Shear Alfven Research Articles

Swing Amplification of Shear Alfvén Waves through Periodical Density Variations in a Conductive Medium

We show that periodical density variations in a conductive medium set up the swing amplification of shear Alfven waves. Consequently, the energy of compressible waves propagating in the medium can be transmitted into the energy of transversal magnetic oscillations. The mechanism of swing energy transformation can be applied to many astrophysical objects.

Generation of field‐aligned currents in the near‐Earth magnetotail

Sudden brightening of aurora occurs at an early phase of substorm onset. Such auroral enhancements are strongly associated with parallel currents or shear Alfven waves. With MHD wave equations, we investigate the generation of field‐aligned currents near the equatorial region of the inner magnetotail, at the boundary between cold and hot plasmas. Our results show that strong localized shear Alfven waves are excited near this boundary via mode conversion when compressional input is assumed. We suggest that this boundary region is strongly associated with the auroral location.

Nonlinear Torsional and Compressional Waves in a Magnetic Flux Tube with Electric Current near the Quiet Solar Photospheric Network

Recent high-resolution observations from photospheric magnetograms made with the SOHO/Michelson Doppler Imager instrument and the Swedish Vacuum Solar Telescope on La Palma showed that magnetic flux tubes in the quiet photospheric network of the solar photosphere are highly dynamic objects with small-scale substructures. We investigate nonlinear waves propagating along a magnetic flux tube in weakly ionized plasmas with high plasma beta (β 1) by using three-dimensional neutral MHD equations. Recently Sakai et al. investigated nonlinear wave propagation along a magnetic flux tube with a weak current for the two cases of uniform density along the flux tube and density inhomogeneity due to solar gravity. They showed that shear Alfven waves are excited by localized, predominantly rotational perturbations and that excited waves with a strong upflow of wave energy can propagate only upward along the flux tube when density inhomogeneity due to gravity is taken into account. In this paper we extend this work by investigating nonlinear torsional and compressional waves in a magnetic flux tube with a strong electric current, i.e., a twisted magnetic field, near the quiet solar photospheric network. If gravity is neglected, the torsional waves are found to propagate in a direction such as to decrease the twist of the magnetic field, while the compressional waves propagate symmetrically. We have found that solar gravity results in the important effect that wave energies excited by both torsional and compressional disturbances can be transferred upward in both untwisted and highly twisted flux tubes and eventually contribute to coronal heating.

Random Scattering and Anisotropic Turbulence of Shear Alfvén Wave Packets

A theoretical model is given of anisotropic magnetohydrodynamic turbulence in the interstellar medium and the solar wind. The model is motivated by observations that show significant deviations from the Kolmogorov power law. Dimensional and heuristic arguments are given and critically assessed. On the basis of the weak turbulence approximation in which three-wave interactions dominate, analytical and numerical results are obtained for the anisotropic energy spectrum produced by the random scattering of shear Alfven waves propagating parallel to a large-scale magnetic field. The energy spectrum is shown to be proportional to k, qualitatively consistent with some observations and wave kinetic theory.

The Role of Nonlinear Alfven Waves in Shear Formation during Solar Magnetic Flux Emergence

Observations show that magnetic flux is constantly emerging at the solar photosphere to expand into the corona. Magnetic buoyancy is essential in bringing the magnetic field from the solar interior to the surface and beyond. In the simulations of buoyancy instabilities reported here, it has been discovered that nonlinear Alfven waves may play an important and dramatic role in the rise of magnetic flux. For initial states, our two-and-a-half-dimensional (2.5D), time-dependent simulations capitalize on the availability of a family of two-dimensional (2D) analytical solutions of isothermal magnetostatic atmospheres threaded by a layer of sheared undulating magnetic field. The magnetic field supports the weight of the atmosphere in an unstable configuration that sets the stage for the demonstration of magnetic flux emergence in a stratified atmosphere. When the system is perturbed, magnetic loops buoyantly rise from the flux layer and shearing motions are found to naturally arise in conjunction with mixed-mode (interchange and undulating) instabilities. The shearing motions take the form of large-amplitude shear Alfven waves that are driven by a component of the magnetic tension force pointing in the invariant direction. The waves are significant in that they transport magnetic flux from the shear layer into the ascending magnetic loops, causing them to become greatly inflated. The presence of such shear Alfven waves in magnetic loops rising through the photosphere provides an explanation for the impulsive shearing motions observed in newly emerged bipolar active regions.

Plasma transport during substorm growth phase and relation to breakup

For ω<ωbi,ωbe, the electron and ion bounce frequencies, the response of a plasma to an externally applied electromagnetic perturbation is nonlocal. This implies, via the quasi-neutrality equation, the development of an electrostatic potential which is constant for a given magnetic field line. In the near equatorial region the corresponding potential electric field is shown to oppose the effect of the induced electric field associated with the externally applied perturbation. Thus the effect of the induced electric field is partially shielded; the total azimuthal electric field (i.e. induced plus potential) tends to be small, which explains why the radial flow velocity is slow during quasi-steady conditions prevailing during the growth phase and after the active phase. The nonlocal response of the plasma also leads to the development of a parallel current that may generate current driven Alfven (CDA) waves, which mode convert into shear Alfven (SA) waves. CDA/SA waves are systematically observed at early breakup; they grow very fast and produce a parallel diffusion of electrons. As soon as the diffusion time is shorter than the bounce time (τd<τb), the nonlocal response vanishes. Thus the shielding disappears, and an enhanced transport is restored at the rate fixed by the induced electric field alone. We show that fast flows effectively occur when CDA waves have enough power to diffuse electrons (over τd<τb). Electron parallel diffusion also leads to an interruption of the parallel current and therefore to a disruption of the perpendicular current.

Incompressible MHD Turbulence

The inertial range of incompressible MHD turbulence is most conveniently describedin terms of counter propagating waves. Shear Alfven waves control the cascade dynamics. Slowwaves play a passive role and adopt the spectrum set by the shear Alfven waves. Cascades composedentirely of shear Alfven waves do not generate a significant measure of slow waves. MHD turbulenceis anisotropic with energy cascading more rapidly along k⊥. than along k∥. Anisotropy increases withk⊥. such that the excited modes are confined inside a cone bounded by k∥ α k⊥2/3. The opening angleof the cone, θ(k⊥) α k⊥ - 1/3, defines the scale dependent anisotropy. MHD turbulence is genericallystrong in the sense that the waves which comprise it are critically damped. Nevertheless, deep insidethe inertial range, turbulent fluctuations are small. Their energy density is less than that of thebackground field by a factor θ2(k⊥) > 1 which accounts for dominance of theshear Alfven waves in controlling the cascade dynamics.

Role of ionospheric effects and plasma sheet dynamics in the formation of auroral arcs

At the ionospheric level, the substorm onset (expansion phase) is marked by the initial brightening and subsequent breakup of a pre-existing auroral arc. According to the field line resonance (FLR) wave model, the substorm-related auroral arc is caused by the field-aligned current carried by FLRs. The FLRs are standing shear Alfven wave structures that are excited along the dipole/quasi-dipole lines of the geomagnetic field. The FLRs (that can cause auroral arc) thread from the Earthward edge of the plasma sheet and link the auroral arc to the plasma sheet region of 6–15 RE. The region is associated with magnetic fluctuations that result from the nonlinear wave-wave interactions of the cross-field current-instability. The instability (excited at the substorm onset) disrupts the cross-tail current which is built up during the growth phase of the substorms and results in magnetic fluctuations. The diversion of the current to polar regions can lead to auroral arc intensification. The current FLR model is based on the amplitude equations that describe the nonlinear space-time evolution of FLRs in the presence of ponderomotive forces exerted by large amplitude FLRs (excited during substorms). The present work will modify the FLR wave model to include the effects arising from magnetic fluctuations that result from current disruption near the plasma sheet (6–15 RE). The nonlinear evolution of FLRs is coupled with the dynamics of plasma sheet through a momentum exchange term (resulting from magnetic fluctuations due to current disruption) in the generalized Ohm's law. The resulting amplitude equations including the effects arising from magnetic fluctuations can be used to study the structure of the auroral arcs formed during substorms. We have also studied the role of feedback mechanism (in a dipole geometry of the geomagnetic field) in the formation of the discrete auroral arc observed on the nightside magnetosphere. The present nonlinear dispersive model (NDM) is extended to include effects arising from the low energy electrons originating from the plasma sheet boundary layer. These electrons increase the ionospheric conductivity in a localized patch and enhance the field-aligned current through a feedback mechanism. The feedback effects were studied numerically in a dipole geometry using the the NDM. The numerical studies yield the magnitude of the field-aligned current that is large enough to form a discrete auroral arc. Our studies provide theoretical support to the observational work of Newell et al. that the feedback instability plays a major role in the formation of the discrete auroral arcs observed on the nightside magnetosphere.

3D Wave Propagation and an Ultra–Low-Frequency Instability in Magnetopause

A model set of equations for the low-frequency electromagnetic perturbations in a magnetized nonuniform plasma is presented. A more convenient and systematic procedure is suggested to treat the fluid equations in order to deduce electrostatic and electromagnetic limits. A general dispersion relation is derived for the waves propagating in 3D under local approximation in nonuniform plasmas, which includes almost all the known modes of cold ion magnetized plasmas in the limit ω < Ω i (where Ω i is the ion cyclotron frequency). Both the limits β ≪ 1 and β ∼ O(1) have been discussed briefly. The shear Alfven waves and electromagnetic ion acoustic waves near ultra low frequency (ULF) range are found unstable in the high β plasma of magnetopause. The results are in complete agreement with the satellite observations.

Comparison of solitary waves and wave packets observed at plasma sheet boundary to results from the auroral zone

The plasma sheet boundary, at distances intermediate between the auroral acceleration region and the regions where energy conversion associated with substorms occurs, is very dynamic with electron and ion beams, field-aligned currents and many types of waves and non-linear structures. We discuss electric and magnetic fields observations of waves occurring at two very different time-scales. At the longer scales (10's of seconds), Wygant (2000) have shown that the observed fields are associated with Alfvenic fluctuations which have their largest electric field normal to the average plane of the plasma sheet (δEN). The simultaneously observed magnetic field perturbations are azimuthal(δBT), resulting in a Poynting flux along the geomagnetic field. The observations are consistent with an incompressible, transverse electromagnetic surface shear Alfven mode at the surface of the plasma sheet boundary. The local δEN/δBT is consistent with VA. The waves provide an intense earthward Poynting flux sufficient to provide the energy necessary for the energization of auroral electron beams. In addition, the large amplitude surface waves are magnetically conjugate (to within 1 degree) to intense auroral emission as determined from the UVI imager, whereas weak aurora are correlated with small amplitude electric fields. Particle detectors simultaneously observe ions flowing up the field line away from the earth, providing further evidence that low altitude acceleration is occurring on conjugate magnetic field lines. At small scales, large amplitude solitary waves are frequently observed, and ion acoustic, lower hybrid, and Langmuir wave packets are sometimes seen. There are clear differences between the solitary wave observations at the plasma sheet boundary and in the low altitude auroral zone. At high altitudes, only electron mode solitary waves have been identified and they occur both in regions of upward and downward field-aligned current, in contrast to the auroral zone where ion solitary waves occur in upward currents and electron solitary waves occur primarily in downward currents. This difference may because the growth of ion acoustic solitons requires that the plasma be strongly magnetized (fce/fpe >>1) which is not the case for the observed high altitude plasma sheet boundary crossings. The high altitude events are associated with a wide variety of electron distribution types, whereas the low altitude events occur in regions of flat-top electron beam distributions. Preliminary evidence suggests that the high altitude events may be BGK electron holes, as has been shown for the low altitude events. For the parameter regime usually observed at high attitudes, electron holes would be stable. In addition, initial work on electron acoustic solitons suggests that these compressive waves would occur only for a limited range of parameters, so they are unlikely to explain the high altitude solitary waves.

Simulation of Nonlinear Waves in a Magnetic Flux Tube near the Quiet Solar Photospheric Network

Recent high-resolution observations from photospheric magnetograms made with the SOHO/Michelson Doppler Imager instrument and Swedish Vacuum Solar Telescope on La Palma showed that magnetic flux tubes in the quiet photospheric network of the solar photosphere are highly dynamic objects with small-scale substructures. We investigate nonlinear waves propagating along a magnetic flux tube in weakly ionized plasmas with high plasma beta ( β 1) by using three-dimensional neutral-MHD equations. We investigate the wave propagation along a magnetic flux tube with weak current for the two cases of uniform density along the flux tube and density inhomogeneity due to solar gravity. It is shown that shear Alfven waves are excited due to localized predominantly rotational perturbations, which might be induced in the quiet photospheric network boundaries. Excited waves with strong upflow of wave energy can propagate only upward along the flux tube when the density inhomogeneity due to the gravity is taken into account. We apply the simulation results to the problem of coronal heating from the quiet photospheric network of the solar photosphere.

ULF resonance structure in the magnetosphere

The cold plasma environment of the Earth's magnetosphere supports the shear Alfven and the fast MHD wave modes. Both these modes encounter natural boundaries in the magnetosphere and can form resonant structures that have the potential of providing routine magnetospheric plasma diagnostic capabilities. The shear Alfven mode has magnetic field guided energy which forms standing field line resonances (FLRs) between conjugate ionospheres while the boundaries for fast mode waves are still unclear although the fast mode turning point as a boundary appears to be undisputed. Excitation mechanism candidates for ULF waves in the magnetosphere must explain the observation of the existence of FLRs almost all the time and at any place (down to L∼1.3) in the dayside magnetosphere. The entry of fast mode wave energy from the bow shock through the magnetopause and down to low latitudes may provide a partial answer. Perhaps FLRs are energised by fast mode resonant structures (cavity/waveguide modes) in addition to “general ULF activity” or “noise” in the system. Despite uncertainties in understanding the excitation of FLRs throughout the magnetosphere, they can be used to estimate the equatorial mass density on high latitudes field lines. Within the plasmasphere, the detection of consecutive FLR harmonics allows the plasma mass density to be determined at discrete, field aligned altitudes without assuming, apriori any density model. This paper reviews current understanding of ULF band, resonant structures in the magnetosphere, emphasizes the ubiquitous nature of FLRs, discusses the structure of fast mode wave resonances and their role in the excitation of FLRs, highlights the diagnostic possibilities available from both the FLR and fast mode resonance structures and identifies some directions for further work.

Parallel electric fields in dispersive shear Alfvén waves in the dipolar magnetosphere

Existing theories do not explain large parallel electric fields that are associated with keV electron precipitation in auroral arcs. The MHD electron response results in an electrical conductivity in the low altitude magnetosphere that is two orders of magnitude greater than is required. We suggest a new mechanism for forming parallel electric fields based on a nonlocal electron response to standing shear Alfvén waves on dipole magnetic fields. Electron trapping is the primary cause of a significant reduction in the collisionless electron conductivity and consequent enhancement of parallel electric fields in the 1–4 mHz frequency range.

Statistical Theory of Anisotropic Magnetohydrodynamic Turbulence: An Approach to Strong Shear Alfven Turbulence by Direct‐Interaction Approximation

We develop a statistical theory of strong, homogeneous, and anisotropic MHD turbulence within a framework of the Eulerian direct-interaction approximation (DIA). Analysis is concentrated on stationary shear Alfven turbulence of which the mean magnetic field is uniform. We assume that timescales of the Alfven wave and the energy cascade in the energy-containing range (ECR) are much larger than the cascade timescale in the inertial range (InR). Thereby, we can obtain DIA equations governing the time evolution of the propagator and the correlation functions in analytically solvable form. The solutions of the DIA equations include an Alfven oscillation factor depending on kz and a relaxation factor depending on k⊥. Here kz and k⊥ are the wavenumbers parallel to and perpendicular to the mean magnetic field, respectively. Applying the result to the DIA equation of spectral energy transfer, we can show high anisotropy of energy cascades; that is, energy cascades to higher kz modes are inhibited, hence only k⊥ cascades occur. Thus, InR extends to much larger k⊥ than ECR while the kz-band broadening is suppressed. Motivated by this, we assume the functional form of the energy spectrum of InR to be E(k⊥,kz) ∝ k-μ⊥δ(kz) and find that μ = 5/2; hence we obtain the corresponding one-dimensional spectrum, k⊥ ∫∞-∞ dkzE(k⊥,kz) ∝ k-3/2⊥. Furthermore, we show the importance of the three-wave resonances for energy cascades in MHD turbulence. Our theory probably suffers spurious convection effects, and therefore so does the resultant energy spectrum. Nevertheless, it can be a good starting point toward refined theories applicable to real astrophysical MHD turbulence.

Dynamics of Alfvén waves in tokamaks

— Theoretical analyses predict that shear Alfven waves may be driven unstable by energetic particles (with energies in the MeV range) in thermonuclear plasmas, e.g., by fusion products. Indeed, these waves have been experimentally observed and – in certain circumstances – found to be responsible of significant energetic particle losses. This fact, together with the possible detrimental effect of these instabilities on the plasma performance – in the perspective of a fusion reactor –, has attracted significant attention on the topic. The present review article is focused on both linear stability and non-linear dynamics of shear Alfven in tokamaks, the presently most successful experimental machines devoted to the study of fusion reactions via magnetic confinement of thermonuclear plasmas. The present theoretical investigation highlights both analytical and numerical approaches to the problem.

Field patterns of Alfven wave resonance cones

One of the fascinating observations from recent rocket and satellite experiments is on the solitary Alfven waves (SAW). SAWs are electromagnetic structures with a spatial width ∼1 km across the Earth's magnetic field B0. The measurements from Freja have revealed that the SAWs are not simply the product of an obliquely propagating plane Alfven wave; instead, they are the radiation (field) patterns of distant Alfven wave sources (AWS) oscillating at frequencies ω &lt; Ωi, the ion cyclotron frequency. The field pattern of an AWS is highly directional in the form of a cone aligned with B0, and with half‐cone angle θc, less than a milliradian or so when ω ≪ Ωi Such radiation patterns are known as resonance cones (RC) or more specifically Alfven wave RC (AWRC), and they are intimately determined by the allowable directions of the group‐velocity vector in the anisotropic plasma. We have studied here the group‐velocity pattern of shear Alfven waves including both warm plasma and inertial effects. It is found that both the kinetic and the inertial Alfven waves show group‐velocity resonance‐cone patterns. Along any direction within the cone there are two group‐velocity vectors having wave vectors with different directions and magnitudes, giving rise to a slow and a fast wave contributing to the propagation. The RC field pattern of a filamentary field‐aligned current source oscillating at frequencies ω &lt; Ωi, is studied. The far‐field pattern shows that within the cone there are two waves propagating at any angle θ &lt; θc as determined by the group‐velocity directions; these waves produce an interference pattern. Near RC surface the interference pattern is given by the Airy function. The scaling laws for the interference pattern and nonlinear effects arising from the pondermotive force are analyzed. Possible applications of the AWRC field pattern, its scaling laws, and the associated nonlinear effects to SAWs are discussed.

Laboratory Observations of Shear Alfvén Waves Launched from a Small Source

Alfven waves are known to be very important in the dynamics of magnetized plasmas in space and in laboratories on earth [1]. They transport electromagnetic energy, may accelerate plasma particles, and are produced in large, dense, magnetized laboratory plasmas or in almost any space plasma environment where there are changes in plasma currents or magnetic field configuration. The experiments described in this Letter are concerned with the shear mode of the Alfven wave launched from sources with transverse scale comparable to the electron collisionless skin depth, d s› cyvped. The shear wave propagates at frequencies below the ion cyclotron frequency svcid, and the associated currents are divergenceless s= j › 0 d with the currents parallel to the background magnetic field, B0, carried by electrons while ions carry the currents transverse to the field through the polarization drift. In a plasma where the ion temperature is much smaller than the electron temperature sTi ? Ted as is typical of the Large Plasma Device (LAPD) discharge plasma, the dispersion relation for shear Alfven waves is [2]

FAST Observations of Inertial Alfven Waves in the Dayside Aurora

Bursts of large amplitude impulsive electric and magnetic field oscillations are a common feature observed from FAST when crossing the dayside auroral oval at altitudes from 1500–2500 km. The oscillations have transverse amplitudes of up to 1 V/m and 100nT and exhibit a parallel electric field component with amplitudes which may be as large as 100mV/m. Calculation of E1/B1 over 100 events yields an average value four times the local Alfven speed. The wave period is usually less than 0.25s with ‘perpendicular wavelengths’ which average to 7.1 electron skin depths (c/ωpe∼80m). Poynting flux calculations indicate predominately downward fluxes with magnitude up 10−2 Wm−2 usually accompanied by a smaller upwards component. Invariably these waves are accompanied by field‐aligned fluxes of down going and sometimes counterstreaming suprathermal electrons. Comparison with theoretical studies indicate that these observations are consistent with the characteristics of a shear Alfven wave with k⟂∼ωpe/c propagating in the inertial dispersive regime and interfering with a reflected component. However the observed large parallel electric field component, if real, has yet to be explained

Spectral Law and Polarization Properties of the Low‐Frequency Waves at the Magnetopause

The magnetic fluctuations, at the magnetopause and in the adjacent magnetosheath, exhibit power law spectra which are very reminiscent of turbulent spectra. In prospect of future modelizations of such a turbulence, new information is brought about the experimental properties of these fluctuations. The power laws spectra previously obtained in the ULF range are shown to hold also in VLF, up to the lower hybrid frequency. Concerning the polarization, 1) the direction with respect to the static magnetic field is shown to be dominantly perpendicular at low frequencies, consistently with Shear Alfven modes in this range, and 2) no right‐hand sense of rotation can be evidenced at frequencies higher than the proton gyrofrequency, although one could expect the fast magnetosonic mode to be dominant in this range. The physical implications of this last observation for the non linear effects at work in the turbulence are briefly discussed.

Auroral density fluctuations on dispersive field line resonances

A model is presented that describes the excitation of density perturbations and parallel electric fields by standing shear Alfvén waves on dipole fields in Earth's magnetosphere. The model includes the effects of electron inertia and gyro‐kinetic dispersion, accounting for field‐aligned variations of the electron and ion temperatures and the ambient plasma density. In a model dipole magnetosphere, it is found that dispersion and nonlinearity determine the depth, spatial structure, and temporal evolution of large‐amplitude density fluctuations near to the polar ionospheres. The characteristics of magnetospheric density cavities and their relationship to auroral luminosity, or field‐aligned currents, is discussed in the context of recent satellite and ground based observations.