Seeded QED cascades in counterpropagating laser pulses

The growth rates of seeded QED cascades in counterpropagating lasers are calculated with first-principles two- and three-dimensional QED-PIC (particle-in-cell) simulations. The dependence of the growth rate on the laser polarization and intensity is compared with analytical models that support the findings of the simulations. The models provide insight regarding the qualitative trend of the cascade growth when the intensity of the laser field is varied. A discussion about the cascade's threshold is included, based on the analytical and numerical results. These results show that relativistic pair plasmas and efficient conversion from laser photons to $\gamma$ rays can be observed with the typical intensities planned to operate on future ultraintense laser facilities such as ELI or Vulcan.

Figure 1

3D PIC simulation snapshot of QED cascades for (a) setup 1 with $a_0=1000$ at $t=90{\omega }_0^{-1}$, (b) setup 2 with $a_0=1300$ at $t=80{\omega }_0^{-1}$, and (c) setup 3 with $a_0=2000$ at $t=46{\omega }_0^{-1}$. The laser pulses are shown through isocontours of the electromagnetic energy. The particles displayed represent only a small fraction of the simulation particles.

Figure 2

Electron energy distribution function at different times for $a_0=500$ in the case of a pure uniform rotating field. The energy distribution is shown at three different times: red solid line at ${\omega }_{0}t=20$, black dash-dotted line at ${\omega }_{0}t=26.3$, and blue dashed line at ${\omega }_{0}t=32.5$.

Figure 3

(a) Growth rate as a function of $a_0$ for different laser polarization. The low $a_0$ model, depicted by a dashed blue (dark gray) line, corresponds to Eq. (11), and the high $a_0$ model, depicted by a dash-dotted green (light gray) line, corresponds to the numerically integrated Eq. (10) with $\overline{\gamma }={\mu }^{3/4}\sqrt{a_S}$ and ${\overline{\chi }}_e=1.24{\mu }^{3/2}$. The model of Bell and Kirl is shown by a dashed red (light gray) dashed line, the model of Bashmakov is shown by a gray (upper) line, and the model of Fedotov is displayed by a dash-dotted brown (light gray) line. (b) Onset of QED cascades for the three setups for $a_0=1000$; the linear polarization setup is shown by the solid blue (dark gray) line, the cw-cw setup by the dash-dotted orange (light gray) line, and the cw-cc setup by the dashed red (dark gray) line.