Nonlinear evolution of 3D-inertial Alfvén wave and turbulent spectra in Auroral region

In the present paper, we have investigated nonlinear interaction of three dimensional (3D) inertial Alfvén wave and perpendicularly propagating magnetosonic wave for low β-plasma (β?m _e /m _i ). We have developed the set of dimensionless equations in the presence of ponderomotive nonlinearity due to 3D-inertial Alfvén wave in the dynamics of perpendicularly propagating magnetosonic wave. Stability analysis and numerical simulation has been carried out to study the effect of nonlinear coupling on the formation of localized structures and turbulent spectra, applicable to auroral region. The results reveal that the localized structures become more and more complex as the nonlinear interaction progresses. Further, we have studied the turbulent spectrum which follows spectral index (～k ^?3.57) at smaller scales. Relevance of the obtained results has been shown with the observations received by various spacecrafts like FAST, Hawkeye and Heos 2.     

Nonlinear kinetic Alfvén wave with Poisson equation correction in the low aurora

Nonlinear kinetic Alfvén waves where m _e /m _i , have been solved both with and without the Poisson equation correction. It is found that the ratio of the perpendicular electric field and magnetic field, and the ratio of parallel and perpendicular electric field increase with deepening of the depressive density soliton. The former ratio may be larger than the Alfvén velocity in the case of a large amplitude solitary kinetic Alfvén wave. The Poisson equation correction is important for the nonlinear kinetic Alfvén wave propagating along the magnetic field, which solves a puzzle of Sagdeev potential to approach infinity in the limit ofK _x 0. This correction causes the solitary KAW possessing an electrostatic character along the direction of wave moving frame. These results have been compared with the observations from the Freja satellite in the low aurora.     

Nonlinear evolution of kinetic Alfvén wave and turbulent spectra: effect of initial conditions

Using the 2D numerical simulation we have studied the nonlinear evolution of kinetic Alfvén wave (KAW) in intermediate β plasmas (β?m _e /m _i ?1). The coupled equations of kinetic Alfvén wave (KAW) and ion acoustic wave (IAW) have been studied with different initial conditions using (1) periodic perturbation, (2) Gaussian perturbation and (3) random perturbation. We have studied the effect of initial conditions on the filament formation and on the turbulent scaling laws. The scale size of the localized structures is also obtained under different conditions.     

Numerical simulations to study kinetic Alfvén wave and whistler wave spectra in solar wind plasma

The numerical simulations of the model equation governing the nonlinear evolution of kinetic Alfvén wave (KAW) in solar wind plasmas are performed. The nonlinear dynamical equation of KAW satisfies the modified nonlinear Schrödinger MNLS equation when the ponderomotive nonlinearity is incorporated in the KAW dynamics. The effect of Landau damping is taken into account in the KAW dynamics. The coherent (in the absence of Landau damping) and damped (with Landau damping) localized structures of pump KAW as a consequence of ponderomotive nonlinearity have been studied in the solar wind at 1 AU. A weak whistler signal propagating in these localized structures is amplified which leads to the development of its own coherent and damped localized structures. Magnetic field (KAW) and electric field (whistler wave) power spectra and their spectral indices are calculated. Our results reveal the change in spectral index because of the damping effect which has good agreement with the observations. These damped structures and steeper spectra may be one of the reasons responsible for the plasma heating and particles acceleration in solar wind.     

Effect of linear waves on kinetic Alfvén wave localization and turbulent spectrum

We have presented the localization of kinetic Alfvén wave (KAW) in intermediate β plasma (m _e /m _i ?β?1) by developing a model based on pump kinetic Alfvén wave and finite amplitude magnetosonic fluctuations. When KAW is perturbed by these background magnetosonic fluctuations, filamentary structures of KAW magnetic field are formed. First, a semi analytical model based on paraxial approximation has been developed to understand this evolution process. Localized structures and magnetic fluctuation spectrum of KAW has also been studied numerically for finite frequency of KAW. The calculated magnetic fluctuation spectrum follows two types of scalings. Above the proton gyroradius scale lengths (in inertial range), spectrum follows Kolmogorovian scaling. Below this scale dispersion starts and the spectrum steepens to about \(k_{x}^{-2.5}\) . The result shows the steepening of power spectra which can be responsible for particle acceleration in solar wind due to the energy transfer from larger to smaller lengthscales. Obtained magnetic turbulent spectra are consistent with observations of Cluster spacecraft in solar wind.     

Quantum treatment of kinetic Alfvén wave

Dispersion properties of kinetic Alfvén wave in quantum magnetoplasma are derived. The quantum contribution to the Landau damping of kinetic Alfvén wave is also derived by using linearized Vlasov equation which contains the Bohm quantum potential. Classical Landau damped kinetic Alfvén waves play an important role in turbulence of astrophysical plasmas. The quantum modification in Landau damping of kinetic Alfvén wave can also play a significant role in changing the scaling law of turbulent spectra as well as the formation of damped localized Alfvénic structures in dense astrophysical plasmas.     

Nonlinear effects associated with the finite frequency pump kinetic Alfvén wave and turbulent spectrum in solar wind

The paper contains a numerical simulation of the nonlinear coupling between the kinetic Alfvén wave and the ion acoustic wave for an intermediate β-plasma (m _e/m _i?β?1). For this study, we have introduced the nonlinear ponderomotive force (due to the finite frequency (ω ₀<ω _ci) kinetic Alfvén wave) in the derivation of the ion acoustic wave. The main aim of the present paper is to study the nonlinear effects associated with the different driving finite frequencies (ω ₀<ω _ci) of the pump kinetic Alfvén wave on the formation of localized structures and a turbulent spectrum applicable to the solar wind around 1 AU. As a result, we found that the different driving frequencies of the pump kinetic Alfvén wave affect the formation of the localized structures. We have also studied the turbulent scaling which follows (～k ^?3.6) for ω ₀/ω _ci≈0.2, (～k ^?3.4) for ω ₀/ω _ci≈0.3 and (～k ^?3.2) for ω ₀/ω _ci≈0.4, at small scales. Further, we have also found that different finite driving frequencies of the pump kinetic Alfvén wave affect the turbulence scaling at small scales, which may affect the heating of the plasma particles in solar wind. The present study is correlated with the observation made by the Cluster spacecraft for the solar wind around 1 AU.     

The Alfvén wave parallel electric field in non-uniform space plasmas

We suggest a two-step mechanism for the generation of the parallel electric field at the Alfvén wave. At the first step, the coupling with the compressional mode due to the magnetic field non-uniformity and finite plasma pressure provides the parallel magnetic field of Alfvén wave. At the second step, the compressional mode acquires the parallel electric field due to coupling with the electrostatic mode as required by the quasi-neutrality condition in kinetics. The parallel electric field acquired by the Alfvén mode is considerably larger than that due to the single-step coupling between the Alfvén and electrostatic modes in kinetics.     

A two-fluid modeling of kinetic Alfvén wave turbulence

We present an analytical model to explore the magnetic field turbulent spectrum by coupled high-frequency kinetic Alfvén wave (KAW) and slow mode of Alfvén wave (AW). The spectrum is computed as a realization of energy cascades from larger to smaller scales for a specific case of solar wind plasma at 1 AU. A two-fluid technique is implemented for the derivation of model equations leading two wave modes. These coupled, nonlinear equations are solved numerically. The nonlinearity in the system arises due to nonlinear ponderomotive force, which is believed to be responsible for the wave localization and magnetic islands formation. The numerical results show that the magnetic islands grow with time and attain a quasi-steady state after the modulation instability is saturated. The magnetic field spectrum and associated spectral indices are computed near the time of saturation of instability. The simulated spectrum in dispersion region follows a power-law with an index of ?2.5. The steeper spectrum could be attributed as energy transfer from larger to smaller scales and helps to study turbulence in solar wind. The magnetic field spectrum and spectral index show a good agreement with the observation of solar wind turbulent spectra.     

Alfvén waves in stellar winds

A mathematical model for undamped, toroidal, small-amplitude Alfvén waves in a spherically-symmetric or equatorial stellar wind is developed in this paper. The equations are reduced to a very simple form by using real Fourier amplitudes and the ratio of the inward and outward propagating wave amplitudes, which is interpreted as a measure of the relative influence of wave reflection in the flow, on the solution at a given point. Asymptotic solutions at large distances are found to depend only on one parameter, = / _P - the ratio of wave frequency and critical (or cutoff) frequency which is a flow characteristic; a = 1 divides solutions into two qualitatively different groups. When 1 the asymptotic (r-) ratio of the inward and outward propagating wave amplitudes does not depend on wave frequency and is equal to unity, while the phase shift between them changes; in this case the wave pattern is a standing wave. If > 1 the converse occurs with the ratio of the amplitudes decreasing rapidly as the frequency increases, and the phase shift equals to -1/2, corresponding to a propagating wave pattern. The result is also expressed in terms of velocity and magnetic field perturbations.Existence of a finite incoming wave amplitude solution at the Alfvén critical point indicates that this point is stable with respect to the perturbations which originate at the critical point and spend an infinite time in its vicinity.Special attention is paid to the applicability of the WKB approximation. It is argued that it can be used only in finite intervals which do not contain the Alfvén critical point, with inward propagating waves taken into account through the boundary conditions. It is shown that despite the presence of reflection, the outward propagating wave amplitude can be described reasonably well by the WKB formula, perhaps with different constants in different regions. In this context = 1 divides solutions which cannot be approximated by the WKB estimate at all at large distances (the first group), from those which can with any given accuracy.As an illustration of the analytical behaviour some numerical results are shown using a cool wind model. These are likely to express qualitatively the features of the Alfvén waves in any stellar wind, since the only assumptions about the flow used in the analytical study of the wave equations were that: the flow has small velocity at the base of the corona; it then passes through the critical point, and reaches its finite non-zero limit at infinity.     

Nonlinear interaction of inertial Alfvén wave with magnetosonic wave and cavitation phenomena

In the present paper, authors have investigated nonlinear interaction of inertial Alfvén wave with magnetosonic wave for low β-plasma (β?m _e /m _i ). Authors have developed the set of dimensionless equations in presence of ponderomotive force due to inertial Alfvén wave in the dynamics of magnetosonic wave. Stability analysis and numerical simulation have been carried out to study the effect of nonlinear coupling between waves which result in the formation of localized structures and density cavity, applicable to auroral region and solar corona. The result reveals that localized structure and density cavity becomes more complex and intense in nature in quasi steady state. From the obtained result, we found the density fluctuations ～0.1n ₀, consistent with the FAST spacecraft observation.     

Cavitation by Nonlinear Interaction Between Inertial Alfvén Waves and Magnetosonic Waves in Low Beta Plasmas

This paper presents the model equations governing the nonlinear interaction between dispersive Alfvén wave (DAW) and magnetosonic wave in the low-β plasmas (β≪m _e/m _i; known as inertial Alfvén waves (IAWs); here \upbeta = 8pn₀T /B₀²\upbeta = 8\pi n_{0}T /B_{0}^{2} is thermal to magnetic pressure, n ₀ is unperturbed plasma number density, T(=T _e≈T _i) represents the plasma temperature, and m _e(m _i) is the mass of electron (ion)). This nonlinear dynamical system may be considered as the modified Zakharov system of equations (MZSE). These model equations are solved numerically by using a pseudo-spectral method to study the nonlinear evolution of density cavities driven by IAW. We observed the nonlinear evolution of IAW magnetic field structures having chaotic behavior accompanied by density cavities associated with the magnetosonic wave. The relevance of these investigations to low-β plasmas in solar corona and auroral ionospheric plasmas has been pointed out. For the auroral ionosphere, we observed the density fluctuations of ∼ 0.07n ₀, consistent with the FAST observation reported by Chaston et al. (Phys. Scr. T84, 64, 2000). The heating of the solar corona observed by Yohkoh and SOHO may be produced by the coupling of IAW and magnetosonic wave via filamentation process as discussed here.     

Nonlinear Evolution of a 3D Inertial Alfvén Wave and Its Implication in Particle Acceleration

A simulation based on a pseudo-spectral method has been performed in order to study particle acceleration. A model for the acceleration of charged particles by field localization is developed for the low-\(\upbeta\) plasma. For this purpose, a fractional diffusion approach has been employed. The nonlinear interaction between a 3D inertial Alfvén wave and a slow magnetosonic wave has been examined, and the dynamical equations of these two waves in the presence of ponderomotive nonlinearity have been solved numerically. The nonlinear evolution of the inertial Alfvén wave in the presence of slow magnetosonic wave undergoes a filamentation instability and results in field intensity localization. The results obtained show the localization and power spectrum of inertial Alfvén wave due to nonlinear coupling. The scaling obtained after the first break point of the magnetic power spectrum has been used to calculate the formation of the thermal tail of energetic particles in the solar corona.     

Alfvén waves in the solar atmosphere

We examine the propagation of Alfvén waves in the solar atmosphere. The principal theoretical virtues of this work are: (i) The full wave equation is solved without recourse to the small-wavelength eikonal approximation (ii) The background solar atmosphere is realistic, consisting of an HSRA/VAL representation of the photosphere and chromosphere, a 200 km thick transition region, a model for the upper transition region below a coronal hole (provided by R. Munro), and the Munro-Jackson model of a polar coronal hole. The principal results are:

1. If the wave source is taken to be near the top of the convection zone, where n _H = 5.2 × 10¹⁶ cm^?3, and if B _⊙ = 10.5 G, then the wave Poynting flux exhibits a series of strong resonant peaks at periods downwards from 1.6 hr. The resonant frequencies are in the ratios of the zeroes of J ₀, but depend on B _⊙, and on the density and scale height at the wave source. The longest period peaks may be the most important, because they are nearest to the supergranular periods and to the observed periods near 1 AU, and because they are the broadest in frequency.
2. The Poynting flux in the resonant peaks can be large enough, i.e. P _⊙ ≈ 10⁴–10⁵ erg cm^?2s^?1, to strongly affect the solar wind.
3. ¦δv¦ and ¦δB¦ also display resonant peaks.
4. In the chromosphere and low corona, ¦δv ≈ 7–25 kms^?1 and ¦δB¦ ≈0.3–1.0 G if P _⊙≈10⁴-10⁵ erg cm^?2s^?1.
5. The dependences of ¦δv¦ and ¦δB¦ on height are reduced by finite wavelength effects, except near the wave source where they are enhanced.
6. Near the base, ¦δB¦ ≈ 350–1200 G if P _⊙ ～- 10⁴–10⁵. This means that nonlinear effects may be important, and that some density and vertical velocity fluctuations may be associated with the Alfvén waves.
7. Below the low corona most wave energy is kinetic, except near the base where it becomes mostly magnetic at the resonances.
8. ?₀ < δv ² > v _A or < δB ² > v _A/4π are not good estimators of the energy flux.
9. The Alfvén wave pressure tensor will be important in the transition region only if the magnetic field diverges rapidly. But the Alfvén wave pressure can be important in the coronal hole.

     

Alfvén waves in the solar atmosphere

The linearized propagation of axisymmetric twists on axisymmetric vertical flux tubes is considered. Models corresponding to both open (coronal hole) and closed (active region loops) flux tubes are examined. Principal conclusions are: Open flux tubes: (1) With some reservations, the model can account for long-period (T 1 hr) energy fluxes which are sufficient to drive solar wind streams. (2) The waves are predicted to exert ponderomotive forces on the chromosphere which are large enough to alter hydrostatic equilibrium or to drive upward flows. Spicules may be a consequence of these forces. (3) Higher frequency waves (10 s T few min) are predicted to carry energy fluxes which are adequate to heat the chromosphere and corona. Nonlinear mechanisms may provide the damping. Closed flux tubes: (1) Long-period (T 1 hr) twists do not appear to be energetically capable of providing the required heating of active regions. (2) Loop resonances are found to occur as a result of waves being stored in the corona via reflections at the transition zones. The loop resonances act much in the manner of antireflectance coatings on camera lenses, and allow large energy fluxes to enter the coronal loops. The resonances may also be able to account for the observed fact that longer coronal loops require smaller energy flux densities entering them from below. (3) The waves exert large upward and downward forces on the chromosphere and corona.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Particle acceleration and Alfvén wave generation by an interplanetary shock

Based on the event observed by ISEE 3 near the Earth’s orbit at 01:21 UT on April 5, 1979, we investigate the diffusive shock acceleration of ions and the generation of Alfvén waves by accelerated particles near the quasi-parallel parts of interplanetary shock fronts within a quasi-linear approach. The theory is shown to give an excessively high level of Alfvén wave generation by accelerated particles at significant deflection angles of the interplanetary magnetic field from the normal to the shock front. At the Earth’s orbit, the Alfve´ n waves produced by accelerated ions are confined within the frequency range 5 × 10^?2?0.5 Hz, and their spectral peak with a wave amplitude δB ≤ B corresponds to a frequency ν = (1?2)×10^?2 Hz. The high-frequency part of the wave spectrum (ν ≥ 0.5 Hz) is subjected to damping on thermal protons. The calculated spectra of the accelerated ions and Alfvén waves generated by them reproduce the main features observed in experiments.     

Kinetic Alfvén waves in extended radio sources

We study a model of extended radio sources (ERS), in particular, extragalactic jets and radio lobes, which are inhomogeneous and where noncompressive Alfvén and surface Alfvén waves (and not shocks and magnetosonic waves) are primarily excited. We assume that a negligible thermal population exists (i.e., the ion density at the low-energy cut-off of the power law distribution is greater than the ion density of the thermal population, if present). Due to internal instabilities and/or the interaction of the ERS with the ambient medium, surface Alfvén waves (SAW) are created. We show that even very small amplitude SAW are mode converted to kinetic Alfvén waves (KAW) which produce large moving accelerating potentials , parallel to the magnetic field. Neglecting nonlinear perturbations, and for typical physical parameters of ERS, we obtaine1 MeV. Wesuggest that these potentials are important in acceleration (e.g., injection energy) and reacceleration of electrons in ERS. We show that energy losses by synchrotron radiation can be compensated by reacceleration by KAW. The relation between KAW acceleration, and previously studied cyclotron-resonance acceleration by Alfvén waves, is discussed.     

Current-driven Alfvén waves in dusty magnetospheric plasmas

It is shown that the sheared flow of electrons and ions in the presence of heavy stationary dust gives rise to unstable Alfvén waves. The coupling of newly studied low frequency electrostatic current-driven mode with the electromagnetic Alfvén and drift waves is investigated. The instability conditions and the growth rates of both inertial and kinetic Alfvén waves are estimated. The theoretical model is applied to the night side boundary regions of Jupiter’s magnetosphere which contain positive dust. The growth rates increase with increase in sheared flow speed. In the nonlinear regime, both inertial and kinetic Alfvén waves form dipolar vortices whose speed and amplitude depend upon the magnitude of the zero-order current.     

Discrete Alfvén waves in planar flux tubes

Properties of discrete Alfvén wave modes are derived, at frequencies up to the ion-cyclotron frequency, for current-carrying plasma slabs with non-uniform densities. It is shown that the essential features of the dispersion relations can be derived by examining the dominant terms in the potential function, when the wave equation is cast in the Schrödinger equation form. Analytical predictions for a class of mass and current density profiles are compared with numerically calculated dispersion relations and wavefields for particular profiles.