The possibility of relatively fast neutron oscillations into a mirror neutron state is not excluded experimentally when a mirror magnetic field is considered. Direct searches for the disappearance of neutrons into mirror neutrons in a controlled magnetic field have previously been performed using ultracold neutrons, with some anomalous results reported. We describe a technique using cold neutrons to perform a disappearance and regeneration search, which would allow us to unambiguously identify a possible oscillation signal. An experiment using the existing General Purpose-Small Angle Neutron Scattering instrument at the High Flux Isotope Reactor at Oak Ridge National Laboratory will have the sensitivity to fully explore the parameter space of prior ultracold neutron searches and confirm or refute previous claims of observation. This instrument can also conclusively test the validity of recently suggested oscillation-based explanations for the neutron lifetime anomaly.
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