Parker's model prediction of an unbounded solution for the supersonic solar wind plasma (SWP) requires a subsonic origin at the solar surface. The transition to supersonic SWP flow is well understood by analogy with the de Laval nozzle. The basic physics, however, of the self-consistent solar surface emission of subsonic SWP is still not very clear. We propose a theoretical model based on a gravito-electrostatic plasma sheath (GES) to investigate the surface emission mechanism of the quasi-neutral SWP. The basic equations for the interior steady state description are solved numerically as an initial-value problem under spherical geometry. A bounded solution for the solar self-gravity distribution is found to exist, meaning that a global quasi-hydrostatic equilibrium is formed at some distance from the heliocentric origin. This defines the solar surface boundary in our model, which lies at radius $ 3.5 (in units of the Jeans length). A minimum speed of $3.0 cm s À1 , corresponding to Mach number $10 À7 , is obtained at this location. Consequently, a subsonic origin of the solar interior plasma flowing radially outward becomes a physical reality. Our model requires a mean electron temperature T e $ 10 7 K (=1 keV) for the numerical results to match the standard solar values. The boundary is found to be negatively biased, with a normalized value of the electrostatic potential s $ À1 (=1 kV ). It is conjectured that our model provides an interesting new physical basis for understanding the collective dynamical coupling processes of solar interior and exterior ( heliosphere) regions through local, as well as global, modes of GES-induced collective waves, instabilities, and oscillations.

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It is recently discussed that a plasma system with drifting ions at near the acoustic phase speed becomes susceptible to weak but finite electron inertial delay effect. In such plasma condition, the linear normal modes of acoustic oscillations undergo resonant linear growth. Such situation exists naturally in transonic zones of boundary plasma layers. The present contribution considers this as a specific case to describe the possible role of an external source driving on the usual ion acoustic soliton solution in the unstable region of the transonic zone assumed to have finite extension. A driven Korteweg-de Vries equation is obtained that is not exactly integrable. It is shown by numerical analysis that the usual acoustic soliton solution exists only for infinitely long wavelength source perturbation. For short wavelength (but within the limit of the long wavelength approximation) source perturbations interesting solutions of single unit of localized oscillatory shock-like structure are obtained. Possible physical interpretations of the results are included in the text.Ã Bharat is an ancient country and is also known as India in recent times.

The pulsational mode of gravitational collapse (PMGC) in a hydrostatically bounded dust molecular cloud is responsible for the evolution of tremendous amount of energy during star formation. The source of free energy for this gravito-electrostatic instability lies in the associated self-gravity of the dispersed phase of relatively huge dust grains of solid matter over the gaseous phase of background plasma. The nonlinear stability of the same PMGC in an infinite dusty plasma model (plane geometry approximation for large wavelength fluctuation in the absence of curvature effects) is studied in a hydrostatic kind of homogeneous equilibrium configuration. By the standard reductive perturbation technique, a Korteweg-de Vries (KdV) equation for investigating the nonlinear evolution of the lowest order perturbed self-gravitational potential is developed in a time-stationary (steady-state) form, which is studied analytically as well as numerically. Different nonlinear structures (soliton-like and soliton chain-like) are found to exist in different situations. Astrophysical situations, relevant to it, are briefly discussed.

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Recently, the practical significance of the asymptotic limit of me∕mi→0 for electron density distribution has been judged in a two-component plasma system with drifting ions. It is reported that in the presence of drifting ions with drift speed exceeding the ion acoustic wave speed, the electron inertial delay effect facilitates the resonance coupling of the usual fluid ion acoustic mode with the ion-beam mode. In this contribution the same instability is analyzed by graphical and numerical methods. This is to note that the obtained dispersion relation differs from those of the other known normal modes of low frequency ion plasma oscillations and waves. This is due to consideration of electron inertial delay in derivation of the dispersion relation of the ion acoustic wave fluctuations. Numerical calculations of the dispersion relation and wave energy are carried out to depict the graphical appearance of poles and positive-negative enegy modes. It is found that the electron inertia induced ion acoustic wave instability arises out of linear resonance coupling between the negative and positive energy modes. Characterization of the resonance nature of the instability in Mach number space for different wave numbers of the ion acoustic mode is presented.

We present a nonlinear stability analysis for an idealistic field-free hydrodynamic model of a self-gravitating massive charged dust molecular cloud in the presence of dust grain velocity convection. Identical spherical dust grains are equally charged, but the cloud as a whole is electrically neutral on the Jeans scale. Application of a multiscale analytical method shows that the self-gravitational potential fluctuation dynamics is governed by a new type of modified Korteweg–de Vries–Burger equation that has a self-consistent linear driving derivative source arising from dust flow convection. A detailed numerical analysis of the eigenmode structures in the steady state is carried out. It is found that the self-gravitational potential fluctuations contribute in the form of new oscillatory shock-like structures because of gravito-electrostatic coupling. The distinctive features of the eigenmode profiles are discussed in detail. In addition, the main conclusions relevant to the astrophysical context are briefly presented.

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