Classical Maxwell Duality, Magnetic Flux String Confinement, and Monopole Dimers as a Classical Dark Matter Model

The original Maxwell equations break electric-magnetic duality due to the absence of magnetic charges and magnetic currents. This purely classical work extends Maxwell equations to fully dual-symmetric form by introducing magnetic charge and magnetic current densities, with all derivations carried out under natural units . Drawing an analogy to classical vortex configurations in type-II superconductors, we construct a magnetic flux string connecting opposite magnetic monopoles, and compute string tension via integrating classical field energy. The effective potential between a monopole and an antimonopole consists of magnetic Coulomb attraction, linear string confinement, and a short-range repulsive core term. Using analytical mechanics, we solve the equilibrium separation and small oscillation frequency of the bound dimer system. Classical thermodynamics predicts a critical temperature above which flux strings vanish, offering a possible classical interpretation for the non-observation of free monopoles in the cold present universe. The monopole dimer is electromagnetically neutral yet carries an electric quadrupole moment. Its scattering cross section with ordinary nuclei is heavily suppressed, consistent with null results from underground dark matter direct detection experiments. Virial theorem analysis reproduces dwarf galaxy core radii at the correct order of magnitude. No quantum field theory or grand unification frameworks are adopted throughout this work. All model parameters are clearly distinguished from quantum counterparts to avoid numerical confusion.