Post-acceleration of electron bunches from laser-irradiated nanoclusters

In this paper the energy gain of attosecond electron bunches emitted during the interaction of intense, few-cycle linearly polarized lasers with nanoscale spherical clusters is determined. In this case electron bunches are emitted from the rear side of the cluster and are then further accelerated while co-propagating with the laser. A previous study has shown how this two-stage process readily occurs for clusters whose radii lie between the relativistic skin depth, δ _r = γ ^1/2 c/ω _p, and the laser spot size σ _L (Di Lucchio & Gibbon, Phys. Rev. STAB 18, 2015). An analytical model for focused light waves interacting with compact, overdense electron bunches in vacuum is derived heuristically from world-line equations of motion of an electron. The functional integral approach is followed under the mathematical point of view of integration with respect to a stochastic variable. The resulting picture of the laser wave crossing the electron's trajectory leads to a finite energy gain of the electron in light–matter interaction in vacuum. The analytical theory is compared with three-dimensional PIC simulations from which trajectories of the electron bunches can be extracted. The effective increase in bunch energy is determined under realistic conditions both for the peak (mode) and the cutoff energy of the emitted bunch, in order to make quantitative comparisons with theory and the experimental findings of Cardenas et al , Nature Sci. Reports 9 (2019). (paper)