Observation of Shell Structure, Electronic Screening, and Energetic Limiting in Sparks

We study the formation of micron-sized spark discharges in high-pressure xenon on the nanosecond time scale. The spark’s energy per length is measured through the expansion dynamics of the generated shock wave, and is observed to scale linearly with the spark radius. At the same time, the surface temperature of the spark channel remains constant. Together, these observations allow us to conclude that the spark channel, up to $40\mu \mathrm{m}$ in overall radius, is actually an energetically hollow shell about $20\mu \mathrm{m}$ thick. Further, the energy per nucleus in the shell is about 15 eV, independent of size and density. To reconcile these findings with the opacity to visible light, we appeal to collective screening processes that dramatically lower the effective ionization potential, allowing a much higher electron density than is otherwise expected. Thus, nanosecond measurements of sparks provide access to the thermodynamics and kinetics of strongly correlated plasmas.

Figure 1

Time-resolved radial cross section of a spark discharge in 42 bar (a) and 10 bar (b) Xe. In (b), a backlight renders the emitted shock wave visible. Temporal (c) and radial (d) lineouts, whose position is indicated by the green dotted lines in (a), reveal brightness saturation occurring both in time and space. A weak femtosecond laser pulse initiates the discharge, indicated by emission at $-8\mathrm{n}\mathrm{s}$ in (a) and (c). The red-dashed curve in (d) is the best-fit super-Gaussian.

Figure 2

Block diagram (b) of the system used to study spark discharges in 10–42 bar Xe. (a) is a time-integrated photograph of a single spark event in 20 bar Xe as captured by CCD1. The pressure chamber contains two $80\mu \mathrm{m}$ diameter tungsten needles held $170\mu \mathrm{m}$ apart perpendicular to the plane of the block diagram, as seen as silhouettes in (a) and charged to 5 kV. CCD1 and CCD2 are used for alignment and diagnostics. Subnanosecond dynamics are resolved by the streak camera (Fig. 1), which images a $\text{6\hspace{0.17em}\hspace{0.17em}}\mu \mathrm{m}$ band across the spark width, indicated as streak slit in (a).

Figure 3

Absolute spectral intensity of Xe discharges at 3 ns for various static pressures. Spectral saturation throughout the measured spectrum occurs for pressures $>10\text{bar}$ and is well fit to a 29 000 K blackbody spectrum (dotted). Simulated spectra (dashed) at 20 bar were calculated for various levels of ionization ($Z=0.3$ and 2) using Eq. (7) at $T_{\mathrm{sat}}=29000\mathrm{K}$ and $l=40\mu \mathrm{m}$.

Figure 4

Plasma radius (solid) and velocity (dashed) as a function of time for 20 and 42 bar discharges. Discharge sizes varied from shot to shot within the range indicated by the shaded regions bounding the radius curves. The radial expansion is fit (black) to Eq. (1) between 3 and 25 ns. A shock wave is released from the plasma surface between 20 and 25 ns as indicated in the shaded region. The plasma velocity is shown normalized to the isothermal speed of sound of a 29 000 K gas ($c_s=\sqrt{k{T}_{\text{sat}}/M_{Xe}}=1.36\mu \mathrm{m}/\mathrm{ns}$).

Figure 5

Scatter plots of (a) $B^2{M}_{Xe}$ and (b) the brightness of the spark channel vs the initial plasma radius for individual discharges at 20 and 40 bar. $B^2{M}_{Xe}$ is proportional to $(R_0-R_{\min })$ and is pressure independent, while the surface brightness is independent of both spark size and pressure.