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Abstract
The shock imparted by a laser beam striking a metal surface can be increased by the presence of an optically transparent tamper plate bonded to the surface. We explore the shock produced in an aluminum slab, for a selection of tamper materials and drive conditions. The experiments are conducted with a single-pulse laser of maximum fluence up to 100 J/cm2. The pressure and impulse are measured by photon doppler velocimetry, while plasma imaging is used to provide evidence of nonlinear tamper absorption. We demonstrate a pressure enhancement of 50x using simple commercially available optics. We compare results from hard dielectric glasses such as fused silica to soft plastics such as teflon tape. We discuss the mechanism of pressure saturation observed at high pulse fluence, along with some implications regarding applications. Below saturation, overall dependencies on pulse intensity and material parameters such as mechanical impedances are shown to correlate with a model by Fabbro et al.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Plasma blowoff from short pulse lasers can generate large impulses within materials. By confining the plasma with an optically transparent material (a tamper) the impulse and pressure can be increased by greater than an order of magnitude depending on material properties and laser drive conditions [1–5]. The tamper confinement process, also referred to as confined laser ablation (CLA), can generate GPa pressure shocks in the material above the plastic deformation threshold (the Hugoniot limit) with moderate energy lasers (a few Joules per pulse). The process is as follows: Ideally, all the laser energy is absorbed by the surface of an absorbing ablator, which is heated to form a dense, low temperature plasma. Expansion of the plasma produces a reactive force on the solid, which imparts a net transfer of momentum, thus launching a shock wave in both directions. The efficiency of momentum transfer is reduced by the rapid adiabatic expansion of the plasma into the surrounding atmosphere, and has been studied through experiment and modeling using the concept of a momentum coupling coefficient [6]. With the presence of a tamper, the plasma blowoff from the target is confined and slowed down. The resulting concentration of energy near the ablation surface increases the recoil pressure, which can intensify shock drive and increase the momentum transfer. In theory, the effectiveness of tamper confinement is limited only by the ability to transmit laser energy through the tamper, i.e. ideally operating below thresholds where nonlinear self-focusing, bulk absorption, or surface breakdown effects degrade laser energy coupling at the target.
An analytic model, assuming all the laser energy reaches the target/tamper interface, was developed by Fabbro et al. [7,8], to provide a semi-quantitative estimate of shock loading. During the pulse, the pressure scales approximately as $P \propto \sqrt {{Z_{net}} \cdot I} $ where I is the laser intensity and Znet is the effective shock impedance of the confinement medium and target, given by 2 Znet-1 = Ztamper-1 + Ztarget-1. (The impedance of a material is the product of the material density and speed of sound.) Confinement also yields an additional advantage, in that the pressure is applied over a period much longer than the laser pulse duration. In the direct, unconfined mode, the pressure profile follows the laser profile, while in the confined mode, the pressure is maintained during adiabatic cooling, even after the pulse. The result is to increase the total impulse momentum per area (pressure integrated over time) delivered to the target. Experiments have shown good agreement with the Fabbro model at low pulse intensity. The present issue occurs at high pulse intensity, where experimental shows that the pressure slows down much faster than the $\sqrt I $ dependence, leading to pressure saturation. Deviation from the model suggests that the salient physics is not captured in the high pulse regime. Indeed, Fabbro et al. showed, using high speed imaging for an aluminum-water target, that the saturation was due to dielectric breakdown of water at the water/air interface [8]. The breakdown produces a plasma that propagates backward, thus absorbing and reducing the laser energy reaching the metal-tamper interface. Consequently, the maximum produced pressure is limited by the tamper absorption of light and optical breakdown.
The pressure enhancement produced by a tamper can extend the range of fundamental material studies using a modest nanosecond laser of a few joules with a beam size of few mm (intensity ∼ 109 W/cm2). The most highly developed technology utilizing CLA is in laser shock peening, to induce compressive stresses to prevent cracks and other surface deterioration effects [9]. More recent applications include launching of miniature flyer plates for dynamic compression studies of materials [10], initiation of high explosives [11], driving large impulse for space propulsion [12,13], synthesis of nanoparticles [14,15], plasma etching of optical surfaces [16], metal spallation [17], and cavitation bubbles in water [18]. One of the most interesting platforms just commissioned is the Direct Laser Impulse (DLI) program at the National Ignition Facility (NIF). DLI uses two of the NIF beamlines with energies of tens of kilojoules to test impulse propagation through large, complex materials with sizes up to 1200 cm2.
In these applications the choice of tamper materials, for which there are both practical and fundamental limitations, plays a key role. Under ideal conditions, the tamper contributes to the increase in magnitude of shock wave pressure by preventing laser-produced plasma from rapidly expanding away from the metal surface. Besides high impedance, the conditions for a favorable confinement medium are optical transparency at the laser wavelength, a high dielectric breakdown threshold, conformability, and chemical inertness with the target. The thickness of the tamper plays a key role, in that thinness tends to inhibit confinement while excessive thickness leads to absorption and distortion of the laser pulse. Sometimes an absorptive layer is inserted between the tamper and target to increase the absorptivity of the target and protect the target surface [19]. For laser peening, the tamper is typically water, due to the favorable conditions noted above [5]. For most applications, however, immersing the target in water is not an option. Glass offers the best performance and can generate an impulse greater than 50x from the studies here, but its rigid structure restricts the use to mostly flat 1D targets. Of the glass materials, silica has been well studied for a tamper material but other commonly used windows such as sapphire and lithium fluoride have not been investigated thoroughly. These materials have even higher impedance than silica, but as we will show, they present other issues that limit the performance. For conformability to a 2D surface, a flexible material is required. One option is to use polymers or plastics which are simple and inexpensive while producing sufficiently high pressure suitable for shock processing studies [20,21]. Our study concentrates on a synthetic fluoropolymer (PTFE) tape, better known as teflon tape, which is used in a variety of photonics applications. For conformability to a 3D surface, not many choices exist. One of these studied here is parylene, which can be deposited directly onto metallic surfaces using chemical vapor deposition.
The goal of this work is to explore the performance of common tamper materials under different laser drive conditions. The metric used to quantify the strength of confinement is based on pressure and impulse measurement using photon doppler velocimetry (PDV). Our experiments directly measure the free surface velocity of the metal, which is proportional to the pressure of the plasma induced at the tamper/metal interface. The impulse, or momentum transfer per area, is the integral of the pressure over time, and is related to the displacement at the back surface. The choice of specifying pressure or impulse depends on the type of experiment. For example, in laser peening and spallation studies, the shock pressure must be higher than the Hugoniot elastic limit to induce plastic deformation in material, and so pressure is a more useful quantity. In laser driven flyers, the final velocity is proportional to the momentum, while in laser propulsion, the thrust is proportional to the momentum. In these applications, impulse is a better metric. Most of our data is shown in displacement (proportional to impulse) with some sections in terms of velocity (proportional to pressure).
The main text compares results for common hard dielectric glass (silica, sapphire, LiF), soft polymers (teflon, parylene, polyethylene tape), and hard plastic (PMMA). These materials are inexpensive, commercially available off-the-shelf parts. We discuss the mechanism of tamper breakdown which leads to pressure saturation at high pulse fluence, and show that the underlying physical processes involved are more complicated than predicted by the Fabbro model. The breakdown mechanisms are different for various materials, as we will show comparing glass and teflon tape. To help understand energy deposition and pressure saturation, we performed experiments using plasma imaging, single-shot transmission measurement, and laser damage testing. As the saturation effect occurs for all optical tampers, an understanding of this will optimize applications utilizing CLA and advanced tamper development.
In the following sections, we describe the model, experimental setup, results, tamper optimization, and our conclusions.
2. Modeling considerations
The system of interest consists of a dielectric tamper directly attached to a target, as illustrated in Fig. 1 (left panel). This is a simplified version of the model developed by Fabbro et al. [7] and will be used for simulations in Section 6. Laser radiation incident on the tamper-target interface ionizes material, sending two shocks propagating, in opposite directions, into the tamper and the target. Plasma confinement by the transparent material increases the pressure on the metal boundary. The rate of growth of the layer is $dL/dt = {u_1} + {u_2}$, with ${u_i} = P/({\rho _i}{D_{i)}},\; $ where ${D_i}$ is the weak shock speed. Using the fact that this is close to the local sound speed, we have
with $Z = 2/({1/{Z_1} + 1/{Z_2}} )$ the net interface impedance (the subscripts 1 and 2 refer to the tamper and target respectively). The energy per area deposited by the laser, I(t)dt, increases the plasma internal energy Eint by d(EintL) and the work done by the pressure according to
Fig. 1. The left panel illustrates the process of tamped ablation described in the model. The right panel is the experimental setup. The laser is focused onto the sample with a f = 300 mm lens. At the metal-tamper interface, the beam size is 1.2 mm 1/e2 super-Gaussian n ∼ 10 profile. PDV is focused onto the back of the sample. An objective collects the plasma emission (green) from the side of the sample and images to an iCCD. The bottom left image shows the actual configuration with the sample, the PDV probe on the back, and imaging objective on the side.
We assume that the thermal energy density is a fraction α of the plasma internal energy estimated experimentally (typically 0.1-0.4). Approximating the plasma as an ideal gas, we have $P = ({2/3} )\,\alpha {E_{int}}$, and
Equations (1) and (3) provide a closed description of the laser-material interaction in CLA experiments.
In equation (2), the mechanical work $P(t )\; dL(t )/dt$ can often be neglected in comparison with the internal contribution, with an error no greater than 10-20%. Rearranging the resulting equations with PL and L as the unknowns, we find that the pressure takes the analytic form:
This approximation is useful for estimates. In general, however, we solve (1) and (3) numerically. For the case of a constant pulse I0, the pressure during the pulse simplifies to:
This gives the dependence of the pressure on a constant laser intensity and net impedance of the target and tamper. The factor 0.01 serves to convert the resulting units to GPa.
The plasma boundary of the material behind the shock expands with a speed u2 = P / Z2. The thickness of the plasma layer into the target increases linearly with time. From reference [7], we have
After the pulse terminates, the plasma continues to expand adiabatically, via P ∼ 1/Lγ ∼ √t, with γ the adiabatic parameter (a typical value is 1.3).
Finally, the impulse, or the momentum per unit area transferred to the target, is the time integral of the pressure:
3. Experiment
3.1 Laser and diagnostics
Laser impulses are generated using a 2 J, 12 ns, 1064 nm laser with a super-Gaussian (n = 10) beam. The 10 Hz repetition rate is synchronized to a shutter that allows for a single shot mode. The laser is focused to a 1.2 mm 1/e2 spot at the interface of the target/tamper sample. At maximum energy, the fluence at the sample was 100 J/cm2, with a peak intensity of about 10 GW/cm2. The fluence and intensity values assumed a flat top spatial distribution. The rear surface moves when the shock arrives at the exit of target. The displacement and velocity of the surface are measured using photon doppler velocimetry [22]. The PDV system outputs a 1550 nm beam focused to about 50 µm 1/e2 diameter at the target 28 mm away. An aluminum target bonded to the tamper reflects this light back to the interferometer. The return light was combined with light from a separate laser operating at 1-2 GHz frequency, offset to provide a heterodyne beat signal that is analyzed using sliding scale FFT [23]. From the analysis, the temporal profile of the free surface velocity and displacement are determined. These are then used to calculate the pressure and impulse. The oscilloscope used was a 4 channel Tektronix 23 Ghz, 100 Gs/s (DPO72304). The laser-induced plasma emission was collected by imaging the side of the tamper using a super-long working distance Mitutoyo objective lens oriented at 90 degrees relative to the beam path. The emission signal was sent to a 1024 × 1024 pixel time-gated intensified CCD (PI-MAX4, Princeton Instruments). Gating the ICCD and varying the delay time relative to the laser pulse allowed the plasma evolution to be captured. Side faces of the tamper samples were polished to allow side view imaging inside the tamper.
3.2 Target
For the targets, we used a simple design with commercially available parts consisting of Al6061 bonded with a tamper. The thickness of Al was nominally 800 µm except as noted for a few experiments. The front surface of the metal (ablation surface) was polished to a smooth finish, and the back surface was mirror-finished to maximize the reflectivity of the PDV signal. The bonding used a UV cured glue (Epoxies 60-7159RCL13) with a transmission of 96% at 1064 nm. A wide variety of tampers was tested consisting of glass, hard plastic, and soft polymers, as listed in Table 1. All tampers were uncoated. Typical dimensions for the glass were 1” diameter round or rectangular (14 × 25 mm2) with a nominal thickness of 3 mm. The teflon fluoropolymers (PTFE) thickness is 125 μm with a 50 μm silicone adhesive while Parylene-C thickness is 30 µm deposited onto aluminum, using vapor coating deposition at Specialty Coating Systems. All tamper materials are transparent to the 1064 nm laser light. They have various densities, sound speeds, and shock impedances as listed in Table 1.
Table 1. Impedances of selected materials
4. Results
4.1 Calculation of peak pressure and impulse from PDV
The pressure generated at the tamper/metal interface by the laser is $P \propto \sqrt {{Z_{net}} \cdot I} $ (see Eq. 5). However, our experiments measure the free surface velocity Vs at the back of the metal. We can relate the velocity measured at the back to the pressure generated at the front by:
and impulse byIn some experiments, a backplate window is attached to the back of the metal for impedance matching studies or to prevent spallation. The factor $K = ({Z_{metal}} + {Z_{backplate}})/2{Z_{metal}}$ is a correction to account for the backplate window. When no backing is used, as in our case, Z2 = 0 and $K = 0.5$ Assuming that all are constants, then $\smallint {V_S}\; dt = \; \Delta x$, the measured displacement. For aluminum, Z = ρ C = 1.733 g/(cm2-µs), and the impulse in units of Pa-s and peak pressure in units of MPa can be approximated as:
Here Δx and Vs are, respectively, the first step displacement and first velocity peak from the initial shock that hits the back surface. Round trip shock reflections subsequently lead to multiple displacement steps and velocity peaks but are not used for the calculations here. Determining the height of the first step is somewhat subjective. In our case, it was chosen at the end of the first step before the rise of the second step (in Fig. 2 this is near x ∼ 160 ns).
Fig. 2. PDV measurements of (A) velocity and (B) displacement for unconfined Al (red) and confined aluminum with a fused silica tamper (red) at 30 J/cm2. In the presence of a tamper, the velocity increases over 20x and displacement increases over 40x. The velocity and displacement are directly related to the pressure and impulse. Also shown on the velocity curve are (a) elastic precursor, (b) maximum velocity peak, and (c) edge effects.
4.2 Shock enhancement with a tamper
We first demonstrate the shock enhancement using Al6061 (800 µm thick) overlaid with a 3 mm thick fused silica (FS) tamper. FS is an excellent choice for the following reasons. First, the impedance is about 10 times the value of water and typical plastics. Second, it is optically transparent from the UV to IR. Third, the laser damage threshold is among the highest of the glass materials and has been characterized extensively [30]. Last, it is an inexpensive, readily available material. FS also serves as a comparison example for the other tamper materials.
When the beam strikes the front surface, there is a delay from the shock transit through the metal, followed by another roughly 100 ns delay through the fiber and interferometer. This delay is subtracted in the analysis, and the signal starts at time zero on the horizontal axis. Figures 2(A) and 2(B) show the velocity and displacement time profile measured at the back free surface of aluminum at 30 J/cm2. The peak velocity measured is 200 m/s for the confined case nearly 20x higher than the unconfined case (red curve, inset). The velocity profile, which is representative of the pressure profile propagating through the material, shows a broadening of about 2x vs the unconfined case. The displacement, and thus the impulse, is about 40x higher for the confined case as expected since the impulse is proportional to the time integral of the pressure. Also captured in the velocity profile is a shoulder before the main peak, attributed to elastic precursors, and a knee during the decay, attributed to edge effects. This shows that additional information can be extracted from PDV measurements [31]. The simple comparison confirms the shock enhancement phenomena with confinement.
4.3 Impulse and pressure for fused silica tamper
Continuing with the fused silica tamper, Fig. 3 shows the displacement and velocity profiles over a wide range of laser fluences (10-75 J/cm2, energy range 110-825 mJ). The fluence values used here correspond to the energy at the entrance of the tamper and do not account for the transmission loss through the tamper. The first velocity peak and first displacement step are shown in (A) and (C). At longer timescales in (B) and (D), multiple velocity peaks (separated by 250 ns) and displacement steps are observed due to round trip shock reflections. The maximum velocity increases with fluence up to 30 J/cm2, saturating between 30-60 J/cm2, and decreasing above that. The velocity profile broadens as the fluence increases, as is associated with a longer pressure pulse. Similarly, in the displacement data, saturation is also observed at high fluence. For a fluence of 30 J/cm2, with a peak velocity of 200 m/s and displacement of 11 μm, this corresponds to a peak pressure of 1.7 GPa, with an impulse of 95 Pa-s from Eqs. (10) and (11).
Fig. 3. PDV measurements for Al with a fused silica tamper, at selected values of fluence. (A) Velocity profile for the first peak, and (B) over long time scales. (C) First step displacement, and (D) over long time scales.
4.4 Comparison of data with simulation for glass tampers
We next include measurements for sapphire and lithium fluoride (LiF) and compare to simulations using the model described in Section 2 (Fig. 4). The tamper thickness was 3 mm, and the metal was 800 µm thick Al, to compare directly with the fused silica sample. According to this model, the impulse is proportional to the net impedance of the tamper-metal target and the square root of the laser intensity (or fluence). In Fig. 4(A), we show the experimental displacement value (solid lines) and simulated value (dashed lines) at 15 J/cm2. These agree reasonably well with the data except in the first 40 ns, where there is a deviation. As mentioned earlier for Fig. 2(A), there is a small shoulder at 10-20 ns prior to the peak of the velocity curve which has been attributed to an elastic precursor [32] but for simplicity is not included in our model.
Fig. 4. (A) Displacement history for selected tampers, according to experiment (full lines) and model (dashed lines). (B) Impulse vs fluence/intensity for FS. Measured values (blue) and values fitted with Fabbro model (red). Saturation in impulse is observed above 30 J/cm2.
The displacement data for a fused silica tamper (from Fig. 3) are plotted in terms of impulse versus laser fluence (or intensity) and fitted to $\sqrt I $, as shown in Fig. 4(B). There is good agreement at low fluence up to 30 J/cm2 between the model (red) and the measured values (blue). Above 30 J/cm2, impulse saturation occurs and even starts to decrease, showing a deviation from the Fabbro model. We note that this effect occurs from optical breakdown of the tamper. The issue of saturation will presently be discussed in more detail.
4.5 Impulse Measurements for Full Selection of Tampers
We now expand the study to include soft and hard polymers such as teflon tape, transparent (polyethylene) tape, parylene film, and PMMA. Figure 5 shows the measured displacement and impulse, as functions of fluence and intensity, for the full selection of tampers. Also included is data for an unconfined 800 µm thick Al, which shows a maximum displacement of 280 nm, corresponding to a greatly lower impulse. The intensity and fluence values assume a uniform flat beam whereas the actual beam is n ∼ 10 super-Gaussian. For the glass tampers, the data was averaged over 5 shots at each fluence. For PMMA and transparent polyethylene tape, we did only two shots at each fluence, as these tampers were not expected to perform well and were used merely as comparison. For parylene, the sample was difficult to obtain and only one shot per fluence was performed. Based on comparing impedance, the model predicts the following order of tampers producing highest to lowest impulse: sapphire > Li > > FS > PMMA > teflon, parylene > polyethylene tape. The results are summarized in Table 2 for the measured impulse vs. predicted impulse relative to FS at 30 J/cm2.
Fig. 5. First step displacement values and calculated impulse for a variety of tampers, as functions of fluence and intensity. The thicknesses of sapphire, FS, LiF, PMMA are 3 mm; teflon 125 µm + 50 µm silicone adhesive; parylene 30 µm; polyethylene tape 125 µm. The metal is Al 6061 with a thickness of 800 µm. The overall behavior of the displacement curves is similar for all the tampers, with an initial rise at low fluence followed by saturation at high fluence, confirming the saturation effect for a wide range of materials.
Table 2. Predicted and measured impulse values relative to fused silica tamper at 30 J/cm2
The overall behavior of the displacement curves is similar for all the tampers, with an initial rise at low fluence followed by saturation at high fluence, confirming the saturation effect for a wide range of materials. Table 2 summarizes the measured impulse versus predicted impulse relative to FS at 30 J/cm2 and the average enhancement factor over unconfined ablation. We now discuss the two regimes.
Regime (I): Low fluences < 30 J/cm2)
The displacement rises as a function of fluence. Sapphire had the highest impulse, averaging about 20% higher than FS, while LiF came in slightly lower than FS. All the plastic/polymer tampers performed more poorly than glass. The measured values for PMMA and teflon tape were about half those of FS, and polyethylene tape was one-third. All but one in Table 2 were close to predictions. The odd one is parylene, which performed substantially more poorly. For parylene, the density is 1.29 g/cm3 and the sound speed is 0.220 cm/µs, giving a shock impedance of about 0.28 g/cm2-μs (see Table 1), similar to Teflon. Thus we had expected similar displacement values. The optical transmission value at 1 µm is 80-90%, which is up to 12% lower than that of teflon [33]. Even if the lower transmission is accounted for, the displacement between the two polymers should be closer. The other difference is the sample thickness of 35 µm, which is 3.5 times thinner than Teflon. As we will discuss later, this thickness is insufficient to confine the plasma.
Regime (II): High fluence > 30 J/cm2)
At high fluences, the displacement begins to saturate and roll over. For most tampers, this threshold is somewhere near 30 J/cm2, but for FS the saturation occurs around 45 J/cm2. For sapphire and LiF, the displacement rolls over rapidly, underperforming FS at high fluence. Data repeatability for FS was fairly good due to the high damage threshold but is rather poor for sapphire and LiF, with a large variability above 30 J/cm2 where it begins to damage.
For the unconfined Al case, saturation is also observed from plasma shielding of laser light at high fluence. However one main difference is that the pressure seems more or less constant without the large decrease or roll over above 30 J/cm2. Besides plasma absorption, he absorptivity and reflectivity of unconfined metal can change as function of power, which can affect the peak pressure generated [34].
5. Experiments to understand pressure saturation
The PDV data shows impulse saturation at high fluence. In this section we describe experiments on transmission, optical damage, and plasma imaging, in order to study energy deposition inside the tamper and to elucidate the saturation effect.
5.1 Self-focusing
We first consider whether the beam, in propagating through the tamper, can undergo deleterious effects such as Kerr self-focusing. For a ns pulse, this issue can be treated in steady state. The instability has a threshold (critical) power ${P_{cr}} = {\lambda ^2}/({2\pi \; {n_0}{n_2}} )$, where ${n_0}$ is the low-intensity index of refraction and ${n_2}$ is the nonlinear index. Even if the power exceeds its critical value, the situation can be benign, since the development of filamentation requires an approximate distance given by [35]:
In the illustrative case of fused silica, for which ${n_0}$ = 1.45, the measured nonlinear index is 2.74 × 10−16 cm2/W and the corresponding critical power is about 4.3 MW [36]. In the experimental setup, the maximum power was about 68 MW (680 mJ for 10 ns). This exceeds the experimental power by a factor of about 15. But because of the large initial beam radius (∼600 µm), the calculated self-focusing distance 260 mm exceeds the tamper thickness by a factor of about 80. Hence self-focusing is not expected.
5.2 Transmission measurements and optical damage studies
To explain the observed saturation, we performed single-shot transmission measurements while monitoring optical damage (Fig. 6). The transmission accounts for energy loss due to absorption, reflection, and scattering through the material. The fluence values shown in the PDV data assume that 100% of the laser energy reaches the tamper-metal interface, which is not the case. A single shot was fired at different fluences, with each shot at a different location on the sample. Experiments were performed in vacuum to prevent dielectric breakdown in air. In addition, since the laser intensity at the exit surface was higher than the entrance (due to focusing of the laser), the exit surface typically damaged first. Damage morphology was analyzed using confocal microscopy.
The transmission data correlates well with the PDV data. Below 20 J/cm2 the dielectrics were completely transparent. Above 20 J/cm2 the tampers behave differently. The loss for FS was very low up to 45 J/cm2, while the loss in sapphire, LiF, and teflon increased much more rapidly. These facts can explain the low impulse saturation threshold. Silica optics are known to have very high nanosecond damage thresholds and are resistant to optical degradation over millions of shots [30,37,38]. The damage threshold on the surface is much lower than that of the bulk due to the high density of extrinsic defects on the surface. Our result is consistent with a picture of material damage through local point defects. At low intensity, these defects are sub-micron sized and not detectable with conventional microscopy. As the intensity increases, more defects are initiated. When the defect temperature approaches the boiling point, a plasma is generated, damage subsequently occurs, and the transmission drops. Fig. 7 (top row) shows the onset of observable damage for FS at the exit surface at 86 J/cm2 and a large site at 105 J/cm2. No bulk damage was observed.
Sapphire and LiF optics damaged at a much lower fluence, and their morphology is also very different. A comparison of the damage sites at 86 J/cm2 is shown in Fig. 6, rows 2 and 3. At this fluence, both the entrance and exit surface damaged, as well as the bulk, causing the transmission to drop sharply before reaching the interface. The materials damaged at a much lower fluence (∼30 J/cm2), but the high fluence image gives an idea of the extent of the damage, especially compared to FS. Damage in the bulk before the surface is known to occur in sapphire optics due to difficulty of growing high quality crystal [39]. Photothermal measurements have verified higher absorption in bulk than silica [40]. The damage morphology for sapphire (Fig. 7, row 2) shows a channel of loosely packed damage sites propagating from the entrance to the exit surface. For LiF, there is damage in the middle of the bulk (Fig. 7, row 3). The LiF entrance and exit damage morphology all have well-defined cracks perpendicular through the middle of the damage site.
Teflon had the lowest damage threshold with damage first observed about 5 J/cm2, although the loss was only a few percent. The transmission drops off rapidly above 20 J/cm2. The damage morphology observed shows multiple large random ablation pits similar to that observed under UV irradiation [41]. We had no way of measuring the transmission of parylene as it is vacuum deposited on the target, but reports from the vendor and others have listed transmissions between 80-90% at 1064 nm, depending on thickness and quality [33,42]. The transmission of PMMA is 92% at 1064 nm and polyethylene transparent tape was above 90%.
5.3 Plasma imaging gives evidence of plasma absorption of laser light
The propagation and evolution of plasma inside dielectric material is a complicated process, particularly in the presence of a metallic workpiece. As the laser intensity increases, the tamper breaks down at the surface or inside the bulk, and a plasma is created, which absorbs the laser pulse. Consequently, the laser energy that reaches the target saturates. More advanced studies have shown that for fused silica, as the dielectric temperature approaches 10,000 K, the optical bandgap ultimately collapses and thus the dielectric behaves as a metal and becomes opaque to the laser light [43,44]. A detailed study of the laser-plasma interaction is beyond the scope of this paper. Nevertheless, in an attempt to understand light absorption, we performed some simple time-resolved plasma imaging to obtain insight on absorption mechanisms. Since plasma emission occurs nearly instantaneously after the laser beam strikes, we are interested in nanoscale time scales relative to the laser pulse. From the plasma images, we can correlate to the transmission data. An objective is used to collect light from the side of the tamper and imaged to an ICCD (Sec. 3). For simplicity, we compare differences between only fused silica and teflon, as representative for glass and thin polymers. These tampers exhibit very different plasma emission behavior.
5.3.1 Plasma imaging of fused silica
Figure 8 shows the plasma emission from the FS tamper at selected fluences. Each image is a new ablation spot. The red arrow shows the approximate air-glass interface. The intensity of the image is set to the same scale. The top panel shows emission from bare fused silica at different fluences (30, 45, 75, 105 J/cm2) at 20 ns from the midpoint of the laser pulse. During the energy absorption stage, the plasma plume expands in air with a velocity of ∼10 km/s, and much slower in silica at a few km/s, resulting in a plasma confining effect. This can be observed by looking at plasma in air which is much larger than in FS. Inside silica, plasma from energy coupling is observed starting at 30 J/cm2, but the transmission loss is still ∼ 1%. At 75 J/cm2, the emission has grown to about ∼ 150 µm with a loss of about 10%. At 105 J/cm2, the plasma ceases to propagate more axially but rather expands laterally due to the high intensity wings of the super Gaussian beam profile. The transmission loss approaches 30%. A white light post-shot image shows damage inside the fused silica corresponding to the plasma image at 105 J/cm2.
Fig. 8. Plasma imaging of fused silica over fluence. The beam size is 1.2 mm 1/e2. Top panel: bare fused silica. Bottom panel: in the presence of Al. Images are acquired at 20 ns relative to the midpoint of the laser pulse with gate width of 3 ns.
Fig. 9. Plasma imaging of 125 µm thick teflon tape with a 50 mm adhesive. Top panel: Bare teflon. The beam size is 320 µm 1/e2. Pairs of images acquired at the same fluence are shown to illustrate the lack of reproducibility at low fluences (13 J/cm2), and the comparative reproducibility at high fluences (40 J/cm2), respectively. As an aid to interpretation the final image shows the teflon post-shot superimposed on the corresponding plasma image. Bottom Panel: in the presence of Al. Beam size is 1.2 mm. Images are acquired at 20 ns relative to the midpoint of the laser pulse with a gate width of 3 ns.
In the presence of Al (bottom panel), interpretation of the plasma emission becomes complicated. The metal lowers the ablation threshold and is itself a source of emission. At the interface light is observed on both sides, but this is not physical, as it results from metal reflections captured by the imaging system. At 75 J/cm2, the plasma shape flattens out similarly to that observed without the Al. At 105 J/cm2, there is a very strong lateral expansion which increases the volume, decreases the plasma density, and contributes to poor confinement. This plasma “leak” which depends on the beam size, target diameter, and confinement medium, has been modeled by Rondepierre et al. for confined ablation studies [45]. A post-shot image shows a similar but larger damage site compared to that of the unconfined case.
5.3.2 Plasma imaging of teflon tape
Although pulsed laser ablation studies of teflon have been done previously, most of the studies have been concentrated on studying damage threshold, chemical process, and UV etching [41,46–49]. Fundamental laser-plasma interactions at the nanosecond timescale has been very limited [50,51]. Here we show that the plasma emission from teflon tape exhibits a dramatically different behavior than silica. For the air/teflon case (Fig. 9, top panel), we used a different setup with higher resolution to image the micron-thin teflon. The laser used here had lower energy, which required focusing the beam down to 320 µm 1/e2 spot to attain a similar fluence. Images are acquired at 20 ns relative to the midpoint of the laser pulse. For low fluence shots, the energy coupling was very unpredictable and interpretation was complicated. Plasma is first observed at 6 J/cm2 inside the teflon but transmission loss was only a few percent. Two red lines are used to indicate the front and back surface of the teflon. At 11, 13, and 19 J/cm2, plasma was observed sometimes at the exit, sometimes at the entrance, and sometimes evenly distributed. A pair of images shown at 13 J/cm2 illustrates the lack of reproducibility, while the labels a, b, c, d on one image show the difficulty of interpreting the image. Our interpretation is: (a) emission at the front surface into air, (b) reflection of the emission from the front surface, (c) reflection of the emission from the back surface, and (d) emission from the back surface into air.
At high fluence (> 30 J/cm2), the emission switches from highly unpredictable to highly reproducible with most of the coupling at the front surface extending 300 um into air. A pair of images shown at 40 J/cm2 illustrates the reproducibility. Why this is the case is not exactly clear, but several explanations exist. Studies have shown that when the laser irradiates the surface of an organic polymer, the light can etch the surface by photodissociation, or melt the surface from thermal processes [48], with the latter resulting in plasma if the temperature is above boiling. Given that polymers do not absorb well in the infrared and that the teflon is thin, it is likely that damage is not caused by absorption, but rather by scattering at or near the front surface. Polymer films are known to scatter light, and at high enough intensity, can lead to optical breakdown at or near the front surface [46]. Based on the transmission results at a similar fluence, over 40% of the energy is absorbed. There is still plasma observed at the exit side and inside the teflon. The velocity of the plasma was about 10 km/s in air. The final square shows a post-shot image with damage site superimposed on the time-resolved image.
In the presence of Al (Fig. 9, bottom panel), we resorted to our standard 1.2 mm beam system. The shape of the plasma was slightly different due to the two different laser beam profiles. Again, it was difficult to determine the interface due to reflections and imaging artifacts, but nevertheless we still observed a large plasma expanding into air.
6. Tamper optimization
In the previous sections, we discussed the dependence of pressure and impulse on laser intensity and intrinsic material properties. In this section we concentrate on experiments relating to effects of different extrinsic, processing parameters that can optimize tamper performance. We include a brief section modeling pressure and impulse based on different laser parameters and scaling laws.
6.1 Tamper thickness
Tamper thickness plays a role in plasma confinement – if too thin, confinement is ineffective, and if too thick, absorption and scattering are excessive. Scattering and reflection are known issues for thin films and polymers such as teflon and parylene. For silica, based on our plasma images on FS, the plasma propagates approximately 150 µm into the bulk after 25 ns, suggesting that the minimum tamper thickness required is 150 µm. For this test, the 110 and 240 µm samples were Willow Glass, while the 1, 3, 5 mm samples were fused silica. Figure 10(A) shows a large increase in velocity from 110 to 240 µm and a slower increase at 1 mm, suggesting an optimal thickness somewhere approaching 1 mm. The 3 mm tamper also performed at peak, indicating that our previous experiments were all near optimal confinement for silica. The 5 mm tamper had a decrease in velocity, pointing to some energy loss with increased tamper thickness.
Fig. 10. Velocity profiles for different sample configurations. (A) Effect of different tamper thickness for (A) fused silica (23 J/cm2), (B) teflon (30 J/cm2), and (C) parylene (30 J/cm2). (D) Comparison of interface gap thickness with glue, without glue, and with 125 µm and 250 µm gap. (E) Comparison of high and low viscosity glue, and no glue (23 J/cm2). (F) Comparison of Al with different thicknesses with teflon tamper. The black arrow points to edge effects from release waves observed on the 400 µm and 800 µm Al. (G) Comparison of SS 830 um thickness with Al 800 um thickness, both with 125 um teflon.
For teflon, we saw an increase in velocity when using 125 µm teflon tamper compared to 50 µm tamper (Fig. 10(B)). Since a thicker teflon tape was not available from the vendor, we stacked two 125 µm teflon strips together to form a 250 µm thick film. The velocity measured was similar to that of a single 125 µm film, but the profile was longer and thus the impulse (pressure over time) was about 15% higher. A thicker teflon should be better optimized for confinement, but there is a compromise since for excessive thickness because the film becomes glazy, scattering increases, and transmission drops. In addition, a thicker teflon tamper may work only at low fluence since at high fluence we observed plasma mostly at the front surface.
For parylene (Fig. 10(C)), comparison was made between the 30 µm film studied earlier (Fig. 5) with a 125 µm film, and the latter had a 50% increase in velocity. Comparing this to 125 µm teflon, the impulse is still about 30% lower, assuming similar pressure widths. Reference [28] gives the impedance of parylene similar to teflon, so one should expect similar results. Several possible explanations are: a) although the two films have similar impedances, the areal density of the teflon is twice of parylene and the density may play a larger role than the model suggested; b) the impedance values may not be correct for the pressure conditions used here; c) chemical vapor deposition over 50 µm thick is difficult, leading to surface defects and low transmission of the film; d) the coating may have degraded over time. Further studies are required to verify these claims.
6.2 Role of glue and interface bonding layer
The role of glue (or bonding layer) is a large unknown factor in confinement. Because of surface imperfections, contact at the interface will have air gaps with large a impedance mismatch, producing reflections which can degrade the pressure. Both metal and FS have a 5-magnitude higher impedance than air. Ideally, the adhesive should be as thin as possible to prevent scattering that can occur at a thick interface. In principle, if the glue impedance is high, it can act as a confinement layer. Since glue is very compressible, however, once it heats up and melts, the impedance can change, as may not be ideal. Figure 10(D) shows comparison for different interface scenarios on a fused silica/Al target: with a glue layer, without a glue layer, with a 125 µm gap, and with 250 µm gap. Without the glue, but with tamper/Al clamped together, the results were quite inconsistent. Sometimes the change was minimal and other times the results decreased by about 30%. When a gap of 125 µm and 250 µm was introduced, the peak velocity dropped. The velocity profile also showed a small step (V ∼ 10 m/s) to 10 ns and 20 ns respectively, caused by reflections from impedance mismatch. The amplitude of the step is similar to the case of an unconfined metal (cyan curve). What is interesting is that this data also shows that there is no effect of a tamper until plasma bounces off the glass.
Figure 10(E) shows a comparison between two types of glue: our standard UV cured with a high viscosity of 450 cps (Epoxies 60-7159RCL13) and a 24 hr room temperature cure with a low viscosity of 100 cps (Epo-Tek 301). The impedance of our standard glue is unknown, but we expect it to be similar to that of the Epo-Tek glue (Z ∼ 0.3 g/(cm2-µs)). Optical profilometry measurements showed a thickness of 3-5 µm for the low-viscosity glue and 5 µm for our standard high-viscosity glue. It was difficult to get a thickness below 5 µm with the higher viscosity glue. We did several measurements which showed a slightly higher velocity with the low-viscosity glue, likely due to the more uniform spread across the sample. Future studies worth investigating would be spin-coating glue for a thinner, more uniform layer.
6.3 Different metal thicknesses
Figure 10(F) compares the effects of different thickness of Al: 265 µm, 400 µm, and 800 µm. With a thinner sample, the shock propagates more axially (thus more 1D) within the target with less attenuation. The respective ratios of thickness to beam diameter are 0.23, 0.33, and 0.67. It has been shown that as the ratio increases, the radial expansion of the plasma becomes non-negligible and shock propagation becomes more 3D [45]. The larger ratio gives rise to edge effects due to discontinuity in pressure between the laser beam and outside the beam (where the pressure is almost zero). This discontinuity results in a release wave generated at the edge of the beam that propagates toward the center of the beam. As the thickness increases, the release wave will catch up before the axial shock propagates to the back surface, thus attenuating the amplitude and degrading the shock. Edge effects are observed in the 400 µm and 800 µm samples in the form of multiple knees in the decay of the velocity profile, while knees are not observed in the 265 µm sample. The model described in Section 2 assumes a 1D geometry and does not apply to edge effects.
6.4 Aluminum vs stainless steel
Here we compare SS6061 (830 um) with Al (800 um) both with 125 um teflon (Fig. 10 (G)). The velocity measured for SS6061 was about half that for Al. SS has a density of 8 g/cm3 and sound speed of 0.6 cm/µs which gives Z∼ 4.8 g/(cm2-µs), about ∼2.8x higher than Al. Although the impedance of SS is much higher than Al, the net impedance (metal + tamper) is actually quite insensitive to the metal. For SS, Znet ∼ 0.72 g/(cm2-µs), which is about 10% higher than for Al (Znet ∼0.69 g/(cm2-µs)), and the square root of Z makes the value only 5% higher. The free surface velocity measured at the back of the metal is related to the pressure by $V = P/{Z_{metal}}$. The pressure generated by the laser at the tamper/metal interface is $P = \sqrt {{Z_{net}}I} $. Assuming the same intensity, then the free surface velocity for SS is ${V_{SS}} = {V_{Al}}\left( {\frac{{{Z_{net,\; SS}}}}{{{Z_{net,\; Al}}}}} \right)\left( {\frac{{{Z_{Al}}}}{{{Z_{SS}}}}} \right) = 0.37\ast {V_{Al}}$ which is close to the value we measured.
6.5 Modeling of pressure and impulse
Here we use the model described in Section 2 to simulate the pressure evolution. Fig. 11 (Top) shows the dependence of the pressure, as calculated from Eqs. (1) and (3), on pulse width and shape, for super-Gaussian pulses with n = 2 (a conventional Gaussian) and n = 10 (a near-flat shape). The maximum pressure is greatest for the shortest selected pulse (8 ns), with a near-flat shape (a hammer). The pulse used in our experiment is modeled as 12 ns, n = 10 (green curve). In our formulation, the momentum transfer of Eq. (7) nominally diverges since the pressure drops slowly with time after the pulse terminates. Hence we must limit the integration by the time at which either plasma recombination or material motion becomes appreciable. Typically, this is about 0.1 µs, insensitive to the precise value. Fig. 11 (Bottom) shows the curves of momentum transfer. Since an integral over time is involved, the results for various pulse parameters do not vary significantly. The nominal best result is achieved by the longest pulse (20 ns), with a Gaussian n = 2. The pressure and momentum transfer differ in optimal pulse length because of their opposite scaling in t.
Fig. 11. Top: Calculated pressure versus time, for super-Gaussian pulses of three widths and two values of n. The fluence is 100 J/cm2. Bottom: Calculated momentum transfer per area versus time.
6.6 Scaling
Scaling is useful if we want to predict how the system will respond given different laser or material parameters. Let us imagine doing an experiment which requires a very high laser intensity that is not accessible. Given a maximum laser energy, what is the optimal pulse duration? The model shows that for a given fluence the pressure produced is proportional to the square root of the pulse duration, so one must increase the pulse duration to get higher pressure. On the other hand, a longer pulse duration means lower intensity which helps avoid dielectric breakdown. As a result, if scaling works, one can avoid doing many experiments at different pulse lengths to determine the optimal drive conditions. It is useful to note that the system scales with respect to the net impedance Z, the fluence F, and the nominal pulse length τ. If the intensity has the customary form $I(t )= ({F/\tau } )f(s )$, where $s = t/\tau $ is the scaled time, then the pressure and momentum transfer scale according to
where the dimensionless quantities $\bar{P}(s )$ and $\bar{M}(s )$ are to be calculated. Thus, the results for a single calculation can be scaled to various choices of impedance, fluence, and pulse length.The plot of Fig. 12 shows data taken from Fig. 4(A), along with modeling results. We scaled the displacement data by dividing by $Z_{\textrm{net}}^{1/2}$ (arbitrary vertical scale) and the results lie nearly atop one another, confirming the scaling with the square root of the net impedance.
Fig. 12. Experimental displacement history for selected tampers from Fig. 4(A), divided by the square root of the net impedance. The vertical units are arbitrary.
7. Conclusions
We have performed a series of impulse measurements on common tamper materials such as glass, hard plastic, and soft polymers. Our results from PDV demonstrate that the dielectric tampers behave similarly, with a rise in impulse at low fluence followed by saturation at high fluence. We show using plasma imaging, transmission measurement, and damage threshold studies that the cause of the saturation is optical breakdown of the tamper, leading to energy degradation at the target. Optical damage at the front surface and in the bulk lowers the saturation threshold. With glass confinement, the impulse can be nearly 50x higher than unconfined Al. The impulse from teflon tape was about half the value of that from fused silica, yet performed well, considering the low cost and ability to conform to simple 2D surfaces. Parylene may be worth exploring as a conformable 3D tamper even though performance was inferior to teflon. Our optimization studies showed that tamper thickness, interface bonding layer, and metal thickness can be optimized to increase the shock enhancement.
Funding
U.S. Department of Energy (DE-AC52-07NA27344); Laboratory Directed Research and Development (19-ERD-027).
Acknowledgments
This work is dedicated to the memory of Alexander (Sasha) Rubenchik who has made seminal contributions in laser-matter interactions, non-linear optics and plasma physics.
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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