Nonlinear kinetic simulations of Jeans instability in a magnetized dusty plasma

The Jeans instability in a magnetized dusty plasma is considered a fundamental process in space, where magnetic fields are common. We investigate the Jeans instability in a magnetized dusty plasma using 1D and 2D particle-in-cell simulations, in which dust grains are treated as particles and the Poisson's equation for the corresponding gravitational and electrostatic potentials is solved in a self-consistent manner. We first confirm that when the magnitude of the dust cyclotron frequency is larger than the Jeans frequency, the Jeans instability is completely stabilized, and the PIC simulation of the stable case shows the existence of cyclotron harmonics in the dispersion relation as predicted by the kinetic linear theory. In unstable cases, we find that the linear growth obtained by the simulations and the fluid and kinetic linear theory are consistent with each other, showing that the linear growth rate decreases as the magnetic field becomes stronger. The magnetized Jeans instability is also qualitatively modified due to the gyromotion of dust grains: (1) a dipole-like structure is observed in phase space and the density peak at the bottom of the gravitational potential is 3 times larger than the nonmagnetized case in the 1D simulation; and (2) dust grains form a filament, which corresponds to the direction in which the gyrating dust grains are accelerated by the gravitational potential, during the linear stage of the instability in the 2D simulation while dust grains condensate at a point in the nonmagnetized case.