Time-Resolved X-Ray Imaging of Anisotropic Nanoplasma Expansion

A complete time-resolved x-ray imaging experiment of laser heated solid-density hydrogen clusters is modeled by microscopic particle-in-cell simulations that account self-consistently for the microscopic cluster dynamics and electromagnetic wave evolution. A technique is developed to retrieve the anisotropic nanoplasma expansion from the elastic and inelastic x-ray scattering data. Our method takes advantage of the self-similar evolution of the nanoplasma density and enables us to make movies of ultrafast nanoplasma dynamics from pump-probe x-ray imaging experiments.

Figure 1

(a) Sketch of the simulation setup with the $R=25\mathrm{nm}$ hydrogen cluster, the virtual detector (defined by a sphere with radius $R_d=290\mathrm{nm}$ around the cluster center), and the incident laser fields. (b)–(d) Time evolution of selected observables during and after the NIR pump excitation. (e) Resulting elastic and inelastic scattered fraction (detection in the $y\text{−}z$ plane) for different x-ray probe delays and the Mie-theory result for an unexpanded cluster for comparison. In the limit $R_d\to \infty$, $S(\mathrm{\Theta })$ specifies the number of x-ray photons scattered into an element of solid angle per incident photon impinging on the initial geometric cluster cross section. (f) Scattered x-ray intensity spectrum (averaged over $60°<\mathrm{\Theta }<90°$) with elastic and inelastic contributions. (g) Mie results showing the minor impact of the finite MicPIC detector distance (black vs red lines) and the size-independent universal envelope of the elastically scattered fraction for weakly absorbing spheres (gray line).

Figure 2

Radial electron and ion density profiles for different pulse delays (as indicated). Solid lines (electron) and shaded areas (ion) show density profiles extracted directly from the MicPIC simulation for directions parallel to (green) and perpendicular to (blue) the polarization direction. Open squares correspond to electron density fits perpendicular to the NIR polarization using the profile given in Eq. (2).

Figure 3

(a)–(c) Time evolution of density profile parameters; lines correspond to direct fits of the MicPIC density for directions parallel to (green) and perpendicular to (blue) the polarization direction using all parameters (solid) or the sharp edge limit $s\to 0$ (dashed); squares denote parameters reconstructed from the scattering pattern in the sharp edge limit (see text). (d) Full NIR–polarization dependent MicPIC scattering pattern (solid lines) and corresponding Born fits (circles) for two delays (as indicated); the inset shows a selective parameter analysis of the Born method for $s\to 0$ (see text).