Laser-Ion Lens and Accelerator

Generation of highly collimated monoenergetic relativistic ion beams is one of the most challenging and promising areas in ultraintense laser-matter interactions because of the numerous scientific and technological applications that require such beams. We address this challenge by introducing the concept of laser-ion lensing and acceleration. Using a simple analogy with a gradient-index lens, we demonstrate that simultaneous focusing and acceleration of ions is accomplished by illuminating a shaped solid-density target by an intense laser pulse at $\sim {10}^{22}\mathrm{W}/{\mathrm{cm}}^2$ intensity, and using the radiation pressure of the laser to deform or focus the target into a cubic micron spot. We show that the laser-ion lensing and acceleration process can be approximated using a simple deformable mirror model and then validate it using three-dimensional particle-in-cell simulations of a two-species plasma target composed of electrons and ions. Extensive scans of the laser and target parameters identify the stable propagation regime where the Rayleigh-Taylor-like instability is suppressed. Stable focusing is found at different laser powers (from a few to multiple petawatts). Focused ion beams with the focused density of order ${10}^{23}{\mathrm{cm}}^{-3}$, energies in access of 750 MeV, and energy density up to $2\times {10}^{13}\mathrm{J}/{\mathrm{cm}}^3$ at the focal point are predicted for future multipetawatt laser systems.

Figure 1

Schematic of the LILA concept: a laser beam propels a thin dense target with nonuniform thickness. Inset: the geometry of the laser reflection from a small target element moving with velocity $\overrightarrow{v}$.

Figure 2

Deformable mirror model of the acceleration and focusing of a thin target propelled by laser pulses of different normalized amplitudes $a_0=10$ ($\mathrm{\Gamma }=0.021$) (a) and $a_0=100$ ($\mathrm{\Gamma }=2.1$) (b), and different target radiuses: $R_0=R_c$ (black curves) and $R_0=(2/3)R_c$ (red curves). Target parameters: $R_c=6\mu \mathrm{m}$, $d_0=300\mathrm{nm}$, and $n_0=100$ $n_c$.

Figure 3

A 3D PIC simulation of LILA. (a) Snapshots of ion densities. Black-dashed lines: target positions from the DM model. The focal spot (peak plasma density) is achieved at $t_f=133.3\mathrm{fs}$ (b) Proton energy spectrum and energy density distribution (in the inset) at $t=t_f$. (c) Proton phase space ($E_k,\theta$) distribution and normalized emittance ${ϵ}_n$ (dotted line) vs energy $E_k$ at $t=t_f$. The laser has a flattop longitudinal profile with a duration $\tau =45\mathrm{fs}$ and a rising edge ${\tau }_{\mathrm{rise}}=3.3\mathrm{fs}$. The simulation box size is $X\times Y\times Z=50{\lambda }_0\times 20{\lambda }_0\times 20{\lambda }_0$, consists of $5000\times 250\times 250$ cells. At the plasma region, each cell contains 160 macroparticles.

Figure 4

Parameter scan of LILA target in 3D PIC simulations. (a) Stable (crosses, bullets) and unstable (triangles) target focusing in the ($\mathrm{\Gamma },R_c$) parameter space. Red dashed lines represent constant acceleration contours (from top to bottom): $g=0.13c^2/{\lambda }_0$, $0.17c^2/{\lambda }_0$, and $0.30c^2/{\lambda }_0$. (b) Focal length $L_f$ and (c) momentum $p_x$ as functions of $\sqrt{\mathrm{\Gamma }}$ from the DM model (solid line) and 3D PIC simulations (crosses, bullets). (d) Example of the unstable acceleration and focusing of the target, corresponds to $\mathrm{\Gamma }=1.6$ and $R_c/{\lambda }_0=10$. (e) Ions’ energy spectrum of the unstable target in (d) at moment $t=133\mathrm{fs}$.