Comment on “Fluid modeling of a high-voltage nanosecond pulsed xenon microdischarge” [Phys. Plasmas 23, 073513 (2016)] Free

We appreciate Levko and Raja's effort¹ to simulate spark breakdown under conditions more appropriate for comparison to our experiments² than they had done previously.³ Our experiments² demonstrate that microdischarges in 10 atm of xenon (Xe) gas are opaque to visible light, which requires an electron density of ∼10²⁷/m³. As they paraphrase in Ref. 1, Levko and Raja's conclusion in Ref. 3 was that “the microdischarge by itself cannot generate fully ionized plasma” as is necessary to explain the opacity. Their simulation—in 1 atm Xe—results in a plasma of only ∼0.01% ionization, and so they suggest that additional “plasma is generated when the electromagnetic radiation [from the laser probe] further increases the plasma density.”³ In Ref. 4, we emphasize that the microdischarge remains opaque in the zero-laser-power limit, and so the laser radiation cannot account for the high electron density. Their more recent simulations¹—in 10 atm Xe—show less than ∼1% ionization and a peak plasma density of ∼10²⁴/m³, still far too low to explain the opacity, and so they offer the alternative explanation that “field emission is another mechanism [that] can be responsible for the generation of a denser plasma.”¹ 

We agree with Levko and Raja that the high electron density must be due to physics that is not included in their software package, but we do not believe it is attributed to field emission. Our group has observed high-opacity phenomena in similar systems that do not have electrodes. For example, a collapsing bubble generates an 11 000 K Xe plasma of collapse density equivalent to 16 bar (4 × 10²⁶/m³)⁵ that is also opaque to visible light. In addition, laser breakdown in 5 bar Xe gas generates a plasma that emits a 13 000 K blackbody spectrum, with emissivity equal to 1 (Ref. 6)—which implies opacity through Kirchoff's Law.

The universality of this high-electron-density state suggests that it has a thermodynamic origin. We believe the explanation is ionization potential lowering due to screening beyond the realm of validity of the perturbative Debye model at these high densities. Our measurements of potential lowering in sonoluminescence plasma,⁷ and more recently in dense Xe sparks⁸ have shown it is substantial, and an approximate thermodynamic theory taking into account such effects leads to runaway ionization,⁹ which parallels phase transitions from weak to strong in electrolytes.¹⁰ 

To our knowledge, density dependent screening effects are not included in the VizGlow software developed by Raja's group and used by Levko and Raja in Ref. 1, whose own brochure¹¹ states it has been “used for applications involving pressures ranging from a few mTorr to several Torr,” and for which no published experimental benchmarks exist at such high pressures. Simulations of Refs. 3 and 1 cannot reasonably be expected to match reality because the physics of this warm, dense regime remains unknown. In the framework of Ref. 1, screening effects would manifest as a reduced, density dependent, electron-ion recombination rate (to single out only one of the many density-independent rate equations input to the model and listed in Table 1 of Ref. 1), which is exactly what Levko and Raja claim limits the peak plasma density in their simulation.¹ However, even in the dilute limit, Saha's equation predicts >50% ionization for the conditions in Ref. 1–10 atm Xe at 2.5 eV (29 000 K)—and first order screening corrections are known to increase the degree of ionization.^12,13 We therefore find the <1% ionization claimed in Ref. 1 to be surprising, and wonder what the physics behind the reduced electron density in their simulation might be.

J.K. thanks Dmitry Levko for valuable discussions. We gratefully acknowledge support from the Air Force Office of Scientific Research and DARPA MTO for research on micro-plasmas.