Low-frequency wave propagations and instabilities are studied taking into account the finite electrical resistivity and viscosity of the neutrino-coupled plasma. It is assumed that the plasma is permeated by magnetic field. The formulation and analysis of the system including the Fermi weak force due to neutrino plasma coupling is done by neutrino magneto hydrodynamics model. The general dispersion relation is derived from the set of perturbed equations to signify the role of dissipative effects on the growth rate and condition of both neutrino instability and self-gravitational instability. To discuss the influence of resistivity and viscosity on the dynamics of the system, the general dispersion relation is reduced for both perpendicular and parallel mode of propagations. The self-gravitating modes are modified by the presence of neutrinos, viscosity, and resistivity in both perpendicular and parallel modes of propagation, while the gravitational instability criterion is modified only by neutrinos. It is also observed that the number density of neutrinos works against the gravitational instability, while the neutrino beam-free energy supports the self-gravitational instability. In the case of perpendicular propagation, the neutrino beam instability criterion and growth rate are affected by dissipative effects.

The effect of non-thermal ion population on self-gravitational instability of magnetized dusty plasma considering electrons are in Maxwell-Boltzmann distribution has been investigated. The dust dynamics is described including polarization force, thermal velocity, and charge fluctuation dust. The modified general dispersion relation has been derived including non-thermal ion population, polarization force, and dust charge fluctuation for self-gravitating dusty plasma system, using the normal mode analysis method. The obtained general dispersion relation is discussed in parallel and perpendicular modes of propagation. The population of non-thermal ion, polarization force and dust charge fluctuation affect the self-gravitational instability criteria in both the modes of propagation while the magnetic field affects the instability criterion only in perpendicular mode of propagation. The domains of instability has been discussed analytically to signify the importance of considered parameters. The stability of the self-gravitating dusty plasma system has been analyzed using Routh-Hurwitz stability criterion. Numerical calculations have been performed to analyze the effects of non-thermal ion population, polarization force, and dust charge fluctuation on the growth rate of self-gravitational instability. The results of the present work can be useful in self-gravitating dusty plasma found in space and the interstellar medium such as the interstellar molecular clouds where non-thermally distributed ions are the species of the plasma matter.

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The ion acoustic solitary and shock waves are studied in strongly coupled nonrelativistic and relativistic plasma. The wave profile has been discussed for the kinetic and hydrodynamic regimes. The ions are considered to be strongly coupled, and electrons as degenerated and relativistic to deal with nonlinear waves using continuity and Poisson’s equations together with generalized hydrodynamical (GH) and quantum hydrodynamical (QH) models. The reductive perturbation method is used to formulate Korteweg–de Vries (KdV) and Korteweg–de Vries Burgers (KdVB) equations in both nondegenerate and degenerated cases. The effects of relativistic, degeneracy parameter and longitudinal viscosity coefficient on the profile of nonlinear waves are discussed. The amplitude and width of a shock in both nonrelativistic and ultrarelativistic cases increase with an increase in the viscosity coefficient, while with an increase in the electron diffraction parameter, the amplitude and width of the shock wave increase, and for a solitary wave decreases in both the nonrelativistic and ultra-relativistic cases. It is also shown that solitary ion acoustic wave propagates with more energy in nonrelativistic plasma than ultrarelativistic. The results of the work will be useful, for example, for astrophysics to understand the process of wave propagation in dense astrophysical bodies.

The effect of radiative heat-loss function on the Jeans instability of an infinitely conducting, homogeneous partially ionized gaseous plasma is investigated. It is assumed that the medium is carrying a uniform magnetic field in the presence of porosity and thermal conductivity. With the help of relevant linearized perturbation equations of the problem, a general dispersion relation is obtained for a such medium using the normal analysis technique, which is reduced for both the transverse and the longitudinal mode of propagation. The longitudinal mode is found to be modified by Alfven speed and parameter of porosity. The thermal mode is obtained separately having the effects of thermal conductivity and arbitrary radiative heat-loss functions. The effect of collision with neutrals and magnetic field have a stabilizing effect, while thermal conductivity has destabilizing influence on the Jeans instability of gaseous plasma. In the transverse mode of propagation, we find the condition of radioactive instability depends on thermal conductivity, magnetic field and the porosity of the medium.