Soft-X-ray harmonic comb from relativistic electron spikes

Pirozhkov, A. S.; Kando, Masaki; Esirkepov, T. Z.; Gallegos, P.*; Ahmed, H.*; Ragozin, E. N.*; Faenov, A. Ya.*; Pikuz, T.; Kawachi, Tetsuya; Sagisaka, Akito; Koga, J. K.; Coury, M.*; Green, J.*; Foster, P.*; Brenner, C.*; Dromey, B.*; Symes, D. R.*; Mori, Michiaki; Kawase, Keigo*; Kameshima, Takashi*; Fukuda, Yuji; Chen, L. M.*; Daito, Izuru; Ogura, Koichi; Hayashi, Yukio; Kotaki, Hideyuki; Kiriyama, Hiromitsu; Okada, Hajime; Nishimori, Nobuyuki; Imazono, Takashi; Kondo, Kiminori; Kimura, Toyoaki*; Tajima, Toshiki; Daido, Hiroyuki; Rajeev, P.*; McKenna, P.*; Borghesi, M.*; Neely, D.*; Kato, Yoshiaki* ; Bulanov, S. V.

We demonstrate a new high-order harmonic generation mechanism reaching the "water window" spectral region in experiments with multi-terawatt femtosecond lasers irradiating gas jets. A few hundred harmonic orders are resolved, giving 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.