Quasimonoenergetic Proton Bunch Acceleration Driven by Hemispherically Converging Collisionless Shock in a Hydrogen Cluster Coupled with Relativistically Induced Transparency

An approach for accelerating a quasimonoenergetic proton bunch via a hemispherically converging collisionless shock created in laser-cluster interactions at the relativistically induced transparency (RIT) regime is studied using three-dimensional particle-in-cell simulations. By the action of focusing a petawatt class laser pulse onto a micron-size spherical hydrogen cluster, a crescent-shaped collisionless shock is launched at the laser-irradiated hemisphere and propagates inward. The shock converges at the sphere center in concurrence with the onset of the RIT, thereby allowing the proton bunch to be pushed out from the shock surface in the laser propagation direction. The proton bunch experiences further acceleration both inside and outside of the cluster to finally exhibit a quasimonoenergetic spectral peak around 300 MeV while maintaining a narrow energy spread ($\sim 10\%$) and a small half-divergence angle ($\sim 5°$) via the effect of the RIT. This mechanism works for finite ranges of parameters with threshold values concerning the laser peak intensity and the cluster radius, resulting from the synchronization of the multiple processes in a self-consistent manner. The present scheme utilizing the internal and external degrees of freedom ascribed to the spherical cluster leads to the proton bunch alternative to the plain target, which allows the operation with a high repetition rate and impurity free.

Figure 1

2D images of (a) electron and (b1)–(b3) ion density distributions for $R_0=0.8\mu \mathrm{m}$ in the $x$-$y$ plane at $z=0$ at different times. The densities are shown as an averaged value over $z=0\pm 0.16\mu \mathrm{m}$ and are normalized by the initial density of the cluster ions or electrons $n_0$. The intensities of the laser electric fields $E_x^2$ along the $y$ axis are shown in red lines.

Figure 2

Temporal evolution for the electron density (blue squares), the ion density (black circles), and the electric field $E_y$ (red diamonds) inside the shock along the $y$ axis at $x=z=0$. The densities are normalized by $n_0$. The time region when the CSA occurs is colored green. The arrow indicates the time when the quasimonoenergetic proton bunch is pushed out via the RIT effect.

Figure 3

(a1)–(a3),(c) One-dimensional cross-sectional views for the charge density distributions of the cluster ions (black lines) and cluster electrons (blue lines) and the intensities of the laser electric fields $E_x^2$ (red lines) along the $y$ axis at $x=z=0$ at different times. (b1)–(b3) 2D images of the kinetic energy distributions of cluster ions in the $x$-$y$ plane at $z=0$ at different times. The ion energies are shown as a value which is averaged in each cell and over $z=0\pm 0.16\mu \mathrm{m}$. The electric fields $E_y$ are also shown as red lines. (d) The phase space distribution of the cluster ions along the $y$ axis at $x=z=0$ at $t=58.9\mathrm{fs}$. The densities in (a1)–(a3), (c), and (d) are normalized by $n_0$. Rectangular broken lines in (a1)–(a3) and (c) represent $n_0$. The vertical broken lines in (a1)–(a3) and (b1)–(b3) represent the location of the quasimonoenergetic proton bunch.

Figure 4

(a) 3D image of the kinetic energy distribution of cluster ions at $t=106.7\mathrm{fs}$. The quasimonoenergetic proton bunch (red) is flying out from the cluster. (b),(d) Proton energy spectra for clusters with (b) $R_0=0.8\mu \mathrm{m}$ and (d) $R_0=1.0\mu \mathrm{m}$ for various laser peak intensities at $t=136.7\mathrm{fs}$. The spectrum for the cluster with $R_0=0.6\mu \mathrm{m}$ at $t=136.7\mathrm{fs}$ is also shown as red dotted line in (b). The proton number is evaluated using a real value by multiplying the particle weight to the PIC particle. (c) The monochromaticity $1/{\sigma }_E$ (black square) and the current $I_c$ (red diamond) for the bunch within ${\sigma }_E$.