High order harmonics from relativistic electron spikes

A new regime of relativistic high-order harmonic generation is discovered [Phys. Rev. Lett. 108, 135004 (2012)]. Multi-terawatt relativistic-irradiance (>1018 W/cm2) femtosecond (~30-50 fs) lasers focused to underdense (few×1019 cm-3) plasma formed in gas jet targets produce comb-like spectra with hundreds of even and odd harmonic orders reaching the photon energy of 360 eV, including the 'water window' spectral range. Harmonics are generated by either linearly or circularly polarized pulses from the J-KAREN (KPSI, JAEA) and Astra Gemini (CLF, RAL, UK) lasers. The photon number scalability has been demonstrated with a 120 TW laser producing 40 μJ/sr per harmonic at 120 eV. The experimental results are explained using particle-in-cell (PIC) simulations and catastrophe theory. A new mechanism of harmonic generation by sharp, structurally stable, oscillating electron spikes at the joint of boundaries of wake and bow waves excited by a laser pulse is introduced. In this paper detailed descriptions of the experiments, simulations and model are provided and new features are shown, including data obtained with a two-channel spectrograph, harmonic generation by circularly polarized laser pulses and angular distribution