Differential Faraday Rotation measurements between the images of same background source, of multiply-imaged gravitational lens systems can be effectively used to provide a valuable probe to establish the existence of large-scale ordered magnetic fields in lensing galaxies as well as galaxy clusters. Estimates of the magnetic field in lens galaxies, based on the radio polarization measurements do not appear to show any clear evidence for evolution with redhsift of the coherent large scale magnetic field between redshift of 0.9 and the present epoch. However, our method clearly establishes the presence of coherent large scale magnetic field in giant ellitpical galaxies.

Here we present a linear stability analysis and an MHD 2D model for the Parker-Jeans instability in the Galactic gaseous disk. The magnetic field is assumed parallel to a Galactic spiral arm, and the gaseous disk is modelled as a multi-component, magnetized, and isothermal gas layer. The model employs the observed vertical stratifications for the gas density and the gravitational acceleration in the Solar neighborhood, and the self-gravity of the gas is also included. By solving Poisson's equation for the gas density stratification, we determine the vertical acceleration due to self-gravity as a function of z. Subtracting it from the observed gravitational acceleration, we separate the total acceleration into self and external gravities. The linear stability analysis provides the corresponding dispersion relations. The time and length scales of the fastest growing mode of the Parker-Jeans instability are about 40 Myr and 3.3 kpc, respectively. In order to confirm the linear stability analysis, we have performed two-dimensional MHD simulations. These show that the Parker-Jeans instability under the self and external gravities evolves into a quasi-equilibrium state, creating condensations on the northern and southern sides of the plane, in an alternate manner.