1. Introduction

When an intense femtosecond laser propagates in transparent media, the beam undergoes self-focusing [1,2]. The self-focusing beam initiated the plasma generation, as the laser intensity is higher than the ionization threshold of the media. Instantaneously, the plasma balances the self-focusing effect, resulting in a high-density plasma channel (1 × 10¹⁶ /cm³ in air) known as the filament [1,2]. The initiated position of the filament zone can be controlled remotely. It can self-sustain for a long distance probably into the km range [3–5]. Next, the plasma recombines back in a picosecond/nanosecond timescale [1,2,6]. Accompanied by the plasma relaxation, a series of nonlinear effects, such as fluorescence emission, chemical reaction, thermal release, shock wave, thermodynamic turbulence, etc., are subsequently generated [7–12], most of which last longer than plasmas in a submicrosecond timescale (shock wave) while the thermodynamic turbulence is even longer, with a timescale of tens of milliseconds [8–11]. During the past few years, femtosecond lasers have been proposed as another alternative and green technique for local weather modulation, e.g., laser-assisted rainmaking and lightning control [13–16].

In 2008, the European Teramobile group shot a 3.5-TW 10-Hz femtosecond laser into humid air both indoor and outdoor, and demonstrated a significant level of water condensation around the filament zone induced by the laser [13,17]. They proposed that besides the high-density plasmas, the by-products of filaments, mainly H₂O–HNO₃ and NH₄NO₃, were important for the triggering of water condensation as cloud condensation nuclei (CCN) [18,19]. In our previous studies, both laser-induced condensation and precipitation were demonstrated [20,21] by using 0.2-TW 1-kHz femtosecond laser pulses in a closed cloud chamber, in which a large temperature gradient was maintained. The thermodynamic airflow motion around the filaments resulting in supersaturation was found to induce precipitation or snow formation [22].

These previous works indicate that the ambitious concept of laser-based rainmaking might be promising in the future. However, for the long-distance filamentation and filamentation-induced water condensation for practical applications, a laser power of dozens of terawatt (TW) or even higher is required. Meanwhile, convincing evidences directly show that laser-induced condensation and precipitation in a time resolved way are sought after. In this work, using high peak power laser pulses of approximately 22 TW (660 mJ and 30 fs), but at a low repetition rate (1 Hz), condensation and precipitation in an open cloud chamber were observed directly in two different time zones, by following the evolution of thermodynamics after strong multiple filamentation.

2. Experimental setup and results

In the present experiment, a 200-TW 1-Hz (3 J, 30 fs, beam diameter of 80 mm) Ti:Sapphire laser, independently developed by the SIOM group, was employed as a pump laser [23]. The output laser power was chosen to be 660 mJ at 30 fs, or 22 TW, to avoid any damage to the output optical window. A lens (L₁) with f = 135 cm was used to initiate plasma channels immediately after the laser output. A reflective mirror (M₁) of 10 cm × 10 cm × 1 cm reflected the focusing beam into the middle of an open chamber. The size of the chamber was 50 cm × 50 cm × 20 cm, with three 10 cm × 10 cm openings. In order to avoid any damages by the reflected lights to the gratings inside the laser compression chamber, L₁ was tilted by a small angle. Therefore, a lens aberration was induced, causing the laser spot to be twisted from vertically elliptical before the geometric focal point (GFP) to round at the GFP and to horizontally elliptical after the GFP. As shown in the inset of Fig. 1(a), when the laser spot was still vertically elliptical before the GFP, a bundle of multiple filaments were generated, which were about 10 cm in length. A 2.0 W solid-state semiconductor green laser was used as a probe beam co-propagating with the femtosecond laser. In order to limit the illuminated area inside the depth of field of the camera as much as possible, the probe beam was expanded and truncated by a vertical slit with a size of 4.0 cm × 0.5 cm.

 

Fig. 1 (a) Experimental setup. (b) Particle density of aerosols created by the 22-TW femtosecond filaments. The top right inset was a typical particle size spectrum of aerosols generated by firing the 1-Hz laser for 5 min.

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Before cooling the cloud chamber, a particle sizer (SMPS3936, TSI) was used to measure the number density of aerosols formed in ambient air, under room temperature (T = 20 °C, relative humidity (RH) = 42%). The particle sizer measured aerosols with diameters in the range of 15–700 nm through up to 168 channels. The insulated inlet pipe of the particle sizer was set with its head ~2.0-cm away from the filaments. Aerosols were sampled every 5 min. As can be seen in Fig. 1(b), the number density of laser-induced aerosols increased sharply from a few hundred up to 2.25 × 10⁶ /cm³ during the first 5 min when the 1-Hz laser was fired, corresponding to an average density of ~7.5 × 10³ /cm³ aerosols formed per shot. The sizes of the new aerosols were typically in the range of 40–200 nm [top right inset of Fig. 1(b)]. The highest particle density, 9.0 × 10⁵ /cm³, was measured for aerosols with a size of 55 nm. These aerosols are believed to be composed mainly of chemicals produced in the filament zone, such as NH₄NO₃, HNO₃, and certain organic compounds [18,19]. It should also be noted that this particle density was comparable with that obtained by spreading AgI @30 nm into clouds in traditional rainmaking methods [24].

Then the open chamber was cooled at its metallic bottom plate (bottom at −45 ± 5 °C and top with an open water bath at room temperature). A measurement by a thermo-hygrometer showed that at approximately 1.0–2.0 cm above the cold plate, a cold zone with a temperature of approximately −5 ± 1 °C and an RH of ~87 ± 3% was formed. The laser was fired into this zone at a vertical height of 1.5 cm relative to the cold plate through an opening of the chamber. A high-speed camera (PCO, Dimax-HS4, monochrome) was installed in the side direction of the filaments [Fig. 1(a)]. Its image resolution was of 2000 × 2000 pixels per frame, corresponding to the maximum frame speed of 2000 fps (frame per second).

During the first period of 0.5 ms < t < 5.0 ms, the laser-induced shock/acoustic wave had decayed away and laser-induced chemicals and the thermal effect remained [10–12]. Figure 2 shows typical images around the filament before and after the arrival of the laser at t $\cong$ 500 μs. In the background [Fig. 2(a)], scattering droplets were already formed in this cold and humid region, due to the existence of background CCN. They distributed uniformly near the cold plate with an estimated size of 20 ± 10 μm [20]. Once the multiple filaments were lunched, in t < 500 μs, “cloud” droplets with an estimated size of 300–400 μm were observed along the filament zone [Fig. 2(b)]. The diameter of these newly formed particles was much larger than that of the background droplets and comparable with the critical diameter of rain droplets in nature (~200 μm) [25]. The generation of these “cloud” droplets was highly repeatable after each laser shot. Occasionally the precipitation process of these droplets was clearly visible [Fig. 2(c); droplets inside the dashed green circles with an arrow pointing toward the ground].

 

Fig. 2 (a) Background. (b–c) Water condensation/precipitation (some being indicated by green circles and arrows) around the filament zone (blue dashed lines) at t $\cong$ 500 μs and t $\cong$ 1.0 ms after the arrival of the laser pulse, respectively.

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Figure 3 shows the time evolution of water condensation around the filaments from 1.0 ms to 5.0 ms after the arrival of the laser pulse. These 300–400 μm large-size droplets, shown in Fig. 2(b), are indicated by solid green arrows in Fig. 3(a). They were located ~2–3 mm from the filament zone center. Apart from the one inside the filament zone, there was another bunch of small-size particles crowding together as a fine “cloud” line. Particles inside the “cloud” line were too small to be recognized by the high-speed camera. They were confined together, and after the large-size droplets vanished at t = 1.5 ms, they were still clearly distinct. However, from t = 1.5 ms to t = 3.5 ms their side scattered light intensity became gradually weaker [Figs. 3(c)-3(f)], and from t = 4 ms to t = 5 ms, the fine “cloud” line was difficult to be recognized by the high-speed camera any more [Figs. 3(g)–3(i)].

 

Fig. 3 (a–j) Time evolution of water condensation/precipitation around the filament zone from t = 1.0 ms to 5.0 ms after the arrival of the laser. Here, in all subsequent figures, the previous location of the multiple filaments is illustrated between two blue dashed lines. The motion of the “cloud” flow around the filament zone is indicated by the yellow dotted arrows.

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There was still another part of condensation as indicated by the yellow dotted arrows in Fig. 3. Unlike the horizontally distributed condensation particles, they distributed vertically relative to the laser axis and moved upward. When they passed through the filament zone, they pushed some of the stationary condensation particles (of both large- and small-size) away vertically.

The next period of activity was between 10 ms < t < 1.0 s when the thermal effect dominated [8,9,12]. As a reference, Fig. 4(a) shows the typical condensation and possible precipitation particles generated in 500 μs after the arrival of the laser pulse. At t = 10 ms, the condensation/precipitation particles around the horizontal filament zone completely disappeared, as shown in Fig. 4(b). Meanwhile, a vertically distributed turbulent “cloud” rose gradually [Figs. 4(c)–4(j)], and moved around the hot filament zone from all sides (indicated by the dotted yellow arrows in Figs. 4(b)–4(j)). Following the strong “cloud” flow, another part of large-size ice particles/droplets appeared and moved in an area slightly above the cold plate (T < −30 °C) at t = 20 ms [Fig. 4(c), the thick line inside the dashed green circles]. The estimated diameter of these particles was even greater than 400–500 μm. At t = 40 ms [Fig. 4(d)], these large-size particles moved further upward, and tangled intensely with other particles carried by the thermal airflow below the filament center. At t = 60 ms, a downdraft emerged below the filament zone [Fig. 4(e), yellow curved arrows below the filament zone]. Most of the large-size particles collided with moist airflow, and, while crashing into them, the direction of their movement changed downward [Fig. 4 and Visualization 1]. Some of these large-size particles coagulated together and formed to be even larger in size [Figs. 4(d) and 4(e), inside the green circles]. At t = 90 ms [Fig. 4(f)], the downdraft became much stronger. The number of the large-size particles inside the field of view decreased nearly to zero, but the “cloud” flow with small-size particles still moved energetically. At t = 120 ms [Fig. 4(g)], the downdraft had already formed a steady vortex motion below the filament zone (see Visualization 1), and most of the large-size particles with a diameter over 100 μm vanished [as shown by the pink arrow in Fig. 4(g) there were still some left]. The velocity of the “cloud” flow (mainly the part moving upwards) was determined by using the same method as given in Ref [13]. The flow “history” is shown in Fig. 4(m). The error bars are obtained from the difference of airflow velocity from different parts of the thermodynamic airflow motion. Figure 4(m) shows that at t = 120 ms, the velocity reached its maximum value of 45 ± 3 cm/s. The turbulence slowed down gradually for t > 120 ms, at t = 200 ms, the velocity decreased to about 15 ± 3 cm/s, and at t = 500 ms the velocity is almost zero. For t > 500 ms [Figs. 4(k) and 4(l)] the turbulence had calmed down. No large-size particles with diameter over 100 μm were captured for t > 120 ms, until the next laser pulse arrived.

 

Fig. 4 (a–l) Time evolution of laser-induced water condensation/precipitation (some being emphasized by green circles) at t = 0.5 ms–1.0 s after the arrival of the laser pulse (see Visualization 1). Typical large-size particles following the “cloud” flow are indicated by green circles or pink arrows.

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3. Discussion

We assumed that 50% of the laser energy (330 mJ) was deposited into the 10-cm-long filament zone [9] as thermal energy, and the thermal conductivity of humid air was assumed to be C = 0.0235 W·m⁻¹·K⁻¹ at −5 °C [26], in Δt = 500 μs, according to the conduction law ΔQ = −CS [(T_f-T_i)/d] Δt, where ΔQ = 33 mJ is the transferred heat, S is the mean surface area of the filament cylinder, T_f = 268 K is the final temperature, T_i = 1400 K is the initial temperature, and d is the diffusion distance [8,9]. The released thermal energy can spread to a distance of d ≅ 1.2 μm from the center of the filament zone, which is still inside the expanded filament zone. Considering binary chemicals, which were mainly composed of HNO₃/NH₄NO₃, their diffusion coefficient D was D = 0.0346 cm²/s (for HNO₃ gas diffusing at the temperature of −5 °C in air) [27]. In 500 μs, HNO₃ gases diffused only within a distance of ~30 nm from the filament center, which was much smaller than the initial filament diameter (~100 μm). Thus, in 500 μs, both thermal release and chemicals contained in the 7.5 × 10³ /cm³ (size of 15–700 nm)/pulse aerosols were supposed to be highly localized inside the filament zone. As each laser shot produced about 7.5 × 10³ /cm³ (size of 15–700 nm) aerosols [Fig. 1(b)] on average, containing ~70% in mass of NH₄NO₃ and HNO₃ [19], >> 0.7 ppm chemicals were produced by each laser shot. They adhered to water droplets around the filament zone and reduced the saturated vapor pressure near the droplet surface [28]. However, due to the high local density of laser-produced chemicals, solution droplets competed with each other equally for the intake of the vapor around. Therefore, numerous small-size particles/droplets might be condensed out owing to the high-density chemicals (>>0.7 ppm), as a fine “cloud” line accompanied by a narrow filament zone [Figs. 3(b)–3(f)] [20,21].

A shock wave, i.e. a strong air disturbance, was created in submicrosecond timescale [10–12]. It propagated cylindrically from the filament center at a supersonic speed and generating a shock pressure of 2–3 bar [8–12]. In approximately 100 ns, it was able to arrive at a position 2–3 mm away from the filament center, and the already existing droplets might be shattered into fragments under the huge instantaneous impact [29]. Meanwhile, the high shock pressure front can easily compress the surrounding moist air to be supersaturated [30]. The fragments, together with the supersaturated surrounding air increased the total collection of water molecules by the surrounding droplets. This would enhance the 300–400 μm particle/droplet formation outside the filament zone [Figs. 2(b) and 3(a)].

The radius of particles/droplets with diameters of 300–400 μm, is comparable with the initial radius of rain droplets in nature, which is about 200 μm. Furthermore, their lifetime under natural evaporation was calculated as 560–980 s (T = −5 °C, RH = 85%) [31,32], which was considerably longer than the 1.5-ms lifetime of existence in the screen. Thus the 300–400 μm particles/droplets settling 2–3 mm away from the filament zone were more likely to precipitate instead of being evaporated naturally, and the shock wave might be the sole reason for this type of precipitation. For droplets with a diameter of 800–900 nm, the evaporation time was about 4–5 ms (T = −5 °C, RH = 85%), which is comparable to the ~4.5 ms lifetime of the “cloudy” line in the screen [Figs. 3(h)–3(i)]. Although the size of particles inside the fine “cloud” line was too small to be determined, we expect it to be much smaller than 10 μm (the best spatial resolution of the high-speed camera), and natural evaporation might be the sole reason for their disappearance.

In the experiment of this study, a strong temperature gradient was preserved inside the open chamber near the cold plate (T = −45 ± 5 °C). When the energetic thermodynamic turbulence from the filament zone (T = −5 ± 1 °C, RH = 87 ± 3%) mixed with the cold moist air above the cold plate (T is approx.. −40–30 °C, RH = 90 ± 3%), supersaturated air with a saturation ratio of S = 1.38–2.05 can be maintained [22]. Condensation can occur efficiently inside the mixed air as the turbulence carrying binary chemicals (NH₄NO₃/HNO₃) was passing through the strong temperature gradient zone. This results in the appearance of a “cloud” flowing nearly perpendicularly to the laser axis (Fig. 3, yellow dotted arrows).

Some special particles with a size of ~400–500 μm [Figs. 4(b)–4(e)] emerged among the tiny particles carried by the thermal airflow motion at t = 20–120 ms after the arrival of the laser pulse. According to the Bigg’s relationship, the freezing temperature of heterogeneous nucleation droplets with a diameter larger than 100 μm, can be higher than −31 °C [33]. As the 400–500 μm particles appeared in an area slightly above the cold plate (T < −30 °C), where the temperature was lower than their freezing temperature, they are very likely to be frozen and formed ice particles. The ice nuclei (IN) near the cold plate, such as organic germs might be rolled into the supersaturated mixed air as well. However, for spherical ice/snow crystals growing into ice/snow particles with a diameter of 400 μm, it took more than 100 s under the surrounding temperature of −12 °C [27]. Therefore these 400–500 μm particles emerging at t ≅ 20 ms might be mainly from the phase transition of the effective condensed droplets, due to the sharp temperature gradient, rather than from background IN. Later, with the maximum probability, they followed the downdraft below the filament and precipitated [Figs. 4(d)–4(e)] (multimedia view) toward the cold plate.The particles/droplets with relatively small size might undergo another circular (vortex) motion [34], and continue to grow in size until they were sufficiently heavy to be spun out as precipitation, which demonstrates that the thermodynamic turbulence, especially the downdraft, is crucial to facilitating large-scale liquid/solid precipitation [20,21].

In practical applications, under an atmospheric environment, it is difficult to find a large temperature gradient in such a small domain. However, it is anticipated that by using TW-level lasers interacting with a cloud full of super-cold droplets, such as cirrus, shock wave and thermodynamic turbulence, filamentation might be able to create large-size droplets (diameter > 100 μm) at the first step, which are then frozen to large-size ice particles in the super-cooled surrounding environment (T < −30 °C). With continuous deposition of ice crystals/particles in a cloud of super-cold droplets, through the Wegener–Bergeron–Findeisen (WBF) process, artificial precipitation might be achieved. As in the present experiment, all possible precipitations apparently terminated at about t = 120 ms, thus we expect that by using the same laser pulses (22-TW 1-Hz at 800 nm) but with the pulse repetition rate of ~10 Hz interacting with a cloud full of super-cold droplets (T < −30 °C), a quasi-continuous deposition of large-size ice crystals (diameter > 100 μm) might be achievable by both the shock wave and thermodynamic turbulence of femtosecond filamentation.

4. Conclusion

A direct visualization of 22-TW multiple-filament-induced water condensation and precipitation was demonstrated in an open cloud chamber for the first time. After each laser shot, both the shock wave and thermodynamic turbulence were found to be able to induce precipitation on a submillisecond or dozens of millisecond timescale, respectively. When the environmental temperature T < −30 °C, condensed droplets with a diameter larger than 100 μm following the energetic thermodynamic turbulence can change their phase from liquid to ice crystals easier than the small-size droplets. By using a 10-Hz 22-TW or even higher-power laser system, continuous deposition of ice crystals might be able to induce locally artificial rain by a chain reaction through the Wegener-Bergeron-Findeisen (WBF) process.