Measurements of ionization states in warm dense aluminum with betatron radiation

Time-resolved measurements of the ionization states of warm dense aluminum via K-shell absorption spectroscopy are demonstrated using betatron radiation generated from laser wakefield acceleration as a probe. The warm dense aluminum is generated by irradiating a free-standing nanofoil with a femtosecond optical laser pulse and was heated to an electron temperature of $\sim 20–25$ eV at a close-to-solid mass density. Absorption dips in the transmitted x-ray spectrum due to the ${\mathrm{Al}}^{4+}$ and ${\mathrm{Al}}^{5+}$ ions are clearly seen during the experiments. The measured absorption spectra are compared to simulations with various ionization potential depression models, including the commonly used Stewart-Pyatt model and an alternative modified Ecker-Kröll model. The observed absorption spectra are in approximate agreement with these models, though indicating a slightly higher state of ionization and closer agreement for simulations with the modified Ecker-Kröll model.

Figure 1

(a, b) Contour plots of the MULTI-fs simulated mass density $\rho (r,t)$ and electron temperature $T_e(r,t)$ of a 50-nm Al foil as a function of the axial position and time, irradiated with a 30-fs laser pulse at an absorbed intensity of $4.6\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ in the laser propagation direction and a wavelength of 800 nm. The laser impinges on the target from the bottom with an angle of incidence of ${40}^{\circ }$ and p polarization. Zero time was defined as the time when the peak of the laser reached the target. (c, d) Spatial line-outs of the mass density and plasma temperature, respectively, for four times as indicated by the dashed white lines overlain on the contour plots. In the simulation, an artificial layer of aluminum vapor ($2\times {10}^{-4}\mathrm{g}/{\mathrm{cm}}^3$) was added at the back of the target to observe the rear expansion. This artificial layer is so dilute that its effect on the mass expansion and heat propagation in the rear side is negligible.

Figure 2

(a) Raw x-ray spectrum (light-blue line) measured at $t=0.5$ ps and a Gaussian smoothed fit to the curve (red line). The FWHM of the Gaussian function for smoothing this measured spectrum was 7 pixels, corresponding to a spectral width of 2.1 eV. (b) The same as (a), but for $t=1$ ps. The FWHM of the Gaussian smoothing function was 9 pixels (2.7 eV). The positions of the observed ${\mathrm{Al}}^{4+}$ and ${\mathrm{Al}}^{5+}$ absorption dips at these two delays are shown by the dashed vertical lines.

Figure 3

  Comparison of the measured transmission curves (dashed green curves) at delays of 0.5 and 1 ps with the simulated transmission curves obtained with different models. The measured transmission curve was normalized to compare with the simulations. The gray area represents the error bar of the measured transmission. (a, b) Simulation results were obtained based on MULTI-fs hydro simulations and spectroscopic calculations with the Stewart-Pyatt (SP), modified Ecker and Kröll (mEK), and ion-sphere (IS) IPD models. (c, d) Simulation results were obtained based on a MULTI-fs simulation with hydro expansion turned off to suppress expansion cooling, using spectroscopic calculations similar to those used in (a) and (b).

Figure 4

Comparison of the $\langle Z\rangle$ of Al at solid density as a function of the temperature derived from different ionization models.