The possibility of relaxation in Quadruple Beltrami states in a four-component magneto dusty plasma

The possibility of relaxation in Quadruple Beltrami states for a system of dusty plasma of opposite polarity dust particles, electrons, and ions has been investigated. The macroscopic magnetic field structures are investigated in alliance with the differential flows of electrons, ions, positively and negatively charged dust grains. For a certain set of Beltrami parameters, it is observed that the system self-organized to Quadruple Beltrami state which is characterized by four eigenvalues. To derive Quadruple Beltrami equation, two different cases are assumed. The system allows a fully diamagnetic structure by considering all the inertial forces. The development of paramagnetic and diamagnetic structures has been observed by just ignoring the inertial effects of electrons. It has been shown that the features (paramagnetic or diamagnetic) of the relaxed structures are significantly modified by the eigenvalues and masses of the oppositely charged dust particles.