Relativistic Attosecond Electron Bunches from Laser-Illuminated Droplets

The generation of relativistic attosecond electron bunches is observed in three-dimensional, relativistic particle-in-cell simulations of the interaction of intense laser light with droplets. The electron bunches are emitted under certain angles which depend on the ratios of droplet radius to wavelength and plasma frequency to laser frequency. The mechanism behind the multi-MeV attosecond electron bunch generation is investigated using Mie theory. It is shown that the angular distribution and the high electron energies are due to a parameter-sensitive, time-dependent local field enhancement at the droplet surface.

Figure 1

Electron isocontour surfaces (1% of $n_{e0}$) of a $R=\lambda /4$ He droplet in a laser pulse of intensity $2\times {10}^{18}\mathrm{W}/{\mathrm{cm}}^2$ at $t=10\mathrm{cycles}$.

Figure 2

Kinetic electron energy (a) and density (b) contour plots (in the $y=0$ plane) of the He droplet of Fig. 1 in a laser pulse of intensity $8\times {10}^{18}\mathrm{W}/{\mathrm{cm}}^2$ at $t=8\mathrm{cycles}$. In the bunch ejected around the pulse maximum, the maximum electron energy is $\simeq 6\mathrm{MeV}$, and $2\times {10}^5$ electrons have an energy $>3\mathrm{MeV}$.

Figure 3

Absolute value of the radial electric field for a 22 times overdense droplet at the droplet surface versus angle $\theta$ and time, as predicted by Mie theory for $R=\lambda /4$ (a) and $R=\lambda /2$ (b) in the $y=0$ plane. The color indicates the electric field in units of the incident field strength $\widehat{E}$. The plots to the right show the electric vector field in the $y=0$ plane at the “optimal” times (indicated by white, vertical lines in the left plots) when the electric field at the droplet surface is highest and pointing inwards, i.e., $t=0.275\mathrm{cycles}$ (a) and $t=0.675\mathrm{cycles}$ (b), respectively.

Figure 4

Angle-resolved ion and electron kinetic energy spectra for the $R=\lambda /4$ droplet [(a) ions and (b) electrons] and the $R=\lambda /2$ droplet [(c) ions and (d) electrons] after $t=9\mathrm{\text{cycles}}$ in a laser pulse of intensity $2\times {10}^{18}\mathrm{W}/{\mathrm{cm}}^2$. The emission angle $\theta$ [indicated in (c)] was determined as $\theta =\arctan (p_x/p_z)$ with $\mathit{p}$ the momentum. The color coding is proportional to the logarithm of the particle number.

Figure 5

Kinetic electron energy (a) and density (b), as in Fig. 2 but for $a=20$ ($8\times {10}^{20}\mathrm{W}/{\mathrm{cm}}^2$). The arrow in (b) indicates an electron bunch which, after the pulse, acquired an energy of $\simeq 130\mathrm{MeV}$.