3.1.1. Flat Target
In
Figure 2A a set of images of the evolution of plasmas formed on a flat target is presented. In addition, the luminous plume front position graph is shown in
Figure 3. The latter data were obtained from horizontal lineouts taken from the centre of the broadband images along an axis normal to the target centre point (or vertex for grooved targets). The expansion length is defined as the distance from the target at which the emission intensity of the plasma was reduced to 5% of the peak emission intensity recorded for the initial plasma position on the sensor at time t = 0 ns.
In that case, the findings suggest the presence of two components: a fast “plasma front” and a slow “primary plasma” similar to the previous observations by Wu and coworkers [
36]. The presence of two components can be attributed to the laser supported detonation (LSD) wave. Specifically on the other hand, the plasma front, which is coupled to the shock wave, expands rapidly outwards due to the extra energy absorbed. Conversely, the primary plasma was left to slowly expand resulting in the observed plume splitting.
According to
Figure 3 the plasma is seen to expand rapidly over the first 40 ns and this can be attributed to the faster plasma front expanding towards the laser pulse. Upon termination of the laser pulse, the plasma front can no longer gain energy to overcome the confinement by the surrounding air at atmospheric pressure. Thus, the plasma front expansion decelerated and began to cool down via radiation losses. In parallel, the primary plasma expanded at a slower rate behind the plasma front and began to be more noticeable at around 60 ns. A flattening of the luminous plume front position curve around 80 ns is noticeable from
Figure 3, indicating that emission from the plasma front was decaying and, as a result, the bright primary plasma becomes the leading edge of the luminous expansion. This switching of the leading edge occurred due to the primary plasma becoming very distinct from the plasma front as can be seen from the image corresponding to the time delay of 100 ns. At a time delay of 160 ns, a deceleration of the primary plasma plume is observed. This is caused by interactions with the plasma front material, along with confinement by the atmospheric pressure air surrounding it. Furthermore, considerable lateral expansion has occurred, and the plasma has assumed a cone shape, characteristic for a laser plasma expanding in air. A sharp interface between the plasma plume and the background can be observed at a time delay of 250 ns, due to strong confinement as the plasma expands into the air at ambient pressure. The plasma then follows a slow diffusion into the surrounding air, as can be observed at 500 ns.
At later time delays, the plasma cools and the more highly charged ions have recombined with electrons to form a plume dominated by neutral and singly charged species. Eventually at 2000 ns, the plasma reached a “stopping distance” of 1.56 mm in agreement with reference [
36] where similar experimental parameters were present. The dependence of the stopping distance on laser parameters such as the pulse energy and wavelength has been studied in reference [
37].
3.1.2. V-Channel Targets
Moving on to the V-channel targets,
Figure 4 includes a set of images of the plasma evolution for each V-channel target. Additionally,
Figure 5 shows the luminous plume front position data for the 30°, 60° and 90° target respectively. From the data presented in
Figure 5 similarities between the 60° and 90° V-channel targets and the flat target are observed at early times. Specifically, the formation of an LSD wave accounted for the plume splitting due to the rapid expansion of the plasma front while the slower moving primary plasma component follows. This plasma front expansion terminated shortly after the end of the laser pulse within 40 ns. At a delay time of 60 ns, two distinct components can be observed, while at 80 ns a dip is present in
Figure 5 for both 60° and 90° V-channel targets. This feature was also observed for the flat target, and it was attributed to the primary plasma becoming the leading edge of the luminous expansion. In the images corresponding to a time delay of 100 ns it can be seen that the plasma front emission decayed considerably such that it became barely visible as the primary plasma emission comes to dominate the image.
At later time delays (t > 100 ns) noticeable differences between the V-channel targets and the flat target can be observed, with the former exhibiting greater directionality as a result of the greater confinement and hence, lower lateral expansion. Such directionality is indicative of collisions that occur within the plasma. More to the point, plasmas expanding from each wall of the V-channel targets will collide at a collision plane or surface. Typically, this would occur in the vicinity of the centre of the V-channel, and the opposing lateral velocity components will cancel. This results in stagnated plasma formation and a net outward growth of the plasma away from the target, with little or no lateral component of expansion and hence greater directionality in the plasma plume expansion.
At a time delay of 160 ns, it can be observed from
Figure 4 that a cylindrical shape corresponds to the V-channel plasmas as opposed to the cone shape observed for the flat target. Confinement by the background air was also evident due to the sharp plasma air interface both in the lateral and outward directions. In the case of 60° and 90° V-channel targets, such confinement created a build-up at the leading edge of the plasma, which was evidenced by the formation of a lobe-like plasma plume component at the leading edge of the plasma (see
Figure 4). At 250 ns, the primary plasma was seen to split into two distinct plasma components, consisting of the lobe-shaped plasma region at the leading edge of the plume, which is now distinct from the other component. At even further time delays, the plasma component within the target vertex remained somewhat stationary, showing little or no expansion. On the contrary, the lobe-shaped plasma plume component expands away from the target. It is proposed that this lobe-shaped plasma component can be explained as follows: the component of the plasma plume located near the vertex of the target creates a pressure gradient, due to the high density, which exerts a force on the plasma region further from the target. The region coalesces into a lobe, which then moves away from the target due to the applied pressure, leading to the appearance of the two plasma components, at long time delays: a stationary plasma, close to the target vertex and a moving plasma lobe. The coalescence of plasma in ambient air into multiple components is a well-known observation going back to the days of the earliest fast photographs of laser plasmas [
38]. Further confinement of the stationary plasma close to the target is attributed to shockwave reflection from the walls of the cavity, as per previous observations [
39,
40].
At even longer time delays, when the stationary plasma and plasma lobe have separated, the electron density and degree of ionisation in both components will be low and so that the Debye length will be long. Hence, Coulombic forces are not expected to affect the separation between the two components.
Turning our attention to the 30° V-channel target, it can be seen from
Figure 4 that no dip is present in the early plasma expansion. Importantly, unlike the other two V-channel targets, it does not seem to exhibit any indication of the appearance of a separate plasma lobe. In addition, as time proceeds, expansion of the plasma plume away from the target continued to slow, and signs of lateral expansion became evident, with the plasma expanding to fill the target vertex region at a time delay of 250 ns. Between 250 and 500 ns, the plume evolved into stationary plasma, similar to the case of the other two V-channels. Furthermore, the component of the plasma plume protruding into the ambient air exhibited a flat and well-defined front edge. This stationary plasma did not expand further and exhibited uniform emission while the plasma cooled.
Assuming a two-component expansion for early times, a single fit to the full expansion data range would not, of course, be satisfactory. Instead, two separate fits of the point explosion model to the luminous front data were required, as can be seen in
Figure 3 and
Figure 5, one for the plasma front (red curve) and one for the primary plasma (blue curve). Thus, for early times the point explosion model was used to fit the plasma front and primary plasma. The formula for the point explosion model is given as [
41]:
where R denotes the shock front position at a time t after plasma ignition. The parameters “α” and “n” are extracted from the fits and are tabulated in
Table 1. More specifically, “n” describes the shape of the shock front and values of 0.4, 0.5 and 0.667, respectively describe spherical, cylindrical or planar shapes. It is clear from the extracted n values that all targets tend towards a cylindrical expansion, in line with the observation that the plasma fronts have a fast, outward expansion, along the incident laser direction, with little evidence of lateral expansion. The “α” values, which are dependent on the energy of the point explosion, indicate that all the V-channel targets show a modest, but distinct increase in this energy as the vertex angle decreases. In addition, the velocities were calculated for the early time delays (0–60 ns) resulting in an increase of 19%, 18% and 24% for the 90°, 60° and 30° V-channel target respectively, due to the increase of the point explosion energy.
Concerning the primary plasma that became dominant after the initial rapid expansion of the plasma front, we tabulated the extracted values also in
Table 1. In that case, we obtained n values of 0.4, for all three vertex angles, meaning that the expansion was quite spherical. Similar to the plasma front case, the V-channel targets give rise to an increased point explosion energy compared to the flat target. This increase in the primary plasma expansion rate supports the proposition that the 30° V-channel target does not show a dip in the luminous expansion data since the primary plasma and the plasma front have expanded at similar rates. As a matter of fact, the two point explosion fits corresponding to the primary plasma (blue curve) and plasma front (red curve) expansions in the 30° V-channel case, overlap each other smoothly. In contrast, for the other targets the two curves were distinct and exhibited a short flat region in the luminous expansion plots as the most distant luminous front swaps from the plasma front to the primary plasma.
Remarkably, at a time delay of 160 ns, an increased degree of lateral confinement is observed as the target geometry became tighter. However, as the plasma remained confined, even when not in contact with target walls, it was proposed that this is not just due to geometric confinement but also arises from the plasmas formed on the target walls. As a result we could state that the tighter the target angle the higher the confinement. When the plasma material arrives at the collision plane the faster lateral expansion components in the 30° and 60° V-channel targets formed well-defined regions or “harder” stagnation, while the slower lateral components from the 90° V-channel formed a less-defined “softer” stagnation.
At longer delay times (t > 600 ns), the fitting of the luminous plasma front position data was performed using the drag force model (green curve). In that case, the equation used to fit the data is given as [
42]:
where R
0 is the stopping distance of the plasma plume and β is the slowing coefficient such that R
0 × β = υ
0 with υ
0 being the initial velocity. The extracted parameters are tabulated in
Table 2. A first point to make, is that the extracted β values, for the 30° and 90° V-channel targets are smaller, thus resulting in longer stopping distances of 1.95 mm and 1.94 mm respectively. On the other hand, the 60° V-channel target exhibits a somewhat smaller stopping distance of 1.84 mm due to the unexpectedly smaller slowing parameter. This observation may be attributed to the fact that these measurements are based on the luminous plasma front position. The emission from the plasma column in the 60° V-channel target was seen to decay away at late time delays and as such this would have a negative going impact on the luminous plasma front position.
By 1000 ns the plasmas have all but stopped expanding and peak intensities are all approximately equal in all cases. However it can be seen that each of the V-channel targets exhibited strikingly different behaviours. The 90° V-channel target had two bright regions of intense emission, the extended plasma lobe and the stationary plasma located near the V-channel vertex. The 60° V-channel target had intense emission from the stationary plasma while in contrast to the 90° V-channel case, the plasma column displayed much weaker emission. The 30° V-channel did not show any indication of a distinct separate lobe formed at any time delay and the entire plasma appeared to behave as one stationary plasma. It is worth pointing out that the stationary plasmas within the V-channels at this point all exhibited similarities in emission intensities and distribution.
At time delays beyond 1000 ns, the intensities of the images for the different targets began to decay at different rates. The 30° and 60° V-channel target intensities fell away at the fastest rates, while the 90° V-channel target was closer to the flat target case. This decrease in emission was proposed to be due to confinement of the targets. More specifically, it was seen that the V-channel targets had an early increase in emitted radiation and this was attributed to confinement increasing the recombination rates, with the rate scaling inversely with the vertex angle leading to a concomitant increase in radiative losses. It is proposed that the increased collisional rates for the 60° and 30° V-channel target plasmas means that the radiative losses occurred more quickly for these cases than the less well confined flat and 90° V-channel cases. This is supported by previous literature studies where time-resolved shadowgraphy was used in tandem with fast imaging (e.g., [
39,
40]). In these papers, which have similar experimental conditions to those present in our work, the authors observe spectral enhancement and persistence in the confined plasma case which scales with the level of confinement. In the case of [
40], they find that as the confinement increases, so too does the spectral enhancement. Thus, this agrees with our observations.
Turning to the individual stationary and lobe plasmas at rather long time delays, when they have been separated for some time, it is observed that the plasma lobe emission intensity decayed more quickly than the emission intensity for the stationary plasma, particularly for the 60° V-channel target case, where the plasma column was not visible in the corresponding image at 2000 ns. Importantly, the stationary plasmas formed at what would be the location of the collision plane from the initial plasmas expanding from the target walls. They exhibited many of the characteristics one would expect from a stagnation layer, for example, they were stationary showing little to no expansion and they had quite uniform intensity distributions, which decayed more slowly than regions further from the target vertex, e.g., in the lobe plasma region.