Magnetic Dipole in a Cuboidal Superconducting Trap

• URL: http://arxiv.org/abs/2606.30808v1
• Date: Mon, 29 Jun 2026 18:32:49 GMT
• Title: Magnetic Dipole in a Cuboidal Superconducting Trap
• Abstract summary: We derive the exact image-dipole potential of a point dipole inside a closed cuboidal superconducting trap.<n>We prove that the image lattice satisfies the Meissner boundary condition on all six walls.<n>Every prediction is verified against finite-element solutions of the same boundary-value problem.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We derive the exact image-dipole potential of a point dipole inside a closed cuboidal superconducting trap. The construction generalises the parallel-plate result to a geometry that confines every translational degree of freedom, and we prove that the image lattice satisfies the Meissner boundary condition on all six walls. For a centred dipole the orientational energy reduces to a diagonal quadratic form whose three coefficients are Epstein-zeta-type lattice sums. We show that in both the infinite and finite rectangular traps the dipole orientation aligns with the \emph{short} cross-sectional axis over a finite range of aspect ratios. The equilibrium orientation in both cases is described by a phase diagram whose degeneracies we classify. Every prediction is verified against finite-element solutions of the same boundary-value problem, with agreement better than $0.16\%$.

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