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Upcoming ultrahigh power lasers at 10 PW level will make it possible to experimentally explore electron-positron (e−e+) pair cascades and subsequent relativistic e−e+ jets formation, which are supposed to occur in extreme astrophysical environments, such as black holes, pulsars, quasars and gamma-ray bursts. In the latter case it is a long-standing question as to how the relativistic jets are formed and what their temperatures and compositions are. Here we report simulation results of pair cascades in two counter-propagating QED-strong laser fields. A scaling of QED cascade growth with laser intensity is found, showing clear cascade saturation above threshold intensity of ~1024 W/cm2. QED cascade saturation leads to pair plasma cooling and longitudinal compression along the laser axis, resulting in the subsequent formation of relativistic dense e−e+ jets along transverse directions. Such laser-driven QED cascade saturation may open up the opportunity to study energetic astrophysical phenomena in laboratory.

A new mechanism of harmonics generation (HG) induced by quantum electrodynamics (QED) effects in extreme intense laser foil interaction is found and investigated by particle-in-cell (PIC) simulations. When two laser pulses with identical intensities of 1.6 × 1024 W cm-2 are counterincident on a thin foil target, harmonics emission is observed in their reflected electromagnetic waves. Such harmonics radiation is excited due to transversely oscillating electric currents coming from the vibration of QED effect generated e-e+ pairs. The effects of laser intensity and polarization were studied. By distinguishing the cascade depth of generated photons and pairs, the influence of QED cascades on HG was analyzed. Although the current HG is not an efficient way for radiation source applications, it may provide a unique way to detect the QED processes in the near future ultra-relativistic laser solid interactions.

The acceleration of electron beams with multiple transverse structures in wakefields driven by Laguerre-Gaussian pulses has been studied through three-dimensional (3D) particle-in-cell simulations. Under different laser-plasma conditions, the wakefield shows different transverse structures. In general cases, the wakefield shows a donut-like structure and it accelerates the ring-shaped hollow electron beam. When a lower plasma density or a smaller laser spot size is used, besides the donut-like wakefield, a central bell-like wakefield can also be excited. The wake sets in the center of the donut-like wake. In this case, both a central on-axis electron beam and a ring-shaped electron beam are simultaneously accelerated. Further, reducing the plasma density or laser spot size leads to an on-axis electron beam acceleration only. The research is beneficial for some potential applications requiring special pulse beam structures, such as positron acceleration and collimation.

The purpose of this paper is to study the existence of weighted boundary limits of the generalized Kobayashi-Royden metrics on weakly pseudoconvex domains in C n {\mathbb {C}^n} and to explore the connections between the limits and the Levi invariants. The main result extends Graham’s result on strongly pseudoconvex domains to a large class of weakly pseudoconvex domains.

We introduce a family of invariants associated with the higher order Kobayashi metrics and study their relations with the regular type in the sense of Kohn and the variety type in the sense of D’Angelo.