The proposed upgrade of the SND@LHC experiment for the High Luminosity phase of the LHC (HL-LHC) will strongly benefit from the presence of a magnetized region, allowing for muon momentum and charge measurement. In this paper we describe an iron core magnet system that is partly integrated with the calorimeter and that is designed to respect the strict constraints from the available space in the experimental cavern, power consumption, and field requirements. Semi-analytical tools are introduced to explore the parameter space, in order to define the primary design options. A full 3-D analysis is then performed in order to validate the optimal choice, and to propose a conceptual design, including sizing of the components, detector performances and stray fields. Several technical options are also discussed, anticipating the design phase.
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