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NASA NTRS1988

The nonlinear breakup of a magnetic layer - Instability to interchange modes

Motivated by considerations of the solar toroidal magnetic field, the behavior of a layer of uniform magnetic field embedded in a convectively stable atmosphere is studied. Since the field can support extra mass, such a configuration is top-heavy and thus instabilities of the Rayleigh-Taylor type can occur. For both static and rotating basic states, the evolution of the interchange modes (no bending of the field lines) is followed by integrating numerically the nonlinear compressible MHD equations. The initial Rayleigh-Taylor instability of the magnetic field gives rise to strong shearing motions, thereby exciting secondary Kelvin-Helmholtz instabilities which wrap the gas into regions of intense vorticity. The subsequent motions are determined primarily by the strong interactions between vortices which are responsible for the rapid disruption of the magnetic layer.

Cattaneo, F.↗

NASA NTRS1988

Comment on 'Generation of broadband noise in the magnetotail by the beam acoustic instability' by P.B. Dusenbery

It is shown here that of the three plasma models for the generation of broadband noise in the magnetotail proposed by Dusenbery and Lyons (1985), two result in the same types of instabilities that are also excited in the Grabbe and Eastman (GE, 1984) model, while the third model introduces other modes not present in the GE model. For the plasma parameters given in the GE model, the ion/ion acoustic instability is a nonresonant one, even though the phase velocity of the excited waves falls within the distribution function of the core ions. The nonlinear saturation mechanism of the ion/ion acoustic instability is the trapping of both the core and the beam ions. In a reply, Dusenbery addresses several ongoing controversies which have resulted from studies of wave particle interactions in the plasma sheet boundary layer.

Omidi, N.↗

NASA NTRS1989

Nonlinear Parker instability of isolated magnetic flux in a plasma

The nonlinear evolution of the Parker instability in an isolated horizontal magnetic-flux sheet embedded in a two-temperature layer atmosphere is studied by using a two-dimensional MHD code. In the solar case, this two-layer model is regarded as a simplified abstraction of the sun's photosphere/chromosphere and its overlying much hotter (coronal) envelope. The horizontal flux sheet is initially located in the lower temperature atmosphere so as to satisfy magnetostatic equilibrium under a constant gravitational acceleration. Ideal MHD is assumed, and only perturbations with k parallel to the magnetic-field lines are investigated. As the instability develops, the gas slides down the expanding loop, and the evacuated loop rises as a result of enhanced magnetic buoyancy. In the nonlinear regime of the instability, both the rise velocity of a magnetic loop and the local Alfven velocity at the top of the loop increase linearly with height and show self-similar behavior with height as long as the wavelength of the initial perturbation is much smaller than the horizontal size of the computing domain.

Shibata, K.↗

NASA NTRS1989

On the three families of instability waves of high-speed jets

An analytical and computational study of the normal-mode small-amplitude waves of high-speed jets is presented. Three families of instability waves have been identified: (1) the familiar Kelvin-Helmholtz instability waves; (2) supersonic instability waves; and (3) subsonic waves. It is demonstrated that the computed wave patterns and propagation characteristics of these three wave types are consistent with the findings of Oetel (1979, 1980, 1982). The subsonic waves are shown to be unstable only for jets with mixing layers of finite thickness.

Tam, Christopher K. W.↗

NASA NTRS1989

Thermal instability accretion disk model for the X-ray transient A0620-00

The limit-cycle thermal instability model for accretion disks is used to study the soft X-ray transient A0620-00. Thermal instability in geometrically thin, Keplerian alpha-model disks is reviewed. The observational constraints on A0620-00 are presented and the parameters chosen for the model are discussed. It is found that, with the adopted parameters, the model requires a central object mass of about 7 solar masses to fit the burst recurrence time. This is consistent with a black hole as the central object. The results suggest that a mass transfer instability may be responsible for outbursts.

Huang, Min↗

NASA NTRS1988

Combustion instability coupling with feed system acoustics

High frequency combustion instability has recently been observed by Rocketdyne in a 40K thrust methane/LOX combustion chamber. The oscillations had frequencies as high as 14,000 Hz with pressure amplitudes in the LOX dome of 500 psi at a chamber pressures of 2,000 psi. At this frequency the wave length associated with a period of oscillation is 2.3 inches in LOX and 1.4 inches in methane. These distances are comparable to the lengths of the injector elements which requires that acoustic waves be considered in the feed systems rather than using lumped parameters as is normally considered for feed system coupled oscillations. To expand the capability of existing models, the Feiler and Heidmann feed system coupled instability model was modified to include acoustic oscillations in the feed system. Similarly the vaporization controlled instability model of Heidmann and Wieber was modified to include flow oscillations that would be produced by feed system coupling. The major elements that control oscillations in a rocket combustion chamber are shown and discussed.

Priem, Richard J.↗

NASA NTRS1989

Electromagnetic instabilities in the plasma sheet boundary layer

Plasma and magnetic field data observed during two ISEE crossing of the plasma sheet boundary layer are studied in conjuction with a linear theory analysis. The plasma distribution functions exhibit three distinct potential sources of free energy: ion/ion relative drifts, electron/ion relative drifts corresponding to nonzero field-aligned current, and large ion temperature anistropies. These observed distributions are used as source functions in a linear Vlasov theory of electromagnetic instabilities at propagation parallel or antiparallel to the average magnetic field. The theory shows that the field-aligned current gives rise to the low frequency kinklike instability, and anisotropies of the flowing ion components give rise to two distinct branches of the ion cyclotron anisotropy instability with spacecraft frame frequencies both below and above the proton cyclotron frequency Omega (p). Analysis of the magnetic field data demonstrates that the appearence of two fast, counterstreaming, anisotropic ion components corresponds to a significant increase in the magnetic fluctuation energy density both below and above Omega(p), in full agreement with the theoretical predictions.

Angelopoulos, Vassilis↗

NASA NTRS1990

Viscous effects on the capillary instabilities of a hollow liquid cylinder

In a microgravity environment, a hollow cylinder of fluid is unstable to axisymmetric disturbances and breaks up to form hollow spheres. These instabilities are due to the surface tension of the fluid. The linear stability analysis presented in this paper shows that the viscosity of the fluid reduces the instability of the configuration, but that, regardless of its magnitude, it can never completely eliminate the instability.

Harvanek, Michael↗

NASA NTRS1990

Surface waves in an incompressible fluid - Resonant instability due to velocity shear

The effects of velocity shear on the resonance absorption of incompressible MHD surface waves are studied. It is found that there are generally values of the velocity shear for which the surface wave decay rate becomes zero. In some cases, the resonance absorption goes to zero even for very small velocity shears. It is also found that the resonance absorption can be strongly enhanced at other values of the velocity shear, so the presence of flows may be generally important for determining the effects of resonance absorption, such as might occur in the interaction of p-modes with sunspots. Resonances leading to instability of the global surface mode can exist, and instability can occur for velocity shears significantly below the Kelvin-Helmholtz threshold. These instabilities may play a role in the development or turbulence in regions of strong velocity shear in the solar wind or the earth's magnetosphere.

Hollweg, Joseph V.↗

NASA NTRS1990

Core instability of the spanwise vortices in a plane mixing layer

A spanwise core instability of the primary vortices in a plane mixing layer has been identified as a viable mechanism for the generation of streamwise vortical structures far downstream of the flow partition. The core instability is excited by a time-harmonic wave train with spanwise phase variation, synthesized by a mosaic of individually controlled surface heaters flush mounted on the flow partition. The flow is visualized in planes of constant cross-stream elevation by means of a schlieren system. As a result of the forcing, the primary vortices undergo spanwise deformations that induce secondary vortical structures, the shape and strength of which depends on the magnitude of the prescribed spanwise phase variation. The appearance of small-scale structures within the large coherent vortices suggests that core instability is an important contributor to mixing.

Nygaard, Kris J.↗

NASA NTRS1990

Ballooning mode instability at the plasmapause

The ballooning mode instability, which can excite hydromagnetic waves at the plasmapause, is studied in the presence of azimuthal plasma flows induced during geomagnetically disturbed periods. A general sufficient criterion for the ballooning mode stability is derived, for a change in the potential energy greater than or equal to 0, which involves the integration over an entire field line. A local stability analysis at the equatorial plasmapause region shows that the ballooning modes could be spontaneously generated via instability under at least two conditions: one is similar to the usual interchange condition, and the second to the quasi-interchange modes. Both of these local instability conditions can be derived from the general stability criterion. Finally an exact solution for the equilibrium state with flow is derived analytically, and the change in the potential energy is computed numerically. It is found that, in the cases studied, the flow does not spontaneously excite the ballooning modes; it only further stabilizes (or destabilizes) the ballooning spectrum if originally the system is stable (or unstable). The analysis would be useful for the interpretation of some of the low-frequency modes observed at the ground and near the equatorial plasmapause.

Lakhina, G. S.↗

NASA NTRS1990

Extensional and compressional instabilities in icy satellite lithospheres

The plausibility of invoking a lithospheric instability mechanism to account for the grooved terrains on Ganymede, Encedalus, and Miranda is presently evaluated in light of the combination of a simple mechanical model of planetary lithospheres and asthenospheres with recent experimental data for the brittle and ductile deformation of ice. For Ganymede, high surface gravity and warm temperatures render the achievement of an instability sufficiently great for the observed topographic relief virtually impossible; an instability of sufficient strength, however, may be able to develop on such smaller, colder bodies as Encedalus and Miranda.

Herrick, David L.↗

NASA NTRS1990

A numerical study of the onset of baroclinic instabilities in spherical geometry

The onset of instabilities in a fluid contained in a rotating hemispherical shell, driven by thermal gradients imposed upon the hemispherical boundaries and by a spherically symmetric radial body force, is numerically studied. Computations are presented for a range of Taylor and thermal Rossby numbers. The analysis indicates the presence of an instability dependent upon the spherically radial gravity alone when the warmest temperatures are at the pole and an additional centrifugal buoyant instability for weak imposed gravity and fast rotation when the temperature decreases poleward.

Miller, Timothy L.↗

NASA NTRS1990

Simulation studies of plasma waves in the electron foreshock - The transition from reactive to kinetic instability

Particle simulation experiments were used to analyze the electron beam-plasma instability. It is shown that there is a transition from the reactive state of the electron beam-plasma instability to the kinetic instability of Langmuir waves. Quantitative tests, which include an evaluation of the dispersion relation for the evolving non-Maxwellian beam distribution, show that a quasi-linear theory describes the onset of this transition and applies again fully to the kinetic stage. This stage is practically identical to the late stage seen in simulations of plasma waves in the electron foreshock described by Dum (1990).

Dum, C. T.↗

NASA NTRS1990

The kink instability in infinite cylindrical flux tubes - Eigenvalues for power-law twist profiles

Simple, accurate methods of calculating ideal MHD instability eigenvalues for infinitely long cylindrical tubes with twist function T(r) are developed. The results show that the most rapidly growing and energetic instabilities occur in the Gold-Hoyle v = 0 field, with the instability progressively weakening with increasing v. However, the maximum force eigenvalue is always small, so that even in the Gold-Hoyle case only a small proportion of the available magnetic energy can be released in the linear phase. The results also confirm that the linear pinch is remarkably weak yet relatively resistant to line-tying. It is shown that the weakness of the force eigenvalue implies that the influence of uniform gas pressure on stability is negligible. Implications for the energy-release mechanism in solar flares are discussed.

Craig, I. J. D.↗

NASA NTRS1990

Nonaxisymmetric instabilities in a slender torus - Two- and three-dimensional simulations

Nonaxisymmetric instabilities in accretion disks are investigated in terms of the slender, non-self-gravitating, ideal fluid torus model. Nonlinear simulations are carried out in two and tree dimensions, using Cartesian-grid finite differencing. The fastest growing instability is the principal mode. This mode saturates with the formation of ellipsoidal density distributions, designated as 'planets'. The simulations provide evidence for nonlinear mode-mode coupling. When several wavenumbers m are unstable, multiple 'planets' form that subsequently merge. Sources of numerical error are examined, and the effects are contrasted with those of the physical instability. The same qualitative evolution is seen in both the two- and the three-dimensional simulations, even though strict vertical hydrostatic equilibrium is no longer rigorously maintained after mode saturation.

Hawley, John F.↗

NASA NTRS1990

Secondary instability in rotating disk flow

Primary instability of the three-dimensional boundary layer on a rotating disk introduces periodic modulation of the mean flow in the form of cross-flow vortices. The stability of this modulated base flow to secondary disturbances is studied. In a three-dimensional boundary layer the threshold primary amplitude for secondary instability is larger than that for a two-dimensional boundary layer. The secondary instability results in a pair of traveling counter-rotating vortices, tilted up and oriented at an angle to the primary cross-flow vortices.

Balachandar, S.↗

NASA NTRS1990

Artificial ion beam instabilities. I - Linear theory. II - Simulations

Some of the important plasma instabilities that result when an artificial ion beam is injected into the ionospheric F region are studied using linear Vlasov theory. The variation in wave spectra at the receiver as the receiver and plasma gun separate perpendicularly to the magnetic field is consistent with a beam density decrease at or near the receiver. At separation distances that are large fractions of the beam gyrodiameter, usually narrow-band waves near the background lower hybrid and H+ gyroharmonic frequencies are measured. These observations are consistent with waves expected to be generated by beam densities on the order of or less than a few percent of the background density. At smaller separation distances, broadband waves are usually observed with frequencies from zero up to and above the lower hybrid frequency. Electrostatic particle simulation studies of the plasma instabilities indicate that the broadband fluidlike lower hybrid instability is the most important for background particle heating. Perpendicular H+ heating is more efficient than perpendicular O+ or parallel electron heating for the drift velocity regime most relevant to past experiments.

Scales, W. A.↗