Dipolar cohesion in densely packed confined columns

We investigate theoretically the dipolar cohesion of densely packed columnar assemblies of identical magnetic spheres confined in a cylinder, whose dipole moments are aligned by a tunable strong external magnetic field. Using exact geometrical solutions and dipolar lattice sums, we analyze how the cohesive energy depends on the cylinder diameter. In the zigzag regime, the cohesion exhibits a pronounced nonmonotonic behavior that can be rationalized in terms of competing radial and longitudinal pressures arising from a breaking of ideal head-to-tail dipolar alignment. This competition leads to a point of weakest cohesion, followed by a stabilization of the densest zigzag structure driven by long-range interchain correlations. At larger diameters, a similar bell-shaped evolution of the cohesive energy is found in the helical regime, together with a striking quasi-degeneracy between zigzag and helical morphologies. Our results are directly relevant to experiments on confined dipolar soft matter, ranging from field-responsive magnetic colloids to paramagnetic granular media.