The magnetic field quantization in pulsar

Magnetic field quantization is an important issue for degenerate environments such as neutron star, radio pulsars and magnetars etc., due to the fact that these stars have magnetic field even more than the quantum critical field strength of the order of 4.4×10¹³G, accordingly the cyclotron energy may be equal or even much more than the Fermi energy of degenerate particles. We shall formulate here the exotic physics of strongly magnetized neutron star. 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.  Here we shall formulate the dispersion equations to govern the propagation of the gravitational waves both in perpendicular and parallel directions to the magnetic field, respectively.  We will depict here that the quantized magnetic field will result in Jeans anisotropic instability such that for perpendicular propagation, the quantized magnetic pressure will stabilize Jeans instability, whereas for the parallel propagation the plasma become more unstable.  We also intend to calculate the corresponding Jeans wave number in the absence of tunneling. 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.