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We study the inverse problem of determining a magnetic Schr\"odinger operatorin an unbounded closed waveguide from boundary measurements. We consider thisproblem with a general closed waveguide in the sense that we only require ourunbounded domain to be contained into an infinite cylinder. In this context weprove the unique recovery of the magnetic field and the electric potentialassociated with general bounded and non-compactly supported electromagneticpotentials. By assuming that the electromagnetic potentials are known on theneighborhood of the boundary outside a compact set, we even prove the uniquedetermination of the magnetic field and the electric potential frommeasurements restricted to a bounded subset of the infinite boundary. Finally,in the case of a waveguide taking the form of an infinite cylindrical domain,we prove the recovery of the magnetic field and the electric potential frompartial data corresponding to restriction of Neumann boundary measurements toslightly more than half of the boundary. We establish all these results by meanof suitable complex geometric optics solutions and Carleman estimates suitablydesigned for our problem stated in an unbounded domain and with boundedelectromagnetic potentials.

Determination of non-compactly supported electromagnetic potentials in unbounded closed waveguide