We study magnetothermal instability in the ionized plasmas including the effects of Ohmic, ambipolar and Hall diffusion. Magnetic field in the single fluid approximation does not allow transverse thermal condensations, however, non-ideal effects highly diminish the stabilizing role of the magnetic field in thermally unstable plasmas. Therefore, enhanced growth rate of thermal condensation modes in the presence of the diffusion mechanisms speed up the rate of structure formation.

In this paper, we investigate the time evolution of quasi-spherical polytropic accretion flow with a toroidal magnetic field. We focus in particular on the astrophysically important case in which the adiabatic exponent γ = 5/3. In this scenario, we have assumed that the angular momentum transport is a result of viscous turbulence and we have used the α-prescription for the kinematic coefficient of viscosity. The equations of accretion flow are solved in a simplified one-dimensional model that neglects the latitudinal dependence of the flow. In order to solve the integrated equations that govern the dynamical behaviour of the accretion flow, we have used a self-similar solution. The solution provides some insight into the dynamics of quasi-spherical accretion flow and avoids many of the strictures of the steady self-similar solution. The effect of the toroidal magnetic field is considered with an additional variable β[= p mag /p gas ], where p mag and p gas are the magnetic pressure and gas pressure, respectively. The solution indicates a transonic point in the accretion flow, that this point approaches the central object by adding the strength of the magnetic field. Also, by adding the strength of the magnetic field, the radial thickness of the disc decreases and the disc compresses. We indicate analytically that the radial velocity is only a function of Alfvén velocity. The model implies that the flow has differential rotation and is sub-Keplerian at all radii.

The present study examines the self-similar evolution of advection-dominated accretion flow (ADAF) in the presence of a toroidal magnetic field. In this research, it was assumed that angular momentum transport is due to viscous turbulence and the α-prescription was used for the kinematic coefficient of viscosity. The flow does not have a good cooling efficiency and so a fraction of energy accretes along with matter on to the central object. The effect of a toroidal magnetic field on such a system with regard to the dynamical behaviour was investigated. In order to solve the integrated equations that govern the dynamical behaviour of the accretion flow, a self-similar solution was used. The solution provides some insights into the dynamics of quasi-spherical accretion flow, and avoids many of the strictures of steady self-similar solutions. The solutions show that the behaviour of the physical quantities in a dynamical ADAF is different from that for a steady accretion flow or a disc using a polytropic approach. The effect of the toroidal magnetic field is considered using additional variable β (= p mag /p gas , where p mag and p gas are the magnetic and gas pressure, respectively). Also, to consider the effect of advection in such systems, the advection parameter f , which stands for the fraction of energy that accretes by matter on to the central object, was introduced. The solution indicates a transonic point in the accretion flow for all selected values of f and β. Also, by increasing the strength of the magnetic field and the degree of advection, the radial thickness of the disc decreases and the disc compresses. The model implies that the flow has differential rotation and is sub-Keplerian at small radii and super-Keplerian at large radii, and that different results were obtained using a polytropic accretion flow. The β parameter obtained was a function of position, and increases with increasing radii. Also, the behaviour of ADAF in a large toroidal magnetic field implies that different results are obtained using steady self-similar models in large magnetic fields.

The purpose of this paper is to explore the effect of magnetic fields on the dynamics of magnetized filamentary molecular clouds. We suppose there is a filament with cylindrical symmetry and two components of axial and toroidal magnetic fields. In comparison to previous works, the novelty in the present work involves a similarity solution that does not define a function of the magnetic fields or density. We consider the effect of the magnetic field on the collapse of the filament in both axial and toroidal directions and show that the magnetic field has a braking effect, which means that the increasing intensity of the magnetic field reduces the velocity of collapse. This is consistent with other studies. We find that the magnetic field in the central region tends to be aligned with the filament axis. Also, the magnitude and the direction of the magnetic field depend on the magnitude and direction of the initial magnetic field in the outer region. Moreover, we show that more energy dissipation from the filament causes a rise in the infall velocity.

The artificial viscosity is reconsidered in smoothed particle hydrodynamics to prevent inter-particle penetration, unwanted heating, and unphysical solutions. The coefficients in the Monaghan's standard artificial viscosity are considered as time variable, and a restriction on them is proposed such that avoiding the undesired effects in the subsonic regions. The shock formation in adiabatic and isothermal cases are used to study the ability of this modified artificial viscosity recipe. The computer experiments show that the proposal appears to work and the accuracy of this restriction is acceptable.