A SYSTEMATIC STUDY OF LASER ABLATION FOR SPACE DEBRIS MITIGATION

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1 A SYSTEMATIC STUDY OF LASER ABLATION FOR SPACE DEBRIS MITIGATION W.J. Burger, A. Cafagna, and C. Manea 3 FBK, Via Sommarive 8, and TIFPA, via Sommarive, 383 Trento, Ital Universit of Trento and TIFPA, via Sommarive, 383 Trento Ital 3 TIFPA, via Sommarive, 383 Trento, Ital ABSTRACT The increase in the number of artificial objects in orbit around the Earth represents a serious threat to the future utiliation of space. The scope and nature of the problem require an international effort. The Trento Institute of Fundamental Phsics and Applications (TIFPA) participates in the stud of laser ablation for space applications, propulsion and space debris mitigation, in the New Reflections program of the Italian Instito di Fisica Nucleare (INFN). An evaluation of the performance of laser ablation for debris removal in Low Earth Orbit (LEO), for different scenarios of ground-based and orbiting sstem configurations is presented. The results are obtained from a simulation developed in the Matlab c environment, which includes the relevant gravitational (Earth onal model, solar and lunar gravit) and atmospheric models. breakup begins, the debris flux in certain regions near earth ma quickl exceed the natural meteoroid flux. Over a longer period the debris flux will increase exponentiall with time, even though a ero net input rate ma be maintained. The Kessler Sndrome, the cascade in the number of collisions rendering the exploitation of space unfeasible for future generations, has led to a large consensus among national space agencies on the importance of the problem []. Ke words: laser ablation, space debris mitigation, simulation analsis. INTRODUCTION The likelihood that the increase of the number of objects launched in space results in an artificial debris belt around the Earth was pointed out b D.J. Kessler and B.G. Cour- Palais in 978 []. The authors developed a model to predict the evolution of the debris population created b satellite collisions based on the available inventor of artificial objects in orbit around the earth (sie, speed, orbit). The process of mutual collisions is similar to the mechanism responsible for the creation of asteroids from larger planet-like bodies. While the time scale of the latter is of the order of billions of ears, the much smaller volume occupied b the earth-orbiting satellites results in a significantl shorter time scale. The authors indicate the inherent risk Collisional breakup of satellites will become a new source for additional satellite debris in the near future, possibl well before the ear. Once collisional corresponding author Figure. The principal space debris populations include a ring of objects in GEO and a cloud of objects in LEO [3]. The number of tracked objects, which exceeds 9,. form two distinct populations: a ring in geostationar orbit (GEO) and a cloud in LEO (Fig.). The information is used b NASA to defined collision avoidance processes for all human space flight missions and for maneuverable robotic satellites in LEO, and within km of GEO []. The satellites and debris in orbit around the earth are subject to the frictional force of the atmosphere and the pressure due to solar activit. A priori the objects in LEO will eventuall deorbit due to these natural effects. One of approaches in active debris removal is to search for technological solutions which would shorten significantl the orbital lifetime of the debris.

2 REQUIRED PERFORMANCE The impulse, applied in the direction opposite (parallel) to the orbital velocit, required to lower (raise) a object in a circular orbit is given b the Hohmann transfer. The momentum change is defined b the difference between the original orbital velocit, and the velocit at the perigee (apogee) of the elliptical transfer orbit tangent to the circle of the lower (higher) altitude orbit. The expression for the momentum change required to displace a mass m in an circular orbit of radius R to an orbit radius R < R is Ratio Impulse with/without Drag Altitude (km) m v = MG R /R () R R + R Figure 3. The ratio of the impulse required to deorbit the debris mass with and without the presence of the atmosphere. where M is the mass of the Earth and G is the gravitational constant. The impulse required to lower the altitude of the satellite R to R equal to the Earth s radius R E, and R E + km are shown in Fig.. The latter represents an altitude where the effect of atmospheric drag will deorbit the mass. The ratio of the impulse with and without atmospheric drag, i.e. the ratio of the impulses required to lower the mass to an altitude of km and to the Earth s surface, are shown in Fig3.. Rplanet. Rplanet. Rplanet x Impulse (Ns) 7 3 t kg kg kg kg. kg 8 Altitude (km) Figure. The impulse required to lower a given mass to a final orbital altitude of km (solid lines) and to the Earth s surface (dashed lines). t Figure. The elliptical orbit in the Geant simulation of the kg mass with a velocit of. km/s. The trajector correspond to 3 h, the period of an elliptical orbit with a semi-major axis equal to Earth radii. Figures and show the orbits of a kg mass which is placed at an altitude of km with the velocities of. and 7. km/s. The corresponding escape velocit at this altitude is. km/s (Fig. ). The change of the perigee altitude produced b an impulse applied in the direction opposite to the orbital velocit (Hohmann), and in the directions along and opposite to the vector drawn from the Earth s center to the debris position at the km altitude, are shown in Fig. 7. Effect of the Impulse Direction The Geant application PLANETOCOSMICS was used to quantif the effect of the direction of the applied impulse. PLANETOCOSMICS performs a detailed simulation of the propagation and interaction of elementar particles in the Earth s magnetic field and atmosphere. The Earth s gravitational field was added to the program. Mean equatorial radius 378 km

3 Rplanet x Figure. The circular orbit at altitude of km of a kg mass with a velocit of 7. km/s. The trajector corresponds 97 min, the period of the circular orbit. Hohmann - radial + radial Perigee Time (min). Rplanet Perigee Altitude (km). Rplanet Impulse (Ns) Figure 7. The change in the perigee altitude ( ) for three different impulse directions: opposite to the orbital velocit of the kg mass (Hohmann), towards the center of the Earth (negative radial) and the local enith (positive radial) are indicated on the vertical axis on the left, the time required to attain the perigee ( ) on the vertical axis on the right. Hohmann transfer, and 3. Ns for the two radial impulses. Above these values, the descent to the ground varies more rapidl with the impulse. Figure. The trajector of a kg mass with a velocit of. km/s at an altitude of km. The mass leaves the simulation volume at distance of Earth radii with a velocit of. km/s in. h. The simulation time is 97 min, corresponding to the period of the circular orbit of the kg mass at an altitude of km (Fig. ). The impulse is applied.7 min after the start of the simulation. The effect of atmospheric drag is absent. A factor larger radial impulse is required to produce a reduction in the perigee altitude comparable to the Hohmann transfer. The two radial impulses result in an elliptical orbit with a perigee altitude lower than the initial km altitude of the initial circular orbit. The altitude reduction produced b the negative radial impulse is -% larger. The perigee time reported in Fig. 7 reflect the relative positions of the perigee and apogee of the elliptical orbits produced b the different impulse directions, illustrated in Figs. 8-. The perigee altitude is attained min after the negative radial impulse is applied; the perigee is displaced to the opposite side of the orbit with the positive radial impulse. The Hohmann transfer results in a perigee position ling between the two radiall directed impulses. The perigee altitude varies monotonicall with the applied impulse below the value required to lower the kg mass to the Earth s surface, 8. Ns for the The simulation results in Fig. 7 are consistent with the impulse values of the Hohmann transfers (Eq. ) of the kg mass from km to km,.3 Ns, and to the Earth s surface, 8. Ns.. Rplanet. Rplanet. Rplanet x Figure 8. The modified trajector of the kg mass in a circular orbit at km (Fig. ) after the Hohmann transfer of 7. N s in the direction opposite to its orbital velocit.

4 3 Atmospheric Densit (g/cm ) -3. Rplanet x. Rplanet. Rplanet Altitude (km) Figure 9. The modified trajector of the kg mass (Fig. ) after the radial impulse of 3. N s in the direction of the Earth s center.. Rplanet Figure. Atmospheric densit from Ref. []. The effect of the atmospheric drag on the debris orbit for the three impulse directions is shown in Fig.. A Hofmann transfer of. Ns results in a deorbit of the kg mass in. The minimal values required to deorbit the mass are.7 and. Ns, respectivel the negative and positive radial impulses; the corresponding deorbit times are. and.8. x. Rplanet Perigee Time (d) 3 Figure. The modified trajector of the kg mass (Fig. ) after the radial impulse of 3. N s in the enith direction. Hohmann - radial + radial - - Perigee Altitude (km) 3. Rplanet Impulse (Ns) Effect of Atmospheric Drag The frictional force acting on a satellite due to the presence of the atmosphere is given b the expression, F = ρcd Av v () where ρ is the atmospheric densit; CD is the drag coefficient, which varies between and ; A and v are the satellite s cross-sectional area and velocit. The force acts in the direction opposite to satellite s orbital velocit. The effect of the atmosphere on the orbit is introduced in the Geant simulation b adding the continuous energ loss process described b Eq.. The kg debris mass is represented b a solid cube of aluminum with a surface area of.3 m. The parameteriations for the troposphere, and the lower and upper stratospheres densities of Ref. [] are used (Fig. ). Figure. The perigee altitude ( ) and time ( ) for the three impulse directions with the presence of the atmosphere. The perigee altitudes, 3- km for the Hohmann transfer and 8-8 km for the radial impulses, shown in Fig. represent the altitudes attained after.3, the simulation time limit. The Hohmann transfer applied to lower the perigee altitude is kinematicall the optimal configuration. In practice, the impulse of a ground-based laser will alwas have a component directed awa from the Earth. A spacebased laser ma engage debris targets at relativel lower and higher altitudes. The results for the radial direction transfers represent the performance lower limits. The modified trajector of the kg mass after a

5 Hohmann transfer of 7. N s in the direction opposite to its orbital velocit is shown in Fig. 3. The applied impulse results in a series of elliptical orbits with progressivel lower perigee altitudes. When the altitude attains the height of the atmosphere each successive passage through the atmosphere produces a further reduction of the orbital velocit. The kg mass falls to the Earth in 7 d after the initial Hohmann transfer.. Rplanet x. Rplanet The corresponding scenarios for negative and positive radial impulses of. Ns are illustrated in Figs. and. The starting position of the debris mass is located in the equatorial plane at - km x.. Rplanet Figure. The kg mass in a circular orbit at km (Fig.) returns to Earth 3 d after a positive radial impulse of. Ns and multiple passes in the atmosphere.. Rplanet DEBRIS MITIGATION WITH LASER ABLATION x. Rplanet. Rplanet Ground-based Sstem Figure 3. The kg mass in a circular orbit at km (Fig.) returns to Earth 7 d after a Hohmann transfer of. Ns and multiple passes in the atmosphere. A ground network of lasers for space debris removal is described in Ref. []. The quoted laser parameters are the energ per pulse Eo > kj, a repetition rate larger than H, a pulse length between and ns, and a beam qualit M less than.. The expected power intensit at the surface of the debris is..8 GW/cm. The impulse is given b the expression, m v = µ Eo Ttel Tatm πφ (R) SCm (3) where φ (R) is the sie of the beam at the range R of the target debris. S and m are the surface area and mass of the target. Ttel and Tatm are the transmission efficienc of the laser emitting telescope and the atmosphere. Cm is the coupling coefficient (N/W) for the conversion of the incident laser pulse energ to kinetic energ.. Rplanet.Rplanet. Rplanet x The measured value of the coupling coefficient for aluminum is N/W for the power densit range between. and.8 GW/cm, at λ =.µm. The vaporiation threshold Po for aluminum is. GW/cm, below threshold m v =. The atmospheric transmission is estimated using the Roenberg model Figure. The kg mass in a circular orbit at km (Fig.) returns to Earth d after a negative radial impulse of. Ns and multiple passes in the atmosphere. Tm = ( Aatm )X with Aatm =.8 at. µm X= cosψz +. e( cosψz ) ()

6 where ψ Z is the elevation angle. Figure shows the variation in the atmospheric transmission with the elevation angle for a.µm wavelength laser beam. Atmospheric Transmission Elevation Angle ψ (deg) Z Figure. The variation of the transmission efficienc of the atmosphere for a.µm wavelength laser beam with the elevation angle, defined with respect to the enith []. The performance has been evaluated for single and multiple pass modes. The results are sensitive to the parameters in Eq. 3, as well as to the tracking precision of the debris objects. The estimated deorbit times range from several hundreds of das to ears. An object is considered deorbited once the perigee altitude reaches km. LASER DEPLOYMENT SCENARIOS The Simulation A simulation developed in Matlab c is used to stud the relative performance of space and ground-based laser sstems. Four laser deploment scenarios are evaluated: a dedicated satellite (SAT), a laser sstem installed on the International Space Station (ISS), and two ground-based sstems located in the equatorial (GEQ) and polar (GPO) regions. The relative performance is evaluated for the same debris mass and orbit. The debris is represented as a point mass M of kg. Consequentl, all forces act on the center-of-mass. The surface area A used for the computation of the frictional drag force is m, ielding a ballistic coefficient β = C D A/M =.. The laser beam delivers a N thrust acting along the lineof-sight between the laser and debris positions. The beam is switched on and off in order to limit the time of operation to periods with advantageous orientations of the beam with respect to the debris velocit vector. The laser is switched on when the debris approaches the ISS or satellite, and the line-of-sight between the space platform and debris is not obscured b the Earth, defined as a spherical volume with radius R = R E + km. For the ground-based sstems, the laser is turned on when the object approaches the laser position, and the angle of elevation (Fig. ) of the line-of-sight ψ Z is greater than. The Jacchia-Bowmann 8 model [7] is used to calculate the air densit at high altitudes. The model takes into account densit fluctuations due to diurnal and seasonal thermal variations. The estimated accurac of the computed densities is better than % based on comparisons with satellite accelerometer data. The epoch Januar,, h.::. is chosen as the starting point in the simulation, in order to use known solar values for the calculation of the atmospheric densit. The debris orbital elements at epoch are listed in Table, which corresponds to an initial position at the apogee of the orbit (8 km). The chosen inclination and altitude is representative of the major part of the debris population in LEO. Table. The orbital elements of the debris object at epoch: semi-major axis a, eccentricit e, inclination i, right ascension of the ascending node Ω, the argument of the perigee ω and the true anomal θ. a e i Ω ω θ 77 km. 8 8 The orbital elements of the satellite and ISS at epoch are listed in Table. The starting point of the satellite is the perigee at an altitude of km. The satellite altitude and inclination angle ma be chosen to optimie the number of debris objects in its line-of-sight. Table. The starting point orbit elements for the dedicated satellite and ISS scenarios. a e i Ω ω θ SAT 88 km ISS 78 km The difference in altitude of the satellite and the debris object (Table ) results in a relative rotation between their orbits due to the J effect of the perturbed gravitational field. The rate of change in time (degree per mean solar da) of Ω, the Right Ascension of the Ascending Node (RAAN) is given b the expression [8] dω dt = ( ) 3. RE ( e ) cos(i) () R E + h where h is the mean distance from the Earth. For the two circular orbits, with mean altitudes of and 8 km, the difference in h results in an increase of Ω with time. The initiall co-planar orbits will become again co-planar in 98 das. All debris objects orbiting

7 7 at the same altitude, and similar, near polar inclinations, will be seen b the satellite in this time interval. The time interval required to return to coplanarit for the higher altitude (- km), near-polar orbit debris objects is shorter. Therefore, the dedicated satellite would be able to target a significant fraction of the near-polar orbit debris in less than 3. A laser sstem installed on the ISS will observe the near-polar orbit debris due to the lower inclination angle of the space station. The position of the equatorial ground-based laser station at epoch is on the x-axis of the Earth Centered Inertial (ECI) reference sstem, which is drawn between Earth s center to the Sun, at a distance of 378 km from the Earth s center. The polar region laser station is at a distance of 37 km from the Earth s center, placed to have the debris (i = ) at its enith at epoch. The orbital direction of the debris (i > 9 ) is opposite to the rotation of the Earth, and to the orbital directions of the satellite and ISS (Table ). Results The results for the four scenarios are presented in Table 3. The satellite (ISS) lasers provide the impulse required to lower the kg mass at 8 kg, to the altitude of the atmosphere ( km), in 3 weeks (3 months). The altitude decrease is significantl slower for the two ground-based lasers. At the end of the month simulation time, the debris perigee altitude decreases b and 7 km for the two ground-based lasers. The total impulse delivered b the polar site laser is a factor. higher. Table 3. The total simulated time t tot, total time laser on t laser, delivered impulse to debris and the final altitude at time t tot. The simulated time was limited to d for the two ground-based laser scenarios. t tot t laser Impulse Alt. Final d h Ns km SAT 3... ISS GEQ GPO The results in Table 3 ma be compared to the impulse required b a Hohmann transfer to lower a kg mass from 8 km to km, 8. Ns. The impulses required for the space-based lasers to lower the kg debris mass to the km perigee altitude are factors.8 and.9 larger. The fractions of time on target, t laser /t tot in Table 3, are.7 (SAT) and.9 (ISS). The orbital descent after d obtained with the polar site, ground-based laser, 8 to 78 km, ma be compared to the d required to deorbit the kg mass in a circular orbit at km, after a Hohmann transfer of. Ns (Fig. ). The corresponding impulse applied in the positive radial direction in the Geant simulation lowers the perigee altitude from to km in.3. Required Laser Performance The impulses quoted in Table 3 represent the sum of the impulse steps delivered each second b the N laser thrust. The corresponding required energ E o can be estimated from Eq. 3 with m v = Ns. For the spacebased lasers (T atm = ), ( )( ) Ns S E o = T tel C m πφ. () (R) The second term in Eq. is the ratio of areas of the debris surface and laser beam spot at the target. With the debris surface of m, a m diameter circular beam spot and a telescope transmission efficienc of 8%, E o is kj, the average power kw. Figure 7 shows the variation of the pulse energ and peak power with repetition rate of the kw laser, for a ns pulse width. The laser peak power is plotted against the peak power densit at the target in Fig. 8. The variation of the same parameters with the pulse width of the kw laser, for a H repetition rate, is shown in Fig. 9. Pulse Energ (kj) Average Power kw Pulse Width ns 8 Laser Repetition Rate (H) Figure 7. The variation with repetition rate of the pulse energ and peak power of the kw space-based laser with a pulse width of ns. The minimum power densit required to produce a momentum transfer b the vaporiation of the material on the surface of the debris (Al) is.gw/cm Ref. []. The laser configurations with peak power densities lower than GW/cm are indicated in red in Figs. 8 and 9. A kw, space-based laser would provide the timeintegrated impulse compatible with the performance presented in Table 3. Two possible laser configurations, which provide the necessar power densit at the target are a relativel low peak power, are listed in Table. Lower pulse energ E o is obtained with a higher repetition rate and narrower pulse width. 8 8 Peak Power (TW)

8 8 8 Average Power kw Pulse Width ns Peak Power Densit (GW/cm ) 8 Average Power kw Rep. Rate H Peak Power Densit (GW/cm ) Peak Power (TW) 8 Peak Power (TW) 8 8 Laser Repetition Rate (H) Laser Pulse Width (ns) 3 Figure 8. The variation of the peak power and the peak power densit at the target with pulse width, for a H repetition rate and an average power of kw. Peak power densities below GW/cm are indicated in red. Figure 9. The variation of the peak power and the peak power densit at the target with repetition rate, for a ns pulse width and an average power of kw. Peak power densities below GW/cm are indicated in red. Table. Laser configurations compatible with the performance of the space-based lasers in the Matlab c simulation (Table 3). P avg E pulse P peak width rate P densit GW kw kj TW ns H cm CONCLUSION An estimate of the required performance for debris mitigation is obtained from the Hohmann transfer required to change the orbital altitude of a satellite. In contrast to a Hohmann transfer, the momentum transferred b a ground or space-based laser will not be concentrated in the direction opposite to the orbital velocit of the debris mass. The Geant simulation was used to compare the perigee altitude of the Hohmann transfer with the altitude change produced b radial impulses directed along, and opposite to the vector drawn from the Earth s center to the debris position, the latter considered as limits for effective operation. A factor larger radial impulse is required to produce a comparable altitude change. Consequentl, for a given intensit, the relative performance would be expected to var from to. depending on the relative positions of the laser and debris target. A first estimate of the required laser characteristics is based on the results of the Matlab c simulation, which takes into account the oblateness of the Earth on the gravitational field, and the diurnal and seasonal thermal variations affecting the atmosphere densit. The N thrust of the space-based lasers lower the perigee altitude of a kg mass from 8 to km, sufficient to produce a deorbit in the atmosphere, in a time varing between 3 weeks and 3 months depending on the laser orbit. The time-integrated impulse required is.-. Ns. The corresponding laser energ E is computed (Eq. ) with the coupling coefficient and threshold peak power densit of the.µm infrared laser reported in Ref. [], and a m diameter beam spot at the target. The average power required is kw. Two pulsed laser configurations are listed in Table. REFERENCES [] Collision Frequenc of Artificial Satellites: The Creation of a Debris Belt, Journal of Geophsics Research, Vol 83, No. A, 979, 37-. [] Inter-Agenc Space Debris Coordination Committee: [3] NASA Orbital Debris Program Office: orbitaldebris.jsc.gov/index.html [] The Threat of Orbital Debris and Protecting NASA Space Assets from Satellite Collisions images.spaceref.com/news/9/ ODMediaBriefing8Apr9-.pdf [] NASA Earth Atmosphere Model, /airplane/atmos.html [] Changes of Space Debris Orbits after LDR Operation E. Wnuk, J. Golebiewska, C. Jacquelard, and H. Haag CLEANSPACE project of EC Seventh Framework Programme (FP7)

9 9 [7] Jacchia-Lineberr Upper Atmosphere Densit Model, NASA Lndon B. Johnson Space Center, 98 A NEW Empirical Thermospheric Densit Model JB8 Using New Solar and Geomagnetic Indices, B. R. Bowman et al., AIAA 8 [8] Orbital Mechanics, V. A. Chobotov, AIAA [9] Removing orbit debris with laser, C. R. Phipps et al. Advances in Space Research 9, APPENDIX: ORBITAL ELEMENTS Figure. The orbital elements inclination i, right ascension of ascending node Ω, the argument of the perigee ω and the true anomal θ.