1 Introduction

Since the launch of the first man-made earth satellite in October 1957, mankind has gone through 65 years of space development and obtained huge benefits, but also produced billions of space debris [1, 2]. Generally, the average speed of space debris is about 10 km/s, they mainly concentrate in low Earth orbit below 2000 km or geostationary earth orbit, and most of them circle around orbital altitudes of 800 km and 1500 km [3]. They are constantly moving around the earth at high speed, forming unique debris environment. Especially, small space debris with characteristic diameters of 1–10 cm formed in low-Earth orbit (LEO) is difficult to track, monitor and protect effectively. Due to the large kinetic energy of such debris, they have caused serious harm to the safe operation of space activities in LEO [4, 5]. At present, how to carry out active removal of small space debris with centimetre scale has become an important task for the international scientific and aerospace communities.

In recent years, a variety of small debris detectors have achieved in-orbit verification, and a large amount of detection data is obtained. However, there are a large number of small space debris in LEO [6]. How to effectively detect the velocity, mass, composition and flux of small debris is still a big challenge. At present, it mainly uses radars, telescopes, sensors and other equipment installed on spacecraft to conduct space-based detection of small debris. Utilizing the detected debris information, the corresponding debris orbit distribution model can be established to provide data for spacecraft structural protection design and debris avoidance. Now, SSN (US Space Surveillance Network) can observe space debris with a diameter greater than 5 cm in the LEO area, and the number of catalogued debris can be tracked exceeds 20,000. Europe's ESA (European Space Agency) system consists of an electromagnetic fence and four telescopes, and the number of tracked and catalogued debris exceeds 17,000. In fact, effectively improving the monitoring capabilities of space debris, especially centimetre sized debris, remains a focus of scientists' attention [7, 8].

Active removal of space debris includes contact and non-contact methods. Comparing the advantages and disadvantages of different removal technologies, the non-contact method has high feasibility and application prospect. The method has gained widespread attention since it was proposed in the early 1990s, and it is mainly divided into two cleaning methods: space-based laser and ground-based laser [9]. However, space-based platform can effectively avoid the influence of atmospheric transmission on laser beam quality, and the required laser energy will be greatly reduced compared with ground-based platform. Figure 1 showed the basic work principle of space-based pulsed lasers irradiating small space debris.

Fig. 1
figure 1

The basic work principle

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With the development of energy system, tracking and positioning, thermal control and management of space-based platform, the feasibility of space-based laser removal solutions has been further demonstrated. Hence, space-based pulsed lasers can be used to investigate the actively removal of small space debris. As an effective method to remove centimetre-level space debris, space-based pulsed lasers can be applied to deal with the debris for protecting spacecraft and space environment. The basic working principle mainly is to use the plasma expansion plumes effect formed during high-energy pulsed lasers irradiate the debris surface to drive the debris deorbit [10]. Namely, the plasma expansion plumes formed by irradiating the debris surface with high-energy lasers, then the debris gains reverse velocity increment under the action of impulse coupling, and the debris orbit is changed. Consequently, the semi-minor axis of the debris around the Earth will also be shorter. After repeated actions of positioning, irradiating and deorbit evaluating, the perigee altitude of the debris gradually is decreased until re-entry conditions are met.

From the point of view of laser-matter interaction, high-energy pulsed lasers irradiate the debris surface to form a plasma expansion plumes for debris removal. Mahmood et al. theoretically analysed the phenomenon of plasma expansion plumes under different environment pressures [11]. Zhu et al. discussed the impulse coupling effects of different mode pulsed lasers by measurement experiments, and investigated the plasma plumes properties under optimal impulse coupling conditions [12]. Phipps and Bonnal investigated laser parameter optimization, impulse evaluation and active deorbit for different debris materials, and believed that space-based laser method were the preferred scheme for debris removal [13]. Tsuno et al. developed an impulse measurement system based on a simple pendulum, and explored efficient constraint of plasma plumes to improve energy efficiency [14]. Munafò et al. established a computational model for nanosecond pulse laser-plasma interactions, and explained that optimal space debris removal efficiency was affected by many parameters [15]. Yang et al. demonstrated a methodology of active space debris removal using space-borne laser systems, and described the interaction process of plasma plumes between pulsed lasers and the debris [16]. May et al. calculated the collision probability of space debris for global broadband constellations by numerical simulation [17]. Zhou et al. discussed the ablation impulse irradiated by nanosecond laser with an Al planar and sphere debris in a large beam spot [18]. Lorbeer et al. also carried out experimental verification for the remote control of high-energy pulsed lasers irradiating space debris [19]. Lu et al. analysed the basic shape classification of space debris with light curves by simulation and experiments [20]. In addition, Fang preliminary explored the dynamic response rules of removing different area–mass ratio small space debris in LEO [21]. In general, scholars have made fruitful studies on the active removal of space debris, which also proved the great potential of laser ablation technology. However, the current research is in the stage of theoretical analysis and experimental verification, and there is still a big gap from practical engineering application. Especially, it is very necessary to further grasp the interaction rules between high-energy pulsed lasers and small space debris in LEO, so as to provide valuable scheme for establishing effectively removal method suitable for engineering application.

With the continuous increase of human spaceflight activities, the harm of small space debris in LEO is becoming increasingly serious to space security, and there is an urgent need to reveal the evolution rules of active removal for small space debris in LEO. In view of the large proportion of aluminium alloy materials in space debris, this article will focus on the evolution rules of plasma expansion plumes when pulsed lasers irradiating small aluminium alloy spherical debris in LEO by numerical calculation, and active deorbit process of the debris under different parameters will be deeply carried out by visual simulation. The results can provide efficient reference for related technical research and task design of clearance small space debris in LEO.

2 Theoretical analysis

The light energy is converted into heat energy when pulse laser beam irradiates on the surface of space debris. Under ideal conditions, assuming the laser spot is completely irradiated on the debris surface, laser spots are evenly distributed, and all the laser energy is absorbed. As the temperature of spot area reaches the vaporisation temperature of the debris, the plasma generated on the debris surface expands outward and flies away. The time from the beginning of laser irradiation to the time when the debris reaches the gasification temperature is called the gasification time, which the gasification time can be approximately expressed as [22]:

$$t \approx \frac{\pi }{4B}\left( \frac{KT}{I} \right)^2$$
(1)

where K denotes the thermal conductivity, T denotes the gasification temperature, I denotes the power density of incident laser, B denotes the thermal diffusivity, and t denotes the gasification time. For aluminium alloy materials, the density is 2.7 g/cm3, the thermal diffusivity is 0.85cm2/s, the thermal conductivity is 2.38W/cm·K, the gasification temperature is 2739 K, and the absorptivity is 0.248, respectively [23].

At the same time, the laser power density has a great influence on the impulse coupling, and the expression of power density during space-based laser transmission is given [24].

$$I = \frac{4E}{{\pi \tau }}\left( {\frac{\lambda L}{{\pi d}} + D} \right)^{ - 2}$$
(2)

where E denotes the single pulse laser energy, d denotes the laser light waist, L denotes the laser transmission distance, D denotes the laser output aperture, λ denotes the laser wavelength, and τ denotes the laser pulse width.

Nanosecond pulse width lasers can generate higher ablation efficiency and laser peak power, and plasma expansion plumes can be obtained effectively. Many experimental measurements were done in the United States from the 1960s to the 1990s, and related theoretical and experimental studies were also carried out in References [25, 26]. The results shown that based on the condition of given pulse width, the laser pulse width needed to reach nanosecond (10−9 s) in order to achieve the optimal power density. Namely, the optimal power density satisfied the below relation [22]:

$$I_{\max } \approx \frac{8.5 \times 10^4 }{{\sqrt {\tau } }}$$
(3)

When pulsed lasers irradiate space debris, two basic physical processes including laser ablation and plasma plumes will be undergone. For debris materials of aluminium alloy, the peak power density of 108 W/cm2 is the threshold from vaporisation to isoionization. When the peak power density ranges from 108 to 1010 W/cm2, the plasma mechanism is again dominant.

From the perspective of debris removal, the amount of impulse that can be obtained per unit area of the debris is very critical. The relevant research results indicate that if the laser pulse width is too short, it is difficult to achieve high-energy output when pulsed lasers irradiating the debris. That is how to make full use of the interaction effect of plasma, vapour, and condensed matter to improve the impulse coupling coefficient also needs to be comprehensively considered. In order to promote the energy utilisation and impulse coupling coefficient of the debris, the laser pulse width should not be too small, and a large laser pulse width within a certain range is necessary for the debris removal efficiently.

After the impulse coupling effect of driving the debris is evolved, the expression of impulse coupling coefficient between the vapour and the debris is given as follows:

$$C_m = \frac{{P\left( {\tau - t} \right)}}{I\tau }$$
(4)

where Cm denotes the impulse coupling coefficient, and P denotes the vapour pressure on the gasification surface.

According to the above analysis, the optimal impulse coupling coefficient between the vapour and the debris can be obtained by substituting Eqs. (1) and (3) into Eq. (4).

$$C^{\prime}_m \approx \frac{{P\sqrt {\tau } }}{8.5 \times 10^4 }\left[ {1 - \frac{\pi }{4B}\left( {\frac{KT}{{8.5 \times 10^4 }}} \right)^2 } \right]$$
(5)

In fact, the impulse coupling process between plasma and incident laser has obvious nonlinear relationship. Based on the best coupling conditions, the variation range of optimal impulse coupling coefficient is about (5.5 ± 2) × 10−5N·s·J−1 for aluminium alloy materials [27]. In this article, the value of impulse coupling coefficient is 6.5 × 10−5N·s·J−1.

Supposing the debris mass remains unchanged before and after laser irradiation. When laser spot is completely irradiated on the debris surface, the optimal velocity increment of the debris is given by combining Eq. (5).

$$\Delta v_{\max } = \frac{{C^{\prime}_m Ik \cdot J}}{m}$$
(6)

where Δvmax denotes the velocity increment obtained by the debris, k denotes the irradiation direction of incident laser, and J denotes the second-order area matrix of the debris.

Based on the Eqs. (5) and (6), the number of laser pulses needed for the debris deceleration is given:

$$n = \frac{{m\Delta v_{\max } }}{{8.5 \times 10^4 C^{\prime}_m A\sqrt {\tau } }}$$
(7)

where n denotes the number of laser pulses, and A denotes the size of laser spot.

The increment of perigee altitude for the debris can be deduced according to the relevant literature [28, 29].

$$\Delta r_p = \left( {1 - e_{\,} } \right)\Delta a - a\Delta e$$
(8)

where e denotes the orbital eccentricity ratio of the debris, Δe denotes the increment of orbital eccentricity ratio, a denotes the orbital semi-major axis of the debris, and Δa denotes the increment of the debris orbital semi-major axis.

3 Simulation model

This section focussed on the process of simulation modelling when pulsed lasers irradiating a small space debris. The geometric shapes of space debris include plate, block, rod and sheet, but most of them are irregular. In this article, a spherical aluminium alloy debris with diameter 2cm was applied to reveal the evolution behaviours of plasma expansion plumes and active deorbit rules, and the main simulated parameters were given in Table 1.

Table 1 The main simulated parameters
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When the incident laser illuminated the debris surface vertically, a geometric model of sphere debris irradiated by pulsed lasers was established, as shown in Fig. 2. In the model, assuming the debris was uniform and isotropic, and the change of viscous resistance during laser action was also ignored.

Fig. 2
figure 2

The three-dimensional geometric model

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Based on the geometric model in Fig. 2, the following established the three-dimensional simulated model for the sphere debris. In the process of simulation calculation, mesh generation is very important for model solution. Finally, the simulated model was established by finite element method (FEM) as shown in Fig. 3.

Fig. 3
figure 3

The three-dimensional simulated model

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For the model in Fig. 3, the tetrahedral elements were applied to calculate the region of vacuum environment, and the prismatic elements were used to the region of debris surface in order to improve the calculation accuracy. As a result, a total of 199,294 tetrahedral elements and 3712 prismatic elements were divided during numerical calculation, and the other grid parameters of the model also were given in the Table 2.

Table 2 The other grid parameters of the model
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Based on the above simulated model, the following developed the simulation platform of space debris irradiated by pulsed lasers, and investigated the interaction process when pulsed lasers irradiating the debris. Due to the advantages of COMSOL in dealing with the coupling problem of multiple physical fields, the interaction physical process of space debris irradiated by pulsed lasers was simulated based on the COMSOL platform. In consequence, a simulation platform of computing plasma expansion plumes was built by COMSOL. The whole platform included three parts: the module developer, parameter setter and calculation processor. As a result, the evolution behaviours of plasma expansion plumes during pulsed lasers irradiated space debris could be analysed efficiently.

4 Results and discussion

According to the current technological development, for large-scale debris with characteristic diameter greater than 10 cm, the spacecraft can be protected by means of orbital manoeuvre. However, it also has considerable kinetic energy for small space debris of about 1–10 cm. This debris is not easy to track and is on active avoidance for a long time, and the cost of installing protective devices is too high. Therefore, it is feasible to use laser irradiation technology for active removal. By numerical calculation and visual simulation, active removal irradiated by pulsed lasers with small space debris in LEO was systematically investigated in this section.

First, the evolution process of plasma expansion plumes formed on the debris under different incident laser powers and action times was analysed in detail. Based on the given parameters in Table 1, whilst the action time was 5 μs, 25 μs and 45 μs, respectively, the evolutionary processes of plasma expansion plumes were simulated when the incident laser powers were 700 kW, 800 kW and 900 kW. Based on the simulation platform, the evolution plots of plasma expansion plumes formed by pulsed lasers irradiating the debris were obtained for different incident laser powers and action times as shown in Fig. 4.

Fig. 4
figure 4

The evolution plots of plasma expansion plumes; a 700 kW, b 800 kW, c 900 kW

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In Fig. 4, the red part represented the plasma region of high temperature and high pressure, most of which were close to the debris surface with the rapid expansion of plasma plumes. The simulated results indicated that the plasma formed after pulsed lasers irradiated the debris was sprayed outwards, the whole plumes area was distributed outward from the centre of the plasma plumes. With the increase of action times and incident laser powers, the plasma continued to expand outward in a mushroom cloud shape.

In particular, by comparing the simulation results in Fig. 4a–c, the velocity of plasma expansion plumes was increased along the laser incident direction, and the plasma expansion plumes were also continued to outwards spread. Then, the speed gradually decreased and tended to be stable owing to the shielding effect of plasma expansion plumes. In addition, by observing the formation and distribution of the plasma plumes, it was found that the high-temperature and high-pressure plasma plumes were concentrated on the debris surface after the end of pulsed lasers irradiation, but the plasma plumes would not survive for a long time due to the surface charging and generation of a Debye sheath. At this time, the pressure of the debris surface was larger, and the recoil impulse formed on the debris was also larger. However, the plasma gradually separated from the debris surface and the density also slowly decreased with the continuous increase of irradiation time. Finally, the recoil impulse of the debris was tardily decreased.

On the basis of the above analysis, the velocity of plasma expansion plumes formed on the debris was also discussed based on different laser parameters. Finally, the variation rules of plasma expansion plumes velocity were obtained for different action times and incident laser powers, and Fig. 5 showed the velocity variation curves of plasma expansion plumes.

Fig. 5
figure 5

The velocity variation curves of plasma expansion plumes

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According to the results in Fig. 5, the increasing trend of plasma plumes speed was very obvious within a certain irradiation times. Especially, when the incident laser power was 700 kW, the plasma expansion plumes reached maximum velocity at the moment of 23 μs, and the maximum value was close to 1.96 km/s. When the incident laser power was 800 kW, the maximum velocity of plasma expansion plumes attained 2.17 km/s at the moment of 22 μs. When the incident laser power was 900 kW, the maximum velocity of plasma expansion plumes achieved 2.36 km/s at the moment of 21 μs. Hence, the optimised laser parameters are very important for improving the flow characteristics and velocity control of plasma expansion plumes.

Furthermore, in order to explore the evolution characteristics of plasma expansion plumes with thermal effects, the temperature changes on the debris surface under different incident laser powers were also discussed. When the incident laser power was 700 kW, 800 kW and 900 kW, respectively, the evolutionary processes of temperature changes on the debris surface were calculated by numerical simulations. Finally, the evolution characteristics of temperature fields on the debris surface with different action times were obtained for different incident laser powers, and Fig. 6 emerged the evolution diagrams of temperature fields on the debris surface whilst the action time was 5 μs, 25 μs and 45 μs, respectively.

Fig. 6
figure 6

The temperature fields on the debris surface at different action times; a 700 kW, b 800 kW, c 900 kW

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According to Fig. 6, the plasma formed by the ablation of the debris was sprayed outward when pulsed lasers irradiated the debris, and the gasification face moved into the debris. Due to the effects of fluid dynamic pressure and electronic thermal conduction, the pressure and temperature of the medium in front of the ablation surface underwent a jump process, which driven a strong shock wave to propagate towards the undisturbed medium. Under the action of high-energy pulsed lasers, the debris absorbed most of the laser energy, and the high temperature and high pressure plasma expansion plumes marked in red was mainly concentrated on the debris surface. As a result, the maximum plumes temperature occurred near the debris surface. Further, by observing the results of Fig. 6a–c, the plasma plumes expanded and did external work with the passage of time, the spatial scale of the plasma expansion plumes was increased rapidly, but the temperature of the plasma expansion plumes was gradually decreased. In the meantime, it was found that the temperature of the debris surface was gradually increased, and the time to arrive at the maximum temperature on the debris surface was also advanced with the increase of the incident laser powers. Especially, when the incident laser power was 700 kW, 800 kW and 900 kW, respectively, the temperature of the debris surface reached a maximum at time 45 μs, which was 7240 K, 8230 K and 9230 K.

Second, based on the orbital dynamics theory and Eqs. (7) and (8), the variation process of the debris orbital semi-major axis with the number of laser pulses was described when the incident laser power was 700 kW, 800 kW and 900 kW, respectively. Eventually, the corresponding variation curves of the debris orbital semi-major axis with the number of laser pulses were obtained as shown in Fig. 7.

Fig. 7
figure 7

The curves of orbital semi-major axis of the debris with the number of laser pulses

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According to the results in Fig. 7, the debris orbital semi-major axis was increased with the increase of the number of laser pulses. Particularly, when the incident laser power was 700kW, the change of the debris orbital semi-major axis reached the maximum. Namely, the maximum increment of the debris orbital semi-major axis was close to 416km whilst the number of laser pulses was 663. When the incident laser power was 800kW, the maximum increment of the debris orbital semi-major axis approached 500km whilst the number of laser pulses was 602. When the incident laser power was 900kW, the maximum increment of the debris orbital semi-major axis approximated 627km whilst the number of laser pulses only was 466. Therefore, it was shown that power 900 kW had an advantage over 700 kW and 800 kW to change the orbital altitude of the debris in the irradiation process of pulsed lasers.

In the meantime, the variation rule of irradiation distance with operation time based on different space-based platforms was carried out. Assuming that the right ascension of ascending node (RAAN) of the debris was 00, and the RAAN of the space-based platform was -1.5° and -4.0°, respectively. As a result, the curves of irradiation distance with operation time were obtained when the incident laser power was 900 kW, as shown in Fig. 8. According to Fig. 8, When the RAAN of the debris was different from the RAAN of the space-based platform, the irradiation distance of the debris emerged significantly downward trend with the increase of operation time. The smaller the RAAN difference between the space-based platform and the debris orbital plane, the less time required for debris removal. Especially, for the space-based platforms with RAAN of − 1.5° and − 4.0°, the debris appeared within the maximum irradiation range of pulsed lasers when the operation time was 1133 s and 1451 s, respectively.

Fig. 8
figure 8

The curves of irradiation distance with operation time

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Further, deorbit process of the debris under non-coplanar condition was demonstrated by numerical calculation. Considering the cost-effectiveness ratio of laser active removal of space debris, the threshold of the perigee altitude of the debris below 200 km has a higher cost-effectiveness ratio. Therefore, 200 km was selected as the criterion condition of debris active deorbit. Assuming that the orbital altitude of the debris was 900 km, the RAAN of space-based platform was − 1.5°, and the incident laser power was 900kW. As a result, the perigee altitude of the debris achieved about 198.4 km by five times passes, and the number of laser pulses reached 862. i.e. the perigee altitude of the debris satisfied the deorbit condition after the fifth time pass, and the active removal process of the debris was realised. Table 3 showed the main orbit elements of the debris after five times passes.

Table 3 The main orbit elements of the debris
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According to Table 3, the perigee altitude of the debris was decreased from 256 km to 198.4 km by five times deorbit processes. That is, the debris entered the space of perigee altitude below 200 km. Finally, the debris gradually entered the atmosphere and burned up, and the purpose of active removal was achieved.

In order to more intuitively describe the orbital manoeuvring of the debris, the following displayed the evolution process of debris deorbit by visual simulation. The visual analysis mainly used STK/Matlab to establish a three-dimensional visualisation scene of debris deorbit, and displayed the whole process of the debris irradiated by space-based pulsed lasers. In the process of visual simulation, active deorbit of the debris mainly included four key phases: track, capture, irradiation and removal. When the pass condition agreed with the laser irradiation range, the orbital manoeuvre process of the debris could be implemented effectively, and Fig. 9 emerged the interaction relationship between space-based pulsed lasers and the debris. In Fig. 9, the blue line represented the debris orbit, and the red line represented the orbit of space-based pulsed lasers platform.

Fig. 9
figure 9

The interaction relationship between pulsed lasers and the debris

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Finally, the interaction process between space-based pulsed lasers and the debris was simulated by five times passes. Figure 10 shown the part images in the process of space-based pulsed lasers irradiating the debris.

Fig. 10
figure 10

The part images in the process of laser pulses irradiating the debris; a phase 1: track, b phase 2: capture, c phase 3: irradiation, d phase 4: removal

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According to the calculated results and three-dimensional running tracks in Fig. 10, when space-based pulsed lasers and the debris were in the same area at the same time, the debris met pass condition of pulse laser irradiation, and the debris was successfully removed after five times passes based on the given parameters. In particular, Fig. 10a denoted a certain position of the debris and laser station in tracking stage, and the debris was identified and tracked at this phase. Figure 10b expressed a scenario where the debris was captured, and the debris reached the working area of the space-based pulsed lasers station at this phase. Figure 10c shows the scene where the debris was irradiated by space-based pulsed lasers station, and the action condition between the debris and the laser was satisfied at this phase. Figure 10d indicates a picture of the debris being removed by dense atmosphere, and the task of debris removal was executed at this phase. In summary, when the orbital semi-major axis and the eccentricity of the debris were 9032.3 km and 0.326, respectively, the perigee altitude of the debris was closed to 198.4 km by five times pulsed lasers irradiation, and the total number of laser pulses reached 862. Therefore, the results showed that the effects of visual simulation were consistent with the results of numerical calculation.

5 Conclusions

Due to intensive development in LEO, there is an important motivation to develop suitable strategies for proactive debris removal. Through numerical calculation and visual simulation, a spherical space debris was applied to systematically address the plasma expansion plumes and active deorbit, and the following conclusions were drawn:

  1. (1)

    The evolution process of plasma expansion plumes formed on the debris was simulated based on different incident laser powers and action times, and the velocity change of plasma expansion plumes formed on the debris was also calculated by numerical calculation. Results showed that the whole area of plasma expansion plumes was distributed outward from the centre of the plasma plumes, and the plasma was sprayed outwards in a mushroom cloud shape with the increase of action times and incident laser powers. At the same time, the plasma plume speed increased within a certain irradiation times with the increase of incident laser powers, and the maximum velocity appeared around 21 μs and reached 2.36km/s when the incident laser power was 900 kW. By exploring the evolution characteristics of plasma expansion plumes with thermal effects, preliminary results showed that the spatial scale of the plasma expansion plumes was rapidly increased, but the temperature of the plasma expansion plumes was gradually decreased with the increase in incident laser powers and action times. As a result, the maximum plume temperature occurred near the debris surface, and the highest temperature on the debris surface reached maximum value of 9230 K at time 45 μs and power 900 kW.

  2. (2)

    The influence rules of the debris orbital semi-major axis with the number of laser pulses were discussed for different incident laser powers, and the variation rules of irradiation distance with operation time were explored for different space-based platforms by numerical calculation. Results indicated that the orbital semi-major axis of the debris was increased with the increase of the number of laser pulses. When the number of laser pulses was 466 and the incident laser power was 900 kW, the maximum increment of the debris orbital semi-major axis achieved 627km. Moreover, the smaller the RAAN difference between the space-based platform and the debris orbital plane, the less time required for debris removal. For the RAAN of -1.5° and -4.0°, the debris appeared within the maximum irradiation range of pulsed lasers when the operation times were 1133 s and 1451 s, respectively.

  3. (3)

    Based on the non-coplanar condition, active deorbit process of the debris was demonstrated by visual simulation, and the results validated that the effects of visual simulation were consistent with the results of numerical calculation. Especially, the perigee altitude of the debris was decreased from 256 km to 198.4 km by five times of passes, and 862 laser pulses completed active removal according to the given parameters. Thus, the results further clarified that the use of high-energy pulsed lasers was an important way to remove small space debris in the future.

  4. (4)

    Optimised laser parameters were essential for improving the flow characteristics and velocity control of plasma expansion plumes. However, in order to establish reasonable and efficient engineering application of laser removal method, it is still necessary to further grasp the interaction rules between high-energy pulsed lasers and space debris under different parameters. These basic tasks mainly include technical issues, such as plasma plumes measurement, active control of space debris, multi-parameter optimization of space-based platform laser, etc. Effective implementation of this work can lay excellent foundation for further engineering application of space debris removal technology.