1. Introduction

2. Methods

Figure 1. Scheme of repetitively pulsed laser irradiation of space debris by a high energy laser ground station for perigee lowering by (a) head-on momentum and, alternatively, (b) outward momentum.

Figure 1. Scheme of repetitively pulsed laser irradiation of space debris by a high energy laser ground station for perigee lowering by (a) head-on momentum and, alternatively, (b) outward momentum.

2.2 Laser-Matter Interaction

For the computation of laser-based orbit modification we employ the commonly used momentum coupling coefficient $c_m$

$$c_m=∆p/E_{\mathrm{inc}}$$

(6)

where $∆p$ is the momentum change of the target due to recoil obtained from the ablation jet and $E_{\mathrm{inc}}$ is the laser pulse energy that hits the target.

Though the predominant fraction of laser-induced heat leaves the target with the plasma jet formed by heated surface material, a residual amount of heat remains in the heat affected zone below the ablated material and dissipates into the bulk. This phenomenon can be quantified using the residual heat coefficient ${\eta }_{res}$ by

$${\eta }_{res}=∆Q/E_{\mathrm{inc}}$$

(7)

where $\mathsf{\Delta }Q$ is the amount of residual heat in the target.

These coefficients of thermal and mechanical coupling, $c_m$ and ${\eta }_{res}$, are material-specific and depend on laser parameters such as wavelength $\lambda$ and pulse duration $\tau$. Moreover, both figures of merit show a strongly non-linear behavior regarding their dependency on the incident laser fluence $\mathsf{\Phi }$, which should be considered for a realistic simulation of a laser-based orbit modification maneuver. Taking this into account we use a parametric fit function of $c_m\left(\mathsf{\Phi }\right)$ based on experimental data for aluminum and stainless steel as relevant target materials [26]. The pronounced dependency of $c_m$ from the incident laser fluence $\mathsf{\Phi }$ can be seen from the respective data shown in Figure 2(a). Experimental data from [27] has been extracted using Image-J and an empirical fit function has been applied. The corresponding fit parameters, cf. [28], serve as input for momentum coupling computation in the raytracing simulations of laser-matter interaction described below.

Figure 2. (a) Momentum coupling as a function of incident fluence of a laser pulse with $\tau =5$ ns pulse duration at $\lambda =1064$ nm wavelength, which is close to the wavelength of our laser configuration (1030 nm). Experimental data from [27] and own simulation results for aluminum, stainless steel, and iron are shown together with corresponding data fits using the empirical fit function for $c_m\left(\mathsf{\Phi }\right)$ derived in [29]. (b) Results from finite-elements-method (FEM) simulations on thermal coupling in laser ablation of aluminum and iron, respectively, for these laser parameters.

Figure 2. (a) Momentum coupling as a function of incident fluence of a laser pulse with $\tau =5$ ns pulse duration at $\lambda =1064$ nm wavelength, which is close to the wavelength of our laser configuration (1030 nm). Experimental data from [27] and own simulation results for aluminum, stainless steel, and iron are shown together with corresponding data fits using the empirical fit function for $c_m\left(\mathsf{\Phi }\right)$ derived in [29]. (b) Results from finite-elements-method (FEM) simulations on thermal coupling in laser ablation of aluminum and iron, respectively, for these laser parameters.

Beyond momentum coupling, laser-induced heat from repetitive laser ablation is of interest regarding possible limitations of laser-based removal. However, corresponding experimental data for the residual heat coefficient ${\eta }_{res}$ was not available for the experiments described in [27]. Instead, we have used results from our own simulations of the laser ablation process, implemented in the commercial finite-elements-method (FEM) software COMSOL Multiphysics^® version 6.1, employing a modeling approach which has been developed in [30], and extended in further research. It comprises laser-induced heat transfer, evaporation cooling, material ablation, Knudsen layer formation, ablation plume gas dynamics, and plasma shielding.

As a preliminary validation for the scope of this work respective simulation results for the same laser parameters as from the experiments [27] are shown in Figure 2(a) (hollow symbols, dotted fit). Basically, there are still some discrepancies between experimental data and simulation results: Results for the ablation threshold of aluminum differ by a factor of two. Nevertheless, we deem this acceptable for our purposes, since experimental data from the literature, however, scatters as well significantly: While for aluminum we find ${\mathsf{\Phi }}_0=1.1$ J/cm² at $\tau =5$ ns [27], $3.2$ J/cm² at $6$ ns [31], and $1.5$ J/cm² at $8$ ns [32], the scatter with stainless steel is even larger exhibiting ${\mathsf{\Phi }}_0=1.7$ J/cm² at $\tau =$ $5$ ns [27], ${\mathsf{\Phi }}_0=7.3$ J/cm² at $\tau =6$ ns [31], and ${\mathsf{\Phi }}_0=0.8$ J/cm² at $\tau =10$ ns [33] whereas one would actually expect ${\mathsf{\Phi }}_0\propto \sqrt{\tau }$ [31].

Moreover, the decrease of $c_m$ due to plasma shielding is predicted at higher fluences (not shown) in the simulations than reported from the experiment. While there is still space for improvement of the simulation regards matching with experimental data, the overall rather good agreement of $c_m$ data between simulation and experiment in the relevant fluence range makes it appear reasonable to use empirical fits of simulation data of ${\eta }_{res}$, cf. Figure 2(b), for this study in order to derive a first estimate on thermal limitations in laser-based removal of space debris.

2.3 Space Debris Simulation Targets

Figure 3. Axis ratios of debris simulation targets. Dimensions X, Y, and Z are defined according to the method of shadow dimensions as described in [34].

Figure 3. Axis ratios of debris simulation targets. Dimensions X, Y, and Z are defined according to the method of shadow dimensions as described in [34].

For our simulations we have chosen four different categories of catalogued debris objects: (i) 1,000 fragments from explosions and collisions with a mass ranging from 1 kg to 50 kg, (ii) 100 medium-sized payloads from 50 kg to 1,000 kg, (iii) a representative selection of 10 large-risk rocket bodies with high priority for ADR according to [35] exhibiting a mass between 1,000 kg and 10,000 kg, and (iv) Envisat, as well listed as high-risk object in [35], which is the largest known debris satellite in LEO. Fragments and medium-sized payloads have been selected from a larger debris population in LEO as of 2 July 2019 comprising objects at mean altitudes between 579 and 1179 km with an orbital eccentricity up to 0.2 and an orbit inclination between 65° and 110°. Orbital data had been retrieved from the catalogue of the United States Strategic Command (USSTRATCOM) [44]. Data on mass and geometry have been provided from the Database and Information System Characterizing Objects in Space (DISCOS) of the European Space Agency (ESA) [43], in particular allowing us for deriving geometric primitives for our simulations, cf. [22] for a description in greater detail. The scatterplot of the geometric axis ratios in Figure 3 underlines the great variety of the investigated debris objects.

Aluminum is attributed as surface material to the 101 payloads while rocket bodies are assumed to consist of stainless steel at their outer shell. Correspondingly, steel is assumed as material of the 287 rocket fragments whereas the remaining 713 payload fragments, among which 342 have arisen from tests of kinetic anti-satellite weapons (ASAT tests), aluminum is selected as simulation material for laser-matter interaction.

3. Results

3.1. Laser irradiation settings

3.1.1 Laser Fluence

Figure 4. (a) Mean fluence in the low Earth orbit (LEO) from a ground-based laser station using coherent coupling of 5,000 laser emitters at 20 J pulse energy each. Laser wavelength $\lambda$ is $1030$ nm, transmitter aperture: $D_{\mathrm{T}}=4$ m. Turbulence compensation is employed using a laser guide star and phase control. (b) Occurrence of the selected 1,111 debris objects.

Figure 4. (a) Mean fluence in the low Earth orbit (LEO) from a ground-based laser station using coherent coupling of 5,000 laser emitters at 20 J pulse energy each. Laser wavelength $\lambda$ is $1030$ nm, transmitter aperture: $D_{\mathrm{T}}=4$ m. Turbulence compensation is employed using a laser guide star and phase control. (b) Occurrence of the selected 1,111 debris objects.

It can be seen from Figure 4 that with our approach for turbulence compensation the threshold fluences for laser ablation of aluminum and steel, which are at 1 to 2 J/cm², corresponding to a beam diameter of 2 – 3 meters, cf. Figure 2(a), can be exceeded at any orbit altitude considered in our study sufficiently well. In particular for the highly frequented altitudes around 800 – 1,000 km, optimum momentum coupling, occurring around 3 to 7 J/cm², equivalent to beam diameters down to 1 meter, can be achieved for a wide range of beam pointing zenith angles. At higher altitudes certain restrictions exist for large zenith angles due to the great distance to the target and the correspondingly decreasing focusability of the beam, while at lower altitudes the momentum coupling coefficient even decreases for small zenith angles due to the high fluences where plasma shielding starts to occur. Most likely, however, this would not give reason for defocusing the beam, since the overall imparted momentum would still increase nearly proportional with the incident laser energy since $∆p=c_m·E_{\mathrm{inc}}$ and, in general, the effective fluence on the surface might be lower due to oblique beam incidence.

3.1.2. Irradiation Interval

The efficiency of momentum generation strongly depends on the irradiation geometry during the station pass of the debris target. For head-on momentum, irradiation under low elevation angles is more beneficial than at small zenith angles regarding the in-track projection $∆p_t$ of the imparted momentum component, cf. Figure 5(a). However, as can be seen from Eq. 1, beam transmission constraints in principle lead to a larger spot size at greater distances between laser and target, which is the case at low elevation angles. In turn, the risk of energy losses by outshining the target increases, moreover, the fluence is significantly lower than at zenith. Hence, obtaining the maximum in-track momentum comes as a trade-off between momentum projection and laser spot size while radial momentum approaches its maximum for small zenith angles for both geometric as well as beam propagation reasons, cf. Figure 5(b).

Figure 5. Aspects of momentum changes in laser-based orbit modification for two debris target examples: (a) in-track (cos β) and radial (sin β) projection of momentum and laser fluence corresponding to the respective distance between laser and target, (b) imparted in-track and radial momentum per laser pulse. Dotted lines indicate Gaussian fit functions of the imparted momentum, see text.

Figure 5. Aspects of momentum changes in laser-based orbit modification for two debris target examples: (a) in-track (cos β) and radial (sin β) projection of momentum and laser fluence corresponding to the respective distance between laser and target, (b) imparted in-track and radial momentum per laser pulse. Dotted lines indicate Gaussian fit functions of the imparted momentum, see text.

Table 1. Fit parameters for determination of the optimum laser irradiation interval of space debris using a pulsed laser at $\lambda =1030$ nm, $\tau =5$ ns and $E_{\mathrm{L}}=100$ kJ. Note that due to the strong non-linearity of $c_m$ removal laser stations with deviating laser parameters or other power beaming performance likely demand for different settings of the irradiation interval.

Table 1. Fit parameters for determination of the optimum laser irradiation interval of space debris using a pulsed laser at $\lambda =1030$ nm, $\tau =5$ ns and $E_{\mathrm{L}}=100$ kJ. Note that due to the strong non-linearity of $c_m$ removal laser stations with deviating laser parameters or other power beaming performance likely demand for different settings of the irradiation interval.

Category	${\mathit{y}}_1\left[°\right]$	${\mathit{m}}_1\left[°/\mathit{k}\mathit{m}\right]$	${\mathit{y}}_2\left[°\right]$	${\mathit{m}}_2\left[°/\mathit{k}\mathit{m}\right]$	${\mathit{y}}_3\left[°\right]$	${\mathit{m}}_3\left[°/\mathit{k}\mathit{m}\right]$
Payload	59.9	-0.0145	17.4	-0.0052	41.1	-0.0105
Rocket Body	68.7	-0.0253	22.9	-0.0099	54.2	-0.0237
Payload fragment	55.7	-0.0113	13.1	-0.0024	34.6	-0.0056
Rocket fragment	57.0	-0.0158	14.9	-0.0046	36.5	-0.0092

Considering the risk of overheating the target, a restriction of the irradiation interval appears to be reasonable in order to avoid laser heating at fluences where the outcome in terms of momentum transfer is rather low. Hence, the magnitude of momentum transfer has been analyzed for the simulated targets at their different altitudes, and a Gaussian has been fitted to the data of momentum as a function of the zenith angle for each target’s pass, cf. Figure 5(b). The related fit parameters show a clear dependency on the orbit altitude, which makes sense from a geometric viewpoint. From the full width half maximum (FWHM) of the Gaussian fit functions, averaged among the different target categories, we have determined the laser irradiation interval by the parameters shown in Table 1. They allow to derive the optimum onset angle ${\zeta }_{\mathrm{in}}=y_1+m_1·h$ and termination angle ${\zeta }_{\mathrm{out}}=$ $y_2+m_2·h$ for head-on irradiation from the object’s orbital altitude $h$. For outward irradiation, a symmetric interval is chosen, i.e., ${\zeta }_{\mathrm{in}}=-{\zeta }_{\mathrm{out}}=y_3+m_3·h$.

3.1.3 Laser Pulse Repetition Rate

As a starting point for our analysis of orbit modification within a single station transit we have selected a laser pulse repetition rate of $f_{\mathrm{rep}}=100$ Hz during the irradiation interval specified in Table 1. However, the resulting number of laser pulses will presumably be too high in terms of laser-induced heat which could endanger the target’s mechanical integrity eventually worsening the space debris situation. To assess this, we analyzed fragments and mechanically intact targets separately regarding their thermal constraints.

For fragments, overheating might eventually lead to uncontrolled target melting and subsequent sphere formation from the initially typically rather flat shape, i.e., yielding a significantly lower optical cross-section and, hence, area-to-mass ratio which might be detrimental for object tracking and removal [16]. Thus, we analyzed target heating at 100 Hz repetition rate, cf. Sect. 2.4, in order to derive an upper limit for the repetition rate in the irradiation interval. For this computation enthalpies of fusion and vaporization have been discarded and the material’s specific heat has been assumed constant at its value for room temperature in order to simplify subsequent downscaling of the laser repetition rate. Moreover, an initial temperature of 273.15 K before laser irradiation has been chosen discarding the fluctuations of debris temperature during the orbital path through sunlight and Earth’s shadow. Finally, we assume that heat distributes rapidly throughout the target before the next laser pulse arrives, which at least for thin metal fragments appears reasonable regarding their high heat conductivity.

Figure 6. Simulated temperature of space debris fragments after irradiation by a 100 kJ high energy laser at 100 Hz pulse repetition rate during the zenith angle range as specified in Table 1 for (a) head-on and (b) outward irradiation, respectively.

Figure 6. Simulated temperature of space debris fragments after irradiation by a 100 kJ high energy laser at 100 Hz pulse repetition rate during the zenith angle range as specified in Table 1 for (a) head-on and (b) outward irradiation, respectively.

It can be seen from the simulation results shown in Figure 6 that the target’s temperature after irradiation increases linearly with its area-to-mass ratio, which can be deduced from Eq. 7 yielding $T_{\mathrm{f}}\approx T_0+\left(A/m\right)\left(1/c_p\right){\sum }_i^N{\eta }_{res}\left({\mathsf{\Phi }}_i\right)·{\mathsf{\Phi }}_i$ where ${\mathsf{\Phi }}_i$ is the fluence at the target surface at the $i^{th}$ pulse, $N$ is the number of laser pulses during the station pass and the heat capacity is assumed to be constant yielding $∆T=$ ${\eta }_{res}{E}_{\mathrm{L}}/\left(m·c_p\right)$. The scatter in the depicted data stems from the various altitudes of the different targets which affect the number of pulses that increases with orbit height by up to more than 80 % throughout the altitude range from 583 km to 1182 km. Moreover, the achievable fluence at higher altitudes is considerably lower, cf. Figure 5(a), which implies greater thermal coupling, cf. Figure 2(b).

Overall, it is evident that the number of laser pulses has to be limited to avoid melting or even vaporization of target in particular when their area-to-mass ratio is rather high. For that purpose, we decided to leave the angular irradiation range unchanged but to reduce the pulse repetition rate which approximately decreases the temperature increment after the pass by the same amount. Choosing a pulse repetition rate of 9 Hz in the case of head-on irradiation and 6 Hz for outward irradiation yields a maximum temperature increment of $∆T\approx 100$ K for aluminum fragments with a very high area-to-mass ratio and $∆T\approx 200$ K for the respective fragments when iron is considered as target material. This temperature increment is less than 20 % of the temperature increase which would yield target melting and seems to be a reasonable limitation of the repetition rate. Afterwards, the acquired heat can be re-radiated into space to allow target cooldown before its trajectory is modified further in a posterior laser station pass.

This assessment of thermal constraints does not hold for non-fragmented targets like payloads or rocket bodies, which are much more complex objects than a target that is treated as homogeneous bulk material. Instead, the outer shell of such an object demands for dedicated consideration. Even for a temperature rise to values substantially below the melting point, heating might already pose a high risk, e.g., in case that stored energy, i.e., not completely discharged batteries or residual propellant, is located inside the object in the vicinity to an outer wall. Since these aspects are not available for a detailed assessment, we restrain our analysis to the computation of the average laser intensity during a station pass.

As an estimate for maximum permissible average irradiation intensity we refer to [40] where an irradiance threshold for lethality against unhardened satellites significantly below $100$ W/cm² was stated. Acknowledging that heat absorbance under laser ablation might be significantly higher than for highly reflective metals, cf. Figure 2(b), we choose $I_{\max }=13.7$ W/cm² as an upper limit for the average intensity during laser irradiation, which equals the hundredfold of the solar constant. To ensure that $I_{\max }$ is not exceeded during irradiation we set the repetition rate for outward irradiation altitude-dependent to $f_{rep}\left(h\right)=I_{max}/{\mathsf{\Phi }}_0\left(h\right)$ where ${\mathsf{\Phi }}_0$ is the laser fluence focused at a target with altitude $h$ in the zenith of the laser station, i.e., $\zeta =0°$. Hence, the applicable laser repetition rate increases nearly linearly from 1.1 Hz at 600 km altitude up to 3.8 Hz at 1,200 km altitude.

While this limitation is reasonable for outward irradiation, where the object is irradiated during a relatively long timespan near zenith, i.e., at high fluences, these values are reached merely at the end of the irradiation interval in the case of head-on irradiation. Therefore, we chose an enhanced repetition rate for head-on momentum which exceeds the repetition rate of outward irradiation at the respective altitude by 50 %. While $I_{max}$ is hence exceeded at the end of the irradiation interval, this is somehow compensated since the arriving laser intensity is significantly lower in the initial phase of the irradiation interval – unlike in the case of outward irradiation, where high intensities are obtained for a relatively long timespan. Overall, this choice gives the same ratio of repetition rates as for fragments, where we had 9 Hz and 6 Hz, respectively. Hence, the selection of repetition rates should yield a nearly similar heat load ratio of the irradiated target for the different irradiation strategies.

3.2. Orbit modification

3.2.1. Orbital velocity changes

Figure 7(a) shows the simulation results for the resulting velocity change of the debris object when the restriction of the repetition rate to 6 and 9 Hz, resp., is applied. Again, a linear dependency of coupling from the object’s area-to-mass ratio is found, which here can be predicted from Eq. 6 as $\mathsf{\Delta }v=\left(A/m\right){\sum }_{i=1}^N{c}_m\left({\mathsf{\Phi }}_i\right)·{\mathsf{\Phi }}_i$. However, the data on laser-induced velocity change exhibits a larger scatter than the data on temperature increment, since beyond the altitude dependency of pulse number and fluence as well the different target shapes are reflected in the raytracing computation of imparted momentum. Overall, the resulting velocity change of a few m/s is about two orders lower than the required $\mathsf{\Delta }v$ for perigee lowering of initially circular orbits for atmospheric burn-up, cf. [39], clearly indicating the necessity of debris irradiation during a multitude of station passes.

Figure 7. Simulation results for (a) velocity change of aluminum fragments and (b) effective momentum coupling coefficient of different object types after repetitive head-on irradiation by a 100 kJ high energy laser. Laser pulse repetition rates depend from target type and irradiation mode, cf. Sect. 3.1.3. The range of irradiation angles is defined in Table 1.

Figure 7. Simulation results for (a) velocity change of aluminum fragments and (b) effective momentum coupling coefficient of different object types after repetitive head-on irradiation by a 100 kJ high energy laser. Laser pulse repetition rates depend from target type and irradiation mode, cf. Sect. 3.1.3. The range of irradiation angles is defined in Table 1.

It should be noted here that the effective momentum coupling coefficient $c_{m,\mathrm{eff}}$ significantly deviates from the experimental data on momentum coupling as of Figure 2(a). Here, we define $c_{m,\mathrm{eff}}$ as a figure of merit for the entire debris removal system, i.e.,

$$c_{m,\mathrm{eff}}=\sum ∆v/\left(N_p·E_{\mathrm{L}}\right)$$

(15)

where $E_{\mathrm{L}}$ is the initially emitted laser pulse energy and $N_{\mathrm{p}}$ is the number of applied laser pulses. Then, it can be taken from Figure 7(b) that the effective momentum coupling is around two to three orders of magnitude below the experimental data, mainly due to the large outshining losses in particular for small targets at beam diameters in the size range of 1 to 3 m. However, what seems here as a massive waste of laser energy is somehow needed for the small objects since the relatively large spot size enables momentum coupling to small objects even in the presence of significant beam pointing jitter. In any case the impact of outshining losses on the effective momentum coupling coefficient should be carefully considered in conceptual studies in order to avoid performance overestimation of any laser-based debris removal system.

3.2.2. Perigee Lowering Method

In the next step of our analysis, our findings on laser-induced velocity change from a station pass have been employed to compute the corresponding perigee change of the respective target’s orbit. The results for head-on irradiation are shown in Figure 8.

Simulation results on perigee lowering after a transit with head-on irradiation are shown in Figure 8. Note that regarding the amount of perigee lowering head-on irradiation outperforms outward irradiation by in average 23 ± 8 %, even though the true anomaly for irradiation has not been optimized for the head-on irradiation, cf. Sect. 2.5, and though outward irradiation benefits from lower zenith angles, i.e., higher fluences yielding an overall velocity change that exceeds the overall $∆v$ resulting from head-on irradiation by ca. 36 ± 5 %.

Frequently, head-on irradiation is treated i the literature as pure deceleration, i.e., $v_r=0$ and perigee lowering is computed using a Hohmann transfer from an initially circular orbit, i.e., assuming $e_0=0$ and $\phi ={\phi }_0=180°$, resulting in a required ${∆v}_t$ for perigee lowering which is about four times lower than the needed ${∆v}_r$ in outward irradiation [39]. From our simulations assuming ${\phi }_0=270°$ we can see that in-track deceleration and imparted radial momentum contribute almost in equal parts to perigee lowering, in particular since the orbit’s initial eccentricity is considered in our simulations. In conclusion, these findings disprove the view that head-on irradiation would be inefficient from ground due to the large displacement between laser source and orbital trajectory.

Figure 8. Simulation results on perigee lowering of space debris after a single station pass with head-on irradiation. Laser pulse repetition rates depend on the target type and irradiation mode, cf. Sect. 3.1.3. The range of irradiation angles is defined in Table 1.

Figure 8. Simulation results on perigee lowering of space debris after a single station pass with head-on irradiation. Laser pulse repetition rates depend on the target type and irradiation mode, cf. Sect. 3.1.3. The range of irradiation angles is defined in Table 1.

3.2.3. Multi-Pass Removal

From the results on perigee lowering in a single transit a rough estimate can be given for the number $N_{\mathrm{pass}}$ of required passes with laser irradiation to achieve the targeted perigee altitude of $h_{p,\mathrm{final}}=200$ km. For this purpose, the progress in the change of the orbit’s eccentricity, semi-major axis, and perigee altitude is monitored for a multitude of station transits until $h_p<h_{p,\mathrm{final}}$. For the sake of simplicity, laser-imparted momentum is not re-computed for each transit. Instead, for each pass the same $∆p$ is used which means that for reasons of computational effort we discard the change $∆a$ of the mean altitude where the irradiation takes place. Otherwise a new set of laser-matter interaction tables would have to be computed for each target at every pass altitude which would increase the overall computational effort of our study by several orders of magnitude. Moreover, we discard the effects of mass loss following the findings in [36].

While discarding $\mathsf{\Delta }a$ for momentum computation is no issue in outward irradiation where we have $\mathsf{\Delta }{v}_t=0\Rightarrow \mathsf{\Delta }a=0$, cf. Eq. 11, due to ${\zeta }_{\mathrm{in}}=-{\zeta }_{\mathrm{out}}$, for head-on irradiation the mean altitude is lowered significantly in a single pass, approximately $∆a/∆r_p\approx$ $0.46\pm 0.02$. Hence, a higher laser fluence and less absolute hit uncertainty is obtained the more the perigee is lowered. Therefore, the number of required passes might in principle be overestimated while, on the other hand, better momentum coupling might as well be associated with higher thermal coupling – which in turn would demand for a stronger limitation of the number of laser pulses during a single transit at a lower altitude. Eventually, this might end up in a similar overall efficiency of the laser irradiation during a single pass. At this point, a more precise assessment is left to be given by more elaborate simulations in the future.

Figure 9. Simulation results for the number of required passes for perigee lowering from LEO down to 200 km with head-on irradiation for (a) fragments and (b) non-fragmented debris objects.

Figure 9. Simulation results for the number of required passes for perigee lowering from LEO down to 200 km with head-on irradiation for (a) fragments and (b) non-fragmented debris objects.

It can be seen from Figure 9(a) that the number of passes for lowering the perigee of fragments is in average 240 ± 130. The lowest values for the number of transits are achieved for targets with a low initial perigee altitude and high area-to-mass ratio, since then a relatively small change of orbital velocity is needed and a relatively large amount of laser energy can be captured for momentum transfer.

In contrast, the resulting number of station passes with laser irradiation is rather high for massive objects, as can be seen from Figure 9(b). As the targets become significantly larger than the spot size, the ratio of spot area to target mass decreases strongly, thus, lowering the capability of laser-induced deceleration. With only a few exceptions, objects larger than 2 meters demand for more than 1,000 passes with laser irradiation while for the high-risk targets between 3,000 and 30,000 irradiations would be needed which cannot be deemed a realistic perspective for their efficient removal at all. Hence, it does not seem to be recommendable to remove larger objects using lasers unless they are rather light-weight and the required perigee lowering is not too high.

4. Discussion

5. Conclusions

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