The design of thin-walled superconducting solenoids for particle physics applications requires the consideration of magnet deformations due to self-induced magnetic forces. We present a reduced-order model for these bidirectional magneto-elastic interactions that exploits the inherent axisymmetry of the problem. The developed simulation code allows for the efficient calculation of stresses and deformations in thin-walled solenoids, as well as the magnetic field map of the deformed solenoid.
The simulation uses two coupled solvers: one for the structural and one for the electromagnetic domain. Magnetic field and Lorentz forces are calculated by a dedicated Biot–Savart solver. The structural solver is based on the Transfer Matrix Method (TMM) for shells of revolution. The coupled problem is solved iteratively by the solvers exchanging updated magnet forces and displacements for increasing current increments. This approach captures geometric non-linearities as well as the non-linear redistribution of magnetic forces due to deformations. The non-linear simulation capabilities are demonstrated by exemplary calculations of the BESS-Polar solenoid. We find deviations up to 1% in magnetic field caused by the solenoid’s deformations. Geometric non-linearity is found to have only a minor effect and may thus be neglected for the calculation of magnet deformations. In parametric studies, the magneto-elastic solver is shown to be an order of magnitude faster than commercial finite element solvers. The proven computational efficiency makes the tool well-suited for the preliminary structural design of superconducting solenoids and for the estimation of magneto-elastic effects in future particle physics experiments like AMS-100.
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