Soft X-ray harmonic comb from relativistic electron spikes

We demonstrate a new high-order harmonic generation mechanism reaching the "water window" spectral region in experiments with multiterawatt femtosecond lasers irradiating gas jets. A few hundred harmonic orders are resolved, giving mu J/sr pulses. Harmonics are collectively emitted by an oscillating electron spike formed at the joint of the boundaries of a cavity and bow wave created by a relativistically self-focusing laser in underdense plasma. The spike sharpness and stability are explained by catastrophe theory. The mechanism is corroborated by particle-in-cell simulations.