Influence of Coulomb screening on wave dynamics and Jeans instability in high-density magnetized dusty plasmas

The Coulomb acoustic mode identified in high-density dusty plasmas by Avinash et al. [Phys. Plasmas 31, 083702 (2024)] is extended to magnetized, self-gravitating plasmas. The linear dispersion characteristics of the Jeans instability and the associated wave dynamics are investigated in a Coulomb-screened dense, magnetized dusty plasma. Coulomb screening gives rise to a dust acoustic mode in the Coulomb regime and significantly modifies the phase speed of low-frequency magnetohydrodynamic waves, as well as the Jeans instability criterion determining the collapse rate of dust clouds. For strong Coulomb screening, the phase speed of the slow magnetosonic mode overlaps with the Alfvén mode, whereas in the weak screening regime, it remains smaller than the Alfvén mode. The additional electrostatic stiffness introduced by Coulomb screening increases the wave phase speed and suppresses the growth rate of unstable gravitational modes. In the transverse propagation, the instability region is strongly suppressed toward the longer wavelengths due to an increase in the dust-to-mass ratio. Numerical calculations of dense astrophysical dust clouds have shown that Coulomb screening increases the effective Jeans length, thereby making the system gravitationally unstable to large-scale perturbations.