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Observation of Shock-Front Separation in Multi-Ion-Species Collisional Plasma Shocks

We observe shock-front separation and species-dependent shock widths in multi-ion-species collisional plasma shocks, which are produced by obliquely merging plasma jets of a He/Ar mixture (97% He and 3% Ar by initial number density) on the Plasma Liner Experiment [S. C. Hsu et al., IEEE Trans. Plasma Sci. 46, 1951 (2018)]. Visible plasma emission near the He-I 587.6-nm and Ar-II 476.5–514.5-nm lines are simultaneously recorded by splitting a single visible image of the shock into two different fast-framing cameras with different narrow bandpass filters (589 ± 5 nm for observing the He-I line and 500 ± 25 nm for the Ar-II lines). For conditions in these experiments (pre-shock ion and electron densities ≈ 5 × 10 cm−3, ion and electron temperatures of ≈ 2.2 eV, and relative plasma-merging speed of 22 km/s), the observationally inferred magnitude of He/Ar shock-front separation and the shock widths themselves are < 1 cm, which correspond to ∼ 50 post-shock thermal ion–ion mean free paths. The experiments are in reasonable qualitative and quantitative agreement with results from 1D multi-fluid simulations using the chicago code. Moreover, the experiment and simulation results are consistent with first-principles theoretical predictions that the lighter He ions diffuse farther ahead within the overall shock front than the heavier Ar ions.

First-principles theory of interspecies ion diffusion and simulations based on the theory predict that lighter ions diffuse farther ahead within a collisional plasma shock (closer to the pre-shock region) than heavier ions [11][12][13][14][15][16][17][18][24][25][26][27][28][29][30]. The diffusion mechanisms are classical diffusion based on the mass concentration gradient, barodiffusion based on the ion pressure gradient, thermodiffusion based on ion and electron temperature gradients, and electrodiffusion based on the electric field (negative gradient of the electric potential). For the He/Ar mixture in our experiments, the various diffusion forces have the same sign except for the relatively small electron thermodiffusion, and we assume that there is no initial concentration separation. Within a shock front, the pressure gradient, temperature gradients, and electric potential gradient point toward the post-shock region. Therefore, in the center-of-mass frame, the diffusion velocity of the lighter ion species (in our case, He) points toward the preshock region, and the diffusion velocity of the heavier ion species (in our case, Ar) points in the opposite direction. In the present research, we directly observe the spatial profile of a plasma shock front containing a He/Ar mixture, offering the opportunity to validate first-principles models of multi-ion-species shock evolution.
We experimentally create multi-ion-species plasma shocks by colliding plasma jets generated from coaxial plasma guns in a 2.7-m-diameter spherical vacuum chamber [34][35][36], building on earlier work using parallelplate railguns [37][38][39][40]. Figure 1 depicts the experimental setup. Initially, the plasma atomic concentration is 97% He and 3% Ar, corresponding to a mass concentration of 76% He and 24% Ar. As the plasma jets propagate toward the chamber center, they expand in vacuum at approximately the sound speed. The two plasma jets merge at a half-angle of 11.6 • , with speeds of 55 km/s corresponding to 11 km/s in the direction normal to the shock and, therefore, a relative normal speed between the jets of v rel = 22 km/s. Before the shock formation, individual jets have electron number densities n e ≈ 5 × 10 14 cm −3 , electron and ion temperatures T e ≈ T i ≈ 2.2 eV, and inferred average ionization states Z of 0.73 for He and 1.15 for Ar. These parameters give  sity [41,42], and emission spectroscopy for temperature and ionization states (data are compared with prismspect non-local-thermodynamic-equilibrium (non-LTE) atomic-modeling calculations [43], as used in earlier research [34][35][36][37][38][39][40]). Figure 2 displays the experimental temperature and density diagnostic results. These pre-shock, experimentally inferred parameters are used to interpret the experimental observations and as input for simulations.
The shock profiles of the different ion species are imaged using a beam splitter to aim the plasma self-emission onto two intensified-charge-coupled-device (ICCD) cameras (10-ns exposure) with narrow bandpass filters [44,45]. Singly ionized Ar-II line emission (near the Ar-II 476.5-514.5-nm lines) is observed with a 500 ± 25-nm filter, and neutral He-I line emission (near the He-I 587.6-nm line) is observed with a 589 ± 5-nm filter. A filter for singly ionized He-II line emission was not used due to the better ICCD camera sensitivity to visible compared to ultraviolet wavelengths and the presence of other stronger lines (Ar-II and/or He-I) near the visible He-II lines. Figure 3 illustrates how the distinct filters are sensitive to the different ion species, based on reference experiments using single-ion-species plasma jet merging. For the 100%-Ar jet merging, the bright region in the Ar-II filtered image correlates to an increase in singly ionized Ar emission. For the 100%-He jet collision, dark bands in the He-I filtered image correlate to a reduction in neutral He emission and a corresponding increase in He ionization. Thus, using these filters, we can separately image the shock profiles of the different ion species. Figure 4 displays the spatial profile of the shock structure produced by merging multi-ion-species plasma jets, which are directly imaged using the narrow bandpass filters for Ar-II and He-I line emission. Normal to the shock front, we take lineouts with widths of approximately 20 pixels (∼1 cm). In the laboratory frame, the shock fronts are moving away from the zero position. The plasma emission intensity is a function of T e and ion density n i . Across the emission spatial profile, the lineout intensities are scaled between 0 (lowest emission) and 1 (peak emission) in the second row. For the Ar-II filtered lineout, 0 corresponds to background (lowest emission of singly ionized Ar), and 1 corresponds to the peak singly ionized Ar emission. For the He-I filtered lineout, 1 corresponds to background (peak emission of neutral He), and 0 corresponds to peak singly ionized He emission (lowest emission of neutral He). Using these lineouts, we infer the shock-front separation between the peak intensities of Ar and He ions. Additionally, we observe the shock width (horizontal bars in the second row of Fig. 4 near the −2 cm position), which we approximate by the transition distance between the middle and peak intensity, here taken as 50%-90% of the peak value. The 50% and 90% values are chosen to reduce the influence of varying background levels and spurious pixel intensities on the measurements. The experimental and simulation results are obtained at 2 µs after the beginning of the plasma jet merging. This time is chosen by analyzing an image time sequence and correlating the density increase over time between the experimental time-resolved interferometry and the simulation results; see the bottom row of Fig. 2.
Using the shock profile lineouts and plasma parameters, we compare the length scales of our collisional plasma shocks. Taking statistics from 34 experimental shock-front profiles, we find a separation between the shock-front intensity peaks to be 0.68 ± 0.17 cm, a He shock width of 0.36 ± 0.09 cm (37 ± 9 post-shock He ion-ion mean free paths), and an Ar shock width of 0.52 ± 0.11 cm (57 ± 12 post-shock Ar ion-ion mean free paths). The experimental uncertainty values are the shot-to-shot standard deviations. These experimental shock widths are somewhat larger than the theoretical prediction of ∼20 post-shock ion-ion mean free paths (for M = 2) [3]. Table I compares the characteristic length scale results for the multi-ion-species plasma jet merging. Post-shock length scales are calculated based on the following plasma conditions obtained from simulations: peak electron number density n e = 2.1 × 10 15 cm −3 , peak T e = 2.4 eV, peak T i,He = 4.6 eV, peak T i,Ar = 5.5 eV, and average ionization statesZ of 0.89 for He and 1.47 for Ar. The post-shock mean free path for an ion (unprimed) colliding with multiple ion species (primed) is [46,47] with thermal velocity v th,i and energy loss collision rate ν i,i . Since we are not in the fast or slow limit, we use the entire collision-rate formula [46]. We compare the experimentally inferred shock width (as defined above) to the ion-ion mean free path rather than to the electronion mean free path because the density jump and ion temperature jump within a shock front is predicted to occur over a distance of a few ion-ion mean free paths, while the electron temperature jump is predicted to occur over a (longer) distance of a few electron-ion mean free paths [3]. The ion-ion interpenetration length is the pre-shock slowing distance over which ions from an individual jet (test particle, unprimed) will stream through the other jet (field particles, primed) before becoming collisional [35,36,39,40,[46][47][48], with relative velocity v rel and slowing-down collision rate ν i,i s . Again, we use the entire collision-rate formula [46]. In our parameter space, the ion-ion slowing dominates over ion-electron slowing, and thus the latter is ignored. Because our jet size is much larger than the interpenetration distance, the merging of the two supersonic plasma jets produces a shock.
The experimental data quantitatively agree with simulation results. We have successfully employed multi-fluid simulations, using the chicago code [31][32][33], in which each plasma jet is modeled as a separate ion fluid that can contain different species, to reasonably model the plasma interpenetration [35,36,38]. chicago is a hybrid particle-in-cell code with the capability to model both ions and electrons as fluid species [31]. The code may also be run in a magnetohydrodynamic (MHD) mode in which electron inertia is neglected. In the present research, the multi-ion MHD approach was found to generate identical results as those of lengthier simulations with electron inertia retained. For the 1D simulation presented in this work, the two jets are given an initial density profile, temperature, and velocity based on input from experimental measurements. propaceos non-LTE data are used for the ion equations of state and opacities [43]. Collisionality between ions and electrons is determined by a Spitzer model. The third and fourth plots in Fig. 4 display the simulated densities and temperatures, respectively, for He and Ar in the individual plasma jets coming from the left and right at 2 µs after the jets start to merge. Simulations indicate a separation between the shock-front density peaks to be 0.50 ± 0.12 cm, a He shock width of 0.44 ± 0.12 cm (45 ± 12 post-shock He ion-ion mean free paths), and an Ar shock width of 0.57 ± 0.12 cm (62 ± 13 post-shock Ar ion-ion mean free paths). The simulation uncertainty values are equivalent to twice the simulation resolution.
The shock-front separation results are consistent among the experiments, simulations, and theoretical predictions of ion species diffusion. As stated earlier: within a shock front, theory predicts that the lighter ion diffusion velocity (in the center of mass frame) points toward the pre-shock region, and the heavier ion diffusion velocity points in the opposite direction. This prediction is Obtaining species concentration measurements across the shock profile in the experiment will require a more detailed spectroscopic study of the emission line ratios in comparison with the prismspect atomic modeling calculations. The general agreement in the present research among experiment, simulation, and theory allows for this experimental data to benchmark other simulation results and motivates studies to further constrain and validate models. As seen in Fig. 4, the experiments show a wider postshock region compared to the simulation. The experiment shock profile ion intensities (Ar-II maximum and He-I minimum) peak away from the zero position (second row in Fig. 4), and we infer a corresponding T e and n i increase at those positions. The experiments then appear to show a decrease in T e at the center position. Comparatively, the simulation results show a peak T e and peak total n i at the center zero position (third and fourth rows in Fig. 4). Possible sources of this discrepancy include the models of collisionality and thermal conduction in the post-shock region used in the simulations. Additionally, the simulation does not capture time-dependent effects of ionization and/or recombination present in the experiments.
In conclusion, within a collisional multi-ion-species plasma shock front containing 97% He and 3% Ar, we experimentally observe shock-front separation and speciesdependent shock widths. Experiments, 1D multi-fluid plasma simulations, and first-principles theoretical predictions are all consistent in showing that the lighter He ions diffuse farther ahead within the overall shock front than the heavier Ar ions. The experimental shock profiles of different ion species were directly imaged using narrow bandpass visible wavelength filters. Multi-fluid plasma simulations allowed for reasonably accurate modeling of the plasma jet merging and multi-ion-species effects. The fundamental experimental data in the present work can be used to validate models and benchmark numerical simulations of multi-ion-species collisional plasma shocks of relevance to HED, MIF, and ICF experiments.