A laser wakefield accelerator is shown to operate in the highly non‐linear bubble regime, following the characteristic scaling of energy gain with density and leading to monoenergetic electron beams with up to 400 MeV and hundreds of pC charge. The bubble acts at the same time as a miniature undulator, causing the electrons to give off a beam of betatron x‐rays with milliradian divergence, μm source size, 1–100 keV photon energy and 1022ph/mm2/mrad2s/0.1% BW.

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