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Abstract
The interaction of plasma (or shock waves) with the uniform sphere shape of polystyrene particles was investigated in this study to observe the effects of confined geometry and energy fluence on propulsion efficiency. The measurements indicate that propulsion efficiency first increases with energy fluence until reaching a maximum at 0.46 J/cm2, then decreases as energy fluency continues to increase. Compared to polystyrene particle propulsion without confined geometry, the propulsion efficiency of polystyrene particles improved due to multiple laser-induced shock wave reflections among the confined geometry internal face; the plasma propelling force also increased perpendicular to the target surface under confined geometry conditions. The results also show that the energy deposited on the plasma affects the energy distribution between the plasma and polystyrene particle. Moreover, a series of experiments was performed to roughly estimate the shock wave expansion shape through the motion direction of the polystyrene particle swarm, where the shock wave was observed to expand spherically.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Laser plasma propulsion in target material is a common phenomenon that was first proposed by Kantrowitz in 1972 [1]. Plasma propulsion has garnered a great deal of research attention due to its numerous advantages such as high payload ratio and low launch cost over conventional chemical or other propulsion systems [2–5]. When a target material surface is irradiated by a laser pulse, high-power energy is absorbed by the target material or the air around the target surface resulting in plasma (or shock wave) formation. The subsequent impact force induced by the expanding shock wave drives target material movement through recoil effect [6]. Generally, plasma propulsion can be roughly divided into two modes: Air-breathing mode and ablation mode [7,8]. In the former, the main propulsive source originates in the laser-induced air plasma (or shock wave) expansion, where air acts as the propellant. In the latter, the propulsive source derives from the expansion of target plasma. The main difference between them is the source of the propellant [9]. Recently, several different techniques have been developed to enhance propulsion efficiency. The momentum coupling coefficient (Cm) and optimum fluence are two key parameters which describe propulsion efficiency; Cm is the ratio of momentum achieved by the target material to the pulse energy [10]. The optimum fluence is the energy fluence at the maximum Cm value.
Many previous researchers have explored propulsion efficiency in regards to geometric structure design, target material properties, laser parameters, and experimental environments [11–13]. Qiang et al., for example, investigated the influence of target properties on propulsion efficiency by employing three different target materials for underwater propulsion; they found that propulsion efficiency is enhanced when plasma is “squeezed” by the surrounding water environment [14]. Fabbro et al. investigated the dynamics of laser-induced plasma in confined geometry, under which conditions both shock wave pressure and duration time increase [15]. Ahmad et al. designed different geometric structures on the surface of ferrites to study their effects on propulsion efficiency. Multiple reflections of shock waves within the walls of ferrites were found to improve the shock wave propagation perpendicular to the ferrite surfaces [16]. The above experiments indicate that the Cm is strongly dependent on target material properties, confined geometry, and laser parameters. In other words, propulsion efficiency can be markedly enhanced by adjusting certain parameters appropriately.
In this study, we investigated the influence of energy fluence and confined geometry on PS particle propulsion efficiency as a dynamic process. We gathered digital images of PS particle moving traces which intuitively represent the propulsion process. We found that an optimal energy fluence does exist in terms of propulsion efficiency. We compared propulsion efficiency with versus without confined geometry to find that the propulsion efficiency of the PS particle is dependent on the energy fluence and confined geometry. We also indirectly estimated the shape of the expanding shock wave through the motion direction of the PS particle swarm.
2. Experimental setup
A schematic diagram of laser plasma propulsion experimental setup is shown in Fig. 1. PS particles as the propelled object were carefully selected and screened under an identical microscope to ensure identical or similar diameter and nearly uniform spherical shape. The calculated weight per particle was about 5.5 × 10−7 g and the diameter was about 100 μm. The PS particle was located on the surface of the silica substrate or placed freely inside a capillary tube (confined geometry) that was fixed on a 3D-translation stage. We used a Nd: YAG laser system as the source which provides 6-nanosecond (around 532 nm) pulse energy at the millijoule order with repetition rate of 6 Hz. The probe laser beam and pump laser beam were derived from the laser pulse with a 50:50 splitter. The laser energy was monitored while the probe laser beam enters the energy meter. The pump laser beam was focused on the front of the PS particle by a 4 × optical objective. Air plasma formed on the front of the particle as the air broke down, which then generated an expanding shock wave to push the PS particle forward through recoil effect. To ensure the PS particle moved along the direction of the incoming laser pulse, we adjusted the relative position of the particle to force the air plasma to impact its center via the 3D-translation stage. The light reflected by the PS particle surface subsequently passed through the optical objective and a 532-nm narrowband filter into the high-speed CCD camera to capture images of the particle dynamics. We also used spectrometers parallel to the plasma expansion direction to collect emission spectra of the air plasma.
3. Results
We explored the feasibility of laser plasma propulsion in this study. In our first experiment, the energy fluence and laser pulse duration were fixed at 0.314 J/cm2 and 6 ns, respectively. Air plasma formed on the front of the PS particle due to air breakdown; the shock wave this produced then generated an impulse that impacted the PS particle to overcome adhesion force (van der Waals force) [17] and propel the particle forward. The movement of a PS particle with 100 μm diameter over a 0.5 ms interval is shown in Fig. 2(a). For clarity, the relation between the motion distance of the particle and time is shown separately in Fig. 2(b). The motion distance and speed of the particle were 42.31 μm and 0.99 × 10−3 Mach at t = 0.125 ms, respectively. The PS particle stops moving at t = 3.25 ms due to the coaction of the friction and air resistance. The kinetic energy from the PS particle cedes to the friction resistance and air resistance (Fig. 2(c)) as the particle stops moving. Other types of resistance may also be involved in the PS particle motion process.
Fig. 2 (a) PS particle movement with energy fluence 0.314 J/cm2 (0.5 ms interval). (b) Distance and velocity of PS particle as a function of time. (c) Kinetic energy of PS particle and resistance as a function of energy fluence.
We conducted a set of similar propulsion experiments with varying laser energy fluence characteristics to further explore the effects on PS particle propulsion efficiency. Results at energy fluence of 0.314, 0.38, and 0.46 J/cm2 with constant PS particle diameter of 100 μm are shown in Figs. 3(a)-3(c). As we expected, the propelled speed (Fig. 3(d)), distance (Fig. 3(d) inset), and momentum (Fig. 3(e) right) of the PS particle monotonically increased with energy fluence, this is due to the laser-induced air plasma or shock wave expanded rapidly as energy fluence increased; in other words, the plasma (or shock wave) expansion velocity increased as laser intensity increased, and accelerated the PS particle via recoil effect.
Fig. 3 PS particle movement process at different energy fluences: (a) 0.314 J/cm2, (b) 0.38 J/cm2, (c) 0.46 J/cm2, (d) PS particle speed as function of energy fluence, inset: Movement distance of PS particle as a function of energy fluence. (e) Momentum coupling coefficient Cm and momentum P as functions of energy fluence.
PS particle movement is attributable to the recoil momentum transfer between the shock wave and particle. Therefore, introducing a key parameter is necessary, the Cm can reflect the recoil momentum transfer. In our experiment, the Cm value first increased with energy fluence until reaching a maximum of 15.2 × 10−7 Ns/J at optimal energy fluence of 0.46 J/cm2, then decreased as fluence continued to increase (Fig. 3(e) left). We attribute this curve to 1) Plasma shielding effect, where the laser energy absorbed by the plasma did not reach the PS particle [18], and 2) plasma superheating of the PS particle layer having caused a “droplet splash” phenomenon. Our experimental results reflect the dependence of energy fluence on propulsion efficiency.
In addition to energy fluence, the momentum transfer and Cm of the PS particle are affected by confined geometry. Zheng et al. [19] tested confined geometry conditions to find that Cm increases when plasma expansion is restrained. In our experiment, we used a cylindrical capillary tube with internal diameter larger than the PS particle serve as the confined geometry and tested its effects on propulsion efficiency. The PS particle diameter and the energy fluence were kept to 100 μm and 0.46 J/cm2. For comparison, under non-confined geometry conditions, the PS particle moved along the laser incoming direction on the substrate surface (Fig. 4(a)). The movement distance, the velocity and the Cm were approximately 1123.52 μm, 8.98 m/s and 15.2 × 10−7 Ns/J, respectively.
Fig. 4 Effects of confined geometry on PS particle propulsion efficiency. Experiments: (a) Without confined geometry (b) With confined geometry. Simulations: (c) Without confined geometry. (d) With confined geometry. (e) Normalized energy intensity distribution.
Under confined geometry conditions, the movement distance, the velocity and the Cm were approximately 1287.89 μm, 10.30 m/s and 17.39 × 10−7 Ns/J, respectively. The obtained values are higher compared to the case without confined geometry. It’s worth noting that the PS particle was broken into pieces while the energy fluence was 0.548 J/cm2 (Fig. 4(bIV)); but the particle remained intact when there was no confined geometry. This behavior revealed that the propulsion efficiency can be enhanced by using confined geometry. Figures 4(a) and 4(b) deduce that multiple reflections of the shock wave among the confined geometry internal face, which ultimately enhanced the propulsion efficiency. We also ran a simulation to illustrate this shock wave propagation characteristic (Figs. 4(c) and 4(d)); we can realize that shock wave confined by a confined geometry was different from free expanding. The multiple reflections of shock wave from the geometry internal face would reheat the plasma, leading to an increase in free electron density, plasma temperature, as well as a higher expansion velocity and intensity of shock wave (Fig. 4(e)). Again, confined geometry enhanced the shock wave propelling force perpendicular to the target surface compared to the same setup without confined geometry [20]. Both the experimental and simulation results suggest that propulsion efficiency can be improved via shock wave confinement [21,22].
4. Discussion
Air plasma generation is generally divided into two stages: (1) The multi-photon ionization regime and (2) the joint action of multi-photon ionization and avalanche ionization [23,24]. In the first stage (M + mhv→M+ + e-), electrons escape from air molecules and turn into free electrons while photon energy exceeds ionization energy. Another stage of the electrons source which was the avalanche ionization stage (M + e-→M+ + 2e-), must be the main free electrons source. Accelerated electrons produced in the first stage serve as the “seed electrons” which impact the neighboring neutral air molecules such that the number of free electrons increases exponentially. In our setup, we consider the plasma to have formed once the free electron density reaches a critical value (1016~1018/cm3), after which point the target material is propelled by the plasma or shock wave expansion [16].
Meanwhile, plasma visualization technology provides valuable information regarding plasma expansion characteristics. Harilal et al. [25] explored the spatial expansion behavior of plasma in a laser irradiating solid target material, where the plasma expansion shape proved to be dependent on the ambient pressure. Chen et al. [26] explored plasma expansion generated by a laser pulse irradiating tin droplets, where plasma expansion velocity increases as incoming angle decreases. In this study, we investigated the effects of energy fluence on the plasma expansion as shown in Fig. 5(a). As per characteristic peak positions in the collected spectra, air is broken down and air plasma is generated; Fig. 5(b) shows an image of air plasma expansion at energy fluence of 0.38 and 0.548 J/cm2 under atmosphere conditions (rows (I)-(II)). As shown in Fig. 5(b), plasma expands to greater extent as energy influence increases, and then accelerated the PS particle via recoil effect (Fig. 5(c)).
Fig. 5 (a) Plasma produced by air breakdown collides with PS particle. (b) Plasma image sequences at different energy fluences: (I) 0.38 J/cm2 (b) 0.548 J/cm2 (c) Uniform PS particle (d) PS particle kinetic (to R5) as a function of energy fluence.
Interestingly, the laser-induced air plasma expansion image shows a classical kidney (or elliptical) shape along the incoming laser, and the larger energy fluence is, the more obviously kidney (or elliptical) the shape is. This is due to a large proportion of laser energy was deposited in the laser direction, and the plasma expanded faster along the incoming laser direction than perpendicular to it [26]. Hence, we inferred that the elliptical formula is suitable for describe the plasma shape. The experimental results also can be used to monitor the changed of the energy partitioned to the PS particle kinetic energy (mv2) and partitioned to the shock wave energy (ρR5/t2). The ratio mv2/R5 can be used to roughly analyze the energy partitioning mechanism. In our case, the ratio reached its maximum value at energy fluence of 0.46 J/cm2, at which point the majority of the energy was assigned to PS particles (Fig. 5(d)). This behavior conforms to the variation tendencies where Cm reaches its limit at the same energy fluence.
Figure 6(a) schematically depicts the origins of driving and resistance forces acting upon the PS particle at the beginning of the movement process. For horizontal propulsion, the sources of the driving force include shock wave pressure F and optical pressure Fo. Plasma pressure F can be expressed as follows [27]:
where ρ0 is density and I is energy intensity. A laser pulse with a wavelength of 532 nm was used as the excitation light, so we assume a = 0.4. Another driving force is optical pressure Fo:where h represents the Planck constant, t is time, v is frequency, ε is photon energy, E is laser pulse energy, and c is the velocity of light. The shock wave pressure F impacting the target was much larger than that of the light pressure Fo induced by wave-particle duality, so we consider Fo to be negligible.Fig. 6 (a) Driving force analysis while the PS particle was impact by shock wave. (b) The resultant and resistance dependent on energy fluence.
Resistance forces also play an important role in PS particle motion. The direction of resistance is opposite to the direction of shock wave propagation. The sources of resistance force include friction f = μmg and air resistance FA = KSv2 which is related to the area and movement speed of the PS particle, where K is a comprehensive coefficient, S is the effective area of the PS particle, and v is the moving speed of the PS particle. The resultant force FR = F-f-FA dominates the driving of the PS particle. Figure 6(b) shows the relationship between propelling and resistance forces during PS particle motion as a function of the energy fluence. The resultant force FR reaches a maximum value of 1.20 N at energy fluence of 0.645 J/cm2. Resistance gradually increased as energy fluence increased due to air resistance FA∝v2.
However, the pressure F produced by the shock wave expansion always greater than the sum of the resistance forces to propel the PS particle. Meanwhile, we also proved that the propulsion process in our setup was dominated by shock wave ejection mechanism. It’s worth noting that the center of the shock wave was not aligned with the center of the PS particle, which was regarded as the major reason that caused the offset of the PS particle during movement. The offset of the PS particle during movement proves the expansion shape of the shock wave indirectly, the spatial distribution (i.e., shape) of the shock wave is discussed below in greater detail.
We predicted shock wave expansion behavior by analyzing the PS particle swarm motion direction (Fig. 7(a)) as an indirect estimation method. We first ensured the output energy fluence was stabilized; then placed the PS particle swarm with an area approximate XY near the focal spot of the optics objective (Fig. 7(b)). Finally, we roughly estimated the shock wave expansion shape based on the PS particle swarm motion direction as captured by high-speed CCD camera. The PS particle swarm scattered after the impact of shock wave expansion (Fig. 7(c)). The shock wave expanded in a spherical shape, as previous researchers have similarly observed [26,28–31]. PS particles closer to the incoming laser direction had larger initial velocity, momentum, and kinetic energy than those in the direction perpendicular to the incoming laser. This was due to a large proportion of energy being deposited in the laser’s incoming path. This phenomenon may be utilized to flexibly manipulate micro particles by adjusting the position of the shock wave; it may also be applied to other disciplines such as particle screening and separation.
Fig. 7 (a) PS particle swarm motion driven by plasma (shock wave) generated by air breakdown. (b) and (c) Shock wave produced by plasma expansion pushes PS particle swarm forward.
5. Conclusion
In summary, we found that propulsion efficiency of PS particles to be crucially dependent on energy fluence and confined geometry. In addition, we effectively predicted shock wave expansion behavior by analyzing the PS particle swarm motion direction. The initial speed, movement distance, momentum, and kinetic energy of the PS particle monotonically increase with energy fluence when there is no confined geometry. The Cm value of the PS particle reaches its maximum at optimal energy fluence of 0.46 J/cm2. Particle propulsion efficiency was also enhanced under confined geometry conditions due to the shock wave reflections within said geometry having increased the force between the shock wave and the particle surface. The mv2/R5 ratio reaches its maximum at energy fluence of 0.46 J/cm2, at which point the most energy possible has transferred to the kinetic energy of PS particles. A similar phenomenon was observed as Cm reaches its limit with increasing energy fluence. We used our observations to roughly estimate the shock wave expansion shape as per the motion direction of the PS particle swarm. We hope that the results presented here may provide workable guidelines for the optimization of plasma propulsion schemes in the future.
Funding
National Key R&D Program of China (2016YFF0200700, 2017YFB0405502); National Natural Science Foundation (NSF) (61635007, 61605031, 11474072, 61775044).
Acknowledgment
The authors are thankful to the Key Lab of In-Fiber Integrated Optics, Harbin Engineering University for providing the research facilities to carry out the research work.
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