Slow Magnetosonic Research Articles

Characterization of Turbulent Fluctuations in the Sub-Alfvénic Solar Wind

Parker Solar Probe (PSP) observed sub-Alfvénic solar wind intervals during encounters 8–14, and low-frequency magnetohydrodynamic (MHD) turbulence in these regions may differ from that in super-Alfvénic wind. We apply a new mode decomposition analysis to the sub-Alfvénic flow observed by PSP on 2021 April 28, identifying and characterizing entropy, magnetic islands, forward and backward Alfvén waves, including weakly/nonpropagating Alfvén vortices, forward and backward fast and slow magnetosonic (MS) modes. Density fluctuations are primarily and almost equally entropy- and backward-propagating slow MS modes. The mode decomposition provides phase information (frequency and wavenumber k) for each mode. Entropy density fluctuations have a wavenumber anisotropy of k ∥ ≫ k ⊥, whereas slow-mode density fluctuations have k ⊥ > k ∥. Magnetic field fluctuations are primarily magnetic island modes (δ B i ) with an O(1) smaller contribution from unidirectionally propagating Alfvén waves (δ B A+) giving a variance anisotropy of 〈δBi2〉/〈δBA2〉=4.1 . Incompressible magnetic fluctuations dominate compressible contributions from fast and slow MS modes. The magnetic island spectrum is Kolmogorov-like k⊥−1.6 in perpendicular wavenumber, and the unidirectional Alfvén wave spectra are k∥−1.6 and k⊥−1.5 . Fast MS modes propagate at essentially the Alfvén speed with anticorrelated transverse velocity and magnetic field fluctuations and are almost exclusively magnetic due to β p ≪ 1. Transverse velocity fluctuations are the dominant velocity component in fast MS modes, and longitudinal fluctuations dominate in slow modes. Mode decomposition is an effective tool in identifying the basic building blocks of MHD turbulence and provides detailed phase information about each of the modes.

Возмущения второго порядка в альфвеновских волнах в плазме с давлением

It is shown first that in finite pressure plasma, just as in cold plasma, Alfvén waves created by an initial perturbation generate plasma flows and decreases in the magnetic field, which propagate along with these waves. Second, at the stage of their interaction, Alfvén waves generate slow magnetosonic (SMS) waves propagating along the magnetic field. These results suggest that at least some of the fast plasma flows observed in the magnetotail can be one of the manifestations of propagating Alfvén waves both in the magnetosphere regions with cold plasma and in the magnetosphere regions with finite pressure plasma. They also provide potential possibility for determining the position of a source of Alfvén disturbance from observations of Alfvén waves and their induced SMS waves.

Second-order perturbations in Alfvén waves in finite pressure plasma

It is shown first that in finite pressure plasma, just as in cold plasma, Alfvén waves created by an initial perturbation generate plasma flows and decreases in the magnetic field, which propagate along with these waves. Second, at the stage of their interaction, Alfvén waves generate slow magnetosonic (SMS) waves propagating along the magnetic field. These results suggest that at least some of the fast plasma flows observed in the magnetotail can be one of the manifestations of propagating Alfvén waves both in the magnetosphere regions with cold plasma and in the magnetosphere regions with finite pressure plasma. They also provide potential possibility for determining the position of a source of Alfvén disturbance from observations of Alfvén waves and their induced SMS waves.

Nonlinear Periodic Wave Propagation of Fast and Slow Magnetosonic Waves in the Presence of Oblique Magnetic Field

Fast and slow magnetosonic cnoidal and solitary wave structures in electron-ion plasmas are studied in the presence of an oblique magnetic field. Under the low-frequency wave assumption, cold ions are taken to be dynamic, while inertialess electrons are assumed as isothermally heated. The two-fluid magnetohydrodynamic model is applied to present the basic set of dynamic equations for magnetosonic waves in the presence of oblique magnetic field. The linear analysis is performed for studying fast and slow modes of magnetosonic waves and also discussed its limiting cases with magnetic field angle. The nonlinear analysis is done via the reductive perturbation method, and the Korteweg-de Vries (KdV) equation is derived with appropriate periodic boundary condition. The cnoidal wave and soliton solutions for both fast and slow magnetosonic waves are presented. The effects of variations of magnetic field angle and plasma beta on both fast and slow magnetosonic cnoidal and soliton wave structures are discussed using the space plasma parameters that exist in the literature.

SPATIAL STRUCTURE OF AZIMUTHALLY SMALL-SCALE MHD WAVES IN ONE-DIMENSIONALLY INHOMOGENEOUS FINITE PRESSURE PLASMA WITH CURVED FIELD LINES

We have studied propagation of hydromagnetic (MHD) waves in one-dimensionally inhomogeneous finite pressure plasma with curved field lines. Magnetic surfaces are considered to be concentric cylinders, where the cylinder’s radius models the radial coordinate in Earth’s magnetosphere. The waves are supposed to be azimuthally small-scale. In this approximation there are only two MHD modes — Alfvén and slow magnetosonic (SMS). We have derived an ordinary differential equation for the spatial structure of the wave field in this model. We have examined the character of the singularity on the surface of Alfvén and SMS resonances and the influence of field line curvature on them. We have determined wave transparent regions. The SMS transparent region was found to essentially broaden as compared to the straight field line case. The very existence of the Alfvén transparent region is caused by the field line curvature and finite plasma pressure; otherwise, the wave structure is represented by a localized resonance.

Пространственная структура азимутально-мелкомасштабных МГД-волн в одномерно-неоднородной плазме конечного давления с кривыми силовыми линиями

We have studied propagation of hydromagnetic (MHD) waves in one-dimensionally inhomogeneous finite pressure plasma with curved field lines. Magnetic surfaces are considered to be concentric cylinders, where the cylinder’s radius models the radial coordinate in Earth’s magnetosphere. The waves are supposed to be azimuthally small-scale. In this approximation there are only two MHD modes — Alfvén and slow magnetosonic (SMS). We have derived an ordinary differential equation for the spatial structure of the wave field in this model. We have examined the character of the singularity on the surface of Alfvén and SMS resonances and the influence of field line curvature on them. We have determined wave transparent regions. The SMS transparent region was found to essentially broaden as compared to the straight field line case. The very existence of the Alfvén transparent region is caused by the field line curvature and finite plasma pressure; otherwise, the wave structure is represented by a localized resonance.

Modulational Instability in the Interaction of Fast and Slow Magnetosonic Modes

The present paper studies the magnetic filaments produced by the interaction between the high-frequency magnetosonic wave and low-frequency magnetosonic wave. These phenomena can be explained by using an envelope solitary wave solution of the nonlinear Schrodinger equation (NLSE). The analytical results from NLSE are in agreement with the numerical result from Ref. Modi et al. (Phys. Plasmas 21: 102305, 2014). Both the linear and the nonlinear modulational instability are studied for the system. Two critical points are obtained. The first critical point gives the regions of both the instability and the stability, while the second one shows that if the perturbed wave number is close to the second critical point, the perturbed wave may be the most stable one. It is also found that all the higher order perturbed waves can be neglected in the stability region when the perturbed wave number is larger than that of the first critical point.

О баллонной неустойчивости в токовых слоях

The problem of instability of azimuthally small-scale Alfven and slow magnetosonic (SMS) waves in the geotail is solved. The solutions describe unstable oscillations in the presence of a current sheet and correspond to the region of stretched closed field lines of the magnetotail. The spectra of eigen-frequencies of several basic harmonics of standing Alfven and SMS waves are found in the local and WKB approximation, which are compared. It is shown that the oscillation properties obtained in these approximations differ radically. In the local approximation, the Alfven waves are stable in the entire range of magnetic shells. SMS waves go into the aperiodic instability regime (the regime of the ‘ballooning’ instability), on magnetic shells crossing the current sheet. In the WKB approximation, both the Alfven and SMS oscillations go into an unstable regime with a non-zero real part of their eigen-frequency, on magnetic shells crossing the current sheet. The structure of azimuthally small-scale Alfven waves across magnetic shells is determined.

Coupled guided modes in the magnetotails: spatial structure and ballooning instability

The problem of the spatial structure of coupled azimuthally small-scale Alfven and slow magnetosonic (SMS) waves is solved in an axisymmetric magnetotail model with a current sheet. It is shown that the linear transformation of these waves occurs in the current sheet on magnetic field lines stretched into the magnetotail. From the ionosphere to the current sheet these modes are linearly independent. Due to the high ionospheric conductivity the structure of coupled modes along magnetic field lines represents standing waves with very different typical scales in different parts of the field line. In most of the field line their structure is determined by the large-scale Alfven wave structure. Near the ionosphere and in the current sheet, small-scale SMS wave field starts to dominate. In these regions coupled modes becomes small-scale. Such modes are neutrally stable on the field lines that do not cross the current sheet, but switch to the ballooning instability regime on field lines crossing the current sheet. An external source is required to generate these modes and this paper considers external currents in the ionosphere as a possible driver. In the direction across magnetic shells the coupled modes are waves running away from the magnetic shell on which they were generated.

Modulational instability and associated rogue structures of slow magnetosonic wave in Hall magnetohydrodynamic plasmas

The modulational instability and associated rogue structures of a slow magnetosonic wave are investigated for a Hall magnetohydrodynamic plasma. Nonlinear Schrodinger equation is obtained by using the multiple scale method, which shows a modulationally unstable slow magnetosonic mode evolving into bright wavepackets. The dispersive effects induced by the Hall electron current increase with the increase in plasma β and become weaker as the angle of propagation increases. The growth rate of the modulational instability also increases with the increase in plasma β. The growth rate is greatest for the parallel propagation and drops to zero for perpendicular propagation. The envelope wavepacket of a slow magnetosonic is widened with less oscillations as plasma β increases. But the wavepacket becomes slightly narrower and more oscillatory as the angle of propagation increases. Further a non-stationary envelope solution of the Peregrine soliton is analyzed for rogue waves. The Peregrine soliton contracts temporally and expands spatially with increase in plasma β. However, the width of a slow magnetosonic Peregrine soliton decreases both temporally and spatially with increase of the propagation angle.

Longitudinal structure of ballooning MHD disturbances in a model magnetosphere

Large-scale toroidal Pc5 pulsations are commonly treated as Alfven oscillations of a magnetic field line. According to observations, their longitudinal structure is described well by theory. At the same time, the longitudinal structure of azimuthal small-scale poloidal Pc5 pulsations is virtually unknown. These pulsations are associated with ballooning disturbances described by a system of coupled equations for Alfvenic and slow magnetosonic (SMS) modes. In this work, the Voigt model is used to describe the equilibrium finite-pressure plasma configuration in an inhomogeneous magnetosphere plasma in a curved magnetic field. Spectral characteristics and the spatial structure of natural ballooning modes are calculated for this model. The model calculations demonstrate the possibility of different longitudinal scales for transverse and longitudinal magnetic components of oscillations near the top of the field line.

Dispersion equation for ballooning modes in two-component plasma

The ballooning magnetohydrodynamic (MHD) modes have been often suggested as a possible instability trigger of the substorm onset, and a mechanism of compressional waves in the outer magnetosphere and magnetotail. Commonly, these disturbances are characterized by the local dispersion equation that is widely applied for the description of ultra-low-frequency oscillatory disturbances and instabilities in the nightside magnetosphere. In realistic situations, especially in the inner magnetosphere, the magnetospheric plasma is composed of two components: background ‘cold’ plasma and ‘hot’ particles. The ballooning disturbances in a two-component plasma immersed into a curved magnetic field are described with the system of coupled equations for the Alfvén and slow magnetosonic (SMS) modes. We have reduced the basic system of MHD equations to the dispersion equation for the small-scale in transverse direction disturbances, and applied WKB approximation along a field line. As a result, we have derived a dispersion equation that can be used for geophysical applications. In particular, from this relationship the dispersion, instability threshold, and stop-bands of the Alfvén and SMS modes in two-component plasma have been examined.

On ballooning instability in current sheets

The problem of instability of the magnetotail current sheet to azimuthally small-scale Alfvén and slow magnetosonic (SMS) waves is solved. The solutions describe unstable oscillations in the presence of a current sheet and correspond to the region of stretched closed field lines of the magnetotail. The spectra of eigen-frequencies of several basic harmonics of standing Alfvén and SMS waves are found in the local and Wentzel–Kramers–Brillouin (WKB) approximation, which are compared. It is shown that the oscillation properties obtained in these approximations differ radically. In the local approximation, the Alfvén waves are stable in the entire range of magnetic shells. SMS waves go into the aperiodic instability regime (the regime of the ‘ballooning’ instability), on magnetic shells crossing the current sheet. In the WKB approximation, both the Alfvén and SMS oscillations go into an unstable regime with a non-zero real part of their eigen-frequency, on magnetic shells crossing the current sheet. The structure of azimuthally small-scale Alfvén waves across magnetic shells is determined.

Transformation and absorption of MHD oscillations in plane-stratified models of the Earth’s magnetosphere

The process of resonant transformation of fast magnetosonic (FMS) waves originating from the solar wind in Alfven and slow magnetosonic (SMS) oscillations in the Earth’s magnetosphere is investigated. The study of this process in a one-dimensional inhomogeneous medium model shows that the presence of a resonant surface for SMS oscillations in the plasma configuration significantly increases the absorption of the energy of FMS waves incident on the magnetosphere. The spatial distribution of the absorption rate of an energy flux of FMS waves is examined. In numerical calculations, the Kolmogorov spectrum was used for FMS waves, which is typical of the waves in the transition layer between a shock wave and the magnetopause. It is shown that the rate of energy absorption of FMS waves due to the resonant excitation of SMS oscillations is by several orders of magnitude greater than the absorption of their energy associated with resonant Alfven waves at the same magnetic shells.

Excitation of low frequency oscillations in a planetary magnetosheath by supersonic shear flow

Abstract. We show that the slow magnetosonic (SM) perturbations generated in the vicinity of the magnetopause, due to the excitation of the Kelvin-Helmholtz (K.-H.) instability in the case of a supersonic flow velocity, are transformed into fast magnetosonic (FM) waves which can propagate into the magnetosheath. Under the conditions discussed in this paper, the FM wave has negative energy in the stationary (magnetospheric) coordinate frame. Due to this the outgoing FM wave increases the growth rate of the K.-H. instability excited at the magnetopause. Within the linear theory, we investigate the influence of the excited FM wave on the growth rate of the K.-H. instability. Simultaneously we predict the transformation of the SM mode into kinetic Alfvén (KA) mode. Thus, in general, two types of waves with different polarizations (the KA wave and the FM wave) should appear in the magnetosheath due to the excitation of the K.-H. instability. At the same time, the SM perturbations are only present in the localized region where the K.-H. instability is excited. To correctly describe the excitation of waves, we use two-fluid (for electrons and ions) magnetohydrodynamics. This approach is more general than the ideal magnetohydrodynamics and allows us to take into account the effects associated with the finite Larmor radius of ions. Also it can be used to investigate the K.-H. instability in a multi-component plasma, or in the case where the frequency of perturbations is of the order of the gyrofrequency of oxygen ions which may occur, for example, at the magnetosheath of Mars.

Transformation and absorption of magnetosonic waves generated by solar wind in the magnetosphere

Resonant transformation of fast magnetosonic (FMS) wave flux into Alfven and slow magnetosonic (SMS) oscillations is investigated in the one-dimensionally inhomogeneous magnetosphere. Spatial distribution of energy absorption rate of FMS oscillations penetrating into the magnetosphere from the solar wind is studied. The FMS wave energy absorption rate caused by magnetosonic resonance excitation is shown to be several orders of magnitude greater than that caused by Alfven resonance excitation at the same surface. It is connected with the spectrum of incident FMS waves. The Kolmogorov spectrum is used in numerical calculations. Magnitude of the Fourier harmonics exciting resonant Alfven oscillations is much smaller than that of the harmonics driving lower-frequency magnetosonic resonance. It is shown that resonant transformation of FMS waves into SMS oscillations can be an effective mechanism of energy transfer from the solar wind to the magnetosphere.

A theory of MHD instability of an inhomogeneous plasma jet

AbstractA problem of the stability of an inhomogeneous axisymmetric plasma jet in a parallel magnetic field is solved. The jet boundary becomes, under certain conditions, unstable relative to magnetosonic oscillations (Kelvin–Helmholtz instability) in the presence of a shear flow at the jet boundary. Because of its internal inhomogeneity the plasma jet has resonance surfaces, where conversion takes place between various modes of plasma magnetohydrodynamic (MHD) oscillations. Propagating in inhomogeneous plasma, fast magnetosonic waves drive the Alfven and slow magnetosonic (SMS) oscillations, tightly localized across the magnetic shells, on the resonance surfaces. MHD oscillation energy is absorbed in the neighbourhood of these resonance surfaces. The resonance surfaces disappear for the eigenmodes of SMS waves propagating in the jet waveguide. The stability of the plasma MHD flow is determined by competition between the mechanisms of shear flow instability on the boundary and wave energy dissipation because of resonant MHD-mode coupling. The problem is solved analytically, in the Wentzel, Kramers, Brillouin (WKB) approximation, for the plasma jet with a boundary in the form of a tangential discontinuity over the radial coordinate. The Kelvin–Helmholtz instability develops if plasma flow velocity in the jet exceeds the maximum Alfven speed at the boundary. The stability of the plasma jet with a smooth boundary layer is investigated numerically for the basic modes of MHD oscillations, to which the WKB approximation is inapplicable. A new 'unstable mode of MHD oscillations has been discovered which, unlike the Kelvin–Helmholtz instability, exists for any, however weak, plasma flow velocities.

Slow magnetosonic oscillations withm>> 1 in a dipole magnetosphere with rotating plasma

[1] A mechanism of excitation of azimuthal small-scale (m 1) slow magnetosonic (SMS) oscillations by the external currents in the near-equatorial region of the terrestrial magnetosphere is proposed. A theoretical study of the structure and spectrum of such oscillations is performed in the model of the magnetosphere with the dipole magnetic field and rotating plasma. In the direction along field lines of the geomagnetic field the oscillations are waves standing between the magnetically conjugated points. The amplitude of the magnetospheric SMS oscillations with m 1 decreases from the equatorial plane to the ionosphere at scales much lower then the field line length. So one is not able to observe the SMS-oscillation field in the vicinity of the ionosphere and on the surface of the Earth. In the direction across the magnetic shells, the standing SMS waves have a structure typical for resonant oscillations. Latitudinal distributions of eigenfrequencies of several first harmonics of SMS oscillations with the polarization similar to the polarization of poloidal and toroidal Alfven waves in the plane perpendicular to the field lines are drawn. INDEX

Magnetosonic resonance in a dipole-like magnetosphere

Abstract. A theory of resonant conversion of fast magnetosonic (FMS) waves into slow magnetosonic (SMS) oscillations in a magnetosphere with dipole-like magnetic field has been constructed. Monochromatic FMS waves are shown to drive standing (along magnetic field lines) SMS oscillations, narrowly localized across magnetic shells. The longitudinal and transverse structures, as well as spectrum of resonant SMS waves are determined. Frequencies of fundamental harmonics of standing SMS waves lie in the range of 0.1–1 mHz, and are about two orders of magnitude lower than frequencies of similar Alfvén field line resonance harmonics. This difference makes an effective interaction between these MHD modes impossible. The amplitude of SMS oscillations rapidly decreases along the field lines from the magnetospheric equator towards the ionosphere. In this context, magnetospheric SMS oscillations cannot be observed on the ground, and the ionosphere does not play any role either in their generation or dissipation. The theory developed can be used to interpret the occurrence of compressional Pc5 waves in a quiet magnetosphere with a weak ring current.

Slow magnetosonic solitons detected by the cluster spacecraft.

Experimental evidence is provided for the existence of slow-mode magnetosonic solitons in the col-lisionless plasma at the magnetopause boundary layer. The solitons were detected by the fleet of Cluster spacecraft at the dusk flank of the magnetosphere as magnetic field depressions (up to 85%) accom-panied with enhancement of the plasma density and temperature by a factor of 2. The solitons propagate 250 km/s with respect to the satellites and have perpendicular size of 1000-2000 km, which is a few ion inertial scale lengths. The comparison with numerical solutions of a theoretical model shows quantitative agreement between the model and observations.