A nonlinear oscillator with an abruptly inhomogeneous restoring force driven by an uniform oscillating force exhibits stochastic properties under specific resonance conditions. This behaviour elucidates the elementary mechanism of the electron energi
zation in the strong electromagnetic wave interaction with thin targets.
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 uJ/sr pulses. Harm
onics 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.
We propose the experiments on the collision of laser light and high intensity electromagnetic pulses generated by relativistic flying mirrors, with electron bunches produced by a conventional accelerator and with laser wake field accelerated electron
s for studying extreme field limits in the nonlinear interaction of electromagnetic waves. The regimes of dominant radiation reaction, which completely changes the electromagnetic wave-matter interaction, will be revealed in the laser plasma experiments. This will result in a new powerful source of ultra short high brightness gamma-ray pulses. A possibility of the demonstration of the electron-positron pair creation in vacuum in a multi-photon processes can be realized. This will allow modeling under terrestrial laboratory conditions neutron star magnetospheres, cosmological gamma ray bursts and the Leptonic Era of the Universe.
