Population-Level Gating in Dusty Plasmas: Charge-Resolved Activation and Collision Kinetics in Polydisperse Granular Media

Abstract

We develop a population formulation of threshold-conditioned grain dynamics in dusty plasmas. The formulation extends the Field-First hypothesis to polydisperse, compositionally heterogeneous populations while distinguishing electric mobilization from magnetic coupling. A charge-resolved activation probability replaces a deterministic single-grain label, and the collision rate retains inactive-inactive, mixed, and active-active encounters. We derive dimensionally consistent electric and magnetic thresholds in the Epstein and Stokes limits, closed population moments for truncated power laws, exact Gaussian charge-tail activation, and probability bounds on the error introduced by independent pair gates. For a prescribed factorized collision closure, the full initial pair rate reduces to three weighted size moments; the familiar active-fraction-squared law is recovered only in a restricted constant-kernel, active-active limit. Reproducible quadrature and independent Monte Carlo integration quantify number-versus-mass activation, response-defined material contrast, and pair-correlation uncertainty. A separate Coulomb-barrier counterexample shows that electrical activation can coexist with forbidden contact, preventing a kinematic gate from being mistaken for an aggregation instability. The results establish a parameter-explicit population framework and a falsifiable calibration protocol. Numerical examples are synthetic closure benchmarks, not experimental confirmation or self-consistent particle-in-cell simulations.