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The invention emits coherent radiation by first generating and transmitting an array of discrete electron beamlets from a nanocathode array along a longitudinal axis. Subsequently, an array of electron beamlets is focused to reduce the spacing that separates the electron beamlets. The transverse-axis spacing of the electron beamlets is then transferred to the longitudinal axis via an emittance exchange beamline, creating a periodically modulated distribution of coherent electronic current. The coherent electronic current can then be directed into a stream of photons to generate coherent x-ray radiation.