Transient stability analysis of the superconducting outsert of a 36 T Series-Connected Hybrid (SCH) magnet being developed at the NHMFL is performed. The latest design version of the SCH outsert primary coil will consists of three radial sections, designated as a low-field, a midfield and a high-field ones, each wound with a different superconducting cable-in-conduit conductor (CICC) using a cable of multi-filamentary $hbox{Nb}_{3}hbox{Sn/Cu}$ strands inside a stainless steel jacket that confines slowly flowing supercritical helium (under 3 atm pressure at 4.5 K). There will be also an outer shield coil wound with a CICC that uses NbTi/Cu strands. The outsert cooling system concept delivers helium to all of the winding layers (each layer has an inlet and outlet), aiming to sustain a wide range of duty cycles required by diverse science experiments, conducted with the magnet. The transient stability is discussed in terms of temperature margin, limiting current, and energy margin as well and analyzed for several operation scenarios/duty cycles and situations resulting in different patterns of deposition and evacuation of heat due to AC losses in the outsert sections.
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