Spark-Induced Shockwave Dynamics Revealed via Nonresonant Four-Wave Mixing

Abstract

We report on the experimental detection of shockwave dynamics produced in a spark discharge, using a nonresonant four-wave mixing optical technique. In particular, we observe the spark-induced local density perturbation across a millimeter-range probe volume, centered on the discharge, via single-shot coherent Rayleigh-Brillouin scattering. We detect the emergence of shock-induced flow velocities, which appear as distinct features in the spectrum, and monitor their dynamic evolution from a few hundred nanoseconds to microseconds after the spark. Finally, we benchmark our measurements against simulations based on a one-dimensional compressible flow model. Our results pave the way for quantitative measurements of highly non-uniform transient flows in challenging environments featuring non-equilibrium gas kinetics.

Figures (5)

• Figure 1: Experimental setup. (a) Schematic illustrating the electrode configuration producing the discharge and the shockwave propagation along the optical lattice. The latter is formed by the interference of two equi-polarized pumps in the gas medium. The probe (out-of-plane, orthogonally polarized) scatters off the lattice at the Bragg angle and the resulting FWM signal carries information on the velocity of gas particles along $\hat{z}$. (b) Current/voltage profiles during the discharge (top) and deposited energy (bottom), shown for the measurements presented in Fig. \ref{['fig:VDF_evolution_symmetric']}. The dashed lines indicate when $99~\%$ of the total energy is deposited. (c) Optical setup configuration. The signal travels $\sim 3$ m before reaching the detection setup (cyan box). M: plane mirror, $\lambda/2$: half-wave plate, TFP: thin-film polarizer, CL: plano-convex lens, BD: beam dump, BP: bandpass filter, PD: photo-diode.
• Figure 2: Detection of the spark. (a) CRBS spectra measured in quiescent (no discharge) conditions ($I_0$, blue), and $\sim0.6~\upmu\mathrm{s}$ after the spark ($I_\mathrm{spark}$, red) in room-temperature, atmospheric $\mathrm{CO}_2$ gas. Both plots are normalized by $I_0^\mathrm{MAX}$. The dashed black curve ($I_\mathrm{theory}$) shows the theoretically predicted spectrum for the quiescent case. The vertical dashed lines indicate the $\mathrm{CO}_2$ speed of sound. (b) Same spectra, each normalized by their corresponding maximum signal intensities, showcasing drastically different gas kinetics in the spark regime, highlighted by supersonic flow velocities.
• Figure 3: Shockwave dynamics. (a) Right: Heatmap plotting the evolution of the CRBS spectrum in $\mathrm{CO}_2$ after the spark. The dashed lines indicate $|v_\mathrm{sound}|$ in quiescent conditions. The probe volume is centered at the discharge channel (see Fig. \ref{['fig:setup']}(a)). Left: Same plots measured in quiescent (no spark) conditions. (b) Selected normalized spectra from (a) highlighting the main differences between quiescent (blue) and spark (red) conditions over time.
• Figure 4: Shockwave evolution revealed in the CRBS spectrum with the electrodes offset such that the probe volume lies mostly on one side with respect to the discharge center. Similar dynamics as in Fig. \ref{['fig:VDF_evolution_symmetric']} are observed, however, primarily positive shock-induced velocities are detected.
• Figure 5: Evolution of shock-induced flow velocity. (a) Experimentally obtained flow velocities as a function of time in the spark regime, extracted from the Doppler-shifted spectra with the probe volume centered (circles) and offset (squares) with respect to the discharge. The blue and red curves plot the shock front and heated channel velocities, respectively, estimated from the gas dynamics model; the dashed curve plots the estimated shock speed from similarity analysis (see text for details). (b) Evolution of the relative density in the shock propagation direction. The dashed line indicates the approximate probe volume length.