Investigations on the effect of target angle on the stagnation layer of colliding laser produced plasmas of aluminum and silicon

Laser produced plasmas have found applications in a wide area of science and technology from extending Moore's law for integrated circuits to colliding galaxies. The latter relies on studies of colliding plasmas, which can be produced in a laboratory by focusing the output of a laser beam that has been split into two to produce two plasmas separated by a few millimeters. Known as colliding laser produced plasmas (CLPPs), these plasmas can act as an experimental basis for investigating astrophysical relevant shocks.^1–5 Better understanding of colliding plasmas can have applications in the study of indirectly driven inertial confinement fusion reactors,^6,7 in which the extreme environment can cause colliding plasmas to form between the core and walls of the chamber, which may limit the performance of the reactor.^8,9 A better understanding of CLPPs can also help to improve the sensitivity of LIBS experiments.^10,11 The aim here is to improve the coupling of the laser to the target and ablated material. In the present work, the authors seek to probe how the colliding plasma parameters vary as the target geometry and material are altered.

In order to engineer the two separate plasmas to interact, a number of geometries have been investigated from planar to orthogonally orientated targets. Collinear targets have been utilized by using two laser pulses separated in time to study the effects of the shock wave generated by the second plasma as it interacts with the first.¹² The most popular diagnostic methods include photographic imaging, time and space resolved spectroscopy,¹³ and laser interferometry.^14,15 Fallon et al.¹⁶ used the motion of the spectral lines of copper to infer velocities as a function of target wedge angle and found that ions move faster than the neutrals and that as the angle of the wedge decreased the growth rate also decreased. While much of the previous work has been done in the visible spectrum,^12,17–21 the work of Harilal²² used a pinhole camera to investigate the XUV emission from the plasma at very early timescales (< 50 ns). Yeates et al.²³ used a Faraday cup technique to measure the dependence of the peak ion current and kinetic energy of the ions as the target atomic mass was varied.

Regardless of the geometry used when the two plasmas overlap, they can either inter-penetrate with little or no interaction between the counterstreaming plasmas, or, at the other extreme, the individual ions and atoms can collide and stagnate. For stagnation to occur, the mean free path (λ_ii) of the atoms must be small. The mean free path for ion–ion interactions is defined as²⁴ 

where m is the mass of the atom, v₁₂ is the relative velocity between the counterstreaming atoms/ions, z is the average charge state of the plasma, ε_o is the permittivity of free space, and $Λ12$ is the Coulomb logarithm. Rambo et al.²⁵ have derived the collisionality parameter, ζ, which is the ratio of λ_ii to the plasma seed separation (D) and indicates whether interpenetration or stagnation is likely to occur. Given that λ_ii is very sensitive to velocity and charge state, larger values of ζ tend to be associated with low ion velocities or higher charge states. In this case, the kinetic energy of the incoming atoms/ions can be converted via collisions into the thermal energy of the stagnation layer, which can lead to reheating effects. A large value of ζ will produce a sharp well-defined stagnation layer, whereas lower values produce a more gradual and diffuse stagnation region.

In the present work, we seek to investigate how the stagnation layer parameters vary over small changes in target mass while simultaneously studying the effect of changing the target geometry and seed separation. We will present time- and space-resolved images of colliding plasmas of Al–Al, Si–Si, and Al–Si as well as a spectroscopic analysis of the stagnation region.

The experimental layout is shown schematically in Fig. 1. It was comprised of a cylindrical vacuum chamber of 50 cm diameter with 8 ports orientated toward the center of the chamber separated by $45°$⁠. Throughout all experiments, the vacuum chamber was kept at a base pressure of $3×10−6$ mbar using a Leybold D&B rotary vane pump as a backing pump and an Edwards EXT250 turbomolecular vacuum pump. The laser pulse was introduced along the z-axis and was focused by a plano-convex lens mounted on an actuator, which controlled the lens-to-target distance. The fast gated camera observed the plasma at $90°$ to the z-axis, while the visible spectrometer was also at $90°$ to the z-axis but on the opposite side of the chamber from the camera. The three actuators used to control the x, y, and z movement of the target holder had a $100 μ$m step resolution. The different thicknesses of the targets were accounted for by the z-actuator, which moved in the direction toward/away from the laser beam. A Q-Switched Nd:YAG Continuum Surelite III-10 laser (⁠$λ=1064,Δt=5.3 ± 0.3$ ns and maximum laser energy of 670 mJ)²⁶ was used to generate the plasmas. A $2°$ wedge prism was used to separate the incoming laser beam into two separate beams as shown in Fig. 2. Two different focal length lenses of 100 and 125 mm were used to produce seed plasma separations of 1.66 and 2.16 mm, respectively. The maximum laser power densities were $4.60±0.9×1012$ and $2.94±0.6×1012W/cm2$ with the f = 100 and 125 mm lens, respectively.

The results in the current work combine the results of two slightly different experimental configurations: time resolved emission imaging covering the range from 375 to 475 nm and time resolved spectra covering the range from 370 to 426 nm. Time-resolved emission imaging was achieved through the use of a Hamamatsu ORCA-05G model ICCD camera, which consisted of a two-dimensional array of 1344 × 1024 pixels of pixel area $6.45×6.45 μm$ yielding an active area of $8.67×6.60 mm2$⁠. The CCD chip is lens-coupled to the MCP, which allowed exposure times of less than 1 ns. The camera had a quantum efficiency of 70% between 500 and 600 nm, which drops to approximately 50% at 400 nm. The use of two bandpass filters centered at 400 nm and 450 nm (FKB-VIS-40 filters from Thorlabs²⁷) helped to isolate the emission in terms of a reduced set of emitting ions and, hence, simplified the interpretation of the images. These filters had a 25 nm bandwidth and a maximum transmission of 50% and 70%, respectively.

The time-resolved spectra were based in the visible region and were recorded by an Acton SP-2756 UV-visible spectrometer from Princeton Instruments fitted with a 0.75m focal length, f/#=9.7, 300 grooves per mm grating using a Czerny–Turner configuration and covering the range of 370–426 nm. The spectra were stigmatic and were recorded with the same Hamamatsu camera as used for the imaging experiments, and hence, the data are not simultaneous imaging/spectral data. A 100 mm uncoated BK7 planoconvex lens, with a diameter of 18 mm, was used to focus the plasmas onto the entrance slit. A dove prism was inserted between the plasma focusing lens and the spectrograph slit in order to orient the expanding plasmas parallel to the slit such that only light from the stagnation layer entered the spectrograph.

This work covers the spectral range from 375 to 475 nm and was done on targets with wedge angles of $180°$(i.e., flat), $120°$⁠, and $80°$ using targets of Al–Al, Si–Si, and Al–Si. Table I lists the lines of interest in the wavelength range from 380 to 475 nm covered by the current work.

The images of the seed and stagnations layers for aluminum and silicon using different wedge angles are presented in Figs. 3–8 taken at intervals of 20 ns from 320 to 420 ns after the laser pulse at a laser energy of 670 mJ. Each image contains a description of the target material, geometry, filter, and time step. In each case, the laser energy was constant giving a power density on the flat targets of $1012 W/cm2$ but was reduced as the wedge angle decreased. The color bar in each of the images is constant to allow direct comparison.

It was difficult to separate the emission from the stagnation layer and seeds at times less than 320 ns, and for this reason, these timescales are excluded. At this point, the plasma will have cooled to temperatures of a couple of eV and little Bremmstrahlung is to be expected. For both target materials, the stagnation layer was visible in almost all of the images. Clearly the effect of decreasing the wedge angle from $180°$ to $80°$ was to increase the brightness of the stagnation layer. The formation of the stagnation layer will depend upon the collisionality parameter, which scales as $ni/T2$ as per Sanchez.¹¹ Given that results later in this paper indicate that these plasmas are typically at low temperature (1.5 eV) and high density (⁠$1017cm−3$⁠), we expect the collisionality parameter to be > 100. Thus, little interpenetration is expected and this is indeed borne out by the images, which show well defined stagnation layers.

For many of the flat target images, the stagnation layer is only weakly defined and grows more intense and sharper as the wedge angle decreases. The length of the stagnation layer is observed to increase as the wedge angle decreases (Table II). Comparing the flat targets to the two wedge targets, the width is generally larger for the wedge-shaped targets. This is evident if we compare the images at 360 ns where the stagnation layer is well defined.

The silicon and aluminum stagnation layers look broadly similar, and there appears to be little dependence on the small change in mass of the target atoms in the stagnation layer. In general, the stagnation layer is less bright, less well-defined, and less persistent when using the 400 nm filter for the aluminum dataset. While there is an Al III line at 415 nm, it is very weak after 380 ns (see Fig. 9) and, thus, we can conclude that most of the emission captured by the 400 nm filter was from the neutral species. This would suggest a lower collisionality parameter caused by the lower charge state captured by this filter. For silicon, the stagnation layer is well defined in both datasets with the 450 nm dataset showing a sharper better defined stagnation layer compared to the broader ones in the 400 nm dataset.

For the heterogenous targets of silicon and aluminum, there is a slight asymmetry in the way the stagnation layer appears to veer toward the silicon target when the targets are flat (Fig. 8). The profile taken along the expansion axis for the flat targets shows that the peak emission occurs about 1 mm from the surface at about 350–360 ns after plasma formation (Fig. 10). The smallest wedge angle of 8° tended to produce the longest stagnation layers. The length of the stagnation layer is defined as the distance between its rising and falling edges at 1/e of the peak. The average length and width of the stagnation layer for the three configurations are shown in Table II for the 450 nm filter.

By analyzing the position of the expanding front away from the target surface with respect to time the velocity of the stagnation layer was calculated. It should be noted that this is not the physical velocity of the stagnation layer as a distinct entity but is more properly the rate at which its visible emission grows with respect to time. Nonetheless this is the term commonly used in the literature and will be maintained here. The velocity of this expanding front in each time interval was observed to increase over time (Fig. 11). This was also reported in the Faraday cup measurements of Yeates et al.²³ where similar velocities of $6.43×106$ cm/s for aluminum and $7.52×106$ cm/s for silicon were observed. This can be explained on the basis of space charge effects where the faster moving electrons will stagnate first and will cause the ions to be accelerated. This is in contrast to the experiments of Min¹² and Mondal¹⁸ who separately reported similar velocities to our experiments but that the velocity remained constant. In the case of Mondal et al., we attribute the different result to the lower power densities and much larger seed separation of 6 mm of their plasmas, whereas for Min et al., the difference is attributed to the fact that their plasmas were collinear.

As the laser energy increases, the expansion of the stagnation layer for the flat targets appears to slow down (Fig. 12), indicating that the stagnation layer is less likely to form at the higher energies. Higher laser energy results in increased velocity of the expanding ions (Sisyuk²⁸). Given that the mean free path is extremely sensitive to this parameter, we explain the slowing down of the stagnation layer as being a result of a greater inter-penetration due to the greater velocity of the atoms and ions. Thus, the higher ion velocity results in increased inter-penetration rather than stagnation. It was also observed that the expansion velocity is slower for the wedged targets compared to the flat target. Again the larger counterstreaming velocity will reduce the level of stagnation, but there will also be an effect from the change in angle of the expanding plasmas since there is less material moving in the axial direction away from the target. The effect of increasing the seed separation is shown to reduce the stagnation layer velocity (Fig. 12). The same observation was documented in Fallon's Ph.D. thesis,³³ while Mondal et al.¹⁸ observe the opposite effect with respect to seed separation, which we again attribute to the different experimental conditions already cited.

The photographic images captured the general evolution of the stagnation layer over time and enabled calculation of the width and length of the stagnation layer under various conditions. A more detailed understanding of the images can be gained by a time-resolved spectroscopic analysis. A series of spectra were captured in a 10 ns interval from 250 to 500 ns with a 50 ns gate time, an example of which is shown in Fig. 9. By tracking the evolution in intensity of a particular emission line over time, it was possible to probe how each ion stage evolved in the stagnation layer. In order to measure the average intensity, the spectra were summed over the length of each emission line to reduce the image to a single intensity vs wavelength array. This was done for each image taken in 10 ns steps from 320 to 500 ns. For these experiments, only the Al–Al and Si–Si targets were used and the wedge target refers to a 90° wedge only.

The time-resolved spectra are shown in Fig. 9. For both silicon and aluminum, we can see that the relative strength of the higher ion stages peaks at earlier times compared to the lower ion stages. The Al III line at 415 nm peaks at 340 ns and decreases thereafter relative to the neutral line at 396 nm, which peaks at a later time of 460 ns. The peak emission as a function of time is measured and shown in Figs. 13 and 14 along with the intensity ratio of the selected ions. The ratio peaks at just under 1.5 for the flat targets but has a higher value of 2.5 for the wedged shaped aluminum targets and is similar in the silicon targets. Mondal et al.,¹⁸ in a similar analysis using the Al II line at 466 nm, observed that the ratio peaks at a value of 12 at 200 ns and then decreases toward one at approximately 500 ns. We attribute this difference to the lower electron densities in those plasmas, and this is supported by results presented later in this paper. Given that the Al III line at 415 nm decreases after 340 ns, we can assume that the same can be said for the Al III line at 451 and 452 nm (and further justified in Sec. III C), which are beyond the wavelength range captured by the spectrograph but were captured in the photographic images. Thus, the 450 nm data in Sec. III A will mostly capture Al II emission at 466 nm.

The silicon spectra contain emission features from Si I up to Si IV. As expected, the Si IV emission peaks first followed by successive ion stages down to the neutral emission at 390.5 nm (Fig. 9). In the case of Si II, Si III, and Si IV, there is more than one emission line and the data in Fig. 14 are averaged over the lines listed in Table I. The ratio of Si III to Si II was measured and is shown in the right hand side of Fig. 14. As with the aluminum data, the ratio is greater than 1 up to about 340 ns and decreases rapidly thereafter to almost zeros at 400 ns.

Referring back to the photographic images from 350 ns onward, we know that Al III has mostly disappeared after 380 ns (see Fig. 9). Thus, the 400 nm dataset for aluminum (Fig. 4) captures emission from Al I. The effect of the wedge is to allow the stagnation layer to exist for longer compared to the flat targets. The 450 nm filter captures higher ionization stages. The persistent emission here at long timescales is assumed to be dominated by the lowest available ionization stage, i.e., the Al II line at 466.3 nm. The slightly sharper stagnation layer in the 450 nm data would be consistent with higher average ionization states as the collisionality parameter is highly dependent on the average charge state (⁠$ζ∝z4$⁠). Similarly the silicon images (Figs. 5 and 6) contain a range of ions, but only the 400 nm filter captures the neutral emission. Thus, the 400 nm dataset presents a less well defined stagnation layer but they are longer lived compared to the slightly sharper stagnation layers associated with the higher average ionization stages captured by the 450 nm filter. In Sec. III C, we show how we have used these results in combination with the calculated electron density in order to infer the temperature of the stagnation layer.

The electron number density of the colliding plasma stagnation layer was determined from the widths of the spectral lines. No self-absorption was apparent from the spectra, and we, therefore, assume that the lines widths are a good diagnostic. The absence of opacity effects in the line shapes was checked by measuring the ratio of two lines and confirming that the ratio of their intensities approached that of their statistical weights. The overall spectral linewidth is typically a combination of Doppler broadening, instrumental broadening, and Stark broadening. The Doppler broadening components are expected to be approximately 0.005 nm for plasmas of 1 eV.¹⁰ Given that we were observing the plasmas perpendicular to the axis of expansion, we do not expect this to be a significant component. Also the instrumental broadening was independently estimated to be about 0.1 nm. The combination of these Gaussian contributions with the Lorentzian contribution from Stark effects will produce a Voigt profile. We have assumed that the Voigt component is completely determined by Stark broadening due to the electron density only, and other components, such as ion broadening, are negligible. The full width at half maximum (FWHM) of the spectral line is related to the electron density through the following relation:

where w is the Stark broadening parameter, n_e is the electron density, and $Δλ1/2$ is the experimentally measured FWHM of the spectral line profile. This analysis was applied to selected lines in the spectra that were relatively intense and well isolated from neighboring lines such that their profiles could be unambiguously determined. In all cases, the width of the spectral lines is constant to within 10%–20% along the z-axis direction away from the target. (The spectra are space-resolved.) This indicates a fairly even density and temperature in the stagnation layer. The spectral lines were sampled at a number of positions along the axis of expansion and the average profile calculated in order to increase the signal to noise ratio. A fitting routine was then used to fit a Voigt profile to each of the line profiles and the Lorentzian width extracted.

The Stark broadening parameters (w) for aluminum and silicon are shown in Table III. Equation (3) was used to calculate the electron density as a function of time, and the results are shown in Figs. 15 and 16 for the flat and wedge-shaped targets of aluminum and silicon. For aluminum, the electron density remains fairly constant with a slight increase at earlier times. At times from 330 to 360 ns, the measurement is derived from the Al III line and shows a slightly higher value (but within the uncertainty limits) compared to later times. There is no obvious difference between the flat and wedge shaped targets in terms of electron densities, but we can see that the emission from the wedge shaped targets persisted longer allowing reliable linewidth measurements up to 550 ns compared with 470 ns for the flat targets. In the case of the silicon targets, the electron density has been averaged over the Si I, II, and IV emission lines listed in Table III. Again the slightly higher values initially are attributed to the higher ionization states (in this case Si IV) that dominate at these timescales. Comparing the aluminum and silicon densities, we can see that the silicon densities are slightly lower compared to those of aluminum. The lack of any temporal change was also the case for the plasmas reported by Luna et al.,¹⁰ and indeed, the electron densities are similar.

The electron density was used to estimate the electron temperature by analyzing the ratio of the intensity of emission lines from consecutive stages of ionization. This technique is only valid if we can assume that the plasma is described by Local Thermodynamic Equilibrium. The McWhirter criterion³¹ specifies the minimum electron density required to satisfy this condition and is given by

For temperatures of 1–2 eV and energies between 1 and 4 eV, the condition is well satisfied. Assuming that a Boltzmann distribution applies to the energy levels, the equation below can be used to calculate the intensity ratio,

where $I$ is the total intensity, g is the statistical weight of the lower level, f is the oscillator strength of the lower charge state ion, λ is the wavelength, and a_o is the Bohr radius. The higher ion stage is denoted by the primed quantities, and $E∞$ is the ionization energy of the lower ion stage. The NIST website³² contains the results of this calculation for a range of electron temperatures and densities, and the data in Fig. 17 are based on these data.

For silicon, the measured ratio of III/II peaked at 1.15 at 310 ns and dropped to less than 0.2 at 380 ns (Fig. 14) and the average electron density is approximately $1×1017 cm−3$ (Fig. 16). From Fig. 17, this would indicate that the temperature was between 1.9 and 2.1 eV. The wavelength dependence of the quantum efficiency of the camera was not taken into account but is not expected to contribute more than $±10%$ to the calculated result. The graph above explains why Mondal et al.¹⁸ obtained a higher value for this ratio given that their experiments were done at lower electron densities (⁠$1016 cm−3$⁠). For both silicon and aluminum, we can see that the higher ionization stages appear earlier in the stagnation layer formation, suggesting that collisional excitation is occurring in this region and then the ions disappear at the expense of the lower ion stages presumably due to recombination. Given that the ionization energy of Si II is 16.3 eV, it is unlikely that this is caused by electron impacts in the stagnation layer. Calculation of ionization rates by Mondal et al.¹⁸ suggest that ionization could be occurring in the stagnation layer at earlier timescales (<200 ns). Alternatively the ions could have been generated in the seed plasmas (Li et al.²¹) and then traveled to the stagnation layer where they undergo collisional excitation. After 350 ns, the silicon stagnation layer is mostly Si I and II.

The effect of target geometry on the formation and evolution of a stagnation layer produced from the interaction of two laser-produced plasmas was studied using time-resolved and space-resolved imaging techniques applied to targets of aluminum and silicon. The geometry of the target has a clear role in determining the brightness, length, and width of the stagnation layer: brighter, longer, and more homogenous stagnation layers were observed when the wedge angle decreased. By analyzing the line widths, the electron densities were calculated showing a relatively constant density over time of $1017cm−3$⁠. From the intensity ratios of consecutive stages, the temperature was deduced to be 1.9–2.0 eV. The time-resolved spectra showed that the stagnation layer emission is dominated by lower ion stages (neutral and singly ionized species) after approximately 370–500 ns. The effect of the mass of the target has been demonstrated in other work²³ where the stagnation layers were analyzed over large target mass ranges. In the current work, the mass change is small from aluminum to silicon and its effect on the stagnation layer parameters is not significant, demonstrating that these parameters change slowly as a function of target material.

The authors wish to acknowledge the Erasmus Mundus Joint Doctorate “EXTATIC” Program under framework partnership Agreement No. 2012–0033 for financial support over the course of this project.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.