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Report presents theoretical study of parametric instabilities of finite-amplitude, circularly-polarized Alfven waves in plasma having pressure anisotropy. Waves studied are observed in solar wind and conjectured to exist in interstellar and other cosmic plasmas.
This paper presents results from the first statistical study of interplanetary directional discontinuities at high heliographic latitudes. Ulysses data showed that the rate of occurrence of interplanetary discontinuities (ROIDs) increased dramatically from the ecliptic plane to high (-80 degrees) heliographic latitudes. The high speed streams included Alfven waves.
We consider the dispersion relation for the parametric instabilities of large-amplitude circularly polarized Alfven waves propagating parallel to the ambient magnetic field. A linear perturbation analysis is employed, and the perturbations are taken to propagate along the ambient field. We present an analysis based on Floquet's theorem. The result is a hierarchy of dispersion relations. However, all the dispersion relations are found to be equivalent to the one obtained via the standard analysis; the differences between them are due only to how ca and k are defined. Thus we conclude that physically there is really only one dispersion relation, namely the 'electrostatic dispersion relation', which is in agreement with earlier works. However, we disagree with Vinas and Goldstein (1991), who obtained additional dispersion relations which they have called the 'electromagnetic dispersion relations'. Their additional dispersion relations are a consequence of first truncating the dispersion relation for obliquely propagating perturbations and then taking the limit of parallel-propagating perturbations.
The non-WKB propagation of Alfven waves has been studied either for harmonic waves, or in terms of the evolution of power spectra. Here we present analytical and numerical solutions for the propagation of pulses, the goal being to understand how waves reflect in a smoothly varying medium. We here limit our discussion to a radial magnetic field. If we launch an outward-propagating delta function, it leaves behind an inward-propagaing signal which is roughly a square wave whose amplitude is proportional to the area under the initial pulse. The inward-propagating signal also reflects, producing an outward propagating pulse which is roughly triangular in shape and which grows with time. These signals also oscillate if v is less than v(A), but they grow if v is greater than v(A). The result reported by us earlier, that the 'ingoing Elsasser variable' can have outgoing phase, is now understood to be a consequence of interference. The inward-propagating signal depends to lowest order on the integral of the outgoing waves which have preceded it. Thus the ingoing signal can be expected to develop as a random walk. This will affect the radial evolution of cross-helicity in the solar wind.
The rate of occurrence of interplanetary discontinuities (ROID) is examined using Ulysses magnetic field and plasma data from 1 to 5 AU radial distance from the Sun and at high heliospheric latitudes. It is found that there are two regions in interplanetary space where the ROID is high: in stream-stream interaction regions and in Alfven wave trains.
The Kelvin-Helmholtz (KH) instability of magnetohydrodynamic surface waves at the low latitude boundary layer is examined using both an eigenfrequency analysis and a time-dependent wave simulation. The analysis includes the effects of sheared flow and Alfven velocity gradient. When the magnetosheath flows are perpendicular to the ambient magnetic field direction, unstable KH waves that propagate obliquely to the sheared flow direction occur at the sheared flow surface when the Alfv\'en Mach number is higher than an instability threshold. Including a shear transition layer between the magnetosphere and magnetosheath leads to secondary KH waves (driven by the sheared flow) that are coupled to the resonant surface Alfven wave. There are remarkable differences between the primary and the secondary KH waves including wave frequency, the growth rate, and the ratio between transverse and the compressional component. The secondary KH wave energy is concentrated near the shear Alfven wave frequency at the magnetosheath with a lower frequency than the primary KH waves. Although the growth rate of the secondary KH waves is lower than the primary KH waves, the threshold condition is lower, so it is expected that these types of waves will dominate at lower Mach number. Because the transverse component of the secondary KH waves is stronger than the primary KH waves, more efficient wave energy transfer from the boundary layer to the inner magnetosphere is also predicted.
Phase mixing has been a popular theoretical mechanism invoked to dissipate the photospheric plane shear Alfven waves hypothesized to penetrate up into the coronal hole and solar wind, thereby maintaining the expanding coronal gas at 1.5 million K and serving as the principal energy source for the solar wind. However, phase mixing requires an ignorable coordinate, which is not available in the presumably filamentary coronal hole. The filamentary density and temperature of the coronal hole couple the waves into a coordinated mode with a unique phase velocity omega/k, which provides the other popular theoretical mechanism, viz, resonant absorption where the local Alfven speed C is equal to omega/k. This provides coronal heating at radial distances O(10 solar radii), where it serves to accelerate the solar wind to high velocity. But it does not provide the principal heat input in the first 1-2 solar radii, required by Withbroe's (1988) analysis of the observed structure of the coronal hole.
The three-dimensional nonlinear simulation of the evolution of a kinetic Alfven wave is presented for simple boundary conditions that resemble those of a discrete auroral breakup arc. The model used is a variant of the reduced megnetohydrodynamic description that includes, in addition, the important dispersive effect of electron inertia. It is found that with a 'generator' boundary condition corresponding to a current generator and a fully conducting 'load' boundary, the wave evolves three-dimensionally through a combination of shear flow and collisionless tearing mode instability.
The possibility that the strong heating produced at temperature-minimum levels during solar flares is due to resistive dissipation of Alfven waves generated by the primary energy release process in the corona is studied. It is shown how, for suitable parameters, these waves can carry their energy essentially undamped into the temperature-minimum layers and can then produce a degree of heating consistent with observations.
A previously developed Vlasov theory is used here to study the role of resonant particle and other kinetic effects on Alfven wave nonlinearity. A hybrid fluid-Vlasov equation approach is used to obtain a modified version of the derivative nonlinear Schroedinger equation. The differences between a scalar model for the plasma pressure and a tensor model are discussed. The susceptibilty of the modified nonlinear wave equation to modulational instability is studied. The modulational instability normally associated with the derivative nonlinear Schroedinger equation will, under most circumstances, be restricted to left circularly polarized waves. The nonlocal term in the modified nonlinear wave equation engenders a new modulational instability that is independent of beta and the sense of circular polarization. This new instability may explain the occurrence of wave packet steepening for all values of the plasma beta in the vicinity of the earth's bow shock.
The objective of this project is to understand the damping, reflection, transmission, and phase mixing of Alfven waves in inhomogeneous plasmas by performing experiments on the Large Plasma Device (LAPD).
Transverse LF oscillations in geomagnetic field observed during January 1967, noting possibility of being second harmonic of magnetospheric standing Alfven waves
The nature of turbulent cascades arising from the parametric instabilities of a monochromatic field-aligned large-amplitude circularly polarized Alfven wave is investigated via direct numerical simulation for the case of low plasma Beta and no wave dispersion. The magnetohydrodynamic code permits nonlinear couplings in the parallel direction to the ambient magnetic field and one perpendicular direction. Compressibility is included in the form of a polytropic equation of state. Anisotropic turbulent cascades, similar to those found in early incompressible two-dimensional simulations, occur after nonlinear saturation of the parallel propagating decay instability. The turbulent spectrum can be divided into three regimes: the lowest wave numbers are dominated by lower sideband remnants of the parametric process, intermediate wave numbers display nearly incompressible dynamics, and the highest wave numbers are dominated by acoustic turbulence.
Correlation coefficients between radial components of interplanetary magnetic field and solar wind velocity from Mariner 5 data due to Alfven waves
The effects of wave amplification (by streaming particle distributions) and damping (by ion-cyclotron resonance absorption) on the nonlinear evolution of Alfven waves are investigated theoretically. The results of numerical simulations based on the derivative-Schroedinger-equation model of Spangler and Sheerin (1983 and 1985) are presented graphically and characterized in detail, with an emphasis on astrophysical applications. Three phases of wave-packet evolution (linear, nonlinear-saturation, and postsaturation quasi-steady) are identified, and nonlinearity is found to transfer wave energy from growing or amplified wavenumbers to wavenumbers affected by damping. It is pointed out that although there are similarities between the solitonlike pulses predicted by the simulations and short-wavelength shocklet structures observed in the earth bow shock, the model does not explain why low-frequency waves stop growing in the vicinity of the bow shock.
Stationary solutions of the derivative nonlinear Schroedinger equation are discussed and classified by using a pseudopotential formulation. The solutions consist of a rich family of nonlinear Alfven waves and solitons with parallel and oblique propagation directions. Expressions for the envelope and the phase of nonlinear waves with periodic envelope modulation, and 'hyperbolic' and 'algebraic' solitons are given. The propagation angle for the slightly modulated elliptic, periodic waves and for oblique solitons is evaluated.
This paper presents a brief report on properties of the parametric decay and modulational, filamentation, and magnetoacoustic instabilities of a large amplitude, circularly polarized Alfven wave. We allow the daughter and sideband waves to propagate at an arbitrary angle to the background magnetic field so that the electrostatic and electromagnetic characteristics of these waves are coupled. We investigate the dependance of these instabilities on dispersion, plasma/beta, pump wave amplitude, and propagation angle. Analytical and numerical results are compared with numerical simulations to investigate the full nonlinear evolution of these instabilities.
CGL relations including the effect of finite ion Larmor radius are used to consider a class of parametric instabilities of finite-amplitude, circularly polarized Alfven waves in high-beta plasmas. The disperison relation governing the instabilities is a sixth-order polynomial which is solved numerically. There are two types of instabilities: a modulational instability at k is less than k(0) and a relatively weak and narrow bandwidth instability at k is less than approximately k(0), where k and k(0) are the wavenumbers of the unstable density fluctuation and the 'pump' wave, respectively. It is shown that these instabilities can occur for left-handed pump waves and that the modulational instability is unstable over a very broad band in k with a maximum growth rate at finite k is not equal to 0.