Formation of multiscale structures in a self-gravitating dusty plasma with matter current

I investigate the formation of multiscale magnetic-field structures in a rotating, self-gravitating dusty plasma comprising electrons, ions, and charged dust grains. By incorporating the gravitomagnetic field, arising from mass currents in rotating astrophysical objects, into a three-component fluid model, I derive a triple-curl Beltrami equilibrium characterized by three distinct spatial scales. These scales emerge from the eigenvalues of a governing cubic equation, reflecting the combined effects of self-gravitation, rotation, and electromagnetic interactions. The model provides novel insights into the role of rotation and gravity in plasma self-organization, with potential implications for star and cluster formation in astrophysical environments. In particular, I estimate that centimeter-sized dust grains in dense rotating molecular clouds can experience gravitational and electromagnetic forces of comparable magnitude, significantly altering the equilibrium magnetic and flow-field profiles.