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Here, we study the behaviour of an inductive superconducting fault current limiter (SFCL) whose secondary is a bulk cylinder with an array of appropriately distributed weak zones. This design allows heat to be removed by conduction from the hot weak zones, which absorb the power dissipation, to the remaining colder parts of the cylinder. Our work highlights the possibility of overcoming the limitations of high power SFCLs based on bulk cylinders, which present recovery time values well beyond the maximum value tolerated in a distribution line.