Jeans anisotropic instability

The effect of quantized anisotropic magnetic pressure, arising due to a strong magnetic field, is studied on the growth rate of Jeans instability of quantum electron–ion and classical dusty plasma. Two dispersion relations are formulated for the propagation of the gravitational waves that are perpendicular and parallel to the magnetic field, respectively. It is shown that for perpendicular propagation, the quantized magnetic pressure is stabilizing the Jeans instability, whereas for the parallel propagation the plasma become more unstable with the increase in the magnetic field or we can say that Jeans instabilities becomes anisotropic in this case. The corresponding Jeans wave number is calculated in the absence of tunneling effect which shows that the magnetic field anisotropy of the Galaxy is connected with Jeans effect. Further, it is shown that the Madelung term leads to the inhomogeneity of the plasma medium. Numerical results are presented to show the effect of the anisotropic magnetic pressure on the Jeans instability.