Dust-ion-acoustic solitary waves and their multi-dimensional instability in a magnetized dusty electronegative plasma with trapped negative ions

A theoretical investigation has been made on obliquely propagating dust-ion-acoustic solitary waves (DIASWs) in magnetized dusty electronegative plasma containing Boltzmann electrons, trapped negative ions, cold mobile positive ions, and arbitrarily charged stationary dust. The reductive perturbation method has been employed to derive the modified Zakharov-Kuznetsov (MZK) equation which admits solitary wave solution under certain conditions. The multi-dimensional instability of these solitary waves is also studied by the small-k (long wavelength plane wave) perturbation-expansion technique. The basic properties (speed, amplitude, width, instability, etc.) of small but finite amplitude DIASWs are significantly modified by the effects of external magnetic field, obliqueness, polarity of dust, and trapped negative ions. The implications of our results in space and laboratory plasmas are briefly discussed.     

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

A Kelvin-Helmholtz instability has been identified numerically on an azimuthally symmetric Alfvén resonant layer in an axially bounded, straight cylindrical coronal loop. The physical model employed is an incompressible, reduced magnetohydrodynamic (MHD) model including resistivity, viscosity, and density variation. 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 Alfvén driving amplitude and inversely proportional to the width of the Alfvén 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 Alfvén resonant layer width, and decreases at higher m's. (m is the azimuthal mode number.)     

Kink instability of a non-static plasma column

Starting with MHD equations we study the linear theory of stability of a plasma column with flow. From the dispersion equation derived, we calculate the dispersion curves and thereby estimate the effect of a flow in the linear theory. We find that, like the toroidal component of the magnetic field, a flow promotes instability: the rate of growth of instability may be increased by one or two orders of magntiude and the wavelength range for instability is also increased. When the flow velocity is large, the m=o and m=1 modes may appear almost together. Finally, a qualitative interpretation of three typical solar events is given on the basis of our results.     

Thermal instability in a weakly ionized plasma

We revisit the problem of clump formation due to thermal instabilities in a weakly ionized plasma with the help of a linear perturbation analysis, as discussed by Nejad-Asghar & Ghanbari. In the absence of a magnetic field and ambipolar diffusion the characteristic equation reduces to the thermal instability described by Field. We derive the critical wavelengths, which separate the spatial ranges of stability and instability. Contrary to the original analysis of Nejad-Asghar & Ghanbari, perturbations with a wavelength larger than the critical wavelength destabilize the cloud. Moreover, the instability regime of isentropic perturbations is drastically reduced. Isobaric modes with real values of the critical wavelength appear only if the density dependence of the cooling rate is more pronounced than the temperature dependence. Isentropic modes arise only if the power of the density in the cooling rate is smaller than 1/2, which is not fulfilled for CO cooling. We find that ambipolar diffusion is not a dominating heating process in molecular gas.     

Filamentation of volcanic plumes on the Jovian satellite Io

Volcanic plumes on the Jovian satellite Io may be a visible manifestation of a plasma-arc discharge phenomenon. The amount of power in the plasma arc (10¹¹ W) is not enough to account for all the energy dissipated by the volcanoes. However, once a volcano is initiated by tidal and geologic processes, the dynamics of the volcanic plumes can be influenced by the plasma arcs. As initially pointed out by Gold (1979), plasma arcs are expected because of 10⁶ A currents and 400 kV potentials generated by the flow past Io of a torus of relatively dense magnetospheric plasma. We utilize our experience with laboratory plasma arcs to investigate the plume dynamics. The filamentation in the plume of the volcano Prometheus and its cross-sectional shape is quantitatively consistent with theories developed from laboratory observation.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

A linear MHD instability analysis of solar mass ejections with gravitation

Solar mass ejections seem, on the basis of many observations, to be divided into two categories: stable and unstable. We use linear magnetohydrodynamic (MHD) instability of a cylindrical plasma in an attempt to search for a theoretical explanation for this phenomenon. The dispersion relation is obtained and solved numerically. It is found that the initial plasma-flow velocity has a significant effect on the instability criteria and growth rate. Also found is that the instability growth-rate is much larger in those cases where plasma flow exists in comparison with the static case. The wave number range where the instability may occur also becomes wider with plasma flow. Further, it is shown that the region of the instability shifts to the short wavelength region with increasing plasma-flow velocity. Therefore, the plasma column may break into small pieces, resembling the melon seed phenomenon that has been suggested as a mechanism for mass ejection in the solar atmosphere. Under the assumption of a thin-tube approximation we show that gravity has little effect on the instability of quasi-horizontal ejection, but it has considerable effect for the vertical ejection. In order to deal with the gravitational force it is convenient to divide the problem into three cases: horizontal, vertical, and oblique. The exact analytical solution exists only in the vertical case. Asymptotic solutions are given in the horizontal and oblique cases.     

Non-linear waves in type-1 comet tails

The non-linear stabilization of Kelvin-Helmholtz instability occurring when disturbance amplitudes become finite is studied. A comet tail is considered as a plasma cylinder with free boundary immersed in the solar wind plasma. Due to Kelvin-Helmholtz instability of kink modes the type-1 comet tail is shown to take stable shape. However the sausage-like modes with wavelength of cylinder circumference cannot be stabilized due to finite amplitudes. The Kelvin-Helmholtz instability of sausage modes leads to the comet tail (or individual ray) losing its regular structure and breaking into individual clouds with the characteristic scale of the order of the cylinder diameter.     

Gravitational instability of suprathermal hydromagnetic plasma

The paper models the suprathermal plasma as the concatenation of two different gravitating fluids each having its own separate density and pressure. One of the fluids has isotropic pressure while the other has an anisotropic pressure. The system is subjected to a uniform magnetic field which is frozen with the fluids. The gravitational instability of the model for low frequency plane waves has been investigated in a linear framework for plasma parameters relevant to the spiral arms of the galaxy and the cosmic gas clouds. The analysis shows that the wavelength of the instability is strongly dependent upon the anisotropy of the non-thermal plasma.     

The Kelvin-Helmholtz instability in the low-latitude boundary layer

The Kelvin-Helmholtz instability on the magnetopause has frequently been invoked as a mechanism for driving geomagnetic pulsations in the Pc3–Pc5 range, as well as to explain the occurrence of surface waves on the magnetopause observed by satellites. Most theories of the instability represent the magnetopause by a sharp boundary with velocity shear. In this paper a linear theory is developed which takes into account the finite thickness of the low-latitude boundary layer on the magnetopause. The theory is in a form suitable for numerical computation and can take into account the effect of gradients in the plasma pressure, magnetic field magnitude and direction, and density. Computations show that the instability is suppressed at wavelengths short compared with the scale width of the boundary. There is thus a wavelength for which the growth rate is maximum. Extensive computations have been carried out and they show that growth can take place for a very wide range of conditions. The computations confirm earlier results snowing that maximum growth occurs for a wave vector which is perpendicular to the magnetic field. For typical solar wind conditions the theory predicts wavelengths on the magnetopause of the order of 10 times the thickness of the low-latitude boundary layer and periods in the Pc3–Pc5 range. The possible non-linear development of the instability is discussed qualitatively. The predicted results are consistent with satellite observations of pulsations.     

The stability of an anisotropic plasma jet

The modified Chew-Goldenberger-Low equations have been used to study the stability of a resistive anisotropic plasma jet surrounded by a non-conducting compressible gas. The dispersion relation has been obtained and discussed in three limiting situations: (i) , the resistivity vanishingly small, (ii) and (iii) short and long wavelength perturbations. In some cases, the limiting situations 1 or 1 ( is the ratio of the density of the plasma jet to the density of the exterior gas) have been discussed. The conditions for instability have been obtained. It has been found that the resistivity introduces new modes which make the plasma jet overstable. In the limit of large wavelength disturbances, the jet with finite but high conductivity is found to be unstable. For small wavelength disturbances, the jet is found to be unstable.     

The shearing instability of ion flow at the high-latitude tail of magnetopause boundary layer

Shearing instability of ion flow in an inhomogeneous plasma background in the magnetopause boundary layer at the high-latitude magnetotail is studied in this paper. By considering tail-aligned currents, we find that the instability excitation strongly depends on the disturbed wavelength. A quasi-critical wave number for instability is obtained. For relatively long perturbations, the instability tends to be excited at the inner edge of the boundary layer. The stable surface waves at the magnetopause and the K-H instability at the inner edge of the boundary layer can exist at the same time. This may contribute to the continuous transfer of momentum toward the magnetosphere.     

Stability of Hamiltonian Systems with Three Degrees of Freedom and the Three Body-Problem

Results are obtained about formal stability and instability of Hamiltonian systems with three degrees of freedom, two equal frequencies and the matrix of the linear part is not diagonalizable, in terms of the coefficients of the development in Taylor series of the Hamiltonian of the system. The results are applied to the study of stability of the Lagrangian solutions of the Three Body-Problem in the case in which the center of mass is over the curve ρ_*, on the border of the region of linear stability of Routh. The curve ρ_* is divided symmetrically in three arcs in such a way that if the center of mass of the three particles lies on the central arc, the Lagrangian solution is unstable in the sense of Liapunov (in finite order), while if the center of mass determines one point that lies on one of the other two arcs of ρ_*, then the Lagrangian solution is formally stable.     

Kelvin-Helmholtz instability of the magnetopause boundary: Comparison with observed fluctuations

We present a numerical investigation of the Kelvin-Helmholtz instability problem, in MHD approximation, for transitions involving continuous variations of both magnetic field and plasma parameters. The variations have been chosen in such a way as to reproduce general features of possible magnetopause transitions. The study, which leads to prediction of a wavelength of maximum instability, has been confronted with recent observational results of surface fluctuations of the magnetopause.     

Dust-ion-acoustic solitary waves and their multi-dimensional instability in a magnetized nonthermal dusty electronegative plasma

A rigorous theoretical investigation has been made on multi-dimensional instability of obliquely propagating electrostatic dust-ion-acoustic (DIA) solitary structures in a magnetized dusty electronegative plasma which consists of Boltzmann electrons, nonthermal negative ions, cold mobile positive ions, and arbitrarily charged stationary dust. The Zakharov-Kuznetsov (ZK) equation is derived by the reductive perturbation method, and its solitary wave solution is analyzed for the study of the DIA solitary structures, which are found to exist in such a dusty plasma. The multi-dimensional instability of these solitary structures is also studied by the small-k (long wave-length plane wave) perturbation expansion technique. The combined effects of the external magnetic field, obliqueness, and nonthermal distribution of negative ions, which are found to significantly modify the basic properties of small but finite-amplitude DIA solitary waves, are examined. The external magnetic field and the propagation directions of both the nonlinear waves and their perturbation modes are found to play a very important role in changing the instability criterion and the growth rate of the unstable DIA solitary waves. The basic features (viz. speed, amplitude, width, instability, etc.) and the underlying physics of the DIA solitary waves, which are relevant to many astrophysical situations (especially, auroral plasma, Saturn’s E-ring and F-ring, Halley’s comet, etc.) and laboratory dusty plasma situations, are briefly discussed.     

Effect of general loss-cone distribution function on electrostatic ion-cyclotron instability in an inhomogeneous plasma: particle aspect analysis

The electrostatic ion-cyclotron instability (EICI) in low β (ratio of plasma to magnetic pressure), anisotropic, inhomogeneous plasma is studied by investigating the trajectories of the particles using the general loss-cone distribution function (Dory-Guest-Harris type) for the plasma ions. In particular, the role of the loss-cone feature as determined by the loss-cone indices, in driving the drift-cyclotron loss-cone (DCLC) instability is analysed. It is found that for both long and short wavelength DCLC mode the loss-cone indices and the perpendicular thermal velocity affect the dispersion equation and the growth rate of the wave by virtue of their occurrence in the temperature anisotropy. The dispersion relation for the DCLC mode derived here using the particle aspect analysis approach and the general loss-cone distribution function considers the ion diamagnetic drift and also includes the effects of the parallel propagation and the ion temperature anisotropy. It is also found that the diamagnetic drift velocity due to the density gradient of the plasma ions in the presence of the general loss-cone distribution acts as a source of free energy for the wave and leads to the generation of the DCLC instability with enhanced growth rate. The particle aspect analysis approach used to study the EICI in inhomogeneous plasma gives a fairly good explanation for the particle energisation, wave emission by the wave–particle interaction and the results obtained using this particle aspect analysis approach are in agreement with the previous theoretical findings using the kinetic approach.     

Boundary layer plasmas as a source for high-latitude, early afternoon, auroral arcs

Simultaneous measurements of hot boundary layer plasma from PROGNOZ-7 and particle precipitation from the TIROS/NOAA satellite in nearly magnetically conjugate regions have been used to study the dynamo process responsible for the formation of high latitude, early afternoon, auroral arcs.

Characteristic for the PROGNOZ-7 observations in the dayside boundary layer at high latitudes is the frequent occurrence of regions with injected magnetosheath plasma embedded in a “halo” of antisunward flowing magnetosphere plasma. The injected magnetosheath plasma have several features which indicate that it also acts as a local source of EMF in the boundary layer. The process resembles that of a local MHD dynamo driven by the excess drift velocity of the injected magnetosheath plasma relative to the background magnetospheric plasma.

The dynamo region is capable of driving field-aligned currents that couple to the ionosphere, where the upward current is associated with the high latitude auroral arcs.

We demonstrate that the large-scale morphology as well as the detailed data intercomparison between PROGNOZ-7 and TIROS-N both agree well with a local injection of magnetosheath plasma into the dayside boundary layer as the main dynamo process powering the high-latitude, early afternoon auroral arcs.     

On the stability of almost perpendicularly propagating ion cyclotron waves

The dispersion relation for the near perpendicular propagation of the electromagnetic ion cyclotron wave, having a wavelength much larger than the ion Larmour radius r_L and a frequency $\text{ω ≈ Ω}{}^{\mathrm{+}}\text{(Ω}{}^{\mathrm{+}}$ is the ion cyclotron frequency), has been derived for a plasma consisting of a hot and a cold ion component. The hot ions and electrons have been described by loss-cone distribution functions; an ordering of the parameters was used to derive the cold ion contributions. Two modes, one with an increasing frequency and another with a constant frequency can propagate in the plasma. The two modes interact resulting in an instability of the former in the wavelength range k_⊥r_⊥ = 0.4?0.6 (for n_C/n_H = 0) and from k_⊥r_L = 0.5?0.8 (for n_C/n_H = 1.0) for a propagation angle of 70°. The instability of the mode is found to decrease with increasing cold ion densities and propagation angles.