Magnetic Loops ◽

The Magnetic Field ◽

Solar Coronal

It is shown that the existence of plasma density inhomogeneities (ducts) elongated along the magnetic field in coronal loops, and of Alfven wave dispersion, associated with the taking into account of gyrotropy U ≡ ω/ωi ≪ 1 (Leonovich et al., 1983), leads to the possibility of a quasi-longitudinal k⊥ < √U k‖ propagation (wave guiding) of Alfven waves. Here ω is the frequency of Alfven waves, ωi is the proton gyrofrequency, and k is the wave number. It is found that with the parameter ξ = ω2 R/ωi A > 1, where R is the inhomogeneity scale of a loop across the magnetic field, and A is the Alfven wave velocity, refraction of Alfven waves does not lead, as contrasted to Wentzel's inference (1976), to the waves going out of the regime of quasi-longitudinal propagation. As the result, the amplification of Alfven waves in solar coronal loops can be important. A study is made of the cyclotron instability of Alfven waves under solar coronal conditions.

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Kinetic Alfvén waves in an inhomogeneous anisotropic magnetoplasma in the presence of an inhomogeneous electric field: particle aspect analysis

Journal of Plasma Physics ◽

10.1017/s0022377899008272 ◽

2000 ◽

Vol 63 (4) ◽

pp. 311-328 ◽

Cited By ~ 11

Author(s):

A. BARONIA ◽

M. S. TIWARI

Keyword(s):

Growth Rate ◽

Dispersion Relation ◽

Electric Field ◽

Alfven Waves ◽

Alfven Wave ◽

Larmor Radius ◽

Alfvén Waves ◽

Temperature Anisotropy ◽

Inhomogeneous Electric Field ◽

Kinetic Alfvén Waves

Kinetic Alfvén waves in the presence of an inhomogeneous electric field applied perpendicular to the ambient magnetic field in an anisotropic, inhomogeneous magnetoplasma are investigated. The particle aspect approach is adopted to investigate the trajectories of charged particles in the electromagnetic field of a kinetic Alfvén wave. Expressions are found for the field-aligned current, the perpendicular current, the dispersion relation and the particle energies. The growth rate of the wave is obtained by an energy- conservation method. It is predicted that plasma density inhomogeneity is the main source of instability, and an enhancement of the growth rate by electric field inhomogeneity and temperature anisotropy is found. The dispersion relation and growth rate involve the finite-Larmor-radius effect, electron inertia and the temperature anisotropy of the magnetoplasma. The applicability of the investigation to the auroral acceleration region is discussed.

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Concerning the Dynamics of Energetic Protons in Coronal Magnetic Loops: Dispersion Effects of Alfven Waves

Symposium - International Astronomical Union ◽

10.1017/s0074180900076105 ◽

1985 ◽

Vol 107 ◽

pp. 559-559

Author(s):

V. A. Mazur ◽

A. V. Stepanov

Keyword(s):

Magnetic Field ◽

Wave Dispersion ◽

Alfven Waves ◽

Alfven Wave ◽

Wave Number ◽

Alfvén Waves ◽

Coronal Loops ◽

Coronal Magnetic Loops ◽

The Magnetic Field ◽

Solar Coronal

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Phase mixing of Alfvén waves in two-dimensional magnetic plasma configurations with exponentially decreasing density

Astronomy and Astrophysics ◽

10.1051/0004-6361/201833639 ◽

2018 ◽

Vol 620 ◽

pp. A44

Author(s):

Michael S. Ruderman ◽

Nikolai S. Petrukhin

Keyword(s):

Magnetic Field ◽

Shear Viscosity ◽

Alfven Waves ◽

Mhd Equations ◽

Alfven Wave ◽

Alfvén Waves ◽

Field Variation ◽

Characteristic Scale ◽

Wave Damping ◽

Magnetic Plasma

We study damping of phase-mixed Alfvén waves propagating in axisymmetric magnetic plasma configurations. We use the linear magnetohydrodynamic (MHD) equations in the cold plasma approximation. The only dissipative process that we take into account is shear viscosity. We reduce the MHD equations describing the Alfvén wave damping to a Klein–Gordon-type equation. We assume that the two terms in this equation, one describing the effect of inhomogeneity and the other the effect of viscosity, are small. Then we use the WKB method to derive the expression describing the wave energy flux attenuation with the height. We apply the general theory to particular equilibria with the exponentially divergent magnetic field lines with the characteristic scale H. The plasma density exponentially decreases with the height with the characteristic scale Hρ. We study the wave damping for typical parameters of coronal plumes and various values of the wave period, the characteristic scale of the magnetic field variation H, and kinematic shear viscosity ν. We show that to have an appreciable wave damping at the height 6H we need to increase shear viscosity by at least six orders of magnitude in comparison with the value given by the classical plasma theory. Another important result is that the efficiency of wave damping strongly depends on the ratio H/Hρ. It increases fast when H/Hρ decreases. We present a physical explanation of this phenomenon.

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FRB coherent emission from decay of Alfvén waves

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa774 ◽

2020 ◽

Vol 494 (2) ◽

pp. 2385-2395 ◽

Cited By ~ 10

Author(s):

Pawan Kumar ◽

Željka Bošnjak

Keyword(s):

Magnetic Field ◽

Wave Packet ◽

Electric Field ◽

Static Magnetic Field ◽

Strong Electric Field ◽

Alfven Waves ◽

Alfven Wave ◽

Alfvén Waves ◽

Radio Waves ◽

Electron Positron

ABSTRACT We present a model for fast radio bursts (FRBs) where a large-amplitude Alfvén wave packet is launched by a disturbance near the surface of a magnetar, and a substantial fraction of the wave energy is converted to coherent radio waves at a distance of a few tens of neutron star radii. The wave amplitude at the magnetar surface should be about 1011 G in order to produce an FRB of isotropic luminosity 1044 erg s−1. An electric current along the static magnetic field is required by Alfvén waves with non-zero component of transverse wave vector. The current is supplied by counter-streaming electron–positron pairs, which have to move at nearly the speed of light at larger radii as the plasma density decreases with distance from the magnetar surface. The counter-streaming pairs are subject to two-stream instability, which leads to formation of particle bunches of size of the order of c/ωp, where ωp is the plasma frequency. A strong electric field develops along the static magnetic field when the wave packet arrives at a radius where electron–positron density is insufficient to supply the current required by the wave. The electric field accelerates particle bunches along the curved magnetic field lines, and that produces the coherent FRB radiation. We provide a number of predictions of this model.

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On Alfvén wave propagation along a circle on dipolar coordinates

Journal of Plasma Physics ◽

10.1017/s0022377819000837 ◽

2019 ◽

Vol 85 (6) ◽

Author(s):

L. M. B. C. Campos ◽

M. J. S. Silva ◽

F. Moleiro

Keyword(s):

Magnetic Field ◽

Wave Equation ◽

Alfven Waves ◽

Alfven Wave ◽

Alfvén Waves ◽

Far Field ◽

Perturbation Spectrum ◽

The Magnetic Field ◽

Zero Frequency ◽

Conformal Coordinates

The multipolar representation of the magnetic field has, for the lowest-order term, a magnetic dipole that dominates the far field. Thus the far-field representation of the magnetic field of the Earth, Sun and other celestial bodies is a dipole. Since these bodies consist of or are surrounded by plasma, which can support Alfvén waves, their propagation along dipole magnetic field lines is considered using a new coordinate system: dipolar coordinates. The present paper introduces multipolar coordinates, which are an example of conformal coordinates; conformal coordinates are orthogonal with equal scale factors, and can be extended from the plane to space, for instance as cylindrical or spherical dipolar coordinates. The application considered is to Alfvén waves propagating along a circle, that is a magnetic field line of a dipole, with transverse velocity and magnetic field perturbations; the various forms of the wave equation are linear second-order differential equations, with variable coefficients, specified by a background magnetic field, which is force free. The absence of a background magnetic force leads to a mean state of hydrostatic equilibrium, specified by the balance of gravity against the pressure gradient, for a perfect gas or incompressible liquid. The wave equation is simplified to a Gaussian hypergeometric type in the case of zero frequency, otherwise, for non-zero frequency, an extended Gaussian hypergeometric equation is obtained. The solution of the latter specifies the magnetic field perturbation spectrum, and also, via a polarisation relation, the velocity perturbation spectrum; both are plotted, over half a circle, for three values of the dimensionless frequency.

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Possible role of magnetosphere-ionosphere coupling in auroral arc generation

Annales Geophysicae ◽

10.1007/s00585-000-1108-5 ◽

2000 ◽

Vol 18 (9) ◽

pp. 1108-1117 ◽

Cited By ~ 5

Author(s):

W. Lyatsky ◽

A. M. Hamza

Keyword(s):

Growth Rate ◽

Plasma Sheet ◽

Alfven Waves ◽

The Other ◽

Alfven Wave ◽

Alfvén Waves ◽

Ionospheric Conductivity ◽

Model Based ◽

Field Aligned Current ◽

Auroral Arcs

Abstract. Three models for the magnetosphere-ionosphere coupling feedback instability are considered. The first model is based on demagnetization of hot ions in the plasma sheet. The instability takes place in the global magnetosphere-ionosphere system when magnetospheric electrons drift through a spatial gradient of hot magnetospheric ion population. Such a situation exists on the inner and outer edges of the plasma sheet where relatively cold magnetospheric electrons move earthward through a radial gradient of hot ions. This leads to the formation of field-aligned currents. The effect of upward field-aligned current on particle precipitation and the magnitude of ionospheric conductivity leads to the instability of this earthward convection and to its division into convection streams oriented at some angle with respect to the initial convection direction. The growth rate of the instability is maximum for structures with sizes less than the ion Larmor radius in the equatorial plane. This may lead to formation of auroral arcs with widths about 10 km. This instability explains many features of such arcs, including their conjugacy in opposite hemispheres. However, it cannot explain the very high growth rates of some auroral arcs and very narrow arcs. For such arcs another type of instability must be considered. In the other two models the instability arises because of the generation of Alfven waves from growing arc-like structures in the ionospheric conductivity. One model is based on the modulation of precipitating electrons by field-aligned currents of the upward moving Alfven wave. The other model takes into consideration the reflection of Alfven waves from a maximum in the Alfven velocity at an altitude of about 3000 km. The growth of structures in both models takes place when the ionization function associated with upward field-aligned current is shifted from the edges of enhanced conductivity structures toward their centers. Such a shift arises because the structures move at a velocity different from the E×B drift. Although both models may work, the growth rate for the model, based on the modulation of the precipitating accelerated electrons, is significantly larger than that of the model based on the Alfven wave reflection. This mechanism is suitable for generation of auroral arcs with widths of about 1 km and less. The growth rate of the instability can be as large as 1 s-1, and this mechanism enables us to justify the development of auroral arcs only in one ionosphere. It is hardly suitable for excitation of wide and conjugate auroral arcs, but it may be responsible for the formation of small-scale structures inside a wide arc.Key words: Ionosphere (auroral ionosphere) - Magnetospheric physics (auroral phenomena; magnetosphere-ionosphere interactions)

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On Alfvén waves in a radial flow and magnetic field

Journal of Plasma Physics ◽

10.1017/s0022377899007801 ◽

1999 ◽

Vol 62 (1) ◽

pp. 1-33 ◽

Cited By ~ 4

Author(s):

L. M. B. C. CAMPOS ◽

N. L. ISAEVA

Keyword(s):

Magnetic Field ◽

Wave Equation ◽

Flow Velocity ◽

Mass Density ◽

Alfven Waves ◽

Uniform Flow ◽

Critical Layer ◽

Alfven Wave ◽

Alfvén Waves ◽

Mean Flow

This paper considers Alfvén waves in a radially stratified medium where all background quantities, namely mass density, magnetic field strength and mean flow velocity, depend only on the distance from the centre, the latter two being assumed to lie in the radial direction. It is shown that the radial dependence of Alfvén waves is the same for two cases: (i) when the velocity and magnetic field perturbations are along parallels, in the one-dimensional case of only radial and time dependence; (ii) in the three-dimensional case with dependence on all three spherical coordinates and time, for velocity and magnetic field perturbations with components along parallels and meridians, represented by the radial components of the vorticity and electric current respectively. Elimination between these equations leads to the convected Alfvén-wave equation in the case of uniform flow, and an equation with an additional term in the case of non-uniform flow with mean flow velocity a linear function of distance. The latter case, namely that of non-uniform flow with flow velocity increasing linearly with distance, is analysed in detail; conservation of mass flux requires the mass density to decay as the inverse cube of the distance. The Alfvén-wave equation has a critical layer where the flow velocity equals the Alfvén speed, leading to three sets of two solutions, namely below, above and across the critical layer. The latter is used to specify the wave behaviour in the vicinity of the critical layer, where local partial transmission occurs. The problem has two dimensionless parameters: the frequency and the initial Alfvén number. It is shown, by plotting the wave fields relative to the critical layer, that these two dimensionless parameters appear in a single combination. This simplifies the plotting of the wave fields for several combinations of physical conditions. It is shown in the Appendix that the formulation of the equations of MHD in the original Elsässer (1956) form, often used in the recent literature, does not apply if the background mass density is non-uniform on the scale of a wavelength. The present theory, based on exact solutions of the Alfvén-wave equation for a inhomogeneous moving medium, is unrestricted as to the relative magnitude of the local wavelength and scale of change of properties of the background medium. The present theory shows that the rate-of-decay of wave amplitude is strongly dependent on wave frequency beyond the critical layer, i.e. the process of change with distance of the spectrum of Alfvén waves in the solar wind starts at the critical layer.

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