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Abstract
Shadowgraphic measurements are combined with theory on gas-dynamics to investigate the shock physics associated with nanosecond laser ablation of cerium metal targets. Time-resolved shadowgraphic imaging is performed to measure the propagation and attenuation of the laser-induced shockwave through air and argon atmospheres at various background pressures, where stronger shockwaves characterized by higher propagation velocities are observed for higher ablation laser irradiances and lower pressures. The Rankine-Hugoniot relations are also employed to estimate the pressure, temperature, density, and flow velocity of the shock-heated gas located immediately behind the shock front, predicting larger pressure ratios and higher temperatures for stronger laser-induced shockwaves.
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1. Introduction
The analysis of laser-induced shockwaves generated during laser ablation (LA) provides important insights into understanding laser-matter interactions between the laser pulse and target material as well as the expansion dynamics of the subsequent plasma plume. In the high-intensity regime of ns laser ablation on solid materials, the laser irradiance (W/cm$^2$) is sufficiently high to rapidly heat the surface material of the target to temperatures well above its boiling point. The temperature of the molten material continues to rise and approach the thermodynamic critical temperature (T$_\text {c}$), where once the target temperature reaches a value near 0.9T$_\text {c}$ the superheated liquid undergoes homogeneous nucleation and a mixture of vapor and liquid droplets are explosively ejected from the surface in a process termed phase explosion [1–3]. This explosive vaporization process results in the formation of a rapidly expanding vapor plume at the laser spot, which grows in size, temperature, and density as the laser continues to ablate the target surface and supply mass and energy to the system. When the electron density of the ionized vapor plume exceeds the critical electron number density, the plasma becomes optically thick and absorbs the laser photons primarily by an inverse Bremsstrahlung process, supplying energy to significantly heat and accelerate the expansion velocity of the plasma plume [4–7]. This rapidly expanding, high-pressure plasma acts as a piston compressing the background gas immediately in front of the plume into a thin shell [8]. As a consequence of this rapid expansion and compression, a strong shockwave is formed; strong shocks are defined to be characterized by an overpressure ($\Delta P$) greater than the ambient pressure by at least a factor of ten ($\Delta P/P_0>10$) [9]. The initial speed of this external shockwave is comparable to the free expansion speed of the plasma, which is largely a function of the initial mass and energy supplied to the plasma during LA as well as ambient gas pressure yet is minimally influenced by the type of background gas [7,10,11].
Following the termination of the laser pulse, the plasma and shockwave continue to expand. The linear free expansion regime transitions to adiabatic expansion, where energy losses to the surrounding atmosphere are primarily a consequence of the work done by the plasma plume and shockwave on the surrounding gas while other loss processes such as heat conduction, diffusion, and radiation are considered negligible [7,12]. Expansion of both the plasma and shock are frequently described by the self-similar solution for an ideal blast wave, where the initial blast energy may be estimated from the analytical equation for the Sedov-Taylor blast wave model [13,14]. The pressure, temperature, and density of the gas-dynamic flow may also be calculated using the limiting equations for a strong shock, although it should be cautioned that Sedov-Taylor theory predicts a density of zero at the plasma core and no upper bound on temperature, which are not physical conditions for laser-induced plasmas. As the size of the shock continues to grow, its velocity decelerates rapidly and propagation ceases as a consequence of resistive forces imparted on the shock by the background gas. Gas pressure and density influence expansion dynamics, where plasma and shock propagation have repeatedly been observed to extend to greater distances and velocities at lower pressures [15–17]. The exponent in the Sedov-Taylor solution has also been shown to increase for lower pressures [18], indicating that propagation approaches linear free expansion that is known to occur at vacuum conditions. These same gas properties also impact when the external shockwave detaches from the plasma contact front, where experimentally this detachment has been observed to occur at later times and further distances from the target surface for lower pressures [15,16]. In nitrogen gas at 10 Torr, this separation between the contact and shock front was observed to occur at around 300 ns [15] while at atmospheric pressure this is believed to occur at less than 50 ns [19]. In addition to gas pressure and density, other parameters associated with the laser ablation environment also influence the shape and expansion dynamics of laser-induced plasmas and shockwaves. Jeong et al. showed that for larger diameter spot sizes (>1 mm) on the same order of magnitude as the shock dimensions that expansion follows a planar shockwave geometry as compared to a spherical geometry at typical LA spot sizes ($\leq$ 500 µm) [20]. The depth of the ablation crater may also alter the dimensionality of the shockwave, where Mach reflections off of the walls of deep craters transform spherical shockwaves into planar shocks [21].
The shock front position may be measured using various different methods including shadowgraphy [22–24], Schlieren imaging [25–27], interferometry [28], probe-beam deflection methods [20,29], and Rayleigh scattering [30]. Shadowgraphy is largely applied as a visual analysis method to image the expansion of laser-induced shockwaves over time, although quantitative shadowgraphy methods have been presented in the literature [31,32] that overcome beam diffraction and angle deflection challenges to measure the physical properties of the gas-dynamic flow [33]. Investigation of the spatial structure of the plasma and position of the plume front are typically obtained through other methods using images of visible emission of the plasma captured using an ICCD camera [34–36], although select works have demonstrated the ability to resolve the plasma contact front using shadowgraphic imaging [37,38]. Imaging of the expansion dynamics of both the laser-induced shockwave and plasma continues to be performed in the literature to explain the evolving spatiotemporal conditions of the post-LA system, where the interaction of this system with its ambient environment provides important insights into the hydrodynamical and chemical processes that govern characteristics of optical signatures measured using spectroscopic techniques [39,40]. Understanding the temporal evolution and response of these spectroscopic signatures to environmental factors has been the focus of recent work with reactive laser-produced cerium plasmas using laser-induced breakdown spectroscopy [41]. This work aims to expand on this previous investigation by presenting the first shadowgraphic measurements of cerium plasmas in ambient gases to characterize the shock dynamics component of the complex physicochemical post-LA system. Focused shadowgraphy is performed to record the propagation and attenuation of laser-induced shockwaves generated by nanosecond LA on a cerium metal target for various irradiances and atmospheric conditions. In addition, the Rankine-Hugoniot relations for an adiabatic shock are applied to estimate the thermodynamic properties of the shock-heated gas immediately behind the shock front.
2. Experimental methods
Focused shadowgraphy is used to image laser-induced shockwaves formed during the laser ablation of a cerium metal target (MSE Supplies, 99.9% purity). All measurements are performed within a custom vacuum chamber where the fill gas composition is varied between air and argon. Blast waves are generated at atmospheric pressure as well as at a reduced pressure (100 Torr) to investigate pressure effects on laser-induced shockwave propagation. The pump-probe setup involves a Q-switched Nd:YAG laser (Continuum Surelite II-10, 7 ns pulse width, 10 Hz pulse rate), where its beam is oriented perpendicular to the sample to perform ns-LA with a spot size of $\approx$250 µm using the fundamental wavelength 1064 nm. The beam energy for the pump laser is set to 20.8$\pm$0.3 mJ, 60.0$\pm$0.4 mJ, and 100.0$\pm$0.8 mJ to study blast wave characteristics at increasing ablation energies. As for the probe laser, the fundamental wavelength (800 nm) of a Ti:Sapphire laser (Coherent Astrella, $\sim$35 fs pulse width, 1 kHz pulse rate) is used. The ultrafast Gaussian beam is first sent through a Galilean telescope to expand the diameter of the beam to $\approx$25 mm, and is then directed across the sample into a plano-convex lens (f=100 mm) that focuses the image onto a CCD camera (Mightex USB2.0 Monochrome CCD Camera). The magnification for this setup is measured at 0.29$\pm$0.01. Absorptive, reflective, and laser line filters are also placed after the sample to reduce the laser and plasma light that reaches the camera. The pump-probe setup is operated at a pulse rate of 10 Hz using a delay generator to sub-sample the 1 kHz repetition rate of the fs laser. The delay time for this system is defined as the duration of time between pulses from the fs- and ns-pulsed lasers, where images are collected for various delays between 30 ns and 10 µs. A simplified schematic of the experimental setup used in this work is shown in Fig. 1. Following shadowgraph collection, the images are post-processed using Fourier analysis to remove artifacts in the image and background subtraction is performed to emphasize features (e.g., ionization front, plasma plume) observed behind the shock front.
Fig. 1. Focused shadowgraphy setup from imaging blast waves formed during laser ablation. Pump-probe measurements are performed in the vacuum chamber for various fill gases (air, argon) and pressures (100 Torr, 760 Torr).
3. Results and discussion
3.1 Laser-induced shockwave propagation in various atmospheres
Shockwaves generated by single-shot LA are recorded using shadowgraphy to investigate the gas-dynamic properties characterizing nanosecond laser-induced cerium plasmas subject to various atmospheric conditions. A series of shadowgraphs collected at atmospheric pressure in air for an ablation energy of 60 mJ is shown in Fig. 2, where the expansion of a hemispherical shockwave is observed. Starting at 400 ns, a second hemispherical feature is also observed behind the shock front, where this feature is believed to indicate the ionization front based on a report by Callies et al. [42]. The ionization front marks the region consisting of shock-heated and ionized gas immediately ahead of the contact front (plasma plume), where the gas located between the ionization and shock front is also shock-heated yet remains non-ionized [42]. For increasing delay times, the separation between the ionization front and shock front becomes greater until the edge of the ionized region can no longer be distinguished from the shadowgraphs around 900 ns. Because shadowgraphy measures the derivative of the density gradient, this behavior indicates a reduction in the change of density between the shocked and ionized regions. For higher ablation energies, the plasma plume can be resolved in addition to the ionization front (see Fig. 3), where for later times (> 2 µs) the position of the plume is observed to remain approximately stationary while the blast wave continues to propagate outwards.
Fig. 2. Shadowgraphic images of the LA shockwave at atmospheric pressure in air for a laser energy of 60 mJ. The ionization front is visible behind the shock front for times 0.4-0.8 µs.
Fig. 3. Shadowgraphic images of the laser-induced cerium plasma and shockwave at atmospheric pressure in air for a laser energy of 100 mJ.
The expansion trajectories of the shockwaves are extracted from the time-resolved shadowgraphs based on the radius of the shock front for air and argon atmospheres (see Figs. 4 and 5). Velocities and Mach numbers ($M=v/c$) are also provided using the derivative of the radius trajectories and the local speed of sound ($c=\sqrt {\gamma RT}$) for the propagation medium, where room temperature is used in this calculation. However, it should be acknowledged that at very early times after laser ablation that X-ray emission from the plasma will preheat the background gas encompassing the early plasma and shock expansion, which will increase the speed of sound for the propagation medium. Therefore, the maximum values for Mach numbers reported in this work may be overestimates. These measurements are performed at ablation energies ranging between 20-100 mJ (40-200 J/cm$^2$) for atmospheric pressure as well as for a reduced pressure of 100 Torr, where these experimental parameters were chosen because they are widely used within the nuclear laser spectroscopy community to measure spectroscopic signatures and image expansion dynamics of laser-produced plasmas [43–47]. The initial expansion of laser-induced shockwaves is known to be linear, after which the shock propagation transitions to adiabatic expansion before slowing down and ultimately transforming into an acoustic wave at late times. During linear expansion, the shockwave is largely unaffected by the background gas and is instead strongly correlated to the energy transferred to the vapor plume and vaporized target material during laser ablation [7,48]. The free expansion trajectory of the shockwave is given by,
where $R(t)$ is the distance, or radius, of the shock front from the target surface, $v_0$ is the free expansion rate and initial propagation velocity, and $r_0$ is a small offset that arises due to experimental uncertainty in delay times. For all experiments performed in this work, the early propagation velocity of the shockwave is measured to be hypersonic and characterized by Mach numbers greater than ten. Shocks generated at reduced pressures are also observed to occur at further distances from the target surface compared to shocks generated at atmospheric pressure and measured at the same delay times. By extension, this means that the measured shocks travel at faster speeds for reduced pressures as well. This behavior has repeatedly been observed in the literature and results from the weaker attenuation of the shockwave at lower pressures [16,17,49]. The background pressure and shockwave attenuation also influences the time at when the shock propagation transitions from free expansion to adiabatic. In this work, shocks are observed to expand linearly for longer times when propagating through lower pressure atmospheres; shock expansion follows the free expansion law for the first 50-100 ns when generated at a reduced pressure of 100 Torr. In contrast, linear expansion is not observed for the measurements recorded at atmospheric pressure, where it is believed that linear free expansion ends at earlier delay times than measured experimentally in this work (i.e., <50 ns).Fig. 4. Blast wave expansion and propagation velocity in air for various laser energies at (a) 100 Torr and (b) 760 Torr. Errors associated with the position of the shock front result from measured variations between individual single-shot ablations while errors provided for the Mach number are estimated from the uncertainty in the fit of the expansion models to the data. Dotted lines indicate an extrapolation of the given properties beyond the experimentally-measured data.
Fig. 5. Blast wave expansion and propagation velocity in argon for various laser energies at (a) 100 Torr and (b) 760 Torr. Errors associated with the position of the shock front result from measured variations between individual single-shot ablations while errors provided for the Mach number are estimated from the uncertainty in the fit of the expansion models to the data.
Following the free expansion stage, the shock continues to expand rapidly. Thermal energy is converted to kinetic energy and as the volume of gas encompassed behind the shock front increases, the velocity and strength of the shock drops rapidly. Over a limited range when energy losses are dominated by the work done by the shock on the surrounding gas, the shock trajectory follows an adiabatic curve and may be described by the Sedov-Taylor blast wave model. This model predicts the radius of an expanding blast wave propagating through an homogeneous atmosphere with constant specific heats and density $\rho _0$, and was derived using self-similar theory assuming a strong point source explosion [50]. The novelty of the Sedov-Taylor solution is that it enables the estimation of the initial energy that goes into producing the blast wave from a simple equation. For spherical blast waves, this exact analytical solution is given by,
where $\xi _0$ is a dimensionless constant that is dependent on the specific heat properties of the atmosphere and $E_0$ is the initial blast energy. Approximate values for $\xi _0$ may be determined using Eq. (3).While the Sedov-Taylor solution is generally assumed as the appropriate model to predict the expansion of blast waves generated by laser ablation, it should be cautioned that the solution yields systematic overestimates on the initial energy [51,52], is only valid in the strong shock limit ($p_1/p_0\gg 1$) and does not hold at later times when the strength of the shock has diminished and the propagation velocity of the shockwave is comparable to the speed of sound for the atmosphere. Hendijanifard and Willis further investigate this limit on the applicability of the Sedov-Taylor solution for laser-induced shockwaves, suggesting that the following criterion must be satisfied for the blast model to be valid [53].
Assuming that the inequality symbol requires $M_0^2$ to be at least a factor of ten larger, the blast model is valid for shock strengths $M_0>7$ and $M_0>5.5$ for air and argon atmospheres, respectively. This criterion was enforced when fitting the Sedov-Taylor blast wave model to the experimental data, where the expansion trajectories for the shocks propagating through gases at atmospheric pressure fit very well and within errors of less than 2%. For higher ablation laser energies, the error between experimental data and optimized fit to the blast model was reduced to as low as 0.512% (100 mJ, 760 Torr argon). The fitting region for this model ranged from 60 ns up to 250 ns, where measurements at the lower laser energies experienced shorter ranges over when the Sedov-Taylor blast wave model was valid due to the generation of weaker laser-induced shockwaves. Generally, all errors reported in this work are observed to be lower for measurements collected at atmospheric pressure as compared to at 100 Torr. This behavior arises because shadowgraphic measurements performed at atmospheric pressure were very reproducible and the position of the shock front was very consistent, while there was greater variation in the shockwave radius at lower pressures.
Further differences between the measurements collected at the two pressures include an observed saturation in the velocity and strength of the laser-induced shockwaves at 100 Torr. This effect has been reported in the literature for higher laser fluences either in the form of a saturation in the shockwave velocities [54] or plasma properties [55], and has been theorized to result from the formation of an optically thick plasma during LA that absorbs a considerable fraction of the incident laser energy until absorption saturates. When this occurs, a self-regulating regime forms that maintains relatively constant plasma temperatures and densities until the end of the laser pulse [5,6]. This process is believed to be pressure dependent, where enhanced plasma shielding has been observed at higher pressures while reduced absorption and increased target ablation have been reported at lower pressures [5,56,57]. However, based on the observed saturation in laser-induced shockwave velocities measured in this work at reduced pressures, the plasma absorption saturation argument does not appear to translate to shock properties. It is known that the ablated target material and vapor plume both play a role in determining the initial velocity of the external shockwave, yet based on the current literature it is unclear on whether these processes have an equal contribution or how the weighting between these processes changes for different pressures and materials. We hypothesize that the ablation rate determines the limiting shock velocity at lower pressures compared to the absorption of the laser photons by the plasma plume at higher pressures, yet further experimentation needs to be performed to explain and test these underlying processes.
When the shockwave transforms into a shock of intermediate strength, its expansion trajectory still follows a power law dependence, although the exponent tends to be greater than the $2/5$ value derived in the Sedov-Taylor solution. The general form of the expansion model is given by,
where $t_0$ was introduced to account for the non-zero initial time value associated with this fitting region. This timing offset was also included when fitting the blast wave model to the experimental data. As the shockwave continues to propagate and decelerate over this expansion region, the exponent is required to increase during the optimization procedure to maintain comparable fitting errors (see Table 1). This same behavior was measured by Buday et al. in [13], and is believed to be an indication of the divergence from adiabatic expansion as a consequence of resistive forces associated with the background gas acting on the shock. Additionally, energy released by ionized species during recombination further slows the deceleration of the shockwave [58]. Throughout this deceleration stage, expansion slowly transitions over to the final expansion regime where the shock trajectory is characterized using the drag model. This model predicts that expansion will cease at a stopping distance ($R_f$) based on a slowing coefficient ($\beta$), where $r_0$ is, once again, an offset term. The expansion of the laser-produced plasma is generally observed to decelerate very rapidly to be characterized by the drag model at times less than 1 µs for pressures greater than 1 Torr [59,60], while the laser-induced shockwave continues to propagate with a power law dependence out to much later times. In this work, the power law dependence is observed to hold for the shock expansion out to times as late as 10 µs, after which the radius of the shock front was larger than the field-of-view of the camera and was not measured. For a laser energy of 20 mJ, the propagation velocities of the shockwaves were measured to be less than the speed of sound in the background gas while the power law model still fit the data with errors of less than 2%. Therefore, it is believed that the shockwave must transform to an acoustic wave and continue to decelerate before the drag model becomes valid.
Table 1. Fitting coefficients determined for the expansion model fits to the shock front trajectories.a
Overall, laser-induced shockwave dimensions and propagation velocities are observed to be larger for higher ablation laser energies and lower pressures. Strong hypersonic shocks are generated for all experimental and atmospheric conditions measured in this work, where a saturation on the shock strength was observed at reduced pressures. Shock front distances and velocities are also generally observed to be higher in air than in argon, where this behavior arises as a result of the lower mass density of air compared to argon [6].
3.2 Characterization and gas-dynamics of the shock-heated flow
The complex gas-dynamical system generated during laser ablation consists of several distinct regions including the vapor-phase plasma, the laser-induced external shockwave, and the compressed background gas located between the plasma and shock front. The previous section focused on characterizing the expansion and deceleration properties of this external shockwave using measurements on the shock front radius, velocity, and Mach number. These same shock dynamics measurements can be combined with theory on gas-dynamics to predict the properties of the compressed and shock-heated gas layer. This layer forms as a consequence of shockwave heating, where bulk kinetic energy is transformed into thermal energy as the supersonic flow rapidly decelerates across the viscous shock front to transition into a subsonic flow. In the stationary shock frame, it is common nomenclature to refer to the cooler incoming flow (i.e., undisturbed gas) as the upstream flow while the hotter, subsonic and outgoing flow (i.e., shock-heated gas) is termed the downstream flow. If the width of the shock front and time for the gaseous flow to pass through the shock front are considered thin and fast compared to the length and timescales of the upstream and downstream flows, then the shockwave may be defined mathematically as a discontinuity, leading to the derivation of the Rankine-Hugoniot relations.
3.2.1 Rankine-Hugoniot relations for an adiabatic shock
The Rankine-Hugoniot relations allow the downstream properties of a shock-heated flow to be defined in terms of the upstream flow properties assuming that the fluxes of mass, momentum, and energy are equal on either side of the shock discontinuity. The combination and manipulation the mass, momentum, and energy conservation laws yields the ratio equations for pressure and density describing an adiabatic shockwave,
where the relations here have been written in terms of the Mach number of the shockwave ($M_0$). Because the definition of a shockwave requires that the shock travels at a velocity greater than the local speed of sound for the propagation medium, it should be understood that the Rankine-Hugoniot relations are only valid for $M_0>1$. In the relations provided here, the properties of the undisturbed gas and upstream flow are denoted by $P_0$ and $\rho _0$, while the properties of the shock-heated gas and downstream flow are given as $P_1$ and $\rho _1$. The adiabatic gas constant $\gamma$ is assumed to be constant and describes both flows. A visual of these label assignments is provided in Fig. 6. The temperature ratio is calculated from the equation of state (i.e., ideal gas law) and is given as a combination of the pressure and density ratios.The Mach number of the subsonic, shock-heated flow may also be calculated using Eq. (10).
The significant assumption made during the derivation of the classical Rankine-Hugoniot relations are that dissipative processes across the shock front are negligible. Therefore, these equations do not hold when dissociation, ionization, radiative emission, chemical reactions, and other dissipative processes are significant. Shockwaves traveling at hypersonic speeds will excite, dissociate, and ionize gas that passes through the shock front [50,61], which will alter the adiabatic gas constant. As a consequence, the ideal gas law can no longer accurately describe the equation of state. Energy source and loss terms must be incorporated into nonadiabatic equations describing the system, requiring a knowledge on the degree of dissociation and ionization present as well as vibrational, dissociation and ionization potentials [61]. In this work, the adiabatic Rankine-Hugoniot relations are being implemented with the analysis of the shock-heated flow behind the laser-induced shockwave to greatly simplify the estimation of the respective shock-heated gas properties, where it should be acknowledged that the use of these relations may yield deviations from the true shock-heated gas properties at early times. Nevertheless, the adiabatic Rankine-Hugoniot relations continue to be applied to the analysis of laser-induced plasmas in the literature [51,62].
Fig. 6. Schematic of a LA plasma system in relation to the variables used in the Rankine-Hugoniot relations. The plasma plume is considered a separate system from the shock-heated and compressed flow, where plasma parameters ($T_e$, $n_e$, $n_i$) are measured using spectroscopic techniques and are not predicted by the Rankine-Hugoniot relations.
3.2.2 Estimation of shock-heated gas properties
The properties calculated using the classical Rankine-Hugoniot relations for the shock-heated gas immediately behind the shock front are shown in Figs. 7 and 8 for air and argon atmospheres, respectively. Pressure and temperature curves resemble trends observed for the Mach number of the laser-induced shockwaves over time, where higher pressures and temperatures are predicted for higher ablation laser energies. A saturation in the pressure and temperature of the shock-heated gas for increasing laser energies is also predicted for the measurements performed at an ambient pressure of 100 Torr because of the dependence of the Rankine-Hugoniot relations on the Mach number. Larger values for pressure and temperature are also observed for air atmospheres compared to argon, where this result arises due to the higher Mach numbers reported in air. The largest pressure estimated in this work is reported as 58.4$\pm$1.3 MPa at 60 ns for atmospheric pressure conditions in air. In contrast, the largest temperature determined occurs for an ambient air pressure of 100 Torr and is given as 62,700$\pm$7,100 K. The density and subsonic Mach number of the shock-heated flow are observed to converge to limiting values, which are predicted by applying the limit for an infinitely strong shock ($M_0\rightarrow \infty$) to Eqs. (8) and (10),
which reduces the equations for the density ratio and $M_1$ to depend purely on the adiabatic gas constant of the background gas. Because of the smaller adiabatic gas constant for air ($\gamma =1.4$ versus $\gamma =1.66$ for argon), a higher limiting density and lower subsonic Mach number are calculated compared to argon. As the laser-induced shockwave decelerates at increasing delay times, the pressure, temperature, and density of the shock-heated flow decay rapidly to approach the properties of the undisturbed ambient gas while the subsonic Mach number increases to meet the shockwave Mach number. The Rankine-Hugoniot relations terminate when both $M_0$ and $M_1$ equal unity.Fig. 7. Time evolution of laser-induced shock-heated air properties for various laser energies at (a) 100 Torr and (b) 760 Torr. Errors provided are estimated from the uncertainty in the fit of the expansion models to the data. Dotted lines indicate an extrapolation of the given properties beyond the experimentally-measured data.
Fig. 8. Time evolution of laser-induced shock-heated argon gas properties for various laser energies at (a) 100 Torr and (b) 760 Torr. Errors provided are estimated from the uncertainty in the fit of the expansion models to the data.
4. Conclusion
In this work, time-resolved shadowgraphic imaging was performed to characterize the shock hydrodynamics of laser ablation cerium plasmas. Measurements were performed for several ablation laser energies, background pressures, and background gas compositions, where images of the shock front position were recorded out to delay times of 10 µs. Stronger and faster shocks were observed for higher laser irradiances as well as lower gas pressures and densities as a result of a larger energy source and weaker attenuation of the blast wave, respectively. Expansion models were fit to the shock front trajectories, where the Sedov-Taylor blast wave model was shown to agree with the experimental data while the strong shock limit was satisfied. The hypersonic shocks weakened to intermediate strength shocks within the first 250 ns, after which expansion was described by a power law dependence. The exponent in the power law was shown to increase for later delay times, where this behavior was attributed to the deviation from adiabatic expansion and attenuation of the laser-induced shockwaves. These results suggest the existence of a transition region between the Sedov-Taylor blast wave model and drag model.
Lastly, the classical Rankine-Hugoniot relations were applied to estimate the gas-dynamic flow properties of the shock-heated gas located behind the shock front. Temperatures calculated using this approach at 60 ns were shown to vary between approximately 10,000 and 70,000 K for the range of experimental and atmospheric conditions studied in this work, indicating that the laser-induced shockwave will dissociate and ionize the background gas surrounding the plasma plume at early times. The characterization of this shock-heated gas layer provides important information on the thermodynamics involved with the intermixing of plasma and ambient gas species subsequent to laser ablation, which influences the oxidation chemistry of reactive LA plasmas and consequentially alters optical signatures measured by techniques such as laser-induced breakdown spectroscopy. The results of this work provide progress towards understanding the physical properties and shock dynamics of ns-LA cerium plasmas to explain the effect of varying experimental and atmospheric conditions on their measured signatures.
Funding
National Nuclear Security Administration (DE-NA0003920); National Science Foundation (CHE1905301); Defense Threat Reduction Agency (HDTRA1-19-1-0025, HDTRA1-20-2-0002).
Acknowledgments
The authors would like to acknowledge the U.S. Department of Defense Science, Mathematics, and Research for Transformation (SMART) Scholarship-for-Service Program for supporting Emily H. Kwapis’ research and studies and the Defense Threat Reduction Agency’s (DTRA) Nuclear Science and Engineering Research Center (NSERC) for providing support for Maya Hewitt’s summer research internship at UF that supported this work. The content of the information does not necessarily reflect the position or the policy of the federal government, and no official endorsement should be inferred.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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