Saturated ablation in metal hydrides and acceleration of protons and deuterons to keV energies with a soft-x-ray laser

Studies of materials under extreme conditions have relevance to a broad area of research, including planetary physics, fusion research, materials science, and structural biology with x-ray lasers. We study such extreme conditions and experimentally probe the interaction between ultrashort soft x-ray pulses and solid targets (metals and their deuterides) at the FLASH free-electron laser where power densities exceeding ${10}^{17}$ W/cm${}^2$ were reached. Time-of-flight ion spectrometry and crater analysis were used to characterize the interaction. The results show the onset of saturation in the ablation process at power densities above ${10}^{16}$ W/cm${}^2$. This effect can be linked to a transiently induced x-ray transparency in the solid by the femtosecond x-ray pulse at high power densities. The measured kinetic energies of protons and deuterons ejected from the surface reach several keV and concur with predictions from plasma-expansion models. Simulations of the interactions were performed with a nonlocal thermodynamic equilibrium code with radiation transfer. These calculations return critical depths similar to the observed crater depths and capture the transient surface transparency at higher power densities.

Figure 1

(a) Experimental setup. The x-ray FEL beam was focused by a mirror onto the sample at normal incidence. Each pulse ejected positive ions from the sample, and a fraction entered the flight tube of the ion spectrometer (horizontal thick solid red arrow). The high-pass filter selected high-energy ions, which hit the particle detector and generate flight-time spectra. Less energetic ions were deflected (dashed arrow).

Figure 2

(a) Scanning electron microscopy image of a crater formed under in-focus conditions in deuterated vanadium (VD) by a single 13.5 nm FEL pulse at about 10${}^{17}$ W/cm${}^2$. (b, c) Atomic force microscopy image and depth profile of the same crater. (d) Scanning electron microscopy image of a crater formed in VD under out-of-focus conditions (below 10${}^{16}$ W/cm${}^2$). (e) Simulated out-of-focus beam profile with fringes caused by scattering off an off-center beam-line aperture.

Figure 3

Averaged ion time-of-flight (TOF) spectra. (a) Entire TOF spectrum obtained from niobium (Nb) with a high-pass (HP) filter setting of 1 kV (inset shows result for HP filter at 2.5 kV). (b) Ion TOF spectra of the light ions (H${}^{+}$ and ${\mathrm{D}}^{+}$) obtained from deuterated vanadium (VD) with different settings on the HP filter (0.3 to 2.0 kV, shown from top down with solid lines). Dotted lines follow the envelope for highest energies; the solid horizontal line shows a 95% confidence level for signal above background.

Figure 4

The highest observed proton energies as a function of power density for various solids. Measurements were performed at an average pulse intensity of 30 $\mu$J at 13.5 nm wavelength. The change in power density was obtained from a variable focus, by moving the sample along the $z$ direction [Fig. 1a; shown on the top horizontal axis, in mm relative to best focus]. The confidence level for detection of signal above the background is at 95%.

Figure 5

Crater depth as a function of power density of the incident x-ray pulse measured using atomic force microscopy. Different power densities in single shots are due to both FEL pulse energy fluctuations and moving the sample through the focus ($z$ shows position of the sample in mm relative to best focus). The solid red line shows a fit of the function $\ln I^n$, with $n=0.9$ for polycrystalline samples (V,VD, NbD) and $n=1.3$ for single-crystal Nb.

Figure 6

Simulated critical depth as a function of power density of the incident x-ray pulse for different materials. Simulations are performed with cretin and show the sample depth where electron density reaches the critical value $N\approx {10}^{22}$ cm${}^{-3}$, presented with dotted blue lines after 0.1 ps and solid red lines after 1 ps. The depths where the electron temperature reaches $T_e=0.3$ eV (dash-dotted purple lines) and $T_e=0.6$ eV (dashed green lines) after 0.1 ps are also shown. The x-ray pulse is 15 fs FWHM and 13.5 nm wavelength.

Figure 7

(a) Simulated ion temperature at the plasma surface 1 ps after the pulse as a function of power density. The inset shows the equilibration of the electron and ion temperatures in VD following illumination with a 15 fs soft x-ray pulse of 13.5 nm and a power density of 10${}^{17}$ W/cm${}^2$. (b) The highest measured proton energies in VD (boxes, confidence level 95%) compared with the simulated electron temperature at the surface (dashed line) and the calculated energy $E_{\max }$ (Eq. (1)) of plasma front expansion for light ions (red solid lines).

Figure 8

(a) Simulated average ionization per atom at the VD surface as a function of power density. At power densities above $4\times {10}^{17}$ W/cm${}^2$, the electron temperature reaches the 500 eV level of the L edge in vanadium. (b, c) Absorption coefficient as a function of photon energy, for the case of cold material (data from The Center for X-ray Optics, CXRO) [31], local thermodynamic equilibrium (LTE), and nonlocal thermodynamic equilibrium (non-LTE), for two different electron temperatures. At high electron temperatures, the non-LTE model leads to a substantial drop in absorption. Electron temperatures of 300 eV are obtained in the sample during the FEL pulse, and a drop in absorption will lead to transparency of the hotter zones of the material and to deeper propagation of radiation into the bulk.