Optimized multibeam configuration for observation of QED cascades

QED cascades in intense electromagnetic field can occur if the dynamical quantum parameter $χ$ of a seed electron, which in Compton units coincides with the electron proper acceleration, attains the order of unity. We derive general expression for $χ$ of an initially slow electron in an arbitrary electromagnetic field for a time range $t\ll 1/ω$, where $ω$ is the field carrier frequency. Using this formula, we consider a special field configuration of multiple colliding focused laser beams and optimize it to provide cascade development at laser power below $10$ PW and intensity of the order of $10^{23}$W/cm$^2$. Such parameters of the beams will be obtained with a new generation of laser facilities, particularly the ELI Beamlines, in the coming years.

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