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Superconducting linear accelerators include a superconducting magnet system for particle beam transportation that provides beam focusing and steering. This system consists of a large number of quadrupole magnets and dipole correctors mounted inside or between cryomodules with SCRF cavities. Each magnet has current leads and is powered from its own power supply. The paper proposes a novel approach to magnet powering based on using superconducting persistent current switches. A group of magnets is powered by the same power supply through the common, for the group of cryomodules, electrical bus, and pair of current leads. Superconducting switches direct the current to the chosen magnet and close the circuit, providing the magnet operation in a persistent current mode. Two persistent current switches were fabricated and tested. The paper also presents the results of magnetic field simulations, decay time constants analysis, and a way of improving quadrupole magnetic center stability. Such an approach substantially reduces the magnet system cost and increases the reliability.