Hydrodynamic disassembly and expansion of electron-beam-heated warm dense copper

Cu foils, $200\mu \mathrm{m}$ in thickness, were heated in two stages by a $\sim 100$-ns-long monoenergetic electron bunch at 19.8 MeV and a current of 1.7 kA ($8.5\times {10}^{14} e^{-}$) in a 2-mm-spot to $T_e\sim 1$ eV. After 45 ns of isochoric heating, the pressure in the foil builds up to $>20$ GPa (200 kbar), it begins to hydrodynamically disassemble, and a velocity spread is measured. Near the end of the electron pulse, the 1550 nm probe is cut off or absorbed. Photonic Doppler velocimetry measurements were made to quantify the expansion velocity, hydrodynamic disassembly time, and pressure of the foil prior to cutoff. Measurements indicate foil motion begins the instant electrons pass through the foil and continues until the particle velocity approaches the ambient sound velocity of Cu and the bulk density exceeds the critical density of the probe. Once the density of the plasma drops below the critical threshold and begins reflecting again, an expansion velocity of the classical plasma is also measured, similar to the point-source solution.

Figure 1

Experimental setup displaying an electron-beam-heated Cu foil (not to scale), an expanding plume (false color), and a PDV probe oriented ${20}^{\circ }$ off normal of the foil face on the downstream side. The expanded plume, shown for reference, is the visible light emitted from the plasma over 90 ns, 20 ns after beam energy deposition begins. Scales are shown for reference.

Figure 2

(a) Zoomed-in version of the measured voltage response on the PDV probe with electrons incident on the foil at $t=0$; the full 10-$\mu \mathrm{s}$ record is shown in the inset. (b) The calculated velocity spectrogram for this 150 ns window is shown indicating the hydromotion of the foil; the full 10-$\mu \mathrm{s}$ spectrogram is shown in the inset. All data for shot number 25901.

Figure 3

lasnex calculation of the axial electron (a) density, (b) temperature, and (c) ionization state for a 200-$\mu \mathrm{m}$ Cu foil at 50 ns intervals from 50 to 200 ns. 10% solid density is indicated in addition to the critical density for PDV in (a).

Figure 4

Red, lasnex calculation, Orange dots: experimentally measured values from the leading edge of the spectrogram in Fig. 2, Green: mean of the experimentally measured spectrogram. (a) particle velocity; (b) foil displacement at the edge and; (c) elastic pressure, from a 200-$\mu \text{m}$-thick copper foil for shot number 25901 vs. EOS pressure at the center of the foil.

Figure 5

An expanded velocity spectrogram out to $1\mu \mathrm{s}$ from the same foil hydromotion from Fig. 2 indicating the temporal velocity spread and cutoff time for shot number 25901.