Magnetic Flux Topology of 2D Point Dipoles

Abstract

Magnetic fields exhibit higher-order, nonlinear singularities in the form of point-dipole singularities. In addition, due to absence of divergence, they feature only a subset of invariant structures from traditional vector field topology. For magnetic fields of sets of point dipoles - widely present in physics and often used as an approximation - we present a technique revealing the topology of magnetic flux. The flux topology is identified with areas covered by field lines that directly connect pairs of dipoles. We introduce the dipole connectrix as a reduced one-manifold representation of those areas. The set of connectrices serves as our concise visualization of the global structure of magnetic flux. In addition, the quantitative values of flux are displayed by the thickness of the connectrices. We evaluate our technique for simulations of ferroparticle monolayers and magnetic gels.