Alfén waves in a thermally stratified fluid

Abstract

The propagation of Alfvén waves along a uniform horizontal field in a highly conducting incompressible fluid, subject to the convective forces produced by a uniform vertical temperature gradient, is treated in a Boussinesq approximation. It is shown that there are exact solutions with large amplitude but restricted form. Their restricted form means that an arbitrary disturbing force produces other motions as well as Alfvén waves. An arbitrary initial disturbance of small amplitude produces waves whose state of polarization varies along the direction of propagation. For large amplitudes, however, any mixtures of polarization states causes scattering into new modes.     

Thermal Generation of Alfvén Waves in Oscillatory Magnetoconvection: Diffusively Modified Modes

Thermal instabilities in the form of oscillatory magnetoconvection representing diffusively modified Alfvén waves in an electrically-conducting Bénard fluid layer of rigid walls in the presence of a vertical magnetic field are investigated. Emphasis of the article is on the transition from a nearly undamped Alfvén wave to diffusively modified Alfvén waves, and on the effect of physically realisable magnetic field boundary conditions on magnetoconvection. It is found that the extra magnetic dissipation in the magnetic Hartmann boundary layers can enhance oscillatory magnetoconvection in the form of strongly modified Alfvén waves. Oscillatory magnetoconvection produced solely by the Alfvén wave mechanism can be the most unstable mode even in the presence of a strong viscous effect. This article also represents the first study on the effect of an electrically conducting wall on magnetoconvection which is associated with a nonlinear eigenvalue problem. We find that the electrically perfectly conducting condition does not yield a good approximation for magnetoconvection with an electrically highly conducting wall. The size of oscillation frequency with an electrically highly conducting wall can be more than a factor of 2 larger than that obtained using the perfectly conducting condition.     

阿尔芬波动特征对卫星磁力仪零位标定的影响

磁通门磁力仪的零位偏移量在卫星轨道上会因诸多因素而发生改变.为此,基于剪切阿尔芬波动不改变总磁场强度这一特征的Davis-Smith方法被提出用于计算磁力仪的零位补偿.实际上,行星际空间中没有纯粹的阿尔芬波动.本文采用数值模拟分析了存在小的压缩波动情况下,阿尔芬波动的幅度、周期和相位以及数据窗口时间长度等对Davis-Smith方法计算零位补偿的影响.我们发现,只有当阿尔芬波动的周期与压缩波动周期相同时,阿尔芬波动的性质会对零位补偿的计算产生不可忽视的误差.阿尔芬波动的幅度越大,零位补偿的误差越小.磁场各分量零位补偿的误差大小还会受到阿尔芬波动初始相位的影响.此外,数据窗口时间长度越长,则零位补偿误差趋于减小至真实值.     

Nonlinear development of phase-mixed alfvén waves

Abstract

We derive an equation governing the nonlinear propagation of a linearly polarized Alfvén wave in a two-dimensional, anisotropic, slightly compressible, highly magnetized, viscous plasma, where nonlinearities arise from the interaction of the Alfvén wave with fast and slow magnetoacoustic waves. The phase mixing of such a wave has been suggested as a mechanism for heating the outer solar atmosphere (Heyvaerts and Priest, 1983).

We find that cubic wave damping dominates shear linear dissipation whenever the Alfvén wave velocity amplitude δv_y exceeds a few times ten metres per second. In the nonlinear regime, phase-mixed waves are marginally stable, while non-phase-mixed waves of wavenumber k_a are damped over a timescale k_uRe ₀|δ v_y/v_A |^?2, Re ₀ being the Reynolds number corresponding to the Braginskij viscosity coefficient η₀ and v_A the Alfvén speed. Dissipation is most effective where β = (v_s /v_A) ² ≈ 1, v_s being the speed of sound.     

The discovery of magnetohydrodynamic waves

The discovery of magnetohydrodynamic waves was a major breakthrough in plasma physics and its applications to space physics and fusion research. The waves were discovered by Hannes Alfvén and are therefore also called Alfvén Waves. The discovery was typical of Alfvén's outstanding ability to derive results of great generality from analysis of specific problems—in this case, the sunspots and the sunspot cycle. It was also typical of his electrodynamic approach to astrophysical problems. It took a long time before his discovery was generally accepted, partly because of the contemporary lack of means to verify the waves experimentally. The experimental verification of the magnetohydrodynamic waves came gradually many years later, beginning with experiments in liquid metals. It was not until the end of the 1950s that experiments were performed in plasmas. These clearly and conclusively demonstrated the existence and properties of magnetohydrodynamic waves, in excellent agreement with the theoretical prediction of Alfvén. The discovery of the magnetohydrodynamic waves opened a whole new field of physics—magnetohydrodynamics, which is of profound importance especially, but not only, in plasma physics. At the same time as the magnetohydrodynamic waves, Hannes Alfvén also discovered another magnetohydrodynamic concept, the frozen-in magnetic field.     

On the spin-up of a stably stratified,electrically conducting fluid. Part 1: Spin-up controlled by the hartmann layer

Abstract

The linear spin-up of a stably stratified, electrically conducting fluid within an electrically insulating cylindrical container in the presence of an applied axial magnetic field is analyzed for those cases in which electric currents generated within the steady Hartmann boundary layer control the fluid interior. It is shown how to obtain the known spin-up times for a homogeneous, nonconducting fluid (τ = E ^-½), a stably stratified, nonconducting fluid (τ = (σS/E, E ^?1) and a homogeneous conducting fluid (τ = α^?1 E ^-½) from the present formulation where τ = v/ωt, E = v/ωL ², σS = vN²/κω² and 2α² = σB²/pω. The problem is solved in the parameter range E?α²?1, α²/E?σS using the Laplace transform and two new spin-up times are obtained. Combined into one expression, they are τ = (1 + δ)α^?1E^-½ where δ = σμv. The spin-up mechanism is investigated and it is found that, in contrast to the homogeneous, conducting case, torsional Alfvén waves may be instrumental in the spin-up of a stratified conducting fluid. The effects of viscous and ohmic diffusion on the torsional Alfvén wave fronts are studied and the following regimes are identified: 0 < δ ?E/α², spin-up by meridional circulation of electric current with no Alfvén waves; E^-½/α ? δ ? 1, spin-up by meridional circulation of electric current with transient Alfvén waves; α/E^½ ? δ ? α²/E, spin-up by meridional circulation of current with weak Alfvén waves; 1 ? δ ? α/E^½, spin-up by strong Alfvén waves; α^½/E ? δ ? α²/E, spin-up by viscous diffusion with transient Alfvén waves; α/E ? δ < ∞, spin-up by viscous diffusion with no Alfvén waves.     

Dependence of the Pc4 magnetic pulsation parameters on the radiated power of the EISCAT HF heating facility

The interaction between the Earth’s ionosphere and magnetosphere in a situation when artificial disturbances are generated in the F region of the auroral ionosphere with the EISCAT/Heating facility is studied. An experiment was performed in the daytime when the facility effective radiated power changed in a stepwise manner. Wavelike disturbances with periods of (130–140) s corresponding to Pc4 pulsations were simultaneously registered by the method of bi-static backscatter and with ground magnetometers. The variations in the Doppler frequency shift were correlated with the changes in the facility power. Incoherent scatter radar measurements at a frequency of 930 MHz (Tromsö) and numerical calculations were used in an analysis. It has been indicated that the ionospheric drift of small-scale artificial ionospheric irregularities was modulated by magnetospheric Alfvén waves. The possible effect of powerful HF radioemission on the Alfvén wave amplitude owing to the modification of the magnetospheric resonator ionospheric edge reflectivity and the generation of an outgoing Alfvén wave above the region where the ionospheric conductivity is locally intensified has been considered.     

Formation of accelerated ion flows in Alfvén disturbances of the magnetotail

This paper shows that there exists a mechanism of longitudinal plasma acceleration which is inherent in the process of the process of resonant conversion of a fast magnetosonic wave freely propagating along the magnetic field into an Alfvén wave. This mechanism is caused by the Ampere force arising due to the interaction between the poloidal component of the current of the compressible disturbance and the generated toroidal disturbance. It is shown that plasma acceleration takes place at the stage of increase in the Alfvén wave amplitude and that the accelerated flow retains its velocity when the process of resonant conversion is over. We describe spatiotemporal structures of plasma flows arising with the transformation of fast magnetosonic waves into Alfvén waves. An interpretation of the presence of fast ion flows in the magnetotail as a consequence of the action of the plasma acceleration mechanism considered in this work is proposed.     

Resonance properties of Psi5/Psc5 in geostationary orbit

It has been indicated that the magnetic field variations, registered by the geostationary satellites in the range 150–600 s after 14 SI/SC events, include transverse wave components that show the spectral—polarization properties of standing Alfvén waves. The amplitude of these waves increases with increasing pulse amplitude, the period increases with decreasing magnetic field magnitude, and the rotation direction and magnetic field vector orientation reverse their signs near the noon and midnight meridians.     

Excitation of Alfvén waves and vortices in the ionospheric Alfvén resonator by modulated powerful radio waves

A review of the artificial excitation of Alfvén waves and vortices in the ionospheric Alfvén resonator (IAR) is presented. In the framework of simplified models of the IAR and the Alfvén vortex instability, we discuss the main physical phenomena arising under the periodic heating of the ionosphere by a powerful HF radio signal with a modulation frequency F which lies in the range of short-period geomagnetic pulsations (F = 0.1–10 Hz). The amplitudes, frequency spectra, and polarization characteristics of artificial pulsations on the ground are found, and a brief comparison with experimental data is made. The Alfvén vortex instability in the IAR is analysed from the point of view of its artificial triggering. Two ways of such a triggering are discussed. The first suggests the use of two spaced transmitter antenna which produce an ionospheric current being in resonance with Alfvén vortices. Existing heating facilities are suitable for this experiment. The second method is based on the change of macroscopic parameters of the ionosphere, such as the conductivity in the instability region. This method is simple, but requires more powerful heaters.     

Interaction between the Alfvén wave and turbulent sheet

The interaction between the Alfvén wave and turbulent sheet (TS) with an anomalous conductivity has been considered. High frequency turbulence causes the appearance of not only anomalous field-aligned plasma conductivity but also cross-field conductivity. Alfvén waves can be partially reflect from TS, be absorbed in this sheet, and pass through TS. When field-aligned conductivity is predominant, the relative effectiveness of these processes strongly depends on a cross-field wave scale. If TS is thin as compared to the Alfvén wavelength, the resistive Alfvén wave (λ _A ) characterized by the field-aligned resistivity and Alfvén velocity above the sheet is the characteristic parameter responsible for the wave-sheet coupling. A comparison of the loss, estimated using the analytical relationships for a thin sheet and numerically calculated based on the complete formulas for a sheet with a finite thickness, indicates that the approximation of a thin sheet results in reasonable estimates at all wave scales except very small ones. The developed model has been applied to the interpretation of the results of the works on Pi2 pulsation damping during the substorm expansion phase, which indicated that the damping decrement increases at large substorm amplitudes. The estimates indicate that this increase in damping is related to the appearance of anomalous resistivity in the case when field-aligned currents exceed the threshold values necessary for excitation of high frequency turbulence.     

Space-time structure of Alfvén resonant disturbances generated by transversally localized FMA wave

This study describes the space-time evolution of the Alfvén resonant disturbance generated by a transversally localized fast magnetoacoustic (FMA) wave induced by impulse action on its localization area. We determine the conditions for the formation of qualitatively different space-time structures of Alfvén resonant disturbances under different relationships between parameters characterizing both dispersion/absorption of Alfvén disturbance and resonant absorption of transversally localized FMA waves. The spatial structures of Alfvén resonant disturbances and their time evolution are described analytically.     

A shell model for anisotropic magnetohydrodynamic turbulence

Abstract

In this paper, starting from the spectral DIA equations obtained by Veltri et al. (1982), describing the spectral dynamical evolution of magnetohydrodynamic (MHD) turbulence in the presence of a background magnetic field B ₀, we have derived an approximate form of these equations (shell model) more appropriate for numerical integration at high Reynolds numbers.

We have studied the decay of an initially isotropic state, with an initial imbalance between the energies for the two signs of the cross-helicity. Reynolds numbers up to 10⁵ have been considered.

Numerical results show that the nonlinear energy cascade behaves anisotropically in the k-space, i.e. in the spectra there is a prevalence of the wavevectors perpendicular to B ₀ with respect to the parallel wavevectors. This anisotropic effect, which is due to the presence of the background magnetic field, can be understood in terms of the so-called ‘‘Alfvén effect''.

A different source of anisotropy, due to the difference of the energy transfer for the two polarizations perpendicular to k, is recovered, but its effect is found to be mainly concentrated in the injection range.

Only little differences have been found, in the inertial range, in the spectral indices from the Kraichnan 3/2 value, which is valid for an isotropic spectrum. A form for the anisotropic spectrum can be recovered phenomenologically from our results. Values of the spectral indices quite different from the Kraichnan 3 2 value are obtained only when we consider stationary states with different forcing terms for the two modes of Alfvén wave propagation.

The comparison of our results with the observations of the v and B fluctuations in the interplanatery space shows that the anisotropy found in interplanetary fluctuations might be attributed only partially to the result of a nonlinear energy cascade.     

Multipoint observations of Pi2 pulsations and correlation with dynamic processes in the near-Earth magnetotail on March 18, 2009

Simultaneous measurements from THEMIS spacecraft,GOES-11 and ground stations(Canadian Array for Realtime Investigations of Magnetic Activity or CARISMA,and 210°magnetic meridian or MM)on March 18,2009 allow the study of dynamic processes in the near-Earth magnetotail and corresponding Pi2 pulsations on the ground in great detail.Fast earthward flows along with traveling Alfvén waves and fast mode waves in the Pi2 band were observed by three Time History of Events and Macroscale Interactions during Substorms(THEMIS)probes(P3,P4 and P5)in the near-Earth plasmasheet.At the mid-to high-latitude nightside,the CARISMA stations located near the foot points of the three probes recorded Pi2s with two periods,about 80 s after the earthward fast flows observed by the P4 probe.The long-period Pi2(140–150 s)belongs to the transient response Pi2(TR Pi2),since the travel time of the Alfvén waves between the plasma sheet and CARISMA stations is very close to half the period of the long-period Pi2.The short-period Pi2(60–80 s)has the same period band as the perpendicular velocity of the fast flows,which indicates that it may relate to the inertial current caused by periodic braking of the earthward fast flows.The 210°MM stations located at the low-latitude duskside also observed Pi2s with the same start time,waveform and frequency,about~120 s after the earthward fast flows.Strong poloidal oscillations are shown by GOES-11(~23 MLT)and the compressional component(Bb)is highly correlated with H components of the 210°MM stations,whereas the other two components(Br and Be)are not.These results confirm that the low-latitude Pi2s are generated by cavity mode resonance,which is driven by an impulsive broadband source in the near-Earth magnetotail.     

On the latitudinal structure of the magnetohydrodynamic Alfvén resonances

According to the data of the IMAGE network of magnetometers the latitudinal profile of the amplitude of the Pc5 geomagnetic pulsations is constructed, which are excited in the Earth’s magnetosphere in the form of the resonance Alfvén magnetohydrodynamic pulsations. The approaches to the solution of two problems are studied on a specific example. The first concerns the anharmonicity of Alfvén’s resonances. The displacement of the peak of the resonance curve towards to the north with the reduction of the amplitude of the pulsations is discovered. Based on the results of measurements, the nonlinear distortion coefficient of the latitudinal profile is determined. The second problem is connected with the magnetotelluric sounding. Information about the resonance structure of the Alfvén pulsations is useful for magnetotelluric sounding. This information gives the possibility of evaluating the accuracy of the sounding with the application of the local impedance relationship and of introducing corrections if necessary.     

Inertial effects in the Earth’s crust and magnetosphere

A review of studies devoted to the problem of exciting magnetic signals in the crust associated with the formation of the major rupture in an earthquake source and with the propagation of seismic waves was given in [Sgrigna et al., 2004]. However, this review contains incorrect citations from original papers and several erroneous statements concerning inertial and inductive mechanisms of conversion of the energy of rock motion into magnetic field energy. These mistakes are analyzed in the present paper. The formal and physical similarity between seismomagnetic waves in the crust and Alfvén waves in the magnetosphere is used in the analysis. A comparative analysis of the inertial and inductive mechanisms of seismomagnetic field generation is performed. The Cherenkov criterion of Alfvén wave generation due to the ionospheric effect of acoustic waves from earthquakes and explosions is derived. Attention is also given to nonlinear phenomena (nonlinearity of a mechanomagnetic conversion in the crust and anharmonicity and self-focusing of Alfvén waves in the magnetosphere).     

The magneto-boussinesq approximation by scale analysis

Abstract

The Magneto-Boussinesq approximation is derived as a set of leading order equations in an asymptotic expansion. An analogous set of equations is derived for the case when the Alfvén speed is comparable to the sound speed.     

Characteristics of the Energy Transfer by Alfvén Waves in the Solar Atmosphere

Geomagnetism and Aeronomy - The propagation of linear Alfvén waves with periods of 10–200 s from the photosphere to the solar chromosphere under the conditions of an isothermal...     

A mechanism of Pc 1 pearl formation based on the Alfvén sweep maser

A self-consistent model for the generation of Pc 1 pearl emissions based on the nonlinear coupling between the magnetospheric and ionospheric resonators for Alfvén waves is considered. Formation of pearls is attributed to the pulsating regime of the Alfvén sweep maser with nonlinear selective mirrors. Such mirrors are formed by the conjugate ionospheres: their reflection coefficient has an oscillatory frequency dependence due to eigenmodes of the ionospheric Alfvén resonator. Nonlinear magnetosphere/ionosphere feedback is provided by the dependence of the value and frequency of the reflection maxima on the flux of energetic protons precipitated into the ionospheres in the course of Alfvén wave generation in the magnetosphere. A nonlinear soliton-like solution of this model is found which corresponds to a single wave packet having the positive frequency drift and oscillating between the conjugate ionospheres. Properties of this solution are shown to explain many observational characteristics of Pc 1 pearls, such as their morningside predominance, correlation with low magnetic activity, spatio-temporal and spectral patterns.     

On the dissipation of atmospheric alfvén waves in uniform and non-uniform magnetic fields

Abstract

We deduce the dissipative Alfvén wave equation in a medium stratified in one direction, with a transverse magnetic field, in the presence of dissipation by fluid viscosity and electrical resistance; the dissipative Alfvén wave equation generalizes earlier results for homogeneous (Cowling, 1960) and inhomogeneous (Campos, 1983a) media, and corrects an error in the literature (Heyvaerts and Priest, 1983). The wave equation is solved exactly in two cases: a uniform magnetic field, and a magnetic field decreasing with height. In both cases the mean state is assumed to be isothermal, with a constant rate of ionization, so that the magnetic diffusivity is constant, but the dynamic viscosity increases with height. There are therefore two regions, a low- (high-) altitude region where electrical resistance dominates fluid viscosity (or vice versa), and an asymptotic regime relevant to the uppermost (lowermost) layers. The two regions are separated by a transition layer, across which the wave field is continuous and whose structure is expressible by hypergeometric functions, with different arguments in the low- and high-altitude regions, and over the whole altitude range. These exact solutions allow the amplitude and phase of the wave field to be plotted as a function of height for a variety of magnetoatmospheric mean states. They show that wave dissipation is more localized and intense when the magnetic field decreases with height than when it is uniform.