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NASA NTRS1994

Beat, modulational, and decay instabilities of a circularly polarized Alfven wave

A circulary polarized low-frequency electomagnetic pump wave propoagating along an ambient magnetic field is known to be unstable to the growth of several parallel-propagating parametric instabilties. If ion-cyclotron effects are retained in a two-fluid description, the dispersion relation is a sixth-order polynomial. We present a series of new analytical approximations to this dispersion relation. We emphasize new results for the beat instability that occurs as an interaction of the forward prpagating upper sideband with the backward propagating lower sideband. The nature of the beat instabitlity depends on beta = (v(sub sound)/v(sub A)(exp 2) and on the sense of polarization of the pump wave. The beat and decay instabilities can occur together if the pump is left-handed (i.e., ion resonant) and if beta is less than or approximately 1, but they cannot occur together if the pump is right-handed. For a left-handed pump the beat mode is the only instability if beta is greater than or approximately 1. If the pump is right-handed and beta is greater than or approximately 1, then the beat instability exists only when the pump amplitude exceeds a threshold value, and the beat will be the only instability if the pump amplitude is large enough to stabilize the modulational instability. If the pump is left-handed and beta is less than or approximately 1, then the beat mode is stabilized when the pump amplitude becomes sufficiently large. The beat instability primarily produces a forward propagating transverse wave in the upper sideband. Thus if beta is greater than or approximately 1, the instabilities considered here do not produce the backward propagating waves which are thought to affect turbulence and the evolution of cross helicity in the solar wind. New analytical results are presented also for the decay and modulational instabilites when beta is approximately equal to 1.

Hollweg, Joseph V.↗

NASA NTRS1993

Lower hybrid turbulence at cometary bow wave and acceleration of cometary protons

The wave measurements at the spacecraft encounters with Comet Halley have shown intense wave activity at the lower hybrid frequency. The excitation of the lower hybrid instability by the pickup cometary ions (protons and water group) in the bow wave region and the quasi-linear diffusion of the ions in these fluctuations are discussed. The quasi-linear diffusion of the pickup protons takes place over a scale length shorter than that of the heavier water group ions. This enhances damping of the waves by protons, and when the pickup proton density is large enough, it can result in the saturation of the instability as this damping balances the heavy ion driven growth. The observed electric field amplitude and the scale length of proton relaxation are in agreement with the theory. For small pickup proton density the instability can saturate due to the wave energy cascade arising from the modulation instability of the large-amplitude lower hybrid waves. This saturation mechanism leads to electron acceleration and suprathermal tail formation.

Shapiro, V. D.↗

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 NTRS1987

Simulation of amplitude-modulated circularly polarized Alfven waves for beta less than one

The nonlinear properties of the amplitude-modulated circularly polarized Alfven wave are studied for beta less than one. The temporal behavior of the wave packet of the electromagnetic hybrid simulation is compared with a numerical solution of the derivative nonlinear Schroedinger (DNLS) equation. It is shown that the left-hand-polarized mode evolves into a shocklike structure due to the modulational instability. However, both cyclotron damping and a snowplow effect near the steepened wave packet suppress its further steepening, contrary to the predictions of the DNLS equation. For the right-hand mode, formation of the shock does not take place, and the initial time development is well described by the DNLS equation. The daughter Alfven wave and ion acoustic waves are excited due to the decay instability at a later time. Heating or acceleration of the particles takes place for both left- and right-hand waves. Energy transfer from the wave to the particles occurs effectively when substantial modulation in the wave amplitude is present.

Machida, S.↗

NASA NTRS1990

Plasma waves associated with the space shuttle

Water molecules outgassed from the Space Shuttle suffer collisional charge-exchange with ionospheric oxygen ions, thereby forming unstable distributions of pick-up water ions and leading to high levels of plasma waves near the Shuttle. Liouville's equation with a charge-exchange source term is solved for the water ion distribution function as a function of position relative to the Shuttle. The observational characteristics of the near zone Shuttle waves are summarized. A linear theory in which beam like distributions of water ions drive Doppler shifted lower hybrid waves via the modified two stream instability is developed. This theory explains many characteristics of the near zone waves. Further work on the effects of wave nonlinearities and spatial inhomogeneity is required to explain the detailed frequency spectrum of the waves. The observed wave levels apparently satisfy the threshold condition for modulational instability of lower hybrid waves.

Cairns, I. H.↗

NASA NTRS1999

Whistler Solitons in Plasma with Anisotropic Hot Electron Admixture

The longitudinal and transverse modulation instability of whistler waves in plasma, with a small admixture of hot anisotropic electrons, is discussed. If the hot particles temperature anisotropy is positive, it is found that, in such plasma, longitudinal perturbations can lead to soliton formation for frequencies forbidden in cold plasma. The soliton is enriched by hot particles. The frequency region unstable to transverse modulation in cold plasma in the presence of hot electrons is divided by stable domains. For both cases the role of hot electrons is more significant for whistlers with smaller frequencies.

Khazanov, G. V.↗

NASA NTRS1999

Whistler Solitons in Plasma with Anisotropic Hot Electron Admixture

Khazanov, G. V.↗

NASA NTRS2016

Influence of Stationary Crossflow Modulation on Secondary Instability

A likely scenario for swept wing transition on subsonic aircraft with natural laminar flow involves the breakdown of stationary crossflow vortices via high frequency secondary instability. A majority of the prior research on this secondary instability has focused on crossflow vortices with a single dominant spanwise wavelength. This paper investigates the effects of the spanwise modulation of stationary crossflow vortices at a specified wavelength by a subharmonic stationary mode. Secondary instability of the modulated crossflow pattern is studied using planar, partial-differential-equation based eigenvalue analysis. Computations reveal that weak modulation by the first subharmonic of the input stationary mode leads to mode splitting that is particularly obvious for Y-type secondary modes that are driven by the wall-normal shear of the basic state. Thus, for each Y mode corresponding to the fundamental wavelength of results in unmodulated train of crossflow vortices, the modulated flow supports a pair of secondary modes with somewhat different amplification rates. The mode splitting phenomenon suggests that a more complex stationary modulation such as that induced by natural surface roughness would yield a considerably richer spectrum of secondary instability modes. Even modest levels of subharmonic modulation are shown to have a strong effect on the overall amplification of secondary disturbances, particularly the Z-modes driven by the spanwise shear of the basic state. Preliminary computations related to the nonlinear breakdown of these secondary disturbances provide interesting insights into the process of crossflow transition in the presence of the first subharmonic of the dominant stationary vortex.

Vortex structure↗

NASA NTRS1972

Linear and nonlinear stability characteristics of whistlers

Linear and nonlinear propagating characteristics of right-hand polarized, slow electromagnetic, magnetoplasma waves (whistlers) are discussed in terms of stability and dispersion. An analysis of the stability of whistlers propagating at an angle to the static magnetic field is presented. A new mechanism is derived for the onset of stimulated emissions, and modulational instability for nonlinear whistlers are discussed.

Brinca, A. L.↗

NASA NTRS1982

Solitons and ionospheric modification

The possibility of Langmuir soliton formation and collapse during ionospheric modification is investigated. Parameters characterizing former facilities, existing facilities, and planned facilities are considered, using a combination of analytical and numerical techniques. At a spatial location corresponding to the exact classical reflection point of the modifier wave, the Langmuir wave evolution is found to be dominated by modulational instability followed by soliton formation and three-dimensional collapse. The earth's magnetic field is found to affect the shape of the collapsing soliton. These results provide an alternative explanation for some recent observations.

Sheerin, J. P.↗

NASA NTRS1983

Self-modulational formation of pulsar microstructures

A nonlinear plasma theory for self-modulation of pulsar radio pulses is discussed. A nonlinear Schroedinger equation is derived for strong electromagnetic waves propagating in an electron-positron plasma. The nonlinearities arising from wave-intensity-induced particle-mass variation may excite the modulational instability of circularly and linearly polarized pulsar radiation. The resulting wave envelopes can take the form of periodic wave trains or solitons. These nonlinear stationary waveforms may account for the formation of pulsar microstructures.

Chian, A. C.-L.↗

NASA NTRS1983

Progress and problems in the theory of type III solar radio emission

The experimental and theoretical status of type III solar radio emission is considered in detail. Very recent developments which are relevant to the underlying plasma physics are emphasized. In particular, the identity of the submegahertz emissions as fundamental, or second harmonic, the degree of correlation between emissivities, electron streams, and plasma (Langmuir) waves, paradoxes concerned with the time-ordering of these phenomena, and the role of background density irregularities and ion-acoustic turbulence in the solar wind, are discussed. From the theoretical point of view, the current picture of the underlying Langmuir turbulence, including such effects as the interaction between Langmuir waves and stream electrons, induced scatter off ions, and strong turbulence effects such as modulational instability and soliton collapse, is discussed.

Goldman, M. V.↗

NASA NTRS1985

Formation of ion acoustic solitary waves upstream of the earth's bow shock

The turbulent plasma development of Lee and Parks is applied to the solar wind approaching the earth's bow shock region. The ponderomotive force contribution is due to ion acoustic waves propagating in the direction of the ambient magnetic field. In this case, the envelope of the ion acoustic wave is shown to satisfy the cubic Schroedinger equation. Modulational instabilities exist for waves in the solar wind, thereby predicting the generation of solitary waves. This analysis further identifies that the ion acoustic waves which exhibit this instability have short wavelengths.

Pangia, M. J.↗

NASA NTRS1985

Statistical theories of Langmuir turbulence. II - Subsonic to sonic transition

The subsonic limit of the quadratic direct interaction approximation (DIA) applied to the Zakharov equations is compared with the cubic DIA applied to the nonlinear Schroedinger equation, which is the subsonic limit of the Zakharov equations. Comparisons with Monte Carlo simulations of a truncated system show that the first theory more accurately describes the regime of stationary turbulence, while the second theory more accurately describes the subsonic evolution of the modulational instability. The weak turbulence limits of the two theories describe the sonic and subsonic regimes, respectively. The addition of vertex corrections to the DIA leads to a hybrid weak turbulence theory that smoothly interpolates between the sonic and subsonic regimes.

Dubois, D. F.↗

NASA NTRS1984

Strong turbulence of plasma waves

This paper reviews recent work related to modulational instability and wave envelope self-focusing in dynamical and statistical systems. After introductory remarks pertinent to nonlinear optics realizations of these effects, the author summarizes the status of the subject in plasma physics, where it has come to be called 'strong Langmuir turbulence'. The paper treats the historical development of pertinent concepts, analytical theory, numerical simulations, laboratory experiments, and spacecraft observations. The role of self-similar self-focusing Langmuir envelope wave packets is emphasized, both in the Zakharov equation model for the wave dynamics and in a statistical theory based on this dynamical model.

Goldman, M. V.↗

NASA NTRS1986

Evidence for nonlinear wave-wave interactions in solar type III radio bursts

Evidence is presented that nonlinear wave-wave interactions occur in type III solar radio bursts. Intense, spiky Langmuir waves are observed to be driven by electron beams associated with type III solar radio bursts in the interplanetary medium. Bursts of 30-300 Hz (in the spacecraft frame) waves are often observed coincident in time with the most intense spikes of the Langmuir waves. These low-frequency waves appear to be long-wavelength ion acoustic waves, with wavenumber approximately equal to the beam resonant Langmuir wavenumber. Three possible interpretations of these observations are considered: modulational instability, parametric decay of the parent Langmuir waves to daughter ion acoustic and Langmuir waves, and decay to daughter electromagnetic waves and ion acoustic waves.

Lin, R. P.↗

NASA NTRS1987

Numerical comparison of strong Langmuir turbulence models

Two models of Langmuir turbulence, the nonlinear Schroedinger equation and the Zakharov equations, are solved numerically for an initial value problem in which the electric field evolves from an almost flat initial condition via the modulational instability and finally saturates into a set of solitons. The two models agree well with each other only when the initial dimensionless electric field has an amplitude less than unity. An analytic soliton gas model consisting of equal-amplitude, randomly spaced, zero-speed solitons is remarkably good at reproducing the time-averaged Fourier spectra in both cases.

Shen, Mei-Mei↗

NASA NTRS1987

Self-modulational formation of pulsar microstructures

A nonlinear plasma theory for self modulation of pulsar radio pulses is discussed. A nonlinear Schroedinger equation is derived for strong electromagnetic waves propagating in an electron positron plasma. The nonlinearities arising from wave intensity induced particle mass variation may excite the modulational instability of circularly and linearly polarized pulsar radiation. The resulting wave envelopes can take the form of periodic wave trains or solitons. These nonlinear stationary waveforms may account for the formation of pulsar microstructures.

Chian, A. C.-L.↗