New Optical Manipulation of Relativistic Vortex Cutter

A new relativistic vortex cutter driven by the Laguerre-Gaussian (LG) mode is carried out for the first time in three-dimensional particle-in-cell simulations. Studies show that the electric fields periodically concentrate and emanate within every laser wavelength for the reflected circularly polarized ${\mathrm{LG}}_p^l$ ($p=0$, $l=1$, ${\sigma }_z=-1$) laser, which works just like a vortex cutter, resulting in a relativistic ultrashort collimated electron cluster with a constant period in space. A single particle model is given and verifies that the cluster formation has a close relation with the parameters of orbital angular momentum ($l$) and spin angular momentum (${\sigma }_z$). Such a relativistic vortex cutter potentially can be applied for the accelerator, generating high-flux particle and coherent radiation sources, and so on.

Figure 1

(a) Vector plot of the electron momentum at $t=44T$. Density distributions of electrons for (b) CP ${\mathrm{LG}}_0^1$ (${\sigma }_z=-1$) and (c) CP ${\mathrm{LG}}_0^1$ (${\sigma }_z=1$). The front surface of the target ($x=29.5\mu \mathrm{m}$) is marked by the dash line. (d) Energetic spectra of the electrons in the region of $x<29\mu \mathrm{m}$, $-4\mu \mathrm{m}<y<4\mu \mathrm{m}$, and $-4\mu \mathrm{m}<z<4\mu \mathrm{m}$ driven by the ${\mathrm{LG}}_0^1$ (${\sigma }_z=-1$) laser (black solid line) and ${\mathrm{LG}}_0^1$ (${\sigma }_z=1$) laser (red dash line). The total electron count in this region is $\sim 0.2\mathrm{nC}$. (e) Corresponding phase-space distribution of electrons for the case of ${\mathrm{LG}}_0^1$ (${\sigma }_z=-1$). The total charge of each bunch (red circle) has been obtained. Here, the electrons in the cube of $1\mu \mathrm{m}(x)\times 4\mu \mathrm{m}(y)\times 4\mu \mathrm{m}(z)$ are counted. The centers of the cubes are at $y=0\mu \mathrm{m}$, $z=0\mu \mathrm{m}$, and $x_{\mathrm{c}}=20.5\mu \mathrm{m}$, $21.5\mu \mathrm{m}$, $22.5\mu \mathrm{m}$, $23.5\mu \mathrm{m}$, $24.5\mu \mathrm{m}$, $25.5\mu \mathrm{m}$, $26.5\mu \mathrm{m}$, respectively. The energy spectrum of the electron cluster center at $x_c=23.5\mu \mathrm{m}$ is shown in the inset.

Figure 2

Trajectories of electrons with initial velocity (in the $x$ direction) (a) $v_{\text{initial}}=-0.2c$, (b) $0c$, (c) $0.4c$, (d) $0.9c$ for ${\mathrm{LG}}_0^1$ (${\sigma }_z=-1$) laser. The interaction happens at $t=0T$. The initial position of the electron is at $x=0\mu \mathrm{m}$, $y=0.5\mu \mathrm{m}$, and $z=0\mu \mathrm{m}$. 3D trajectories for the elections at different initial position of (e) $x=0\mu \mathrm{m}$, $y=\pm 0.5\mu \mathrm{m}$, $z=0\mu \mathrm{m}$ and (f) $x=0\mu \mathrm{m}$, $y=0\mu \mathrm{m}$, $z=\pm 0.5\mu \mathrm{m}$. The initial velocity $v_{\text{initial}}=0.9c$. The laser travels in the $x$ direction.

Figure 3

3D trajectories of electrons at different initial positions ($x=0\mu \mathrm{m}$, $y=0\mu \mathrm{m}$, and $-4\mu \mathrm{m}<z<4\mu \mathrm{m}$) for the (a) ${\mathrm{LG}}_0^1$ (${\sigma }_z=-1$) and (b) ${\mathrm{LG}}_0^1$ (${\sigma }_z=1$) laser. The corresponding vector plot of the electric fields in one lase duration for (c1)–(c6) ${\mathrm{LG}}_0^1$ (${\sigma }_z=-1$) and (d1)–(d6) ${\mathrm{LG}}_0^1$ (${\sigma }_z=1$) laser.