This paper presents a comprehensive review of dispersive Alfven waves in space and laboratory plasmas. We start with linear properties of Alfven waves and show how the inclusion of ion gyroradius, parallel electron inertia, and finite frequency effects modify the Alfven wave properties. Detailed discussions of inertial and kinetic Alfven waves and their polarizations as well as their relations to drift Alfven waves are presented. Up to date observations of waves and field parameters deduced from the measurements by Freja, Fast, and other spacecraft are summarized. We also present laboratory measurements of dispersive Alfven waves, that are of most interest to auroral physics. Electron acceleration by Alfven waves and possible connections of dispersive Alfven waves with ionospheric-magnetospheric resonator and global field-line resonances are also reviewed. Theoretical efforts are directed on studies of Alfven resonance cones, generation of dispersive Alfven waves, as well their nonlinear interactions with the background plasma and self-interaction. Such topics as the dispersive Alfven wave ponderomotive force, density cavitation, wave modulation/filamentation, and Alfven wave self-focusing are reviewed. The nonlinear dispersive Alfven wave studies also include the formation of vortices and their dynamics as well as chaos in Alfven wave turbulence. Finally, we present a rigorous evaluation of theoretical and experimental investigations and point out applications and future perspectives of auroral Alfven wave physics.

/pdf/small-scale-alfvenic-structure-in-the-aurora-3hopdgfj09.pdf

Small scale alfvénic structure in the aurora

Kinetic Alfven waves have been invoked is association with auroral currents and particle acceleration since the pioneering work of Hasegawa. However, to date, no work has considered the dispersion relation including the full kinetic effects for both electrons and ions. Results from such a calculation are presented, with emphasis on the role of Landua damping in dissipating Alfven waves which propogate from the warm plasma of the outer magnetosphere to the cold plasma present in the ionosphere. It is found that the Landua damping is not important when the perpendicular wavelength is larger than the ion acoustic gyroradius and the electron inertial length. In addition, ion gyroradius effects lead to a reduction in the Landua damping by raising the parallel phase velocity of the wave above the electron thermal speed in the short perpendicular wavelength regime. These results indicate that low-frequency Alfven waves with perpendicular wavelengths greater than the order of 10 km when mapped to the ionosphere will not be significantly affected by Landau damping. While these results based on the local dispersion relation, are strictly valid only for short parallel wavelength Alfven waves, they do give an indication of the importance of Landua damping for longer parallel wavelengthmore » waves such as field line resonances. 26 refs., 5 fig.« less

On the kinetic dispersion relation for shear Alfvén waves

A general stability analysis is performed for the Kelvin-Helmholtz instability in sheared magnetohydrodynamic flow of finite thickness in a compressible plasma. The analysis allows for arbitrary orientation of the magnetic field B0, velocity flow v0, and wave vector k in the plane perpendicular to the velocity gradient, and no restrictions are imposed on the sound or Alfven Mach numbers. The stability problem is reduced to the solution of a single second-order differential equation, which includes a gravitational term to represent coupling between the Kelvin-Helmholtz mode and the interchange mode. In the incompressible limit it is shown that the Kelvin-Helmholtz mode is completely stabilized for any velocity profile as long as the condition is satisfied, where V0 is the total velocity jump across the shear layer. Numerical results are obtained for a hyperbolic tangent velocity profile for the transverse (B0 ⊥ v0) and parallel (B0∥v0) flow configurations. Only modes with kΔ < 2 are unstable, where Δ is the scale length of the shear layer. The fastest growing modes occur for kΔ ∼ 0.5-1.0. Compressibility and a magnetic field component parallel to the flow are found to be stabilizing effects. For the transverse case, only the fast magnetosonic mode is destabilized, but if k · B0 ≠ 0, the instability contains Alfven-mode and slow-mode components as well. The Alfven component gives rise to a field-aligned current inside the shear layer. In the parallel case, both Alfven and slow magnetosonic components are present, with the Alfven mode confined inside the shear layer. The results of the analysis are used to discuss the stability of sheared plasma flow at the magnetopause boundary and in the solar wind. At the magnetopause boundary, the fastest growing Kelvin-Helmholtz mode has a frequency of 0 (V0/2Δ), which overlaps with the frequency range of geomagnetic pulsations (Pc 3-5). It is suggested that the MHD Kelvin-Helmholtz instability could serve as a dynamo process driving small-scale field-aligned currents in the presence of the sheared plasma flow in the magnetosphere.

Nonlocal stability analysis of the MHD Kelvin-Helmholtz instability in a compressible plasma. [solar wind-magnetosphere interaction]

A new scenario of AMPTE/CCE observation of substorm onset and current disruption and the corresponding physical processes is presented. Toward the end of late growth phase plasma beta increases to greater than or equal to 50 and a low-frequency instability with a wave period of 50-75 seconds is excited and grows exponentially to a large amplitude at the onset of current disruption. At the current disruption onset, higher-frequency instabilities are excited so that the plasma and electromagnetic magnetic field form a turbulent state. Plasma transport takes place to modify the ambient plasma pressure and velocity profiles so that the ambient magnetic field recovers from a tail-like geometry to a more dipole-like geometry. To understand the excitation of the low-frequency global instability, a new theory of kinetic ballooning instability (KBI) is proposed to explain the high critical beta threshold (the high critical beta threshold is greater than or equal to 50) of the low-frequency global instability observed by the AMPTE/CCE. The stabilization is mainly due to kinetic effects of trapped electrons and finite ion Larmor radii which give rise to a large parallel electric field and hence a parallel current that greatly enhances the stabilizing effect of field line tension tomore » the ballooning mode. As a result, the high critical beta threshold for excitation of KBI is greatly increased over the ideal-MHD ballooning instability threshold by greater than or equal to O(10 exp 2). The wave-ion magnetic drift resonance effect produces a perturbed resonant ion velocity distribution with a duskward velocity roughly equal to the average ion magnetic (gradient B and curvature) drift velocity. Higher-frequency instabilities such as cross-field current instability (CCI) can be excited by the additional velocity space free energy associated with the positive slope in the perturbed resonant ion velocity distribution in the current disruption phase.« less

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1998GL900093

Kinetic ballooning instability for substorm onset and current disruption observed by AMPTE/CCE

First results from a high-resolution three-dimensional nonlinear numerical study of the kink oscillation are presented. We show in detail the development of a shear instability in an untwisted line-tied magnetic flux tube. The instability produces significant deformations of the tube boundary. An extended transition layer may naturally evolve as a result of the shear instability at a sharp transition between the flux tube and the external medium. We also discuss the possible effects of the instability on the process of resonant absorption when an inhomogeneous layer is included in the model. One of the implications of these results is that the azimuthal component of the magnetic field of a stable flux tube in the solar corona, needed to prevent the shear instability, is probably constrained to be in a very specific range.

Nonlinear instability of kink oscillations due to shear motions

The nonlinear dynamics of a shear flow and its subsequent evolution in the equatorial plane of the inner plasma sheet is studied. A linear analysis of the ideal MHD equations reveals a hybrid vortex instability which appears because of the coupling of Kelvin-Helmholtz (KH) and Rayleigh-Taylor instabilities. The hybrid vortex mode grows faster than a KH mode, extracts ambient potential energy, and leads to vortex cells that have a larger spatial extent than a simple KH vortex. In the nonlinear stage, vortices become surge-like and may destroy the shear flow region. The relevance of this model to vortex generation and auroral arc intensifications at the inner edge of the plasma sheet is discussed.

/pdf/coupling-of-shear-flow-and-pressure-gradient-instabilities-58z1bxfd4p.pdf

Coupling of shear flow and pressure gradient instabilities

Magnetohydrodynamic, field line resonances in the Earth's magnetosphere can have very large velocity shears and field-aligned currents. Auroral radar measurements of high-latitude resonances indicate that the velocities associated with the resonances in the E and F regions are often substantially greater than 1 km/s, and that the frequencies are in the interval from 1 to 4 mHz. Assuming that these resonances are oscillating at the fundamental mode frequency, and mapping these velocity fields along magnetic field lines to the equatorial plane shows that the velocity shears in the equatorial plane are of the order of 200 km/s over a radial distance of less than 2000 km (the amplitude of the velocity fluctuations is 100 km/s). Using a three-dimensional magnetohydrodynamic computer simulation code, we show that the resonances evolve through the development of Kelvin-Helmholtz instabilities near the equatorial plane. Within this framework, the instability is taking place on dipole magnetic field lines, and the resonances form a standing shear Alfven wave field due to the boundary conditions which must be satisfied at the polar ionospheres. We find that the nonlinear evolution of the Kelvin-Helmholtz instability leads to the propagation of vorticity from the equatorial plane to the polar ionosphere and that the vorticity leads ultimately to the dissipation of the resonance. This occurs within a quarter wave period of the shear Alfven field associated with the resonances.

/pdf/the-nonlinear-evolution-of-field-line-resonances-in-the-3dh2o7irke.pdf

The nonlinear evolution of field line resonances in the Earth's magnetosphere

A three-dimensional compressible resistive magnetohydrodynamic simulation code, with inclusion of the fully generalized Ohm's law, has been developed to study the nonlinear evolution of field line resonances in Earth's magnetosphere. A simple Cartesian box model of an inhomogeneous plasma with straight geomagnetic field lines is used, and the Alfven velocity increases monotonically from the magnetopause boundary layer toward Earth. A monochromatic fast mode compressional oblique wave is applied from the direction of the magnetopause boundary layer, pumping energy into the magnetosphere. The fast mode wave, while propagating toward Earth, is partially reflected at the turning point (located at radial distances between 8 and 10 RE in the equatorial plane) and then couples to shear Alfven waves, leading to the formation of large-amplitude field line resonances near Earth. The field line resonances are observed to narrow to several electron inertia lengths within several wave periods of the driver wave, and electron inertial effects become important at this stage. Final profiles near the resonance are very similar to Airy functions, indicating that electron inertial effects become important before possible nonlinear effects. The electron inertial effects lead to oscillating parallel electric field which might be potential accelerators for electrons in some types of auroral arcs.

https://era.library.ualberta.ca/items/e9dad511-54bb-459b-ab8b-84b0aa97f749/view/d471e584-f687-4cb6-b775-9b2343a3325e/JGRSP_99_A6_11265.pdf

Electron inertial effects on geomagnetic field line resonances

We present theory and numerical simulations of strong nonlinear effects in standing shear Alfven waves (SAWs) in the Earth`s magnetosphere, which is modeled as a finite size box with straight magnetic lines and (partially) reflecting boundaries. In a low beta plasma it is shown that the ponderomotive force can lead to a large-amplitude SAW spatial harmonic generation due to nonlinear coupling between the SAW and a slow magnetosonic wave. The nonlinear coupling leads to secularly growing frequency shifts, and in the case of driven systems, nonlinear dephasing can lead to saturation of the driven wave fields. The results are discussed on the context of their possible relevance to the theory of standing ionospheric cavity wave modes and field line resonances in the high-latitude magnetosphere.

/pdf/nonlinear-standing-shear-alfven-waves-in-the-earth-s-28toxjkbua.pdf

Nonlinear standing shear Alfven waves in the Earth`s magnetosphere

Using a compressible, three-dimensional resistive magnetohydrodynamic (MHD) computer simulation code, we examine the evolution of standing wave field line resonances (FLRs) in the nightside of the Earth's magnetosphere. The MHD code that is used allows for a full nonlinear description and enables us to follow the evolution of FLRs to large amplitude. We take as our MHD driver a source of fast-mode waves incident from the direction of the magnetopause boundary layer. The ambient density and geomagnetic field are such that the fast mode waves have turning points at radial distances between 8 and 10 Re in the equatorial plane. The fast-mode angle of incidence is selected such that tunneling of the wave from the turning point to the resonance point leads to resonant mode conversion of energy from congressional waves to shear Alfven waves. We determine whether kinetic effects or finite electron inertia effects are likely to become important during the nonlinear evolution of the FLRs. For this to occur, the FLRs must narrow to the point where the radial scale size is several ion gyroradii or less or to the point where the equatorial width of the resonance maps to several electron inertia lengths in the polar magnetosphere. It is shown that the resonances do narrow to the point where kinetic effects are likely to be important and that, in contrast to estimates in previously published work indicating that narrowing would take hundreds of wave cycles, this occurs within a few cycles of the driver field, consistent with observations of FLRs in the high-latitude ionosphere.

https://era.library.ualberta.ca/items/3e78a10d-f736-48c6-8921-9ececfe845a4/view/15eec243-c12c-4c9c-87aa-4cd64ea24c25/JGRSP_98_A12_21341.pdf

P. Frycz

Papers

Coupling of shear flow and pressure gradient instabilities

The nonlinear evolution of field line resonances in the Earth's magnetosphere

Electron inertial effects on geomagnetic field line resonances

Nonlinear standing shear Alfven waves in the Earth`s magnetosphere

Simulations of driven field line resonances in the Earth's magnetosphere