Limitations on the Attainable Intensity of High Power Lasers

It is shown that even a single $e^{-}{e}^{+}$ pair created by a superstrong laser field in vacuum would cause development of an avalanchelike QED cascade which rapidly depletes the incoming laser pulse. This confirms Bohr’s old conjecture that the electric field of the critical QED strength $E_S=m^2{c}^3/e\hslash$ could never be created.

Figure 1

Evolution of quantum dynamical parameter $\chi$ along the particle trajectory for $a_0=3\times {10}^3$, $\hslash \omega =1\mathrm{eV}$ in three cases: head-on collision of two elliptically polarized plane waves (solid line); collision at 90° of two linearly polarized plane waves with orthogonal linear polarizations (dashed line); single tightly focused $e$-polarized laser beam (dotted line).

Figure 2

Pair production as a function of $\mu$. The solid curve corresponds to the number $N_e$ of pairs produced by a single cascade process. The dotted curve shows the number of pairs produced by multiple cascades generated by pairs created by two colliding circularly polarized 10 fs laser pulses. The branching point corresponds to the threshold value of $\mu$ where the spontaneous pair production begins. The dash line shows the limit for $N_e$ determined by the energy of the laser pulse. The laser frequency $\hslash \omega =1\mathrm{eV}$. The inset shows the magnified region of intersection of the curves.