Inertial Alfven Waves Research Articles

Retraction Note to: Numerical simulation of inertial alfven waves to study localized structures and spectral index in auroral region

In the present paper, the numerical simulation of Inertial Alfven wave (IAW) in low- $$\beta $$ plasma applicable to the auroral region at 1700 km was studied. It leads to the formation of localized structures when the nonlinearity arises due to ponderomotive effect and Joule heating. The effect of perturbation and magnitude of pump IAW, formed the localized structures of magnetic field, has been studied. The formed localized structures at different times and average spectral index scaling of power spectrum have been observed. Results obtained from simulation reveal that spectrum steepens with power law index $$\sim -3.5$$ for shorter wavelength. These localized structures could be a source of particle acceleration and heating by pump IAW in low- $$ \beta $$ plasma.

Inertial Alfvén waves in auroral acceleration region with H+, He+ and O+ ions plasma

The propagation of inertial Alfven wave is investigated in cold, low- $\beta $ , homogeneous and bi-Maxwellian plasma consisting of multi-ions (H+, He+ and O+). Kinetic approach is adopted to derive the dispersion relation, damping rate, group velocity and growth/ damping length of the wave. Figures are exhibited with respect to ${ck_{\bot }} / {\omega _{pe}}$ . Effects of density variation with multi-ions are analysed on frequency, damping rate, parallel and perpendicular components of group velocity and growth/ damping length of the inertial Alfven wave. It is found that varying densities of multi-ions significantly influence the frequency, damping rate and group velocity of inertial Alfven wave. The wave frequency is observed between 0.5 to $18~\mbox{s}^{- 1}$ pertaining to observational data. The increasing density of heavy ions reduces the frequency of waves. The presence of He+ and O+ enhances the damping of wave showing more transfer of energy from wave to particles leading to increase in electron acceleration. The order of parallel and perpendicular group velocity is found to be $10^{9}~\mbox{cm}/\mbox{s}$ and $10^{5}~\mbox{cm}/\mbox{s}$ respectively. Maximum perpendicular growth length is observed corresponding to the minimum damping rate of wave at ${ck_{\bot }} / {\omega _{pe}} <1$ , signifying the dynamics in transverse direction to the magnetic field which are more significant in the present analysis. The parameters relevant to auroral acceleration region are used for graphical analysis. The applications of present study may be towards the electron acceleration in the dynamics of auroral acceleration region consisting of heavy ions in background plasma.

RETRACTED ARTICLE: Numerical simulation of inertial alfven waves to study localized structures and spectral index in auroral region

In the present paper, the numerical simulation of Inertial Alfven wave (IAW) in low-\(\beta \) plasma applicable to the auroral region at 1700 km was studied. It leads to the formation of localized structures when the nonlinearity arises due to ponderomotive effect and Joule heating. The effect of perturbation and magnitude of pump IAW, formed the localized structures of magnetic field, has been studied. The formed localized structures at different times and average spectral index scaling of power spectrum have been observed. Results obtained from simulation reveal that spectrum steepens with power law index \(\sim -3.5\) for shorter wavelength. These localized structures could be a source of particle acceleration and heating by pump IAW in low-\( \beta \) plasma.

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 Alfven 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 Alfven 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 Alfven 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.

The range of Alfvénic turbulence scales in the topside auroral ionosphere

The minimal scale of the Alfvenic turbulence transverse to the external magnetic field in the topside auroral ionosphere is investigated using electric field observations of the FAST spacecraft (the resolution 512 s–1). The events in which the power law form of the electric fluctuation spectra with a 2.0–2.5 slope (typical of Alfvenic turbulence) remains unchanged down to acoustic gyroradius ρs or ion gyroradius ρi local values are illustrated for the first time. In this case, the character of spectrum variation does not change at the electron inertial length λe, which is much larger than ρs and ρi for FAST altitudes (apogee ~4000 km). We have tried to explain this experimental fact by consideration of the known scenarios of the appearance of a small transverse scale in an Alfvenic perturbation. It has been noted that the effects of front steepening in an inertial Alfven wave with a finite amplitude, which propagates at an angle smaller than (me/mi)1/2 with respect to the transverse direction, can result in small transverse scales comparable with acoustic gyroradius appearing in a perturbation.

Numerical study of density cavitations by inertial Alfvén waves

In this manuscript, we study the localization and density cavitations using inertial Alfven wave (AW) and fast AW in the auroral ionosphere. We first develop a system of equations semi-analytically for both wave modes by using two-fluid model and then solve the model equations numerically using two-dimensional pseudo-spectral approach to analyze the localized structures and cavity formation at different instant of time. The ponderomotive force associated with the pump wave changes the background density and as the inertial AWs propagate through the modified density channel it gets localized. Therefore, the inertial AW splits up into filamentary/localized structures. A low frequency fast AW traveling through these complex structures created by inertial AW, is intensified having its own filamentary structures. The filamentary structures grow with time until the instability acquires steady state. We notice that the density cavities are also accompanied by the high amplitude magnetic fields. The amplitude of the strongest density cavity is estimated as ∼0.26n 0 (n 0 is unperturbed plasma number density). We also discuss the implications of the present study in the context of auroral ionosphere.

Localization of 3D inertial Alfvén wave and generation of turbulence

The present paper deals with the nonlinear interaction of Inertial Alfven wave (IAW) and fast magnetosonic wave in the low beta plasma, where beta is the ratio of thermal pressure to the background magnetic pressure. In this paper, the localization and turbulent spectra of IAW along with the density dips correlated with the fast magnetosonic wave have been investigated. Variation of parallel electric field along and across the field lines has also been studied. Taking ponderomotive nonlinear effect in the dynamics of fast magnetosonic wave, couple of dimensionless equations has been derived. These coupled equations have been simulated numerically using the pseudo-spectral method. The obtained results reveal that the Kolmogorov scaling is followed by a steeper scaling in magnetic power spectrum, which is consistent with the observations by the FAST and Hawkeye spacecraft in auroral region. The relevance of present investigation has been discussed for auroral plasmas.

Localization of finite frequency inertial Alfvén wave and turbulent spectrum in low beta plasmas

In the present paper, we have investigated nonlinear interaction of inertial Alfven wave with ion acoustic wave, for low β-plasma (β≪m e /m i ) where β is the thermal to magnetic pressure ratio. We have developed the dynamical equation of inertial Alfven wave by considering the finite frequency as well as finite ion temperature correction. The dynamical equation of ion acoustic wave, propagating at an angle with respect to the background magnetic field, in the presence of ponderomotive nonlinearity due to inertial Alfven wave is also derived. Numerical simulation has been carried out to study the effect of nonlinear coupling between these waves which results in the formation of localized structures and turbulent spectrum, applicable to auroral region. The result reveals that the localized structures become complex and intense in nature (quasi-steady state). Further, we have studied the turbulent spectrum which follows spectral index (∼k −4.46) at smaller scales. Relevance of the obtained results has been shown with the observations reported by various spacecrafts like Hawkeye and HEOS-2 (Highly Eccentric Orbiting Satellite-2).

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 Alfven 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 Alfven 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.

Properties of dispersive Alfvén waves: 3. Hydrodynamics (Very Low, Intermediate, and Low Density Plasmas)

The behavior of dispersive Alfven waves (DAWs), including inertial and kinetic Alfven waves, in astrophysical plasmas of very low, intermediate, and low pressure is investigated in the hydrodynamic approximation. New full solutions are obtained. Our results are analyzed and compared with those from the kinetic approach. It is shown that one general solution for the DAWs in plasmas of very low, intermediate, and low pressure can be obtained in the framework of the hydrodynamic approach, as opposed to the kinetic one. In the very low damping region, the kinetic and hydrodynamic solutions agree very well; but there are parameter regions where the solutions are essentially different. The influence of the astrophysical medium parameters on the DAW behavior and properties is analyzed. All main wave characteristics—the dispersion, damping, polarization, density perturbations, and charge density perturbations—are obtained, whose the consideration is very important for the observation and detection of these waves, as well as for a more correct understanding of their behavior and role in various astrophysical processes taking place in the cosmic medium.

Inertial Alfvén wave induced turbulent spectra in aurora

In the present paper, we investigate the localization of weak inertial Alfven wave (IAW) in the presence of finite amplitude magnetosonic fluctuations in low β plasmas (β≪m e /m i ). When IAW is perturbed by these fluctuations, localized structures of IAW magnetic field intensity are formed. We have developed a semi analytical model based on paraxial approximation to study this interaction. Numerical method has also been used to analyse the localized structures and magnetic fluctuation spectrum of IAW. From the obtained results, we find that the magnetic turbulent spectrum upto k x λ e ≈3 fits power law spectrum with an index consistent with the Kolmogorov $k_{x}^{ - 5/3}$ law, here λ e is the electron inertial length. Furthermore, at shorter wavelengths the spectrum steepens to about $k_{x}^{ - 3.8}$ . Energy transfer from larger lengthscales to smaller lengthscales through this mechanism may be responsible for the observed parallel electron heating in auroral region. Results obtained from the simulation are consistent with the observations recorded from various spacecrafts like FAST, Hawkeye and Hoes 2.

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

In the present paper, authors have investigated nonlinear interaction of inertial Alfven wave with magnetosonic wave for low β-plasma (β≪me/mi). Authors have developed the set of dimensionless equations in presence of ponderomotive force due to inertial Alfven 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 ∼0.1n0, consistent with the FAST spacecraft observation.

Properties of dispersive Alfvén waves: 1. Kinetics (very low, intermediate, and low density plasmas)

The work is devoted to the study of the behavior of dispersive Alfven waves, including inertial and kinetic Alfven waves, in astrophysical plasma of very low, intermediate, and low pressure. New and full solutions were obtained. The solutions for “ordinary” and inertial Alfven waves were shown to be particular cases of the general solution. The effect of the parameters of the astrophysical medium on the behavior and properties of dispersive Alfven waves was analyzed. All the main wave characteristics were obtained, namely, the dispersion, fading, polarization, density perturbations, and charge density perturbations, whose consideration is essential for observation and detection of these waves and for more adequate understanding of their role in different astrophysical processes that occur in the space environment.

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 Alfven waves. The coupling of newly studied low frequency electrostatic current-driven mode with the electromagnetic Alfven and drift waves is investigated. The instability conditions and the growth rates of both inertial and kinetic Alfven 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 Alfven waves form dipolar vortices whose speed and amplitude depend upon the magnitude of the zero-order current.

Study of gradient effects on inertial Alfvén waves in plasma sheet boundary layer region—kinetic approach

Inertial Alfven waves are investigated using Maxwell-Boltzmann-Vlasov equation to evaluate the dispersion relation and growth/damping rate in inhomogeneous plasma. Expressions for the dispersion relation and growth/damping rate are evaluated in inhomogeneous plasma. The effects of density, temperature and velocity gradient are included in the analysis. The results are interpreted for the space plasma parameters appropriate to the plasma sheet boundary layer. It is found that the inhomogeneities of plasma contribute significantly to enhance the growth rate of inertial Alfven wave. The applicability of this model is assumed for auroral acceleration region and plasma sheet boundary layer.

Inertial Alfven waves in an inhomogeneous bi-Maxwellian plasma

Abstract The Vlasov kinetic equation is solved using gyrokinetic theory and the dielectric tensor for non-relativistic, magnetized, bi-Maxwellian plasmas is calculated. A generalized dispersion relation for kinetic Alfven waves is derived taking into account the density inhomogeneity and temperature anisotropy. The modified dispersion relation thus obtained is then used to examine the propagation characteristics of the kinetic Alfven waves in the inertial regime. The importance of density inhomogeneity and temperature anisotropy for Solar corona is highlighted. The growth rate of the inertial Alfven wave proves that density inhomogeneity acts as a source of free energy.

Coupling of electrons and inertial Alfven waves in the topside ionosphere

A one‐dimensional kinetic model is constructed to simulate the electron acceleration by inertial Alfven waves. The electrons are divided into cold and hot electrons and treated separately. Cold components are described by the fluid equation and hot ones by the Vlasov equation, both carrying field‐aligned currents. Intense variation of Alfven speed has been introduced by inclusion of cold electrons. The model results show that the exponential decrease of the plasma density plays a key role, which leads to the sharp gradient of both Alfven velocity and electron inertial length. When Alfven waves encounter this sharp gradient at lower altitudes, the electrons accelerated by the waves become super‐Alfvenic, and the width of burst structures becomes much wider than the electron inertial length. Consequently, the background electrons carry the oppositely field‐aligned current due to plasma oscillation. It is demonstrated that the current carried by the electrons exceeding the wavefront is balanced by the reverse current carried by background electrons. This mechanism can be used to reasonably explain observations of the electron bursts accompanied by little net field‐aligned current. Furthermore, our simulation indicates another type of Alfven wave reflection due to mirror force and wave‐particle interaction.

Three dimensional particle-in-cell simulation of particle acceleration by circularly polarised inertial Alfven waves in a transversely inhomogeneous plasma

The process of particle acceleration by left-hand, circularly polarised inertial Alfven waves (IAW) in a transversely inhomogeneous plasma is studied using 3D particle-in-cell simulation. A cylindrical tube with, transverse to the background magnetic field, inhomogeneity scale of the order of ion inertial length is considered on which IAWs with frequency 0.3ωci are launched that are allowed to develop three wavelength. As a result time-varying parallel electric fields are generated in the density gradient regions which accelerate electrons in the parallel to magnetic field direction. Driven perpendicular electric field of IAWs also heats ions in the transverse direction. Such numerical setup is relevant for solar flaring loops and earth auroral zone. This first, 3D, fully kinetic simulation demonstrates electron acceleration efficiency in the density inhomogeneity regions, along the magnetic field, of the order of 45% and ion heating, in the transverse to the magnetic field direction, of 75%. The latter is a factor of two times higher than the previous 2.5D analogous study and is in accordance with solar flare particle acceleration observations. We find that the generated parallel electric field is localised in the density inhomogeneity region and rotates in the same direction and with the same angular frequency as the initially launched IAW. Our numerical simulations seem also to suggest that the “knee” often found in the solar flare electron spectra can alternatively be interpreted as the Landau damping (Cerenkov resonance effect) of IAWs due to the wave-particle interactions.

Nonlinear dispersive scale Alfvén waves inmagnetosphere-ionosphere coupling: Physical processes and simulation results

Dispersive Alfven waves (DAWs) have been demonstrated to play a significant role in auroral generation of the magnetosphere-ionosphere coupling system. Starting from a two fluid reduced MHD model, we summarize the frequency, temporal and spatial characteristics of magnetospheric DAWs. Then, the nonlinear kinetic and inertial scale Alfven waves are studied, and we review some theoretical aspects and simulation results of dispersive Alfven waves in Earth’s magnetosphere. It is shown that dispersive standing Alfven waves can generate the field-aligned currents which transport energy into the auroral ionosphere, where it is dissipated by Joule heating and energy lost due to electron precipitation. The Joule dissipation can heat the ionospheric electron and produce changes in the ionospheric Pedersen conductivity. As a feedback, the conducting ionosphere can also strongly affect the magnetospheric currents. The ponderomotive force can cause the plasma to move along the field line, and generate ionospheric density cavity. The nonlinear structuring can lead to a dispersive scale to accelerate auroral particle, and the Alfven waves can be trapped within the density cavity. Finally, we show the nonlinear decay of dispersive Alfven waves related to two anti-propagating electron fluxes observed in the auroral zone.

Nonlinear evolution of inertial Alfvén wave turbulence

Some recent experimental observations have been shown that inclusion of electron collisions damping in inertial Alfven wave (IAW) dynamics may be important for laboratory as well as space plasmas. This paper presents the numerical simulation of model equation governing the nonlinear dynamics of IAW in low-beta plasmas. When the nonlinearity arises due to the ponderomotive force and Joule heating driven density perturbations, the model equation turns out to be a modified nonlinear Schrodinger equation (MNLS). The electron collisions are introduced only in the electron momentum equation. The damped localized structures of IAW with sidebands are obtained. Also, the effect of collisional damping on power spectra of magnetic fluctuations with different scaling laws has been studied. These turbulent structures may be responsible for particle acceleration in laboratory and space plasmas.