Exact and Computationally Robust Solutions for Cylindrical Magnets Systems with Programmable Magnetization

Magnetic systems based on permanent magnets are receiving growing attention, in particular for micro/millirobotics and biomedical applications. Their design landscape is expanded by the possibility to program magnetization, yet enabling analytical results, crucial for containing computational costs, are lacking. The dipole approximation is systematically used (and often strained), because exact and computationally robust solutions are to be unveiled even for common geometries such as cylindrical magnets, which are ubiquitously used in fundamental research and applications. In this study, exact solutions are disclosed for magnetic field and gradient of a cylindrical magnet with generic uniform magnetization, which can be robustly computed everywhere within and outside the magnet, and directly extend to magnets systems of arbitrary complexity. Based on them, exact and computationally robust solutions are unveiled for force and torque between coaxial magnets. The obtained analytical solutions overstep the dipole approximation, thus filling a long-standing gap, and offer strong computational gains versus numerical simulations (up to 10⁶ , for the considered test-cases). Moreover, they bridge to a variety of applications, as illustrated through a compact magnets array that could be used to advance state-of-the-art biomedical tools, by creating, based on programmable magnetization patterns, circumferential and helical force traps for magnetoresponsive diagnostic/therapeutic agents.