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NASA NTRS1987

Current-driven magnetohydrodynamic thermal instabilities in sheared fields

Approximate analytic solutions are sought for the dispersion relation for the MHD stability of magnetized medium in current-driven filamentation modes such as those observed in the solar atmosphere. The magnetic field is assumed to have a self-consistent sheared equilibrium structure. The analysis is carried out in the small wavenumber regime, where shear length is similar to the mode wavelength. Instability is found to depend on the ratio between the thermal and magnetic diffusivities, i.e., the Prandtl number, which identifies the unstable transverse wavenumbers. The instability conditions are expressed in an algebraic equation amenable to numerical solution. Results are provided from use of the model to determine the maximum growth rate and typical scale lengths of instabilities in a precoronal atmosphere and the lower transition region.

Bodo, G.↗

NASA NTRS1987

Numerical study of the spectrum of broadband electrostatic noise in the magnetotail

A numerical study of the spectrum of broadband electrostatic noise (BEN) generated by ion beams in the plasma sheet boundary layer (PSBL) is presented, in which two cases are analyzed. The first case is concerned with a single hot-electron species. In the second case, a second population of cold electrons (arising from diffusion from the lobe into the PSBL) is introduced. The presence of the second electron component in the dispersion relation for generating BEN was found to significantly increase the upper frequency range of the unstable spectrum, enhancing the associated growth rates. It is shown that ion beam instabilities can explain most major features of the observed BEN spectrum. The results explain the gradual rise in the upper frequency range of BEN as a spacecraft approaches the plasma sheet from the lobe, and the sudden jump in that frequency up to near the plasma frequency upon crossing the PSBL.

Grabbe, Crockett L.↗

NASA NTRS1986

Relationship between directions of wave and energy propagation for cold plasma waves

The dispersion relation for plasma waves is considered in the 'cold' plasma approximation. General formulas for the dependence of the phase and group velocities on the direction of wave propagation with respect to the local magnetic field are obtained for a cold magnetized plasma. The principal cold plasma resonances and cut-off frequencies are defined for an arbitrary angle and are used to establish basic regimes of frequency where the cold plasma waves can propagate or can be evanescent. The relationship between direction of wave and energy propagation, for cold plasma waves in hydrogen atmosphere, is presented in the form of angle diagrams (angle between group velocity and magnetic field versus angle between phase velocity and magnetic field) and polar diagrams (also referred to as 'Friedrich's diagrams') for different directions of wave propagation. Morphological features of the diagrams as well as some critical angles of propagation are discussed.

Musielak, Zdzislaw E.↗

NASA NTRS1987

MPD thruster plasma instability studies

Results of an ongoing experimental/theoretical effort to understand the influence of plasma waves and instabilities upon coaxial plasma thruster performance and longevity are discussed. An experiment which permits measurement of the plasma dispersion relation plus a suite of plasma parameters for each one millisecond quasi-steady discharge is described. This investigation is guided by a linearized Boltzmann-Poisson kinetic numerical model which can accommodate the effects of collisions, inhomogeneities and the magnetic field. Preliminary tests reveal the presence of the low-frequency branch of an ion cyclotron wave. Although the stability of these waves still has to be established through spatial growth rate measurements, it is well known that they are prone to 'current-driven' instabilities. 'Current-driven' instabilities in the collisional tensor conducting plasma of the MPD thruster are analytically discussed and their relevance to the MPD plasma is illustrated by estimating a critical total current at which their onset occurs.

Kelly, A. J.↗

NASA NTRS1987

A linear MHD instability analysis of solar mass ejections with gravitation

The linear MHD instability of a cylindrical plasma is used to investigate the origin of solar mass ejections, and the dispersion relation is solved numerically. The initial plasma-flow velocity is found to have a significant effect on the instability criteria and growth rate, and the instability growth-rate is shown to be larger in cases where plasma flow exists, relative to the static case. Results suggest that the plasma column may break into small pieces. Assuming a thin-tube approximation, gravity is found to have little effect on the instability of quasi-horizontal ejection, but to have considerable effect on the vertical ejection. In considering the gravitational force, an exact analytical solution is found for the vertical case, while asymptotic solutions are given for the horizontal and oblique cases.

Song, M. T.↗

NASA NTRS1987

On the thermal instability of galactic and cluster halos

The paper presents a detailed study of thermal instabilities in cooling flows associated with galaxies and clusters of galaxies. In the case of purely radiation-driven accretion onto a central object such as the cD galaxy M87, it is found that the gas is largely subject to overstability, rather than to monotonic instability. If thermal conductivity is taken into account, the flow is stabilized on scales of several kiloparsecs, even if the conductivity is appreciably reduced (e.g., about 1 percent) with respect to the Spitzer value. In no case are the globular perturbations (i.e., perturbations with comparable radial and azimuthal dimensions) found to be monotonically unstable. The paper presents numerical solutions of the local dispersion relation for the cooling flow in M87 and discusses the possible consequences of the results for a correct understanding of cooling flows.

Malagoli, A.↗

NASA NTRS1987

Absolute instability of the Gaussian wake profile

Linear parallel-flow stability theory has been used to investigate the effect of viscosity on the local absolute instability of a family of wake profiles with a Gaussian velocity distribution. The type of local instability, i.e., convective or absolute, is determined by the location of a branch-point singularity with zero group velocity of the complex dispersion relation for the instability waves. The effects of viscosity were found to be weak for values of the wake Reynolds number, based on the center-line velocity defect and the wake half-width, larger than about 400. Absolute instability occurs only for sufficiently large values of the center-line wake defect. The critical value of this parameter increases with decreasing wake Reynolds number, thereby indicating a shrinking region of absolute instability with decreasing wake Reynolds number. If backflow is not allowed, absolute instability does not occur for wake Reynolds numbers smaller than about 38.

Hultgren, Lennart S.↗

NASA NTRS1988

Thermal filamentation instability driven by the auroral electrojet current

A thermal instability leading to the filamentation of auroral electrojet currents and giving rise to purely growing magnetic field-aligned density irregularities in the E region of the high-latitude ionosphere is investigated. The physical process of the instability is through the modification of the electron-neutral collision frequency due to the electron temperature perturbation in the electrojet. A dispersion relation of the instability is derived, from which the threshold electrojet current and the growth rate of the instability are determined. It is found that they become independent of the scale sizes of the irregularities for scale sizes larger than about 13 m. The proposed instability can thus be considered to be one of the mechanisms responsible for observed relatively large-scale E region irregularities (Pfaff et al., 1984).

Kuo, S. P.↗

NASA NTRS1988

The velocity structure and turbulence at the center of the Orion Nebula

Using the Coude Feed System of the Kitt Peak National Observatory at its highest possible dispersion and a CCD detector with wide dynamic range it was possible to examine in detail the radial and turbulent velocities of the Orion Nebula at the seeing limit. For the first time, multiple components of the spectral lines were resolved and the Gaussian profiles fit to them. Using four different observing runs, two circular areas 2 minutes in diameter were observed, the first centered on the theta sup 1 Orionis and the second centered on theta sup 2 Orionis. The velocity resolution of 1 km/s combined with the angular resolution of 2 seconds allowed observation in detail at line splitting as well as the location and measurement of high internal motions, about -50 km/s with respect to the bulk of ionized matter. Because over 900 different positions were measured, modern statistical techniques were used for the analysis of turbulence, so that the dispersion relation and the structure function could be calculated and compared with predictions of the Kolmogorov theory. The random motions showed correlation with spatial separation, as expected for turbulence; but comparison with predictions of the classical theory for nebular turbulence showed poor agreement. If Kolmogorov theory applies, then the energy must be input at many scales.

Castaneda, Hector O.↗

NASA NTRS1988

Nature and the nonlinear evolution of electrostatic waves associated with the AMPTE solar wind releases

The nonlinear evolution of the electrostatic waves observed during the AMPTE (Active Magnetosphere Particle Tracer Explorers) solar wind releases is investigated. Previous linear studies indicate two distinct sets of instabilities may be responsible for the generation. One set consists of ion-acoustic type instabilities which are insensitive to the presence of a background magnetic field, while the other group corresponds to the modified two stream instabilities and requires the solar wind flow to be across the ambient magnetic field. To establish which set of instabilities is more viable a detailed linear Vlasov theory has been conducted by numerically solving the full electromagnetic dispersion relation. In addition both the plasma wave as well as the magnetic field measurements by the IRM (Ion Release Module) spacecraft were used to correlate the frequency and the power of the observed waves with the magnitude and the direction of the solar wind magnetic field. The results of these analyses indicate that the ion-acoustic type instabilities have growth rates that are an order of magnitude or more larger than those of the modified two stream instabilities. Results show that both the solar wind protons and the released ions may be heated and accelerated in the directions oblique to the solar wind flow velocity.

Omidi, N.↗

NASA NTRS1988

Filamentation instability of large-amplitude Alfven waves

An instability that leads to the filamentation of large-amplitude Alfven waves and gives rise to purely growing density and magnetic field fluctuations is studied. The dispersion relation of the instability is derived, from which the threshold conditions and the growth rates of the instability are analyzed quantitatively for applications to the solar wind plasma. Their dependence on the filamentation spectrum, the plasma beta, and the pump frequency and intensity was examined for both right-hand and left-hand circularly polarized Alfven waves. The excitation of filamentation instability for certain cases of interest is discussed and compared with that of the parametric decay and modulation instability. The relevance of the proposed instability to some observations is discussed.

Kuo, S. P.↗

NASA NTRS1989

Absorbing boundary conditions for second-order hyperbolic equations

A uniform approach to construct absorbing artificial boundary conditions for second-order linear hyperbolic equations is proposed. The nonlocal boundary condition is given by a pseudodifferential operator that annihilates travelling waves. It is obtained through the dispersion relation of the differential equation by requiring that the initial-boundary value problem admits the wave solutions travelling in one direction only. Local approximation of this global boundary condition yields an nth-order differential operator. It is shown that the best approximations must be in the canonical forms which can be factorized into first-order operators. These boundary conditions are perfectly absorbing for wave packets propagating at certain group velocities. A hierarchy of absorbing boundary conditions is derived for transonic small perturbation equations of unsteady flows. These examples illustrate that the absorbing boundary conditions are easy to derive, and the effectiveness is demonstrated by the numerical experiments.

Jiang, Hong↗

NASA NTRS1989

The electron beam instability revisited: Growth above and below f sub p

The growth of electrostatic waves near the plasma frequency (fp) due to an unstable electron beam is investigated by solving the unmagnetized electrostatic dispersion equation numerically. The numerical solutions are compared with analytic theories for reactive (or fluid-type) and kinetic versions of the beam instability, and for the O'Neil/Malmberg connection of the beam and Langmuir modes. Conditions for growth significantly above or below fp are given. Three general results are found: (1) The unstable waves do not grow on a mode with Langmuir dispersion except in the limit of a very dilute beam with growth on O'Neil/Malmberg's connected mode; (2) The properties of the unstable mode depend strongly on beam parameters such as beam density, speed and temperature; and (3) The frequency of maximum growth frequently lies significantly above or below fp, and differs significantly from that predicted by the Langmuir dispersion relation. Results imply important consequences for theories of strong turbulence and nonlinear wave-wave processes, and observational identification of fp from observed wave frequencies.

Cairns, I. H.↗

NASA NTRS1989

Observations of gravity waves in the mesosphere with the MU radar

Wind motions were observed at 60 to 90 km altitudes with the MU radar during daylight hours (0800 to 1600 LT) from 13 to 31 October 1986. Quasi-monochromatic gravity waves were evident on 16 of the 19 days of observations. They were characterized by typical vertical wavelength of 5 to 15 km and intrinsic periods centered at about 9 hours. The propagation direction of the gravity waves, determined by the gravity wave dispersion relation, was mostly equatorward. The vertical wave number spectra of the horizontal components of the mesoscale wind fluctuations are explained well by saturated gravity wave theory. The frequency spectrum of vertical wind component has a slope of + 1/3, while the oblique spectra have a slope of -5/3 up to 4 x 10(-3) (c/s); these agree fairly well with model gravity wave spectra. Doppler shift effects on the frequency spectra are recognized at higher frequencies. Upward flux was determined of horizontal momentum flux induced by waves with periods from 10 min to 8 hours, and westward and northward body forces of 5.1 and 4.0 m/s/day, were estimated respectively.

Tsuda, T.↗

NASA NTRS1988

Surface and body waves in magnetic flux tubes

The dispersion relation of surface and body waves in a magnetic flux tube is studied in detail. The properties of the fast and slow bodywaves are described in terms of the filtering characteristics of the flux tube. In addition to the axisymmetric and nonaxisymmetric distinction between the modes, an additional distinction is made between the fundamental mode and the rest of the modes. New results concerning the thin and large flux tube approximation are derived. The behavior of surface and body waves in the solar convection zone, photosphere, and corona is discussed.

Abdelatif, T. E.↗

NASA NTRS1989

Magnetohydrodynamic waves and particle acceleration in a coronal loop

A model is presented for the acceleration of electrons in a flaring solar coronal loop. It is suggested that the primary energy release event in the flare establishes a spectrum of MHD waves within the loop which accelerate electrons by wave-particle resonant interactions. The nature of the MHD oscillations are described and numerical and analytic solution of the dispersion relation are examined. It is found that the behavior of a particle depends on whether or not it is in resonance with the wave spectrum. Resonant particles follow chaotic trajectories and can diffuse in velocity space between wave effective potentials, thereby gaining energy.

De La Beaujardiere, Jean-Francois↗

NASA NTRS1988

Current driven instabilities of an electromagnetically accelerated plasma

Quantitative measurements of the plasma instability that strongly affects the efficiency and lifetime of electromagnetic plasma accelerators were obtained. Experimental results are presented for the dispersion relations (wave phase velocities), spatial growth rates, and stability boundaries of accelerators. The measured critical wave parameters are found to agree well with theoretical predictions. A kinetic theoretical model was used to study current driven instabilities which are intrinsic to the high-current-carrying magnetized plasma of a magnetoplasmadynamic accelerator. Under certain conditions, marginally stable waves travelling almost perpendicular to the magnetic field are found which travel at a velocity equal to that of the electron current.

Kelly, A. J.↗

NASA NTRS1989

Interfacial wave theory for dendritic structure of a growing needle crystal. I - Local instability mechanism. II - Wave-emission mechanism at the turning point

The complicated dendritic structure of a growing needle crystal is studied on the basis of global interfacial wave theory. The local dispersion relation for normal modes is derived in a paraboloidal coordinate system using the multiple-variable-expansion method. It is shown that the global solution in a dendrite growth process incorporates the morphological instability factor and the traveling wave factor.

Xu, Jian-Jun↗