Mechanisms of carbon dimer formation in colliding laser-produced carbon plasmas

Laser-produced plasmas (LPPs) at moderate laser intensities have garnered much interest in a diverse expanse of applications including laser induced breakdown spectroscopy (LIBS) for material composition and detection analysis, pulsed laser deposition (PLD) for thin film deposition, development of photon sources with various energies for a wide range of applications such as EUV and x-ray sources for advanced nanolithography and biomedical applications, and simulation of plasma/wall interactions during transient events in magnetic fusion reactors.^1–5 

The research on colliding plasmas has witnessed increased interest over the past decade due to their distinct characteristics and plasma chemistry which set them apart from conventional single plume LPPs. Colliding plasmas are currently a subject of interest in several plasma fields where their unique nature can give rise to optimal conditions for nanostructure formation⁶ and EUV photon emission^7,8 or can lead to hard contamination of the chamber environment in an inertial fusion device.⁹ For example, in inertial fusion devices, the thermonuclear burn of the DT pellet and the resulting products are contained by the first wall of these devices, which utilize carbon and other materials. The intense radiation and energetic ions produced in thermonuclear burn could vaporize the wall material, leading to low-temperature plasma converging toward the center of the reactor chamber. The formation of large molecules during the collision of such plasmas at the cavity center poses a threat to the necessary spatial and temporal uniformity of this heating since carbon macromolecules are susceptible to scattering, absorbing, or otherwise perturbing of x-ray light. With a standard device operating with a repetition rate of 10 Hz, the long dwell time of these large carbon structures could disrupt the necessary vacuum condition required for obtaining efficient DT burn. Inquiry into the colliding regime of carbon plasmas is necessary to properly access the eminence of these concerns.

The formation of large carbon fullerene structures from the laser ablation of graphite has also been implemented favorably for the systematic production of carbon nanotubes (CNTs). A common technique utilizes a laser oven method in which controlled ablation of the graphite is conducted at around 1200 °C ambient in a flowing inert gas buffer.^10,11 Other design modifications such as introducing 1% Ni and 1% Co impurities into the graphite matrix as carbon nanotube (CNT) growth catalysts¹² and employing a double-pulse scheme have shown improvements.¹³ Using colliding plasmas for this purpose is only recently being explored.

The presence of free electrons and ions in the colliding plasma environment manifests quite unique chemistry which should be understood to most effectively tailor the plasma for relevant technologies. Laser-produced plasmas in vacuum first undergo isothermal heating during the pulse duration which is quickly followed by subsequent adiabatic expansion of the plasma plume. In the adiabatic expansion stage, the plasma plume rapidly rarefies and cools. In colliding plasmas, two distinct plasmas interpenetrate, resulting in the formation of a degree of stagnation of the two plumes. The stagnation volume in colliding plasmas may persist for several hundred nanoseconds while retaining plasma temperature and density. The unique conditions in the stagnation of two colliding plasmas require a further detailed study to better understand their natural occurrence and to develop new techniques to implement colliding plasmas for novel technologies and research techniques.

Numerous experimental studies of colliding plasmas allowed the prediction of fundamental characteristics of the stagnation layer formed by LPPs from different laser energies. Time averaged electron densities and temperatures for various laser beam intensities were found from the analysis of line broadening for various ion emissions and from the relative intensity of lines produced by different transitions.^14,15 Measurements of kinetic energies of ions showed the ability of colliding plumes to accelerate ions in vacuum chamber conditions.^15,16 Spectral images obtained across the visual range and within the narrow bandwidth belonging to specific ion and molecular vibration emission lines showed spatial evolution of stagnating plasmas produced from various target materials in different ambient conditions.⁹ 

While the above measurements allow the accurate estimation of averaged parameters in the case of plasmas in local thermodynamic equilibrium (LTE), time- and space-resolved plasma characteristics in the stagnation layer require a more detailed analysis. The above technique for plasma density and temperature measurement cannot be used for non-LTE conditions produced by higher intensities of laser beams. Parameter averaging, used in this technique, is not appropriate for transient non-LTE plasmas with highly non-homogeneous distributions of density and temperature.

Modeling LPPs can help in this regard. Limitations of empirical and simple theoretical methods necessitate comprehensive and integrated computational modeling of experimental findings. However, to our knowledge, not many modeling efforts have been devoted to colliding plasma studies due to strict requirements to numerical analysis such as full 3D models for the description of plasma physics processes and simulations of relatively large spatial domain evolution over full plume lifetime.

The theoretical description of carbon dimer multiple bonding and dissociation on an ab-initio basis is still a very challenging task due to the existence of many valence bond structures and complex full configuration interactions in ground and excited electronic states.^17,18 Different ab-initio calculations with various levels of sophistication such as a coupled cluster technique,¹⁸ density functional methods,¹⁹ and quantum Monte Carlo²⁰ are used for the prediction of molecule configuration and dissociation forms. Complex C₂ activity calls for the challenging analysis of dimer formation dynamics with a strong dependence on plasma conditions. The Swan emission spectrum is well defined and has been used, e.g., for plasma diagnostics for many years.²¹ We used in our current analysis a combination of experimental methods with well-established methods for plasma modeling and diagnostics to describe carbon behavior in colliding plasmas.

The analysis shown in this paper is based on the integration and correlation of measurements at Center for Materials Under eXtreme Environment (CMUXE) experimental facilities and modeling results obtained with the HEIGHTS simulation package for the 3D modeling of LPPs developed at CMUXE. Such an approach permits both the temporal and spatial resolution of main plasma parameter distribution and explains the effect of laser beam intensity on colliding plasma evolution and properties. It has been demonstrated that the hot stagnation region formed from the collision of laser-produced carbon plasmas is rich with carbon dimers which can be synthesized into large carbon macromolecules such as carbon fullerene onions and nanotubes.

Colliding plasmas occur from the collision of two partially expanded seed plasmas as they propagate into each other. Since an evolving LPP expands in both longitudinal and lateral directions, different collisional regimes may arise. Laterally, colliding plasmas and cross-collisional plasmas are described in greater detail in the literature.^7,9–16 Certain parameters dictate the manner of stagnation of the two colliding plasmas, namely, the characteristic plasma dimension (i.e., the separation between the colliding plumes) and the ion-ion mean free path. The “collisionality” parameter is the ratio of the plasma dimension to the ion-ion mean free path (ζ = D/λ_ii) and is given by

where $ni0$ and $Te0$ are the ion density and electron temperature at the ablation surfaces.²² Hard stagnation (ζ < 1) is characterized by plasma interpenetration, whereas soft stagnation (ζ > 1) is highly collisional and involves the agglomeration of the seed plasmas into a single hot, dense plasma where expansion energy converts into thermal energy. The ensuing conversion of the thermal energy to molecular synthesis in colliding plasmas created from carbon targets is the subject of our analysis.

It is well documented from experiments that carbon allotropes form in plasma environments rich with C₂ dimers.^23,24 A plasma may produce C₂ via two mechanisms: (i) fragmentation of large C_n (n ≫ 2) clusters ejected from ablation or (ii) molecular synthesis via interacting carbon species in recombination processes.²⁵ Carbon neutrals are integral to many of these processes and therefore play a significant role in the formation of C₂ and larger carbon structures. In standard single-pulse LPPs, fragmentation predominates at low laser fluence, whereas the recombination processes dictate formation when using high laser fluence. The laser-plasma interaction and plume evolution influence the formation of large carbon molecules by changing local concentrations of carbon species and therefore C₂.

The precise mechanism of carbon fullerene formation is hard to predict,²⁶ especially for transient LPP conditions. A general description usually entails the formation of linear carbon chains which in turn may begin to form cyclic aromatic structures via π-conjugation, concluding with cage closure. The precise timescale for the formation of carbon fullerenes via this mechanism is still not fully understood, but the necessity of high carbon density, continual resupply of C₂, and high temperature is emphasized.²⁷ Particle confinement and fluid thermodynamics of collisional plasmas are quite unique from single-pulse plasmas in that regions with high temperature and carbon density may be retained for relatively long timescales, which allows appreciable intermixing of various charge states of carbon. The ensuing discussion of this paper will help elucidate the formation mechanism of C₂ in cross-collisional carbon plasmas taking into account plume emissions and dynamics.

A schematic of the experimental setup is shown in Fig. 1. Seed plasmas were produced using a single laser pulse (1064 nm, 6 ns Nd:YAG) which was split into two arms bearing equal pulse energy (150 mJ). The laser pulse was split using an ensemble of two waveplates and two cube polarizers which allowed for fine tuning of pulse energy. The energy was measured at each respective chamber entrance using an Ophir NOVA II laser power-energy monitor to rectify for energy loss along the beam path. The two individual beams entered the chamber in mutually orthogonal directions (one from above and the other laterally along the tabletop). They were separately focused using two 40 cm planoconvex lenses onto orthogonal surfaces of a two planar carbon target (graphite, Alfa Aesar) which together formed a wedge (see the inset in Fig. 1). Ablation occurred such that the two plasmas were created each 5 mm from the wedge corner, possessing intersecting targets normal such that skew collisions were avoided. Three different focal spot sizes (250, 500, and 1000 μm) were investigated corresponding to three different laser intensities (∼5.1 × 10¹⁰, 1.3 × 10¹⁰, and 3.2 × 10⁹ W/cm²). The pressure during data collection was maintained at ∼0.1 Torr of air ambient.

A combination of plume imaging and spectroscopy diagnostics was used to provide empirical insights into the collision of carbon plasmas. Fast photography was done using an integrated charged couple device (ICCD) camera (PI-Max, Princeton Instruments) which provided detailed time-resolved observations of the colliding plasma within the time domain of plume expansion and collision. A focusing objective (Nikon) was used to obtain the focused view of the plasma plume. These observations provide a useful qualitative tool to understand plume dynamics (i.e., plume stagnation and interpenetration). Further imaging involved selective placement of one of two different bandpass filters (656 or 510 nm and 10 nm bandwidth) in front of the camera to perform monochromatic imaging. This permitted discriminatory observation of carbon C⁺¹ ions and molecular C₂ dimers (viz., Swan band emission) from integrated spectral images. For each imaging series, a fixed (non-incremental) gate width of 20 ns was used to facilitate the absolute comparative assessment of emission intensities across the whole-time domain in the observed spectral window. Optical emission spectroscopy (OES) was performed using a 0.5 m Czerny-Turner type spectrograph (Acton SP-2500, Princeton Instruments) with 150 grooves/mm grating at a fixed 30 μm slit width. OES spectra likewise used a constant gate width (25 ns) for collection. OES was used in tandem with monochromatic imaging to present complementary time- and space-resolved indication of carbon species emission. Triggering of the ICCD was accomplished using spectroscopy software delay settings and a 1 GHz digital oscilloscope.

Verification and explanation of experimental results and further benchmarking of plasma physics models were done using the CMUXE's in-house multi-physics simulation tool, the HEIGHTS computer package.^28,29 The package includes detailed models of all main processes for the description of laser produced plasma (LPP) development, dynamics, and collision. The solution of the general equation set detailing a full description of the LPP system is split to solve five major components separately: laser energy deposition, target heating and erosion, vapor/plasma hydrodynamics, thermal conduction in plasmas, and radiation transport. Various numerical methods are employed for the description of each of the above processes. The package self-consistently integrates Monte Carlo models for laser beam interactions with the solid target, vapor, and plasma; Monte Carlo modeling of plasma radiation and photon transport; explicit high order schemes for target evolution and vapor/plasma dynamics; and implicit solution of thermal transport in vapor/plasma. Atomic properties and optical coefficients are calculated using the self-consistent Hartree-Fock-Slater (HFS) method and the collisional-radiative equilibrium (CRE) model. HFS calculations determine the structure of atomic energy levels, wave functions, transition probabilities, ionization potentials, oscillator strengths, broadening constants, photoionization cross-sections, and other atomic characteristics.³⁰ The CRE model is used to calculate the populations of atomic levels and the ion and electron plasma concentrations. Ion and electron concentrations found from the CRE model are used in the equations of state to calculate the pressure and internal energy. A detailed description of all the methods integrated in the HEIGHTS computer package can be found elsewhere.³¹ The package was benchmarked and used for the optimization of LPPs for EUV and soft x-ray sources.²⁹ 

The self-consistent and integrated models implemented in the HEIGHTS package allow the accurate simulation of the entire process of LPP evolution. All laser photon interactions with target/media are described using Monte Carlo techniques. Initially, the laser beam propagates through the optically transparent chamber environment interacting with the solid target only. Laser photon absorption/reflection from the target surface is determined based on experimental optical constants. Subsequent material heating and evaporation lead to target surface recession and vapor expansion described by fluid dynamics. This leads to laser photon interactions with vapor based on the collision-induced absorption mechanism and initiates photon absorption in an evolving plasma by inverse bremsstrahlung. The macrocharacteristics of the evolved plasma are determined from the pre-calculated and tabulated optical and thermodynamic data using HFS/CRE approaches. The energy distribution in the vapor/plasma domain is determined by five processes: evaporated particle kinetics, laser energy deposition, fluid dynamics of the vapor/plasma, electron thermal conduction, and plasma radiation and transport. A suitably small time-step allows consequent simulation and integration of all processes without any oscillations and with the accurate prediction of laser energy deposition in the target and vapor/plasma.

Three-dimensional simulations of a relatively large LPP system for modeling colliding plasma experiments up to a microsecond were conducted on a multi-processor system. Various algorithms were developed and optimized for task distribution among several processors. A non-uniform mesh was also used for fine spatial resolution of the target surface region that allowed accurate simulations of target evolution. Exact experimental parameters were used in the modeling of colliding plasmas.

ICCD fast-gated plume imaging was used in this study to assess the dynamics of the colliding plume fronts of the two seed plasmas from the graphite targets. In addition to integrated spectral images, plume imaging was done using bandpass filters, and so, specific emission features could be spatially mapped within the collision plane of the two plasma plumes. In all imaging scenarios, laser focal spot sizes of 250, 500, and 1000 μm were used (corresponding to intensities ∼5.1 × 10¹⁰, 1.3 × 10¹⁰, and 3.2 × 10⁹ W/cm², respectively). Imaging is provided for the 500 μm spot size case, which enables comparison with HEIGHTS modeling. Figure 2 shows the plume evolution of the colliding plasma from emission over the visible spectrum. The ablation sites indicate the dimensional scale of the colliding plasma scheme (each being 5 mm from the collision center). At ∼100 ns, it is seen that the carbon plasma produces soft stagnation along the collision midplane of the two seed plumes. As time progresses, the stagnated plasma plume expands outward while being confined along its lateral dimension. This could be explained by continual pressure being supplied by the seed plumes. With the gradual abatement of seed plume expansion, lateral confinement of the stagnated plasma is lost after 500 ns.

It was discussed in the introduction that the purported mechanism for C₂ and larger C_n formation is assisted by a high density of carbon neutrals. Our experiments could not detect carbon neutrals within the plasma since the most prominent emission lines of carbon neutrals lay outside the spectral range of our imaging apparatus. We used comparative diagnostics of the Swan spectrum and ion emission to distinguish molecule formation areas in colliding plasmas. C₂ molecular dimers were located using a 510 nm bandpass filter to transmit 0–0 Swan band emission. The 0–0 Swan band provided high luminosity making it suitable for imaging. Monochromatic imaging for C₂ can be seen in Fig. 3. The most intriguing trend that can be discerned from the images is present at 350 ns. At the bottom of the stagnation plume, a high intensity region forms, occurring several hundred nanoseconds after the collision of the seed plasma has already transpired. This marked behavior is not seen from the integrated spectral images shown in Fig. 2. We posit that this region corresponds to the onset of C₂ formation in the colliding plasma. At later time steps, this region grows and extends upward along the collision midplane. This can be interpreted as either the spatial relocation of C₂ continually being formed or as the drift motion of C₂ already synthesized (or some combination thereof). We believe that this is principally due to C₂ drift due to carbon neutral species being highly localized near the bottom of the stagnation plume (as is seen in modeling results presented in Subsec. V B). Loss mechanisms for C₂ are not reconciled in this experimental investigation, and so, further diagnostics are needed in future studies to present a comprehensive theory.

It should be mentioned as a caveat that several C¹⁺ ionic lines (due to 2s2p(³P°)3p-2s2p(³P°)3s transitions) reside in this window with non-negligible luminosity, but they only present a concern at early times when C¹⁺ is greatly abundant. At such times, C¹⁺ ionic line transitions would give false positive indication of C₂ Swan band emission. Time-resolved contour mapping of C¹⁺ species was employed to enable the accurate distinction of regions exhibiting C₂ formation.

To locate C¹⁺ ions, a 656 nm bandpass filter was used to selectively transmit 2s²3p-2s²3s emission lines which are well-segregated from competing emissions. Imaging for C¹⁺ ions can be seen in Fig. 4 where it is shown that C¹⁺ ions exist most abundantly in the region of most intense stagnation. After approximately 350 ns, the stagnation volume has largely cooled and the ion population recedes commensurately as the stagnation plume relaxes. C¹⁺ imaging results do not conflict with the previous discussion regarding C₂ formation, showing no indication of appreciable emission after 350 ns. This increases confidence that this emission is indeed Swan band emission and that the onset of C₂ dimer formation begins at such times. Spectroscopy results presented later will further reinforce this assessment. The observed trends reoccurred across all three spot sizes.

Beginning at 350 ns, the region of intense Swan emission expands along the stagnation column. At approximately 500–700 ns, the region with high C₂ density showed the greatest brilliance. This was observed for all three laser fluences. However, the peak magnitude of emission was shown to vary, being least for high laser fluence.

Three-dimensional modeling allowed a detailed analysis of the developed plasma plumes and stagnation layer, spatial and temporal distribution of plasma parameters, and species. Figure 5(a) shows that the laser beam with an energy of 150 mJ, a duration of 6 ns (FWHM), and a spot size of 500 μm creates the plasma from graphite with a maximum temperature of around 35 eV at the peak of laser pulse intensity. Energy redistribution by collisions of plasma species in the expanding plumes and by radiation transport result in the temperature decrease to ∼10 eV before the seed plumes contact. Subsequently, hydrodynamic pressure driving the two plumes leads to increased particle collisions at the intersection of two plasma fronts, resulting in an increase in temperature in the developing stagnation layer [Fig. 5(b)].

Plasma species distributions at the initial interpenetration of two plasmas showed prevailing concentrations of C²⁺ - C⁴⁺ ions in the stagnation layer and in the plasma front layers [Fig. 6(a)]. Only the near surface area with a high concentration of neutrals can be the source for carbon molecule formation at this time [Fig. 6(b)]. C²⁺ - C⁴⁺ ions were found in the core of the stagnation layer up to 350 ns, corresponding approximately to the confinement time of this plasma layer.

Experimental results showed that the initiation of C₂ molecule formation in the area of the stagnation layer corresponds to the time of ∼250 ns after laser pulse for the considered laser parameters and ambient conditions. Continuing expansion of original plasma plumes and plasma species recombination lead to the increased concentration of neutrals surrounding the stagnation layer at this time. However, relatively high pressure of the expanding plumes prevents fast cooling of the core of the stagnation layer that leads to the prevailing concentration of carbon ions (mostly C¹⁺) in this area. These conditions continue for a relatively long time, around hundred nanoseconds, without significantly changing the stagnation layer properties (Figs. 4 and 7).

Modeling of colliding plasma experiments provides a good opportunity to test integrated models comparing plasma dynamics and species distributions for a wide span of plasma/particle interactions. Given in Figs. 4 and 7 are the results showing the long-term existence of C¹⁺ ions in the stagnation layer predicted in modeling and in spectroscopic images of C¹⁺ ions emission at a wavelength of 656 nm.

The temporal evolution of the stagnation layer properties and neutral accumulation can be described by plasma hydrodynamics with incorporated mechanisms of electron thermal energy distribution and plasma species ionization/recombination. Initially, expanding plumes create a dense layer at the intersection with temperature higher than in the surrounding plasma. This layer lasts for a relatively long time due to continued pressure being applied from the original plumes [Fig. 8(a)]. When radiative cooling and plume expansion processes reduce significantly the seed plasma pressure, high pressure in the core of the stagnation layer initiates the expansion of the stagnation layer [Fig. 8(b)]. Energy redistribution in the rarefied layer leads to a significant reduction of plasma temperature that finally leads to the prevailing neutral concentration and preferred temperature for carbon molecule formation.

A comparison of plasma temperature distribution at 500 ns and 750 ns (Fig. 9) with Swan emission intensity found in the experiments (Fig. 3) permits the indication of favorable conditions for carbon molecule formation and persistence within the plasma lifetime. These conditions describe regions with a relatively high concentration of carbon neutrals and with plasma temperatures between 0.7 and 1.1 eV. At earlier time, 500 ns, the high intensity of Swan emission is found close to the bottom edge of the stagnating plasma column due to relatively high plasma temperatures in the top area [Figs. 3 and 9(a)]. Further expansion and cooling of the stagnation layer lead to larger area with optimum conditions for a high reaction rate [Figs. 3 and 9(b)].

The above analysis showed that stagnation layer evolution and properties can be determined by the interplay of two processes: (1) stagnation layer expansion due to high pressure in the core of this layer and (2) pressure from two seed plasma plumes due to continuous expansion of these plasmas. The higher energy accumulated in the stagnation layer in the case of more intense lasers leads to faster expansion and rarefaction of the colliding plasma layer that reduces the neutral concentration in the area with optimum temperatures for molecule formation and persistence.

A slight temperature increase at the intersection of two plumes occurs also for less energetic plasma flows created by lasers with intensities two times less than those considered above [Fig. 10(a)]. However, much less energy is accumulated in thin intersection layer due to lower pressures of seed plumes. Such conditions lead to slower expansion of the stagnation layer created by less energetic plasmas. Thus, the combination of two phenomena, lower energy in the stagnation layer in the case of less intense lasers and continuing supply of neutrals from the expanding seed plumes, prevents fast rarefaction of this layer that results in a high neutral concentration in the areas with optimum plasma temperatures for carbon macromolecule formation. Figure 10(b) illustrates the uniformity of conditions in the stagnation layer in the case of less intense lasers, showing pressure distribution at the stage of layer expansion.

The maximum plasma temperatures in the stagnation layer varied from ∼2.5 eV at 400 ns to 1.2 eV at 700 ns (in the case of 1.3 × 10¹⁰ W/cm² laser intensity). Other researchers showed similar slow cooling of the stagnation plasma for approximately the same laser parameters.¹⁴ While experimental results predicted temperatures along the longitudinal distance averaging this parameter along the lateral distance, our modeling results enabled the prediction of the 3D temperature distribution in the entire layer. A comparison of modeling results with the previous experiments mentioned above and with our current experimental results regarding time-resolved ion emission images gives us confidence in the correctness of used methods for the modeling of colliding plasma experiments. Theoretical validation for the hydrodynamical description of such a plasma arises from the relatively high Mach numbers of the considered flows.³² 

Monochromatic and fast ICCD imaging were used in tandem with HEIGHTS modeling of the colliding plasmas to provide a robust description of plume hydrodynamics. However, monochromatic imaging is limited in that it cannot image carbon neutrals, whereas HEIGHTS modeling package currently does not incorporate molecule formation. Between the two, an intuitive understanding of the underlying mechanism can be conjectured, but this assessment can be further supported through obtaining emission spectra. Optical emission spectroscopy was used to assess the emission spectrum in the plume location of high carbon neutral density (i.e., the bottom edge of the stagnation plasma column). This was performed for all three spot sizes.

It was previously mentioned that monochromatic imaging may conflate multiple dissimilar emission sources. Earlier than 100 ns, Bremsstrahlung emission tends to dominate the spectrum. Shortly thereafter, a locus of C¹⁺ lines occupying the spectral range centered around 514 nm emits concurrently with Swan emission if both C¹⁺ and C₂ species are present. Monochromatic imaging provides useful qualitative information about chemical species existing in the plasma but may lack definitiveness when competing emission sources exist. Optical emission spectroscopy permits absolute identification and quantitative metric of Swan emission to verify the production of C₂ dimers and improve the fidelity of our proposed interpretation of experimental monochromatic imaging results.

Emission spectra for the carbon plasma were acquired in the 375–525 nm window to include numerous strong C¹⁺ and C²⁺ emission lines and prominent 1–0 and 0–0 Swan bands. Unfortunately, carbon does not possess prominent neutral line emission in the visible range (the two most prominent nearby emission lines being at 248 and 834 nm). It should be noted that the 656 nm C¹⁺ ionic line used for the monochromatic imaging of C¹⁺ ions resides outside the selected spectral window. However, preliminary spectra showed this line to be well segregated from other emission sources. For persistence purposes, the 392 nm C¹⁺ ionic line possesses only marginally less emission intensity to the 656 nm line and may be used for the proxy comparison.

Figure 11 shows time varying spectra for the colliding plasma. As seen from monochromatic imaging (Fig. 3), the lower edge of the stagnated plasma column shows the earliest onset of C₂ production. The spectrometer slit was positioned onto this region of interest. Per expectation, early time was dominated by ionic line emission. C²⁺ lines (namely, 465 nm) were relatively short-lived with C¹⁺ lines (392 and 427 nm) persisting longer. To corroborate C₂ imaging from Fig. 3, the 0–0 Swan band was assessed. Nominally, the molecular band should retain the shape over time if no other emission sources in that wavelength window are present [as is seen in Fig. 11(c)]. When high laser intensities are employed, a greater number of ions achieve high charge states, which leads to increased ionic line emission. This is seen in Fig. 11(a) as an anomalous peak due to the C²⁺ line contribution to the measurements of the 1–0 Swan band. In Figs. 11(a) and 11(b), this is seen as unwonted curvature of the rising slope of the 0–0 band measurements. The curvature in Fig. 11(b) is only slight at 250 ns, and so, we can claim that monochromatic imaging after this time correctly depicts the 0–0 Swan band emission of C₂ dimers.

In all three scenarios, Swan band emission appears at approximately 250 ns and persists for roughly 500 ns. Persistence curves for the 0–0 Swan band are shown in Fig. 12. The greatest yield of Swan emission occurs when the lowest laser fluence is used. Swan emission was shown to decrease with increased laser intensity with fixed pulse energy. A combination of several factors contributed to the overall yield of C₂ in the plasma environment created by lasers with the same energy and different spot sizes. Less material was ablated from the graphite target when a higher laser intensity was used due to both the smaller ablated area and enhanced plasma shielding effect. Modeling results predicted two times less eroded mass in the case of 500 μm laser intensity in comparison to a larger, 1 mm spot. Alternatively, more laser energy is converted into ionization and kinetics of plasma species. The net effect is enhanced energetics of the expanding plasma and expedited rarefaction of the developing plume due to quick cessation of seed plume pressure. It should be understood that processes giving rise to C₂ formation favor plasma temperatures around 0.5–1 eV. Relatively high temperatures in the core of the stagnation layer, preserved for a long time, may disfavor recombination processes which lead to C₂ synthesis (Fig. 7). The spatiotemporal optimization of the plume evolution is appropriately dependent upon lab parameter pulse energy and intensity (and therefore also spot size).

Spectra for individual single seed plumes were also briefly evaluated but showed little C₂ generation. The plumes evanesced rather quickly without giving rise to prominent Swan band emission. In the low laser fluence scenario, Swan emission persisted for several hundred nanoseconds albeit with much lower luminosity than that seen from colliding plasmas.

The slit of the spectrograph was aligned vertically (in reference to ICCD images provided), which consequently is 45° from the axis of outward propagation of the stagnated plasma. Alternatively, a dove prism could be used to align the slit either transversely or longitudinally along the column of the stagnated plasma but with significant loss of the spectral signal. For the purposes of this inquiry, the chosen configuration adequately characterizes the local emission, which is our concern. The slit was centered on the bottom edge of the stagnated plasma column, the region previously shown to exhibit high carbon neutral density and Swan emission [see Figs. 3(c), 3(d) and 9].

Modeling results were used for a further analysis of the conditions at the location of high Swan intensity during the period of increase in the emission intensity (Fig. 13). Experimental results shown in Fig. 12(b) correspond to the location at x = 0 and z = 0 in Fig. 13. Changes in the velocity directions show that an increase in the C₂ concentration during the time from 350 ns to 500 ns is most likely due to increase in the formation rate at this particular location rather than drift from other areas. Future experiments supported by modeling will be conducted to provide details of carbon dimers and higher structure formation in the entire stagnation plasma layer.

Based on the above analysis, preferable conditions for C₂ formation in LPPs can be described as a high neutral concentration along with relatively high, 0.7–1. eV, electron temperatures, confined in the volume not surrounded by hot plasmas, and lasting for a long, hundreds of nanoseconds, time. Such conditions can be created by multiple beams with relatively large spot sizes, having, however, enough intensity to create and confine the colliding layer that can also be controlled by the setup geometry. Thus, the development of optimum colliding LPPs for the synthesis process depends on the interplay of several parameters, e.g., laser intensity which determines the amount of the evaporated material and seed and colliding plasmas velocities, laser spot size which determines collision dynamics along the stagnation layer, and ambient conditions and setup geometry which affect plasma confinement.

We integrated our experimental and modeling efforts for the investigation of colliding plasma formation, expansion, and properties. Detailed inquiry into the precise mechanism in colliding plasmas which gives rise to C₂ formation was undertaken in this study. Monochromatic imaging of the colliding plasmas mapped C¹⁺ and C₂ species within the plasma and was compared to modeling results showing contour plots of atomic C, C¹⁺, and higher carbon charge states. Optical emission spectroscopy corroborated results from monochromatic imaging, showing the late onset of Swan band emission at around ∼250 ns. Our comparative analysis showed that the process of carbon molecule formation is assisted by local plasma temperature of ∼0.7–1 eV. More energetic seed plasma flows created by more intense lasers lead to faster expansion of the stagnation layer, reducing the concentration of carbon neutrals in areas with temperatures favorable for molecular formation and persistence.

The findings of this study ultimately suggest that the reduced laser interaction with the early plasma corresponds to an enhancement of C₂ formation. Future work will explore the role of the irradiation wavelength in the collisional plasma regime. In-situ and ex-situ experimental methods will be used to track carbon radical species in the plasma and to determine the production yield of CNTs. Having shown that 3D hydrodynamics and radiation transport modeling can accurately describe stagnation layer evolution, HEIGHTS will continue to provide valuable insights into colliding plasma research.

This work was supported by the National Science Foundation, PIRE Project. We gratefully acknowledge the computing resources provided by the Blues cluster operated by the Laboratory Computing Resource Center at Argonne National Laboratory.