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An intense laser pulse in a plasma can accelerate electrons1, 2, 3, 4 to GeV energies in centimetres5, 6, 7. Transverse betatron motion8, 9 in the plasma wake results in X-ray photons with an energy that depends on the electron energy, oscillation amplitude and frequency of the betatron motion10, 11, 12. Betatron X-rays from laser-accelerator electrons have hitherto been limited to spectra peaking between 1 and 10 keV (ref. 13). Here we show that the betatron amplitude is resonantly enhanced when electrons interact with the rear of the laser pulse14, 15. At high electron energy, resonance occurs when the laser frequency is a harmonic of the betatron frequency, leading to a significant increase in the photon energy. 108 gamma-ray photons, with spectra peaking between 20 and 150 keV, and a peak brilliance >1023 photons s−1 mrad−2 mm−2 per 0.1% bandwidth, are measured for 700 MeV beams, with 107 photons emitted between 1 and 7 MeV. Femtosecond duration gamma-rays may find uses in imaging, isotope production, probing dense matter, homeland security and nuclear physics16

Gamma-rays from harmonically resonant betatron oscillations in a plasma wake