Numerical and analytical investigations of thermosolutal instability in rotating Rivlin-Ericksen fluid in porous medium with Hall current

Numerical and analytical investigations of the thermosolutal instability in a viscoelastic Rivlin-Ericksen fluid are carried out in the presence of a uniform vertical magnetic field to include the Hall current with a uniform angular velocity in a porous medium. For stationary convection, the stable solute gradient parameter and the rota- tion have stabilizing effects on the system, whereas the magnetic field and the medium permeability have stabilizing or destabilizing effects on the system under certain condi- tions. The Hall current in the presence of rotation has stabilizing effects for sufficiently large Taylor numbers, whereas in the absence of rotation, the Hall current always has destabilizing effects. These effects have also been shown graphically. The viscoelastic effects disappear for stationary convection. The stable solute parameter, the rotation, the medium permeability, the magnetic field parameter, the Hall current, and the vis- coelasticity introduce oscillatory modes into the system, which are non-existent in their absence. The sufficient conditions for the non-existence of overstability are also obtained.

Instabilities in a Self-Gravitating Magnetized Gas Disk

A linear stability analysis has been performed onto a self-gravitating magnetized gas disk boundxed by external pressure. The resulting dispersion relation is fully explained by three kinds of instability: a Parker-type instability driven by self-gravity, usual Jeans gravitational instability and convection. In the direction parallel to the magnetic fields, the magnetic tension completely suppresses the convection. If the adiabatic index γ is less than a certain critical value, the perturbations trigger the Parker as well as the Jeans instability in the disk. Consequently, the growth rate curve has two maxima: one at small wavenumber due to a combination of the Parker and Jeans instabilities, and the other at somewhat larger wavenumber mostly due to the Parker instability. In the horizontal direction perpendicular to the fields, the convection makes the growth rate increase monotonically upto a limiting value as the perturbation wavenumber gets large. However, at small wavenumbers, the Jeans instability becomes effective and develops a peak in the growth rate curve. Depending on the system parameters, the maximum growth rate of the convection may or may not be higher than the peak due to the Jeans-Parker instability. Therefore, a cooperative action of the Jeans and Parker instabilities can have chances to over-ride the convection and may develop large scale structures of cylindrical shape in non-linear stage. In thick disks the cylinder is expected to align its axis perpendicular to the field, while in thin ones parallel to it.

Absolute and Convective Instabilities of Two-Plasmon Decay in an Inhomogeneous Magnetized Plasma

Three-wave resonant parametric decay instability of extraordinary wave decay into two upper hybrid waves in an inhomogeneous plasma is studied theoretically. Analytical expressions of the local absolute growth rate, convective amplification factor and threshold intensity are obtained. The calculated results show that the effects of magnetic field and ky （ICy is the component of the wavenumber of upper hybrid wave perpendicular to pump wave k0） on the growth rate, amplification factor and threshold intensity are extremely dependent on their strength. The absolute growth rate and convective amplification factor increase with the plasma density while the threshold decreases. Moreover, the expression indicates that the inhomogeneity scale length of density and linear damping will reduce the convective amplification factor.