We report an observation of essentially full spatial coherence in a high average power soft-x-ray laser. Rapid coherence buildup due to strong refractive antiguiding in a long plasma column is experimentally demonstrated. This allows the generation of fully coherent, milliwatt-level average power soft-x-ray radiation by a tabletop device. The peak brightness of this laser reaches 2x10(25) photons s(-1) mm(-2) mrad(-2) within 0.01% spectral bandwidth, making it one of the brightest soft-x-ray sources available.
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