Shear Alfven Mode Research Articles

On the coupling of fast and shear Alfvén wave modes by the ionospheric Hall conductance

There are two low frequency, magnetised, cold plasma wave modes that propagate through the Earth’s magnetosphere. These are the compressional (fast) and the shear Alfven modes. The fast mode distributes energy throughout the magnetosphere with the ability to propagate across the magnetic field. Previous studies of coupling between these two modes have often focussed on conditions necessary for mode coupling to occur in the magnetosphere. However, Kato and Tamao (1956) predicted mode coupling would occur for non-zero Hall currents. Recently, the importance of the Hall conductance in the ionosphere for low frequency wave propagation has been studied using one dimensional (1-D) models. In this paper we describe effects of the ionosphere Hall conductance on field line resonance and higher frequency, 0.1–5 Hz waves associated with the Ionospheric Alfven Resonator (IAR). The Hall conductance reduces the damping time of field line resonances and Joule dissipation into the ionosphere. The Hall conductance also couples shear Alfven waves trapped in the IAR to fast mode waves that propagate across the ambient magnetic field in an ionospheric waveguide. This coupling leads to the production of low frequency magnetic fields on the ground that can be observed by magnetometers.

Coherent structures, intermittent turbulence, and dissipation in high-temperature plasmas

An unsolved problem in plasma turbulence is how energy is dissipated at small scales. Particle collisions are too infrequent in hot plasmas to provide the necessary dissipation. Simulations either treat the fluid scales and impose an ad hoc form of dissipation (e.g., resistivity) or consider dissipation arising from resonant damping of small amplitude disturbances where damping rates are found to be comparable to that predicted from linear theory. Here, we report kinetic simulations that span the macroscopic fluid scales down to the motion of electrons. We find that turbulent cascade leads to generation of coherent structures in the form of current sheets that steepen to electron scales, triggering strong localized heating of the plasma. The dominant heating mechanism is due to parallel electric fields associated with the current sheets, leading to anisotropic electron and ion distributions which can be measured with NASA's upcoming Magnetospheric Multiscale mission. The motion of coherent structures also generates waves that are emitted into the ambient plasma in form of highly oblique compressional and shear Alfven modes. In 3D, modes propagating at other angles can also be generated. This indicates that intermittent plasma turbulence will in general consist of both coherent structures and waves. However, the current sheet heating is found to be locally several orders of magnitude more efficient than wave damping and is sufficient to explain the observed heating rates in the solar wind.

Low frequency collective modes in dense relativistic-degenerate strongly coupled plasma

It is shown that low frequency electrostatic ion mode couples with electromagnetic shear Alfven mode in a dense plasma containing strongly coupled non-degenerate ion and relativistic degenerate electron fluids. By employing the appropriate fluid equations, a linear dispersion equation is obtained which shows modifications due to ion correlations and electron relativistic degeneracy. The results are discussed in the ultra-relativistic and weak-relativistic limits and implications of the results in dense degenerate plasmas of astrophysical origin (e.g., white dwarf stars) are pointed out with possible consequences.

Coupled modes in magnetized dense plasma with relativistic-degenerate electrons

Low frequency electrostatic and electromagnetic waves are investigated in ultra-dense quantum magnetoplasma with relativistic-degenerate electron and non-degenerate ion fluids. The dispersion relation is derived for mobile as well as immobile ions by employing hydrodynamic equations for such plasma under the influence of electromagnetic forces and pressure gradient of relativistic-degenerate Fermi gas of electrons. The result shows the coexistence of shear Alfven and ion modes with relativistically modified dispersive properties. The relevance of results to the dense degenerate plasmas of astrophysical origin (for instance, white dwarf stars) is pointed out with brief discussion on ultra-relativistic and non-relativistic limits.

Relationship between ULF wave mode mix, equatorial electric fields, and ground magnetometer data

[1] The magnetized plasma of near-Earth space supports the shear and fast Alfven, ultralow-frequency (ULF; 1–100 mHz), magnetohydrodynamic wave modes. The fast mode may propagate across the magnetic field, spreading ULF wave energy throughout the magnetosphere, and couple with the shear Alfven mode to form field line resonances (FLRs). The FLR electric field in the magnetosphere may have sufficiently large amplitudes to energize electrons and enhance radiation belt particle diffusion rates. Ozeke et al. (2009) recently described a technique that related the observed north-south ULF magnetic component at the ground, bνg, with the radial electric field component in the equatorial plane of the magnetosphere, eνeq, via the fields in the ionosphere. In this paper we use a fully coupled ULF wave model to determine the ratio eνeq/bνg for a 5 mHz FLR formed at high latitudes. We find that Ozeke et al. (2009) underestimated the ULF wave magnetic field on the ground which varies with ionosphere Hall conductance. This difference is found to be caused by assuming a decoupled wave mode model for the ionosphere fields. Any relationship that involves ULF wavefields in the ionosphere must include the effects of ULF wave mode mixing.

Observations of Pi2 pulsations by the Wallops HF radar in association with substorm expansion

[1] We report the first sub-auroral Pi2 pulsations observations by a SuperDARN type HF radar. The Wallops radar LOS measurements obtained at ionospheric altitudes, ∼56° magnetic latitude, 23 hour magnetic local time, are shown to be highly correlated with ground magnetic field perturbations obtained at Ottawa. The period of the Pi2 pulsations is 118 s and the m-number is ∼2.3. The availability of both ionospheric LOS measurements and ground based magnetic field perturbations enable us to constrain the properties of the wave. A predominantly shear Alfven mode wave is able to explain both the amplitude and phase relations of our observations. Although the solar wind dynamic pressure is fairly stable the IMF Bz is highly variable thereby preventing an unambiguous identification of a solar wind trigger. Rather, magnetotail observations of a clear dipolarization and an intensification of the auroral westward electrojet producing a modest ground magnetic bay indicate that the wave is associated with the onset of a weak substorm.

Radial dependence of magnetohydrodynamic continuum modes for an incompressible plasma

The spatial structure of the magnetohydrodynamic shear Alfven and cusp continuum modes in axisymmetric toroidal geometry is analyzed for an incompressible plasma. The normal component ξ ψ of the plasma displacement is found to have an oscillatory type of singularity, ξ ψ ∼ (ψ - ψ 0 ) δ ∼ sin(|δ|ln|ψ - ψ 0 | + const), or, for example, in the case of up/down symmetry, a purely logarithmic behavior. This result was also obtained in the more general case of a compressible plasma (Salat, A. and Tataronis, J. A. 1999 Phys. Plasmas 6, 3207). However, in that work the incompressible limit could not be taken because the continuum equations were written in terms of a variable that becomes ill-defined in the limit. The present ab initio derivation shows that, in general, the incompressible limit in the previous work, γ → ∞, where γ is the ratio of the specific heats, does give the correct spatial dependence. Furthermore, we prove that it is possible to recover the oscillatory type of singularity for the cylindrical screw pinch from the logarithmic singularity of an up/down symmetric torus.

A hall dynamo effect driven by two-fluid tearing instability

A quasi-linear prediction of the two-fluid dynamo effect is analyzed with the use of tearing eigenfunctions obtained for force-free equilibrium. In the range of parameters of practical interest, the basic shear Alfven mode is decoupled from fast compressional Alfven and slow magneto-acoustic modes. Kinetic Alfven modification of the shear Alfven wave drives an instability with a growth rate ∝δ1/3ρ s 2/3 , where δ is the electron skin depth and ρs is the ion-sound gyroradius. A net dynamo effect parallel to the magnetic field is calculated at ρ s ≫δ for large values of the stability factor \(\Delta '\rho _s^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} \delta ^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} \gg 1\). The dynamo effect caused by the j×B Hall term dominates the contribution from the v×B term (the alpha effect) by a factor ∝(ρs/δ)2 in the narrow electron layer, while in the broader ion layer these contributions are comparable. The results are compared with the case of a strong guiding field where ρ s ≪δ and the tearing instability is described by resistive MHD.

The phase structure of very low latitude ULF waves across dawn

Ultralow frequency (ULF) waves at the geomagnetic equator are studied by using a small magnetometer array and a one‐dimensional electromagnetic wave model. Most ULF waves observed at low latitudes have been associated with shear Alfven mode hydromagnetic resonances in the plasmasphere. Near the equator it is difficult to excite these resonances, and the wave activity is attributed to fast mode waves. The phase difference data recorded at longitudinally spaced, equatorial magnetometers shows a marked change around dawn when one station is sunlit while the other is still in darkness. The phase structure with latitude also shows large phase shifts near the equator, in agreement with previous studies. A model of ULF wave propagation through the equatorial ionosphere is presented and used to compare with the observed amplitude and phase properties. It is shown that the observed frequencies are in the vicinity of the wave cutoff frequency where the phase structure becomes complicated. For frequencies above the cutoff, the phase structure across dawn is directly related to dawn‐associated changes in electron density in the ionosphere.

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.

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.

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.

Convergence of an unconditionally stable semi-implicit scheme for linear incompressible MHD equations

Semi-implicit methods have been introduced by Harned et al. to solve magneto-hydrodynamic equations (MHD) with numerical schemes which are unconditionally stable with respect to fast and shear Alfven modes. They prove the stability of their scheme for linear ideal MHD equations with periodic boundary conditions, and with some technical assumptions. In this paper, we prove convergence of the numerical approximation (time discretization), under the same hypothesis, but looking for solutions on any regular bounded open set of R 3 with appropriate boundary conditions, and introducing finite resistivity and viscosity.

Simulation of Alfven-wave-resonant-particle interaction

New numerical simulations are presented on the self-consistent dynamics of energetic particles and a set of unstable discrete shear Alfven modes in a. tokamak. The code developed for these simulations has been previously tested in simulations of the bump-on-tail instability model. The code has a Hamiltonian structure for the mode-particle coupling, with the superimposed wave damping, particle source and classical relaxation processes. In the alpha-particle-Alfven-wave problem, we observe a transition from a single mode saturation to mode overlap and global quasi-linear diffusion, which is qualitatively similar to that observed in the bump-on-tail model. A considerable enhancement in the wave energy due to the resonance overlap is demonstrated. The effect of global diffusion on the energetic particle losses is also demonstrated

Relative intensity of toroidal and compressional Pc 3‐4 wave power in the dayside outer magnetosphere

Active Magnetosphere Particle Tracer Explorers/Charge Composition Explorer (AMPTE/CCE) magnetic field data are used to study the excitation mechanism of local toroidal harmonic field line resonances (FLRs). Enhanced toroidal fluctuations can exhibit either clear harmonic resonance signatures or broadband power enhancements. This may indicate that two different processes are operating. To assess the differences between toroidal harmonic and broadband events statistically, we examined data from 56 dayside orbits and selected intervals that displayed either clear toroidal harmonics (Harmonic) or primarily broadband (Broadband) toroidal power. The resulting database consisted of 878 intervals, each 26.5 min long. Spectral power was integrated from 10 to 50 mHz to obtain radial, PR, toroidal (eastward), PE, and compressional (northward), PN, power levels. Absolute toroidal power levels were comparable for both Harmonic and Broadband events, ranging from 0.1 to 20 nT² for both categories. To minimize the influence of activity variations in power level, we examined power ratios, for example, PE/PN, rather than the absolute power levels. The Harmonic events have an average PE/PN of 2.28±0.07, whereas PE/PN averages 1.51±0.05 for the Broadband events. The average radial power is essentially equal to the compressional power: average PR/PN is 1.04±0.04 for Harmonic and 1.00±0.04 for Broadband events. That toroidal power is enhanced for the Broadband as well as Harmonic events suggests that resonance effects occur in the Broadband events but that the resonances are not sufficiently developed to be apparent as harmonics in power spectra. For the Harmonic events PE/PN decreases with L, whereas for Broadband events PE/PN is constant or rises with L, also suggesting that their sources are different. There are three ways to interpret these results. First, one can attribute the Harmonic events to coupling of compressional modes to local FLRs. Since the observed FLRs occur over a continuous range in frequency, one must assume, however, that the cavity eigenfrequency spectrum is also nearly continuous, that is, the number of eigenmodes is very large. The Broadband events are not readily accounted for in the cavity mode picture, however. Alternately, if the magnetospheric system is considered to be a relatively poor global resonator, low Q, due to Joule dissipation and/or a Poynting flux directed out of the cavity, there are two possible explanations. In the first low‐Q scenario, harmonic toroidal fluctuations are driven by the high‐latitude entry mechanism of Engebretson et al. (1991), whereas the Broadband events are due to coupling of propagating compressional waves with the shear Alfven mode. The second low‐Q scenario attributes both Harmonic and Broadband events to local FLR excitation by propagating compressional waves, but the Harmonic events correspond to local FLRs excited by longer wavelength perturbations at the magnetopause, yielding better coupling to the local FLRs and hence more fully developed resonance signatures.

Radial energy transport by magnetospheric ULF waves: Effects of magnetic curvature and plasma pressure

The “radial” transport of energy by internal ULF waves, stimulated by dayside magnetospheric boundary oscillations, is analyzed in the framework of one‐fluid magnetohydrodynamics. (The term radial is used here to denote the direction orthogonal to geomagnetic flux surfaces.) The model for the inhomogeneous magnetospheric plasma and background magnetic field is axisymmetric and includes radial and parallel variations in the magnetic field, magnetic curvature, plasma density, and low but finite plasma pressure. The radial mode structure of the coupled fast and intermediate MHD waves is determined by numerical solution of the inhomogeneous wave equation; the parallel mode structure is characterized by a WKB approximation. Ionospheric dissipation is modeled by allowing the parallel wave number to be complex. For boundary oscillations with frequencies in the range from 10 to 48 mHz, and using a dipole model for the background magnetic field, the combined effects of magnetic curvature and finite plasma pressure are shown to (1) enhance the amplitude of field line resonances by as much as a factor of 2 relative to values obtained in a cold plasma or box‐model approximation for the dayside magnetosphere; (2) increase the energy flux delivered to a given resonance by a factor of 2–4; and (3) broaden the spectral width of the resonance by a factor of 2–3. The effects are attributed to the existence of an “Alfvén buoyancy oscillation,” which approaches the usual shear mode Alfvén wave at resonance, but unlike the shear Alfvén mode, it is dispersive at short perpendicular wavelengths. The form of dispersion is analogous to that of an internal atmospheric gravity wave, with the magnetic tension of the curved background field providing the restoring force and allowing radial propagation of the mode. For nominal dayside parameters, the propagation band of the Alfvén buoyancy wave occurs between the location of its (field line) resonance and that of the fast mode cutoff that exists at larger radial distances.

Shear Alfven wave excitation by direct antenna coupling and fast-wave resonant-mode conversion

Antenna coupling to the shear Alfven wave by both direct excitation and fast-wave resonant-mode conversion is modelled analytically for a plasma with a one-dimensional linear density gradient. We demonstrate the existence of a shear Alfven mode excited directly by the antenna. For localized antennae, this mode propagates as a guided beam along the steady magnetic field lines intersecting the antenna. Shear Alfven wave excitation by resonant-mode conversion of a fast wave near the Alfven resonance layer is also demonstrated and we prove that energy is conserved in this process. We compare the efficiency of these two mechanisms of shear Alfven wave excitation and present a simple analytical formula giving the ratio of the coupled powers. Finally, we discuss the interpretation of some experimental results.

Destabilization of the shear Alfven mode by alpha particles and other high energy ions

Toroidal Alfven eigenmode (TAE) and elliptical Alfven eigenmode (EAE) instabilities in plasmas with high energy ions are considered in the context of local theory. The instability growth rate is found for cases when waves are excited by alpha particles or by ions produced as a result of neutral injection or RF heating. Electron and ion Landau damping due to the toroidal sideband wave-particle interaction is also calculated. The electron damping rate is shown to be much lower than the generally accepted value. The TAE instability observed in the experiment with neutral beam injection on TFTR is analysed and the principal experimental features of TAE instability are explained

Nonresonant resistive dissipation of compressible magnetohydrodynamic waves

view Abstract Citations (25) References (15) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Nonresonant Resistive Dissipation of Compressible Magnetohydrodynamic Waves Califano, Francesco ; Chiuderi, Claudio ; Einaudi, Giorgio Abstract The effect of compressibility on the propagation and resistive dissipation properties of magnetohydrodynamic waves in nonuniform media is studied by using a normal mode analysis. The paper concentrates on wave models for which the resistivity acts over the entire system, thus excluding localized resonant absorption. The wave modes in nonhomogeneous situations are identified in term of their familiar homogeneous counterparts and it is shown that only the shear Alfven and slow magnetosonic modes survive in the resistive regime. The most promising heating agents in the astrophysical context are shown to be the shear Alfven waves that behave almost incompressibly. Publication: The Astrophysical Journal Pub Date: May 1992 DOI: 10.1086/171306 Bibcode: 1992ApJ...390..560C Keywords: Compressibility; Magnetohydrodynamic Waves; Wave Attenuation; Wave Propagation; Analytic Functions; Magnetosonic Resonance; Mathematical Models; Propagation Modes; Shear; Plasma Physics; MAGNETOHYDRODYNAMICS: MHD full text sources ADS |

Excitation of high-n toroidal shear alfven mode due to alpha-particle ripple losses in tokamaks

The alpha-particle effects on high-n toroidal shear Alfven mode are investigated analytically. The mode can be driven to unstable when the alpha-particles have an anisotropic distribution function due to ripple losses in tokamaks. The growth rates of the instability in both "fast" and "slow" plasma heating cases are calculated, and the conditions for the excitation of the modes are also studied.