Nonlinear Force-Free Vlasov-Maxwell Equilibria in Dusty Plasmas: The Role of Fluctuating Dust Charge in the Presence of Maxwellian Electrons and Ions

The conditions for force-free, nonrelativistic, translationally invariant one-dimensional Vlasov-Maxwell equilibria in dusty plasmas (Maxwellian electrons and ions, dust with fluctuating charge) are investigated. The equilibrium equations reduce to a pseudoparticle in a conservative pseudopotential proportional to a diagonal pressure tensor component. Including dust charge fluctuations adds a Hamiltonian term representing work done during charging in a varying electric potential. A necessary pseudopotential condition for force-free equilibria is derived. Numerical orbit-motion-limited charging simulations show that linear force-free solutions correspond to an attractive central pseudopotential modified by dust charging. Three dynamical regimes emerge based on the ratio of charging to pseudoparticle oscillation frequency: adiabatic (force-free persists with altered parameters), resonant (force-free destroyed), and slow (fluctuations frozen). The pseudopotential’s transformation property is verified numerically, showing how the same force-free trajectory can arise from different pressure functions despite dust effects. Sensitivity to dust density, grain size, and temperature ratios offers observational diagnostics for dusty plasmas.