Multi-Domain Generalization of Operational Phase Basins: From Celestial Mechanics to MHD Wave Coupling and Vacuum Field States

Traditional paradigms of interplanetary trajectory optimization treat robust flight corridors as empirical products of brute-force numerical searches rather than deterministic consequences of underlying variational geometry. This paper introduces a profound multidomain generalization of the B2 operational phase basin framework, lifting it from discrete N-body point-mass dynamics to continuum magnetohydrodynamic (MHD) plasma flows and quantum-geometric vacuum fields. The proposed unified framework formalizes navigation corridors as open sets in parameter space governed by a generalized stationarity condition of the action principle (δS/δϕ = 0) coupled with positive definite second-order variational curvature (δ2S/δϕ2 > 0). In the gravitational domain, this framework maps launch epochs to asymptotic arrival geometries, yielding a 16.65% flight-time reduction for Earth–Jupiter transfers and a 4–5× reduction in the trajectory-correction maneuver (TCM) budget, validated down to rare-event failure tails (Pf ∼ 10−6 ) via Importance Sampling. Transitioning to continuous media, we prove the existence of an MHD phase basin (∆ϕMHD = ±12.8◦) where resonant impedance matching with Alfvenic wave fields suppresses initial position dispersion by a factor of 9 over 30 days without reactive mass expulsion. Finally, we formulate a phenomenological effective action for vacuum polarization states, identifying a stable vacuum phase basin (∆ϕvac = ±7.1◦ ) where a spacecraft tracks localized energy-density minima via the principle of least action. These parallel derivations demonstrate that operational phase basins are not numerical artifacts of specific astrodynamical setups, but universal mathematical operators of stationarity that bridge celestial mechanics, plasma physics, and field theory into a single non-propulsive navigation framework.