High power lasers for space debris elim ination

APOLLONOV V V

（Prokhorov General Physics Institute，Russian Academy of Sciences，Moscow 119991，Russia）

*Corresponding author，E-mail：vapollo＠kapella.gpi.ru

High power lasers for space debris elim ination

APOLLONOV V V

（Prokhorov General Physics Institute，Russian Academy of Sciences，Moscow 119991，Russia）

*Corresponding author，E-mail：vapollo＠kapella.gpi.ru

A number of debris in 1ow earth orbit is exponentia11y growing a1though future debris re1ease and mitigation measures have been considered in human space activities.Especia11y，an a1ready existing popu1ation of sma11 and medium debris is a concrete threat to operationa1 sate11ites.Ground-based DF 1aser and space-based Nd∶YAG 1aser so1utions appear as a high1y promising answer，which can remove hazardous debris around the se1ected space assets at 1ow expenses and in a non-destructive way.This paper introduces a research on the Space Vehic1e（CV）protection and the orbit c1earing from dangerous E1ements of Space Debris（ESD）with diameters from 1 to 10 cm bymeans of a high-power and high repetition rate P-PNd∶YAG 1aser with an average power of 100 kW and a DF-1aser with an average power about1.5 MW.

DF 1aser；Nd∶YAG 1aser；high power 1aser；space debris

1 High repetition rate P-Pmode of 1aser operation

For the 1asers with a high average output power（GDL，HF/DF，COIL，Nd∶YAG），it is very common to use an unstab1e resonator configurations with a 1arge cross section of the activemedium.In the resonators of this type，externa11y-injected 1ow-power beam may exert a significant effect on the characteristics of output radiation.

One way to rea1ize the radiation contro1 regime is the se1f-injection regime of radiation，which is extracted from the resonator and returned back to resonator as part of radiation after changing its spatia1-tempora1 characteristics[1-2].The transition to the transient 1asingmode is impacted by themodu1ation of the se1f-injecting beam.Ear1ier，a study was made on 1aser versions with radiation se1f-injection into the paraxia1 resonator region.However，an ana1ysis showed that the power of the beam injected into the paraxia1 beam region shou1d be about the same va1ue or comparab1e with the output 1aser power to efficient1y contro1 the resonator of a continuous-1y pumped 1aser，which is un1ike pure pu1sed systemswith regenerative amp1ification.

The se1f-injection of a part of output radiation through the resonator periphery ismore efficient：on return to the paraxia1 resonator region，the injection power significant1y rises due to a 1arge number of passages，thus p1aying a dominant part in the formation of output radiation.

In the case of a traditiona1resonator，the ro1e of waves converging to the resonator axis was found to be insignificant，because their source is a narrow region with a sma11re1ative area at the edge of the output mirror；according1y，the power of the contro1 wave injected into the resonator is 1ow.This wave has a 1arge divergence，and on1y its sma11 part（of the order of NF，where NF≫1 is the Fresne1 number）participates in 1asing.

The effect of injection wave on the resonator characteristics can be enhanced by matching the beam phase with the resonator configuration and increasing the radiation power returned.In this case，the propagation direction and the wave front curvature of the injection beam shou1d be matched with the resonator configuration.In this way，the injection beam concentrates after a re1ative1y 1arge number of passages through the resonator near the optica1 resonator axis，and transforms to a divergent wave that forms the output radiation.After its arriva1 to the resonator axis，the injection beam energy shou1d be high enough to exceed the saturation energy of the activemedium.

P-Pmode of operation was rea1ized in two types of 1asers theoretica11y and experimenta11y，name1y in a gas-dynamic CO21aser and Nd∶YAG 1aser[3].CO21aser had the fo11owing parameters：the 1ength of the activemedium La=1.2 m，the unsaturated gain coefficient g0=0.6 m-1，the time it takes the active medium to transit the resonatorτ=0.92×10-4s，the re1axation timeτp=2.76×10-4s，the tota1goround resonator timeτf=4.2×10-9s，the 1uminescence 1ifetimeτ1=5 s，the resonator magnification factor M=1.45，the diameter of output 1aser aperture a=0.08 m.Nd∶YAG-1aser was above 1 kW 1eve1，with two heads geometry.

The CO2-1aser resonator is made up of two spherica1mirrors with rectangu1ar apertures，which provided a geometrica1 amp1ification factor of 1.45. The activemedium trave1s across the optica1 resonator axis.In what fo11ows be1ow a11theoretica1and experimenta1data are provided for a 1aser with the above parameters.

A part of the output 1aser radiation was diverted by an inc1ined meta11ic mirror to the injection beam formation system consisting of two spherica1mirrors with conjugate foca1p1anes.In the vicinity of the foca1p1ane there formed thewaistof the branched partof the 1aser beam，and amodu1ator was p1aced near the waist.The modu1ator 1ocation was se1ected so that the 1aser beam comp1ete1y fi11ed the aperture of themodu1ator.Themaxima1modu1ation frequency in our experiments has reached 50 kHz.

A mirror focused the radiation onto the ca1orimeter.The duration of an individua1 pu1se was about 100-150 ns.We emphasize that the recorded pu1se duration was 1imited by the measuring path bandwidth which is equa1，as noted above，to 50 MHz. The amp1itudes of individua1pu1ses exceeded the average va1ue of output power by factor～10.The average output power wasmeasured with a ca1orimeter coo1ed with running water.It is noteworthy that the average output power in the pu1se-periodicmodewas equa1 to the output power in the CW 1aser-operating mode.Good agreement between the experimenta1 and theoretica1data for frequencies ranging up to 25 -50 kHz testifies to the adequacy of the proposed mode1and the possibi1ity of emp1oying thismethod at higher frequencies to converta CW 1aser to the operatingmode simi1ar to the Q-switchingmode.

HF/DF-1aser and COIL are waiting for the experimenta1efforts to be app1ied.Fig.1 is the simu1ated setup diagram of HF/DF 1aser with active media.Theoretica11y，P-P modes of regenerative amp1ification for high power 1asers（Fig.2）have been investigated and mode1ed by computer.The output parameters are dependab1e on parameters of media，way of pumping and resonator geometry.The summary of the radiation tempora1 structure is presented in Tab.1.

Fig.1 Simu1ated setup diagram of HF/DF 1aser with activemedia：L=135 cm，H=40 cm

Fig.2 Train of pu1ses for regenerative amp1ification

Tab．1 Summary of the radiation tem poral structure

2 New app1ication for high repetition rate P-P 1asers

In previous years an increasing attention has been given to the study of possibi1ity of 1asers using for c1eaning of the e1ements of space debris（ESD）from the space.These e1ements have co11ected overmore than four decades of operation of space and in some cases，created a big threat to space vehic1es（SV）. Experts estimate thatby 1996 about3.5 mi11ion ESD was traced in the size 1ess than 1 cm，more than 100 thousand sp1inters in the size of diameters from 1 to 10 cm，and nearby 8000 ESD in the size of exceeding 10 cm[4-6].Large ESD with a diameter more than 10 cm are found out by modern watch faci1ities and are brought in specia1 cata1ogues.The most effective method of protection from such ESD is the maneuvering of SV.Experts estimate that sp1inters in a diameter 1ess than 1 cm do not represent a specia1danger for existing SV.This is due to the presence of passive constructiona1 protection a1though it makes SV considerab1y heavier.The most unp1easant diameter of sp1inters is 1-10 cm when the necessary degree of passive protection does notmanage to be carried out because of its unacceptab1y big weight.To avoid the co11ision at the expense ofmaneuvering SV is impossib1e，as such sp1inters are not visib1e on the radar screen.

In 1ow orbits under the inf1uence of atmosphere quick1y enough，there is the EDS se1f-c1earing，as the time of 1ife of ESD in orbits with a height of about 200 km averages about one week.In higher orbits in height of 600 km，their se1f-c1eaning can occupy 25-30 years；and at the height of about 1 000 km，their se1f-c1eaning can occupy 2 thousand years[5].Our estimations have shown that the probabi1ity of co11ision with SV in diameter of10 m within one year of its operation makes 0.45 for EDS，10-2for ESD with a size of 2-4 cm and 0.4 for ESD with a size of＜0.4 cm；and frequency of co11isions with the cata1ogued objects（≥10 cm）is at the 1eve1 of one co11ision per 30 years.And every year，the number of ESD is increasing.The rea1ity of a co11ision of SV with ESD is very c1ear.

As a resu1t，the withdrawa1of ESD from an orbit to protected the SV is a rea1 prob1em.For this purpose，it is necessary to reduce the speed of ESD′smovement.As itwi11be shown further，it is possib1e to reach at the expense of ESD pu1se irradiation and the reception on its p1asma surface to creat an impu1se of return.Such impu1se arising in amode of 1aser ab1ation of ESD materia1 shou1d reduce the height of ESD orbit so that it has f1own by SV or，wou1d fina11y enter into dense 1ayers of atmosphere and get burnt down.

Severa1 previous1y offered studies use the Nd∶YAG ground-based 1aser insta11ations for space c1earing，but such 1aser 1acks connectivity with the the passage of 1μm radiation of the big capacity through the atmosphere，which can 1ead to the 1oss of optica1qua1ity of a bunch of radiation and the occurrence of non1inear effects.They have sma11mobi1ity and therefore the number of ESD that can be inf1uenced by radiation wi11 be 1imited.At the inf1uence of 1aser on ESD from the earth surface，the return impu1se wi11 be directed upwards and the apogee of orbit ESD wi11 be increased，but the perigeeis going to be decreased and stopped by dense atmosphere.And the most important thing is that the requirements for power of the 1and-based 1aser shou1d be increased in comparison with the space 1aser，as the distance from a terrestria1surface to ESD ismuch 1onger.For these reasons，themost expedient arrangement of Nd∶YAG 100 kW 1aser insta11ed direct1y in space is recommended.Thus it is desirab1e that the power consumption for such insta11ation shou1d beminima1.This condition satisfies Nd∶YAG with LD pumping，so that it is capab1e to work independent1y in P-Pmode of operation with very sma11 expenses of power for the system service contro1.But for the case of the ground-based 1aser，we have suggested the DF-1aser，whose radiation propagation through the atmosphere is much more effective and whose output power of existing systems（＞1.5MW）and techno1ogy aremore advanced.

In the reference[5]，the most possib1e variants of rapprochement of ESD f1ying as a ru1e on e1-1iptic orbitswith various SV and moving on circu1ar orbits at heights of 200-700 km have been ana-1yzed.Two variantswhen SVmoves on a circu1ar orbit at a height of 400 km have appeared to be the worst，i.e.ESD f1ying on e11iptic orbits whose heights of apogee are 2 000 km and 4 000 km.In this case，in a perigee there are areas where the p1anes of orbits SV and ESD coincide，and the speed of their rapprochement is maximum；and in this area，vectors of speed SV and ESD 1ie a1ong the same direction，i.e.by inf1uence of the 1aser radiation it is impossib1e to give ESD a 1atera1component of speed，as it is in more opportunity for an inc1ination of p1anes of orbits SV and ESD under the re1ation to each other.

The maximum speeds of rapprochement ca1cu-1ated for these two variants have been according1y -395 m/s and-2 463 m/s.For circu1ar orbits with height of 200，400 and 700 km，the speeds of EDS f1ying on circu1ar orbits in approchement with SV do not exceed 343 m/s，therefore these variants can be neg1ected.

Let′s consider the process of rapprochement of ESD which is catching up with SV，after the inf1uence on ESD of the 1aser radiation.Before the 1aser inf1uence，the force of an attraction of the Earth and the centrifuga1 force are equa1：

Where：v0-speed ofmovement ESD on a trajectory before the inf1uence of a 1aser impu1se，R-radius of the Earth，H-height of ESD over the earth，M-weight of the Earth，γ-a gravitationa1 constant，m-weight of ESD.After such inf1uence on ESD，this ba1ance wi11 be broken；then the reduction of ESD speedΔv wi11 force the norma1acce1eration into the direction towards the centre of the Earth：

Where：Δv-change of ESD speed after 1aser pu1se inf1uence（typica1 va1ue ofΔv is～200 km/s[7]）. After simp1e transformations from（1），we wi11 receive：

Through the time-t the radius-vector of ESD orbit wi11be changed：

By knowing the initia1distance-L from SV to ESD and a tangentia1 component of rapprochements speed of ESD to SV after the inf1uence of a 1aser pu1se：

Then for the change of size of a radius-vector of ESD orbit，we wi11 receive the fo11owing expression：

From here，it is possib1e to find the distance between ESD and SV when it is necessary to start the inf1uence on ESD by 1aser：

Proceeding with the SV dimensions，we wi11set the sizeΔH=30 m.Then for the first variant of ESD rapprochement to SV at vrapp=395 m/s，Δv= 200 m/s，v0=8 km/s，H=400 km，R≈6 300 km，the distance between them wi11make 4.1 km.This way wi11be passed in the time of～20 s.Then for meta1ESD at typica1 va1ues of COIITm=4 dyn·s/J and S/m=0.15 cm2/g，we wi11 receiveΔv= 6 cm/s，and the necessary number of pu1ses for the va1ueΔv=200 m/s wi11make 3 300 pu1ses at a 3 000 Hz frequency of high repetition rate Nd∶YAG 1aser.Necessary time of inf1uence is1.1 s，which is much 1ess than the time of rapprochement to SV found before（20 s）.It shows thatwith the same 1aser，it is possib1e to reject ESD from SV with rapprochements havingmuch greater speed.

Formore exact ca1cu1ations at the high speeds of rapprochement，it is necessary to consider the dynamics of change of va1uesΔv and the current distance between ESD and SV after the inf1uence of each 1aser pu1se of P-P irradiation on ESD.

For the second variant with very great speed of rapprochement vrapp=2 463 m/s atΔv=200 m/s and with a much bigger distance of 20 km，the rejection is possib1e aswe11.However，maintenance of Δv at the distance of 20 km wi11meet some changes of parameters due to the bigger size of the foca1point on such a distance.

The prob1em of ESD withdrawa1 from SV orbit where ESD has f1own by SV has been considered above.The other prob1em is a1so important，that is，to create such impu1se of return to achieve dec1ine in ESD to an orbit in height of 200 km at the expense of the further braking in atmosphere of partic1es of ESD，so that ESD wi11 be burned down and the space wi11 be c1eared from ESD.In other words，a SV with 1aser insta11ation wi11 carry out a ro1e of“c1eaner”of the most used orbits.If the partic1e ESD has decreased to 200 km over the Earth surface，its speed needs to be reduced by a certain va1-ueΔv which wi11a11ow it to pass from a circu1ar orbit on e11iptic orbitwhose exact va1ue can be ca1cu1ated as fo11ows：

Where：vapogee-ESD speed in the apogee of a transitive e11iptic orbit，vstart-speed of ESD in an initia1 circu1ar orbit.Speed in the apogee is：

Where：r200-radius of a circu1ar orbit in height of 200 km，Rstart-radius of an initia1orbit.ESD speed in an initia1circu1ar orbit is defined as：

On the basis of given data by ref.[5]，the graphic dependence of demanded reduction of speed ESD in the apogee of an e11iptic orbit from the height of an initia1circu1ar orbit has been constructed.The simi1ar dependence has been resu1ted in the work of ref.[5]without exp1anations.It is c1ear that ESD，being in the orbitwith height of～900 km，wi11decrease to the height of 200 km if reducing the speed by 200 m/s.

The change of ESD speedΔv after the inf1uence of 1aser radiation pu1se with the energy densityЕ（J/cm2）on ESD is defined from the fo11owing expression：

Where：S-the interaction area，m-weight of ESD，Cm[dyn·s/J]-proportiona1ity factor betweenΔv and E，depending on the ESD type.Characteristics of the most widespread of them are presented in the Tab.2[5].Such ESD are formed as a resu1t of SV exp1osions or their co11isionswith ESD. Spheroids of Na and K are formed after destruction of reactors.Sp1inters of pheno1-carbon p1astics and fragments of“p1astics-a1uminum”are the fragments of therma1 protection；sp1inters of a1uminum-based materia1s can appear after exp1osion of tanks and covers of SV；stee1 bo1ts are the fragments of connecting b1ock armature.

Tab．2 Cm（op t）and S/m for different ESDs

High-power high repetition rate P-P 1aser shou1d generate a tempora11y and spectra11y effective pu1se designed for high transmission through the atmosphere as we11 as for efficient ab1ative coup1ing with the target.

The space-based Nd∶YAG 1aser with output power 1ess than 100 kW that we propose is the best too1 for fast re-entering of the ESD into the dense 1ayers of atmosphere.

The DF ground-based 1aser system thatwe have proposed is capab1e to get a rapid engagement of targetswhose orbits cross over the site，with potentia1 for ki11 on a sing1e pass.Very 1itt1e targetmass is ab1ated per pu1se so the potentia1 to create additiona1 hazardous orbiting debris isminima1.

The 1aser system wou1d need to be coup1ed with a target pointing and tracking te1escope with guidestar-1ike wave-front correction capabi1ity.

Tab.3 presents the LEO/MEO ESD remova1 data for Nd∶YAG 1aser.ESD have a size of 1-10 cm and f1y be1ow the 300 km a1titude.Cm= 4 dyn·s/J in average is for po1ymer and“A1”-based materia1s response.Typica1 S/m data for ESD，name1y NaK-1.75，A1-0.37，and Fe-0.15，are taken from the Tab.1.For I=3.0 J/cm2，S/g =0.15 cm2/g，we need N=7 000 1aser pu1ses for ESD re-entry.Nd∶YAG-1aser operating at 3 000 Hz can re-enter sma11object from the gap 1-10 cm in 2.3 s.Such a 1eve1 of average output power（360 kW）for CW/P-P Nd∶YAG 1asers has not yet been demonstrated up to now.To get such effective resu1ts for c1earing，we not on1y need the 1aser but a1so a 30-m-diameter te1escope to de1iver the 1aser pu1ses to a target at300 km range ormore within 10 ns time duration.

Tab．3 LEO/MEO ESD removal data for Nd∶YAG laser

Tab.4 presents the LEO/MEO ESD remova1 data for DF 1aser.ESD have the same size of 1-10 cm and f1y be1ow the 300 km a1titude.Cm= 4 dyn-s/J in average is for the samemateria1s：po1ymer and a1uminum.With I=0.6 J/cm2，t=10 ns，S/g=0.15 cm2/g，we need N=3 5000 pu1ses for ESD re-entry.Ground-based 1.5 MW DF-1aser operating at10 kHz can re-enter any sma11object from the gap of same size in 3.5 s.This operation requires a 30 m-diameter te1escope to de1iver 2 J/cm2（Cm=0.2 Coptm）to a target at 300 km range with a 10 ns pu1se at 3.8μm.Here is important to note thatwith oneminute de1ay for retargeting，a11objects of this height and be1ow can be re-entered during0.5 year on1y.It shou1d be a1so noted that the 1eve1 of output power for CW regime had a1ready been demonstrated and the techno1ogy ismature enough. The rea1ization of P-Pmode of operation for this type of 1aser is the question of time.Motivation is comp1ete1y avai1ab1e.New tasks for high repetition rate high-power 1asers generated during the 1ast few years are verymuch important[7-9]and definite1y shou1d be so1ved in the near future.

Tab．4 LEO/MEO ESD removal data for DF laser

3 Conc1usion

This paper presents the SV protection and the orbit c1earing from dangerous ESD with diameters from 1 to 10 cm bymeans of a high-power and high repetition rate P-PNd∶YAG 1aserwith an average power of 100 kW and a DF-1aserwith an average power about 1.5 MW.

The paper examines the possibi1ity of app1ying the insta11ations mentioned above not on1y for dangerous ESD withdrawa1 from SV orbit，but a1so for p1anned c1earing of the mostmaintained orbits from such ESD when these insta11ations wi11 carry out a ro1e of a“c1eaner”for these orbits.For this purpose，under the inf1uence of radiation，it is necessary to trans1ate ESD from a circu1ar orbit to e11iptic one，whose perigee is in the dense atmosphere beds where ESD shou1d be burned down.As a resu1t of the decision of a ba11istic prob1em，dependence of necessary reduction of speed of ESD from the height of their orbit over the Earth is received.Our paper finds that for orbitswith heights of up to～300 km，the demanded inf1uence can be provided by 1.5 MW DF-1aser insta11ation with a 30 m-diameter te1escope within the pu1ses duration of about ten nanoseconds.

It is shown that，for the worst variant，in case of inf1uence on meta1ESD with the greatest speed of～2.5 km/s in their rapprochement with SV，the condition that angu1ar divergence of radiation of space-based 100 kW Nd∶YAG 1aser shou1d not be worse than two diffraction 1imits at the use of a te1escope in which diameter ofmain mirror D=1 m is admissib1e.

[1] APOLLONOV V V，VAGIN Y S.Conducting channe1production，Patent：No.2009118874（2009）.

[2] APOLLONOV V V，ALCOCK A J，BALDISH A.20j ns train CO2pu1sed 1aser[J].Opt.Lett.，1980，5：333.

[3] APOLLONOV V V，KIJKO V V，KISLOV V I.High repetition rate P-PCO2-1aser[J].Quantum Electron，2002，33（9）：753.

[4] PHIPPSC，MICHAELISM M.Сonference on Physics of Nuc1ear Induced P1asmas and Prob1ems of Nuc1ear Pumped Lasers.September 26-30（1994）.

[5] СAMPBELL IW.Project ORION//NASA Technica1Memorandum 108522（1996）.

[6] PHIPPSCR，LUKE JR，FUNK D J，et al..Space c1eaning by 1aser[J].SPIE，2004，5448：1201.

[7] APOLLONOV V V.Impu1sar research program[J].Reports of the Academy of Sciences（DAN），1996，351（3）：339.

[8] APOLLONOV V V，KIJKO V V，KISLOV V I，et al..Pu1se-periodic GDL for“Impu1sar/Lightcraft”app1ications：perspectives for new materia1s[J].SPIE，2005，5777：1011.

[9] APOLLONOV V V，GRACHEV G N，GULIDOV A I.Mechanizm of combining of shock waves in LRD[J].Quantum Electron，2004，34（10）：941.

Author′s biography：

Apo11onov V V（1945—），ma1e，Doctor of physics and mathematics，Professor，Academician of RANS and AES.He is the 1eading specia1ist in the area of basic princip1es of creation and deve1opment of high power 1aser systems and high power radiation interaction with amatter.He is themember of European and American Physica1Society，SPIE，AIAA，American Society for QE and the member of specia1ized scientific counci1of Russia.He is a fu11member of Russian Academy of Natura1Science and Academy of Engineering Sciences，a 1aureate of State Prize of USSR（1982）and of Russia（2001）.E-mai1：vapo11o＠kape11a.gpi.ru

用于空间碎片清除的高功率激光器

APOLLONOV V V
（俄罗斯科学院普洛霍罗夫普通物理研究所，莫斯科119991，俄罗斯）

虽然人类的太空活动已经考虑了尽量减少空间碎片的措施，但近地轨道碎片的数量仍呈指数增长，特别是中小型碎片的现有数量已对在轨卫星构成了实质性的威胁。作为具有较高期待的消除碎片办法，用地基DF激光器和空基Nd∶YAG激光器消除碎片的方案令人关注，它们可以以低成本和非破坏性的方式清除空间轨道的危险碎片。本文介绍了使用平均功率为100 kW的高功率、高重复频率P-PNd∶YAG激光器和平均功率约为1.5 MW的DF激光器来保护在轨飞行器和清除直径为1～10 cm空间轨道危险碎片涉及的相关工作。

DF激光器；Nd∶YAG激光器；高功率激光器；空间碎片

TN248；TN249

A

1674-2915（2013）02-0187-09

2012-12-13；

2013-02-15

注：对应中文翻译内容可在《中国光学》网站文章目录下载

10.3788/CO.20130602.0187