Resolving Ultrafast Heating of Dense Cryogenic Hydrogen

We report on the dynamics of ultrafast heating in cryogenic hydrogen initiated by a $\lesssim 300\mathrm{fs}$, 92 eV free electron laser x-ray burst. The rise of the x-ray scattering amplitude from a second x-ray pulse probes the transition from dense cryogenic molecular hydrogen to a nearly uncorrelated plasmalike structure, indicating an electron-ion equilibration time of $\sim 0.9\mathrm{ps}$. The rise time agrees with radiation hydrodynamics simulations based on a conductivity model for partially ionized plasma that is validated by two-temperature density-functional theory.

Figure 1

Schematic of the experimental setup. Horizontally polarized FEL radiation at 92 eV, 10 Hz pulse repetition rate, and duration of $\tau \lesssim 300\mathrm{fs}$ is geometrically divided by a split-and-delay unit [19]. Likewise, a time delay $\mathrm{\Delta }t$ between the x-ray pulses is introduced with few-fs precision. The pulses are subsequently focused to a $20\times 30\mu {\mathrm{m}}^2$ spot using an ellipsoidal mirror, yielding intensities up to $(27\pm 0.6)\mathrm{TW}/{\mathrm{cm}}^2$ for the variable-delay branch and $(19\pm 0.4)\mathrm{TW}/{\mathrm{cm}}^2$ for the fixed branch. The FEL pulses hit a $(9\pm 2)\mu \mathrm{m}$ radius hydrogen jet with mass density of $0.08\mathrm{g}/{\mathrm{cm}}^3$ and temperature of 20 K. Scattering is collected at 90° relative to the incident FEL radiation in the vertical plane. To discriminate between the scattered XUV photons and plasma self-emission or energetic particles, we employ a variable line space grating spectrograph [22, 23].

Figure 2

Experimental scattering spectra as function of time delay. The inset shows two 16-bit raw spectra, each $25\times 50$ pixels of ${(13.5\mu \mathrm{m})}^2$ size, with a horizontally oriented spectral axis corresponding to the graph, where the spectral profiles are integrated along the vertical axis.

Figure 3

Simulation of the temporal evolution of the plasma parameters and the structure factor. The temperatures of the electronic and atomic-ionic subsystems are calculated using the 1D radiation-hydrodynamics code HELIOS and a Saha-based EOS. Also shown is the structure factor at $k=0$. No temporal evolution in the initial ion density is observed. The ionization ranges between 4%–6%, temporally following the electron temperature dependency.

Figure 4

Shown is the calculated pair distribution function $g(r)$ as a function of the radial interparticle distance $r$ for different time delays and temperatures. For cryogenic hydrogen ($\mathrm{T}=20\mathrm{K}$), a peak at $r\sim 0.75\AA$ indicates the distance in the ${\mathrm{H}}_2$ molecule. With increasing temperature the molecular bonds break and the intensity of the peak drops.

Figure 5

Temporal evolution of the measured and simulated x-ray scattering. A total of 300 exposures were grouped together by delay, and their errors resemble their root mean square deviations. For the blue data points, ranging from $\mathrm{\Delta }t=0\mathrm{ps}$ to 1 ps only, the more intense $27\mathrm{TW}/{\mathrm{cm}}^2$ pulse pumps the target, while it is probed by the $19\mathrm{TW}/{\mathrm{cm}}^2$ pulse. The red data points, ranging from 0 to 5 ps, resemble the inverse case where the pump was less intense ($19\mathrm{TW}/{\mathrm{cm}}^2$) than the probe ($27\mathrm{TW}/{\mathrm{cm}}^2$). In both cases, the signal increases within 1 ps, and for the more intense pump the amplitude is larger. Simulations based on QEOS (gray) predict no delay dependence for $S(0)$.