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NASA NTRS1973

Finite beta drift Alfven instability

We propose a means by which the theory of drift instabilities can be extended to plasmas of arbitrary beta. We then concentrate on the drift Alfven instability driven by an electron temperature gradient, proposed by Coroniti and Kennel (1970) to be a source of Pi 1 micropulsations on auroral lines of force. Even at relatively low beta the full finite beta theory differs considerably from previous low beta theories and produces better agreement with observation.

Chance, M. S.↗
NASA NTRS1993

Modulational and decay instabilities of Alfven waves - Effects of streaming He(2+)

The parametric instability of a circularly polarized Alfven wave propagating along the background magnetic field are considered, with emphasis on the effects of a second ion species, He(2+), which drifts relative to the protons. Even though its abundance is small, the He(2+) modifies the dispersion relation of the 'pump' Alfven wave and introduces a new sound wave (alpha sound) in addition to the usual sound wave carried primarily by the electrons and protons. Instabilities which are close to the He(2+) gyroresonance are found. This may provide a means of directly transferring Alfven wave energy to the alpha particles, if the alphas are able to resonantly extract energy from the unstable waves without quenching the instability altogether. Instabilities which are close to the alpha particle sound speed are also found.

Hollweg, Joseph V.↗
NASA NTRS1992

Parametric Instabilities Of Alfven Waves

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.

Hamabata, Hiromitsu↗
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 NTRS1991

Kelvin-Helmholtz instability in an Alfven resonant layer of a solar coronal loop

A Kelvin-Helmholtz instability has been identified numerically on an azimuthally symmetric Alfven resonant layer in an axially bounded, straight cylindrical coronal loop. The set of equations is solved numerically as an initial value problem. The linear growth rate of this instability is shown to be approximately proportional to the Alfven driving amplitude and inversely proportional to the width of the Alfven resonant layer. It is also shown that the linear growth rate increases linearly with m - 1 up to a certain m, reaches its maximum value for the mode whose half wavelength is comparable to the Alfven resonant layer width, and decreases at higher azimuthal mode number.

Uchimoto, E.↗
NASA NTRS1986

Parametric instabilities of the circularly polarized Alfven waves including dispersion

A class of parametric instabilities of large-amplitude, circularly polarized Alfven waves is considered in which finite frequency (dispersive) effects are included. The dispersion equation governing the instabilities is a sixth-order polynomial which is solved numerically. As a function of K identically equal to k/k-sub-0 (where k-sub-0 and k are the wave number of the 'pump' wave and unstable sound wave, respectively), there are three regionals of instability: a modulation instability at K less than 1, a decay instability at K greater than 1, and a relatively weak and narrow instability at K close to squared divided by v-sub-A squared (where c-sub-s and v-sub-A are the sound and Alfven speeds respectively), the modulational instability occurs when beta is less than 1 (more than 1) for left-hand (right-hand) pump waves, in agreement with the previous results of Sakai and Sonnerup (1983). The growth rate of the decay instability of left-hand waves is greater than the modulational instability at all values of beta. Applications to large-amplitude wave observed in the solar wind, in computer simulations, and in the vicinity of planetary and interplanetary collisionless shocks are discussed.

Wong, H. K.↗
NASA NTRS1993

Parametric instabilities of circularly polarized Alfven waves in high-beta plasmas

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.

Hamabata, Hiromitsu↗
NASA NTRS1992

Parametric instabilities of large amplitude Alfven waves with obliquely propagating sidebands

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.

Vinas, A. F.↗
NASA NTRS1974

Excitation and dissipation of Pc-1 micropulsations

A theoretical model based on hydromagnetic instabilities (including Alfven firehose and magnetoacoustic mirror instabilities), in the region where the electrons are in the transition from collisional to collisionless and ions are in the collisionless region, is proposed as a possible wave emission mechanism for Pc-1 pulsations. The model is compared with recent observations with good agreement between the theory and observations, especially for an emission source located at a distance L less than 5. Furthermore, a suggestion is made that the hydromagnetic instabilities could be relevant to the night and early morning hours emissions while the ion cyclotron instabilities could be responsible for the daytime emission of Pc-1 pulsations.

Hung, R. J.↗
NASA NTRS1992

Alfvenic drift Kelvin-Helmholtz instability in the presence of an equilibrium electric field

The Alfvenic drift Kelvin-Helmholtz instability of a high-beta plasma in the presence of equilibrium magnetic and electric fields perpendicular to each other are studied. The plasma components are assumed to have 2D sheared velocity in y and z directions. The dispersion relation is derived, and the instability criterion is determined. It is shown that the equilibrium electric field has either stabilizing or destabilizing effect depending on certain conditions discussed in the paper.

Sharma, Avadhesh C.↗
NASA NTRS1993

On the dispersion relations for parametric instabilities of parallel-propagating 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.

Yajanti, Venku↗
NASA NTRS1978

Modulational instability of finite-amplitude, circularly polarized Alfven waves

The simple theory of the decay instability of Alfven waves is strictly applicable only to a small-amplitude parent wave in a low-beta plasma, but, if the parent wave is circularly polarized, it is possible to analyze the situation without either of these restrictions. Results show that a large-amplitude circularly polarized wave is unstable with respect to decay into three waves, one longitudinal and one transverse wave propagating parallel to the parent wave and one transverse wave propagating antiparallel. The transverse decay products appear at frequencies which are the sum and difference of the frequencies of the parent wave and the longitudinal wave. The decay products are not familiar MHD modes except in the limit of small beta and small amplitude of the parent wave, in which case the decay products are a forward-propagating sound wave and a backward-propagating circularly polarized wave. In this limit the other transverse wave disappears. The effect of finite beta is to reduce the linear growth rate of the instability from the value suggested by the simple theory. Possible applications of these results to the theory of the solar wind are briefly touched upon.

Derby, N. F., Jr.↗
NASA NTRS1985

Nonlinear astrophysical Alfven waves - Onset and outcome of the modulational instability

The nonlinear development of Alfven waves is numerically studied, with applications to Alfven waves in astrophysical plasmas. It is found that amplitude-modulated Alfven wave packets undergo a collapse instability in which the wave packets become more intense and of smaller spatial extent. The wave packet steepening is eventually halted in a process most aptly described as soliton formation. A simple analytic model based on the method of characteristics can account for many of the results of the numerical calculations. The instability probably cannot prevent particle pitch angle isotropization due to self-generated Alfven waves. Nonlinear effects of the collapse may modify the process by which energetic electrons are reaccelerated by plasma turbulence. The model calculations can semiquantitatively account for properties of shock-associated Alfven waves in the solar system.

Spangler, S. R.↗
NASA NTRS1974

Further remarks on plasma instabilities produced by ions born in the solar wind

Whistler and Alfven wave instabilities produced in the solar wind by newly born ions of planetary or interstellar origin are examined, and it is shown that the dispersion equation considered by Wu and Davidson (1972) contains another class of complex roots which imply stronger instabilities than previously noted. The applicability of the proposed theoretical models is discussed together with the implications of the results for the interaction of planetary and interstellar He+ ions with the solar wind.

Wu, C. S.↗
NASA NTRS1993

Parametric instabilities of parallel-propagating Alfven waves: Some analytical results

We consider the stability of a circularly polarized Alfven wave (the pump wave) which propagates parallel to the ambient magnetic field. Only parallel-propagating perturbations are considered, and we ignore dispersive effects due to the ion cyclotron frequency. The dissipationless MHD equations are used throughout; thus possibibly important effects arising from Landau and transit time damping are omitted. We derive a series of analytical approximations to the dispersion relation using A = (Delta B/B(sub O))(exp 2) as a small expansion parameter; Delta B is the pump amplitude, and B(sub O) is the ambient magnetic field strength. We find that the plasma beta (the square of the ratio of the sound speed to the Alfven speed) plays a crucial role in determining the behavior of the parametric instabilities of the pump. If 0 less than beta less than 1 we find the familiar result that the pump decays into a forward propagating sound wave and a backward propagating Alfven wave with maximum growth rate gamma(sub max) varies A(sup 1/2), but beta cannot be too close to 0 or to 1. If beta approx. 1, we find gamma(sub max) varies A(sup 3/4), if beta greater than 1, we find gamma(sub max) varies A(sup 3/2), while if beta approx. 0, we obtain gamma(sub max) varies A(sup 1/3); moreover, if beta approx. 0 there is a nearly purely growing instability. In constrast to the familiar decay instability, for which the backward propagating Alfven wave has lower frequency and wavenumber than the pump, we find that if beta greater than or approx. equal to 1 the instability is really a beat instability which is dominated by a transverse wave which is forward propagating and has frequency and wavenumber which are nearly twice the pump values. Only the decay instability for 0 less than beta less than 1 can be regarded as producing two recognizable normal modes, namely, a sound wave and an Alfven wave. We discuss how the different characteristics of the instabilities may affect the evolution of Alfven waves in the solar wind. However, for a solar wind in which beta approx. 1 the growth times of the instabilities are probably too long for these instabilities to have an appreciable effect inside 1 AU.

Jayanti, V.↗
NASA NTRS1994

Theoretical studies of the solar atmosphere and interstellar pickup ions

Solar atmosphere research activities are summarized. Specific topics addressed include: (1) coronal mass ejections and related phenomena; (2) parametric instabilities of Alfven waves; (3) pickup ions in the solar wind; and (4) cosmic rays in the outer heliosphere. Also included is a list of publications covering the following topics: catastrophic evolution of a force-free flux rope; maximum energy release in flux-rope models of eruptive flares; sheet approximations in models of eruptive flares; material ejection, motions of loops and ribbons of two-ribbon flares; dispersion relations for parametric instabilities of parallel-propagating; parametric instabilities of parallel-propagating Alfven waves; beat, modulation, and decay instabilities of a circularly-polarized Alfven wave; effects of time-dependent photoionization on interstellar pickup helium; observation of waves generated by the solar wind pickup of interstellar hydrogen ions; ion thermalization and wave excitation downstream of the quasi-perpendicular bowshock; ion cyclotron instability and the inverse correlation between proton anisotrophy and proton beta; and effects of cosmic rays and interstellar gas on the dynamics of a wind.

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