Non-Linear Advective Electrodynamics, Magnetic Vorton Reconnection, and Topological Energy Partition in Dense Plasma Vacua

This treatise unifies electrodynamics and fluid mechanics within an incompressible fluid vacuum substrate: Advective Field Coupling: Replaces static partial time derivatives with convective material derivatives in Maxwell's system, absorbing electromagnetic and gravitational energy density gradients into a generalized pressure that sources zero spurious vorticity. Discrete Magnetic Vortons: Models continuous fields as chains of solenoidal circulation dipoles paired with proportional magnetic moments, proving that magnetic amplification is driven purely by fluid vortex stretching rather than linear magnetic self-growth. Circulation-Flux Conservation: Proves the exact conservation of generalized canonical circulation, demonstrating that fluid circulation and magnetic flux undergo continuous, reversible topological conversion. Fast Reconnection Invariant: Resolves the Sweet-Parker reconnection bottleneck by proving that the normalized plasma inflow rate across the reconnection vertex is a universal geometric constant independent of the Lundquist number. Weak Distributional Surgery: Formulates field interactions in weak integral form, regularizing continuum gradient blow-ups through an anomalous dissipation defect measure. Super-Alfvénic Plasmoid Propulsion: Proves that reconnection of curved horseshoe flux tubes converts half of trapped magnetic energy into directed kinetic energy, launching autonomous toroidal plasmoid rings at super-Alfvénic speeds. Deterministic Particle Acceleration: Derives a universal non-thermal particle power-law spectrum with an index of minus two directly from inductive acceleration at the unmagnetized null without stochastic tuning. Self-Energy Regularization & Applications: Eliminates infinite bare-mass divergences by truncating electrostatic self-energy at the autonomous vorton lattice scale, providing a unified resolution for solar flares, Parker Solar Probe magnetic switchbacks, and tokamak edge filaments.