L'ADROIT - A space borne ultra violet laser system for space debris clearing

13 Pages·2.059 MB·English

by  Phipps C.R.

ActaAstronautica104(2014)243–255
ContentslistsavailableatScienceDirect
Acta Astronautica
journal homepage: www.elsevier.com/locate/actaastro
L'ADROIT – A spaceborne ultraviolet laser system for space
debris clearing
Claude R. Phippsn
PhotonicAssociates,LLC,200AOjodelaVacaRoad,SantaFe,NM87508,USA
a r t i c l e i n f o a b s t r a c t
Articlehistory: Small(1–10cm)debrisinlowEarthorbit(LEO)areextremelydangerous,becausethey
Received27May2014 spreadthebreakupcascade.Pulsedlaseractivedebrisremovalusinglaserablationjetson
Receivedinrevisedform target is the most cost-effective way to re-enter the small debris. No other solutions
6August2014 address the whole problem of large ((cid:1)100cm, 1t) as well as small debris. Physical
Accepted8August2014
removalofsmalldebris(bynets,tethersandsoon)isuneconomicalbecauseoftheenergy
Availableonline19August2014
costofmatchingorbits.Inthispaper,wepresentacompletelynewproposalrelativeto
Keywords: ourearlierwork.Thisnewapproachusesrapid,head-oninteractionin10–40sratherthan
Spacedebrisremoval 4 minutes, using 20–40kW bursts of 100ps, 355nm UV pulses from a 1.5m diameter
Laserablation apertureonaspace-basedstationinLEO.Thestationemploys“heat-capacity”lasermode
Laser-producedplasma
withlowdutycycletocreateanadaptable,robust,dual-modesystemwhichcanloweror
Neodymiumlaser
raiselargederelictobjectsintolessdangerousorbits,aswellasclearoutthesmalldebris
Ytterbiumlaser
Thirdharmonic in a 400-km thick LEO band. Time-average laser optical power is less than 15kW. The
combinationofshortpulsesandUVwavelengthgiveslowerrequiredfluenceontargetas
wellashighermomentumcouplingcoefficient.Anorbitingsystemcanhaveshortrange
becauseofhighinteractionratederivingfromitsvelocitythroughthedebrisfield.This
leadstomuchsmallermirrorsandloweraveragepowerthantheground-basedsystems
wehaveconsideredpreviously.Oursystemalsopermitsstrongdefenseofspecificassets.
Analysisgivesanestimatedcostlessthan$1keachtore-entermostsmalldebrisinafew
months,andabout280k$eachtoraiseorlower1-tonobjectsby40km.Webelieveitcan
dothisfor2000suchlargeobjectsinaboutfouryears.Laserablationisoneofthefew
interactionsinnaturethatpropeladistantobjectwithoutanysignificantreactiononthe
source.
&2014IAA.PublishedbyElsevierLtd.Allrightsreserved.
1. Background 300mgpieceofsmalldebrishasakineticenergydensity
of113MJ/kg,23timesthatofdynamite.Itskineticenergy
Asthemovie“Gravity”dramaticallyillustrated[1],the is83timesthatofa9mmLugerround.
instability predicted by Kessler and Cour-Palais [2] is While improved debris tracking and orbit prediction
propagated between big objects by small debris. The can temporarily improve threat avoidance via maneuver-
instability has now reached the point where collisional ing[3,4],effectivedebris-clearingstrategieswillbeneces-
cascadesthreatentheuseofLEOspace.Thesmallonesare sary. For very large objects like the 8-ton ENVISAT, an
asignificantthreat.Withrelativeimpactvelocitiesoforder effective maneuver is to lower or raise it about 40km,
15km/s and mass areal density of order 1kg/m2, a 2cm, resulting in less collision probability as well as less
perceivedrisk[seeSection3.2].
Four cataloged events have now occurred in which a
nTel.:þ15054663877. debris collision terminated an active satellite. Thirty-five
E-mailaddress:[email protected] cataloged satellite breakups are of unknown cause, and
http://dx.doi.org/10.1016/j.actaastro.2014.08.007
0094-5765/&2014IAA.PublishedbyElsevierLtd.Allrightsreserved.
244 C.R.Phipps/ActaAstronautica104(2014)243–255
manyofthesearesurelyduetocollisionswithuntracked Few concepts have progressed to the point where
debris. However, the main urgency is to mitigate future accurate costs can be calculated, but Bonnal [9] has
risks. Morethan one hundred 1400-kg Cosmos 3M third estimated a cost of 13–17M$ per object for deorbiting
stageswithupto300kgofresidualpropellantarestillin large targets. Any mechanical solution will involve a
Δ
LEO and medium-Earth orbit (MEO), waiting to sponta- comparable v from Earth, so we take this estimate as
neouslyexplode,astheyhavefivetimes.Basedon[5],we representative of removal cost per large item with
estimate the cumulative probability of ENVISAT's debris- mechanicalmethods.
inducedfailureat8%/decade.Itscatastrophicfailurewould
jeopardizeuseofsun-syncorbits,andthreatentheregion
2.2. Laserinteractioncategories
around 766km altitude in the long term. It will take a
decade to implement an effective debris removal system,
At low intensities below the ablation threshold, lasers
sonowisthetimetobegin.Largedebrismustberemoved.
havebeenproposedtodivertdebristhroughlightpressure
They are the main source of additional debris when hit.
[10].Inthiscase,theproposedhardwarearrangementwill
Small debris must also be removed. Theyare much more
deliveratmostafewtimestheintensityofthesuntothe
numerous and so are the main threats because of the
debris,andthatonlyduringafewminutes'timewhilethe
additional debris they create when they collide with a
debris passes above the laser site, rather than all day.
larger object. These were the main conclusions of a 45-
Sunlight produces a larger time-integrated effect. This
studentstudyattheInternationalSpaceUniversity[6].The
method does not effectively address the debris growth
chancethatsmalldebriswillstrikealargeLEOspaceasset
problem.
is 45 times as high as the hazard from large objects [7].
Laser ablation is more effective by several orders of
Table1summarizestheseconclusions.
magnitude. But, at the focal plane intensity required for
continuous(CW)laserablation,thenecessarylaserpower
isdaunting[seeSection4.3],andsplashingislikely.
2. Proposedsolutions
Pulsedlaserablationisanoptimumuseoflaseraverage
powerbecausetheablationimpulseandefficiencycanbe
2.1. Absorbingorchangingorbitsofdebris
optimized for each type of target material, and removes
nmofmaterialperpulse.
Solutions that have been proposed for large objects
A NASA headquarters concept validation study [11]
include chasing and grappling, attaching electrodynamic
concludedthatitisfeasibletousepulsedlaserstoremove
tethers, deploying nets, and deploying clouds of frozen
essentially all dangerous orbital debris in the 1–10cm
mist,gasorblocksofaerogelinthedebrispathtoslowthe
rangebetween400and1100kmaltitudewithintwoyears,
debris.Someofthesearedifficulttoimplement,costlyand
andthatthecostofdoingsowouldbemodestcompared
addressonlyoneorafewobjectsatatime.Forexample,
to that of shielding, repairing, or replacing high-value
anaerogel“catcher'smitt”designedtoclearthedebrisin
spacecraft that would otherwise be lost todebris impact.
twoyearswouldrequireaslab50cmthickand13kmona
Webelievethisisstilltrue,andthatthetimeforactionhas
side. Such a slab would weigh 80kt, cost $1T to launch
arrived.
(Table 2), and require a steady 12kN average thrust to
opposeorbitaldecayoftheslabagainstrampressure,even
inanellipticalorbit[8]. 3. Laserdebrisremovalsystemdesign
Table1 3.1. Systemgoals
LEOdebriscategories.
Reasonable goals for a laser debris removal (LDR)
LEODebris Small Large
system are that it should removesmall debris, as well as
Size(cm) 1–10 10–1000 reducethethreatoflargedebrisbyraising/loweringthem
AccessibleTargets 100k 2.2k into a less hazardous orbit, work fast, have the best cost
NumericalRatio 45 1
perdebrisobjectandavoidtheperceivedrisksassociated
Characteristic Mainthreat Mainsource
with LDR. These are: unpredictable re-entry location on
Table2
ExamplesofproposedLEOdebrisclearingsystems.
Applicableto ) Large Small Disadvantages Advantages
Approach + Debris Debris
ElectrodynamicTethers Yes No LargeΔvtoreachsuccessiveobjects,(cid:1)17M$/object Goodforfew,largeobjects
AerogelBlocks Yes Yes 1T$costtolaunch&maintain,Cluttersspace Shieldindividualobjects
Nets Yes No LargeΔvtoreachsuccessiveobjects,(cid:1)17M$/object Goodforfew,specificobjects
GroundbasedLaserActiveDebris Yes Yes Weather,self-focusing,stimulatedRamanscattering, Goodforall,lowcostpersmall
Removal(LODR,ORION) turbulence,largetelescopes,adaptiveoptics object
SpacebasedLaserActiveDebris Yes Yes Launchcost;difficulttorepair Goodforall,smalloptics,very
Mitigation(“L'ADROIT,”thispaper) lowcostpersmallobject
C.R.Phipps/ActaAstronautica104(2014)243–255 245
the ground for large objects that might survive re-entry, rather than up from the ground, also provides a much
unintended dazzling of spaceborne sensors and injuring bettermomentumexchangegeometry.
peopleontheground.Thedesignwepresentinthispaper Wewilluse“heat-capacity”lasermodewithlowduty
willachievethesegoals. cycle to create an adaptable, robust, dual-mode system
which can lower or raise large derelict objects into less
3.2. L'ADROITsystemconcept dangerousorbits,aswellasclearoutthesmalldebrisina
400-km thick band in LEO. Heat capacity mode means
We call the concept we introduce in this paper Laser momentarily operating a solid state laser in a mode
Ablative Debris Removal by Orbital Impulse Transfer. It beyond its continuous capability for heat dissipation in
achievesthesystemgoalsinsixspecificways. itscomponents,usingtheirthermalcapacity,andcooling
First, we will lower or raise large objects rather than later. Time-average laser optical power in small target
attemptingtore-enterthem,untilwehavedemonstrated modeisabout2kW.
precisionoperationofoursystem,toeliminateoneofthe Fig.2showsthatinthispolarorbit,typicaldebrishave
perceived risks. Lowering ENVISAT by 40km will reduce a15km/svelocityrelativetoourstation.
thethreattoitbyafactoroffour[12]. Fig. 3 shows the L'ADROIT system. It is launched into
Second, we use 100ps ultraviolet pulses at the 3rd apolarorbitwitheccentricitye¼0.028,inclinationi¼901,
harmonicofneodymium(Nd)at355nmor,possibly,that argument of the periapsis ω¼–1801, maximum altitude
ofytterbium(Yb)at343nm.Theshorterwavelengthand 960km and minimum altitude 560km. Altitude at the
μ
pulsewidth (compared to the 1.06 m, 10ns pulses we poles is 760km. In this orbit, it will eventually intersect
used in previous work) give a factor of 9 less fluence theorbitsofalldebrisinthebandh¼760 7200kmand,
(J/cm2)requiredontargettoproduceoptimummechanical atthepoles,repeatedlyintersectthealtitudeofmanysun-
impulse coupling, and an improved impulse coupling synchronous orbits, especially that of ENVISAT. Its orbit
coefficient. Diffraction at 355nm gives a 3-times-smaller matchestheconditionsofFigs.1and2.
illumination spot for a given range (Section 4.4). Lower Fig. 4 shows the components of the system. Two
fluenceontargetcorrespondstolowerlaserpulseenergy telescopes are used. One is a wide field of view passive
required from the laser. Further, atmospheric attenuation acquisitionsensor,usingdaylightscatteredfromthetarget
at355nmis0.3/km[13],sothattransmissiononatangent to detect its position. On average, a target is in daylight
path to Earth from space is only 2.5E-9, preventing eye half the time. The telescope is aspheric, with a design
injuries on the ground. This choice also gives low back- describedinthenextsection.
groundilluminationanddark,absorptivetargets. The second is an off-axis Cassegrain with a 6mrad
Third, we put the system in LEO rather than on the (0.341) field of view (FOV) which is used to project the
ground,wheretheorbitalsweepvelocitygivesacompara- laser beam. For acquisition, the laser pulse energy is just
tivelylargetargetaccessratewithablackbackgroundfor 1J, but for pushing on large targets it can be as large as
bettertargetdetection.Higheraccessrate,inturn,permits 3kJ.Thistelescopeissteeredtothepositionindicatedby
usingmuchsmallerlaserrange,oforder250kmforsmall the passive acquisition sensor, and the focus can be
objects, and smaller, lighter optics to project the beam, zoomed slightly to match the beam waist diameter and
compared to the groundbased alternative. For large tar- positiontothetargetpositionasitapproaches[15].
gets,wecanusethesameopticsandlargerpulseenergy
with rangeof order600km,because largetargetsdo not 3.3. Targetaccessrate
requiresmallilluminationspots.Inspace,wehaveperfect
pathtransmission,andnoscintillationornonlinearoptical In order toachieve adequate target detection rate, we
effects, so that we can dispense with adaptive optics require a passive sensor with a large FOV. For N targets
Δ
outsidethelasersystemitself. uniformlydistributedinaband hthickataltitudeh,the
Fourth, we interact with small debris head-on to rateatwhichapassivedetectionsystemwithfieldofview
produce re-entry in 10s (rather than the 4min intervals moving at velocity v , range z, thickness Δz, and field of
o
Ω
usedin[7]),withshort,highpowerburstsofpulseswith view accessestargetsis:
even higher momentary power from a 1.5m diameter dN=Ndt¼v Ωz2Δz=½4πðR þhÞ2Δh(cid:3): ð1Þ
aperture. We do not have to reacquire the small targets o E
after the interaction. For large targets, we use many 40s InEq.(1),R istheEarth'sradius.
E
interactions over four years to lower/raise all of them, Toobtainausefulaccessrateforsmalltargets,letalone
and here we can rely on groundbased tracking for thelessnumerouslargeones,wefoundthatweneededat
reacquisition. least a 601 FOV (0.87 sterrad) for the acquisition optic.
Fifth, we set a polar, elliptical orbit which will access Fig. 5 shows how this is possible with two computer-
mostLEOdebris.Fig.1[14]showsusthat,onapolarorbit, generatedconicsectionsobtainedbyrevolvingtheFigure
the azimuth range 7301 will encompass most of the about the vertical axis [16]. A 1:1 correspondence exists
debris.Asweremovethese,otherswillfillinthedistribu- betweenapositiononthearraydetectorandadirectionin
tionuntilallaregone. thefield ofview. Köseetal.obtaineda 1261 FOV in their
Sixth, our laser is mainly aimed horizontally. This, design, much more than we require. This is a modern
together with the UV wavelength eliminates dazzle of exampleofasetofconicsectionswhichgavea1801FOVin
μ
reconnaissancesensors,whichlookdownandmostlyuse [17]. We chose 72 rad FOV for one pixel, leading to a
infrared wavelenghs. Operating head-on into our targets, 212Mpixelvisiblewavelengtharraywith10cmdiameter.
246 C.R.Phipps/ActaAstronautica104(2014)243–255
Fig.1. Source-wiseandtotaldebrisfluxford41cmonanERSorbit[i¼98.61,h¼773(cid:4)789km],asafunctionoftheimpactazimuthA(classwidth
ΔA¼31)[ResultsofESAMASTER-2009model(H.Krag,DLR2014),usedbypermission.Seehttps://sdup.esoc.esa.int.Acronyms:EXPL:explosionfragments.
LMRO:launchandmissionrelatedobjects,intact.SRMS:solidrocketmotoraluminumoxideslag.SRMD:solidrocketmotoraluminumoxidedust.EJEC:
hypervelocityimpactejects.CLOUD:fragmentationclouds.MLI:multilayerinsulation.COLL:collisionfragments.PAFL:paintflakes.MTB:meteoroid
background.Amajorityofthedebrisisincludedwithina7301azimuthrelativetotheorbitingADROITstation.
Fig.2. Source-wiseandtotaldebrisfluxford41cmonanERSorbit,[I ¼98.61,h¼773(cid:4)789km],asafunctionofimpactvelocityΔv(classwidth:
Δv/v¼0.25km/s)[H.Krag,DLR(2014)updateofH.Klinkrad, SpaceDebris,ModelsandRiskAnalysis,SpringerPraxis(2006), Fig.4.4,p.127]usedby
permission,acronymssameasforFig.1.
Table3givesouraccessrateresultsforsmalltargetsat We employ a minimum range of z¼175km to not
different ranges. For small debris, we use range exceed this maximum transverse angular rate and avoid
z¼250775km to combine good acquisition rate ((cid:1)20/ heroic target tracking rates. Test volume thickness
min),reasonablepulseenergy(380J),spotsizelargerthan Δz¼150km gives 10s operation time per target
alltargets(0.22m)andreasonabletransverseangularrate approaching at 15km/s. For this analysis, we assume
fortargetsmovingwithin 7301ofourpath(1.71/s). NS¼100k small debris distributed uniformly within the
C.R.Phipps/ActaAstronautica104(2014)243–255 247
3.4. Targetpassiveacquisitionindaylight
Acccessisnotacquisition.Acquisitionimpliesnotonly
targetaccess,butachievementofadequatesignaltoback-
groundratio(S/B)andadequatephotoelectronnumberN
pe
perdetectorarraypixel. We take N ¼10.Tables 5 and 6
pe
show these results for small and large targets acquired
passively. Values used for these calculations are given in
[7]. In those tables, R is the diffuse reflectivity (per
diff
sterradian).
The values we used for background and source irra-
dianceBλandIλaregivenintheheaderofTable6[18–20].
Δ
Iλissourcebrightnessduetosolarradiation,and tisthe
target residence time on one pixel. We see that all cases
giveadequateN andS/Bratio,evenat900kmrange,so
pe
long as the debris are in sunlight. Relevant relationships
are[7]:
S=B¼RdiffIλ=Bλðd=dspÞ2 ð2Þ
Finigcl.in3a.tLio'AnDcRoOvIeTrssytshteemaltiintuodrebirta.nAgseli5g6h0tl–y7e6c0ckenmt.ricpolarorbitwith901 Npe¼1d6sνp?ηczπ2IðλhΔc=λλÞðdDbqffiRffiffidffiffiiffifffiffifffiÞ2 ð3Þ
In Eq. (3), the parameters are photon energy hc/λ, target
velocityv? transversetothefieldofview(whichsetsthe
exposuretimeperpixel),detectorphotoelectricefficiency
η
, viewing spot size of one pixel d and optical band-
e sp
widthΔλ.Forexample,with250kmrange,dsp ¼18m.In
the visible, we take η ¼75%. At the extreme range
e
z¼900km used for large targets, d ¼65m. Having
sp
located a target's transverse positionpassively with solar
illumination to within this accuracy, we then switch to
activeacquisitiontorefinethepositionfurther.
3.5. Targetactiveacquisition
The active array sensor is a 3000(cid:4)3000 pixel array
μ
with total FOV 6mrad and 2 rad FOV per element. At
250kmrange,oneelementhas25cmresolution.Inactive
acquisition, we steer the Cassegrain telescope shown in
Fig.4. ComponentsoftheL'ADROITsystem.Awidefieldofviewpassive Fig. 4 until it points in the direction indicated by an
acquisitionsensoridentifiestargetsusingsolarillumination.A355nm, elementoftheFig.5passiveacquisitionsensor,andrefine
6mradnarrowFOVactiveacquisitionandfiringunittracksthetarget, its pointing until it follows the track indicated by the
obtainsreturnsfromit,focusesonitandfiresrepeatedlytoalteritsorbit.
acquisition array. When the track is stabilized, wesend a
Because the outgoingpulse ispolarized, itpasses through the splitter
trainof 1J, 355nm pulses tothe target. The laser is now
withzeroloss,whilethereturnpulsesuffersa50%loss.Onlytheactive
telescopeissteered.Section5providesmoredetailsofthedesign. commandedtofireatprogressivelyincreasingenergyper
pulse, its pointing direction optimized and its focal spot
minimized until we see the blue flash of plasma on the
altitude band Δh¼400km centered on h¼760km. The target.Duringahighpowerburst,wewillbeabletoverify
resulting spatial number density times the swept area target position along the beam to 77.5mm, so we will
times relative velocity v¼15km/s corresponds exactly to know when we have changed its velocity enough for
thefluxshowninFig.1addedupacrosstheazimuthbins reentry or, if we are making its path less desirable, to
between 7301. We assume NL¼2000 largedebris in the ceasefiring.Then,wemoveontothenexttarget.
band [7]. Section 5 provides more detail on pointing Tables 7 and 8 give our results at two ranges, for the
accuracy. return from a 1J laser pulse. A narrowband filter helps
Table4givesaccessrateresultsforlargetargets.Wesee providethesignaltobackgroundratioslisted.IntheTable,
thatarangez¼6007300kmisagoodchoicetocombine weassumerangegating,thatis,gatingthedetectorarray
good acquisition rate rate ((cid:1)1.5/min), reasonable pulse to respond only during the period Δz/c during which a
energy (2kJ), laser spot diameter appropriate for all target signal return will be seen. More array elements
targets ((cid:1) 0.5m) and reasonable transverse angular rate wouldgivemoreprecision,withevenmoreS/Bratio.From
(0.91/s). Test volume thickness Δz¼600km gives 40s the last column in Tables 7 and 8, the benefit of a space
operationtimepertargetapproachingat15km/s. backgroundisveryclear.Wenotethat,in[7]and[11],we
248 C.R.Phipps/ActaAstronautica104(2014)243–255
Table3
Smalltargetaccessrateandrequiredpulseenergyforvariousranges.
Range TestvolumeA*Δz Targetnumberintest Targetsaccessed Maxtransverse Singlepixelprojectionat Requiredpulse
(km) (km3) volume number/min ratedeg/s targetds(m) energyW(J)
175 3.98Eþ06 1.6 9 2.46 0.16 188
250 8.12Eþ06 3.2 19 1.72 0.22 380
325 1.37Eþ07 5.4 32 1.32 0.29 630
500 3.25Eþ07 12.7 76 0.86 0.43 1410
AssumednumberofsmalltargetsN¼100k.AltitudebandΔh¼400km,h¼760km.TestvolumethicknessΔz(smalltargets)¼150km.A¼sweptareaΩz2.
Thelastcolumngivespulseenergyrequiredtomakeaplasmaandachieveoptimumcouplingatgivenrange.“Requiredpulseenergy”isexplainedin
Section4.
Table4
Largetargetaccessrateandrequiredpulseenergyforvariousranges.
Range Testvolume Targetnumberin Targetsaccessed Maxtransverse Singlepixelprojectionat Requiredpulse
(km) A*Δz(km3) testvolume number/min ratedeg/s targetds(m) energyW(kJ)
300 4.68Eþ07 0.37 0.55 1.43 0.26 540
600 1.87Eþ08 1.01 1.52 0.86 0.54 1950
750 2.92Eþ08 1.46 2.19 0.72 0.61 2850
900 4.21Eþ08 3.29 4.93 0.48 0.70 3790
AsinTable3,butassumednumberoflargetargetsN¼2k,altitudebandΔh ¼400km,h ¼760km,testvolumethicknessΔz ¼600km.Despitelower
number,muchlargertestvolumestillgivesreasonableaccessrateforlargetargets.
Table5
Photon Budget, Passive Daylight Acquisition: S/B and Npe (λ¼550nm, 250km range) [Iλ¼1000 Wm(cid:5)2sr(cid:5)1μm(cid:5)1, Bλ¼2.7μWm(cid:5)2sr(cid:5)1μm(cid:5)1Rdiff¼0.25,
Db¼1.5m,Δt¼dsp/vperp¼2.4ms,pixelFOV¼72mrad,dsp¼18m,arrayFOV1¼1.05rad.
Debrisd(m) ApertureDb(m) Dbd√R Npe/pixel S/B
1 1.5 0.75 8.81Eþ06 2.86Eþ05
0.3 1.5 0.225 7.92Eþ05 2.57Eþ04
0.05 1.5 0.038 2.20Eþ04 7.14Eþ02
0.01 1.5 0.008 8.81Eþ02 2.86Eþ01
Note:Thisisa212MpixelVISdetectorarrayarray,10cmdia.
Fig.5. Thewidefieldofviewopticmadefromconicsectionsusedinthepassiveacquisitionsystem.AdaptedfromE.KöseandR.Perline(2014),“Double-
mirrorcatadioptricsensorswithultrawidefieldofviewandnodistortion,”Appl.Opt.53,528–536,Fig.6[usedbypermission].
C.R.Phipps/ActaAstronautica104(2014)243–255 249
Table6 Table9
Photon Budget, Passive Daylight Acquisition: S/B and Npe (λ¼550nm, OpticsSteeringReactionWheel.
900km range) [Iλ¼1000 Wm(cid:5)2sr(cid:5)1μm(cid:5)1, Bλ¼2.7μWm(cid:5)2sr(cid:5)1μm(cid:5)1
Rdiff¼0.25, Db¼1.5m, Δt¼dsp/vperp¼2.4ms, pixel FOV¼72mrad, dsp¼ OpticsmassM 1000 kg
65m,arrayFOV1¼1.05rad. MomentR 1 m
MomentofinertiaI 1000 kg-m
Debrisd(m) ApertureDb(m) Dbd√R Npe/pixel S/B Retargettime 120 s
Accel/deceltime 60 s
1 1.5 0.75 2.45Eþ06 2.21Eþ04 Totalangle 0.52 rad
0.3 1.5 0.225 2.20Eþ05 1.98Eþ03 Angularacceleration 2.9E-4 rad/s2
0.05 1.5 0.038 6.11Eþ03 5.51Eþ01 Torque 0.29 N-m
0.01 1.5 0.008 2.45Eþ02 2.21Eþ00 Reactionwheelcapacity 17.5 N-m-s
Note:Thisisa212MpixelVISdetectorarrayarray,10cmdia.
Table10
Table7 TypicalImpulseCouplingCoefficients(8ns,1.06μm).
PhotonBudget,ActiveAcquisition:S/B(W¼1J,λ¼355nm,250kmrange)
[Iλ¼540Wm(cid:5)2sr(cid:5)1μm(cid:5)1,Bλ¼1.5μWm(cid:5)2sr(cid:5)1μm(cid:5)1Rdiff¼0.25,Db¼1.5m, Material Cmopt(N/MW) Refnc
ΔΔtλ¼¼Δ0.z2/ncm¼]8.30μs, pixel FOV¼2mrad, dsp¼0.5m, array FOV1¼6mrad, Polyethylene,Kaptons 50 19
AluminumAlloys 75 20–23
Debris Laser Signal Background S/B Kevlars 160 24
d(m) photons photons photonsafter
ontarget/ received/ filter,splitter,
pulse pulse rangegate
active optics system, well within current commercial
1 7.15Eþ18 1.61Eþ07 1.20E-05 1.34Eþ12 capability[seeTable9].
0.5 1.79Eþ18 4.02Eþ06 1.20E-05 3.34Eþ11
0.2 2.86Eþ17 6.44Eþ05 1.20E-05 5.34Eþ10
4. Laserablationimpulsegeneration
0.1 7.15Eþ16 1.61Eþ05 1.20E-05 1.34Eþ10
0.05 1.79Eþ16 4.02Eþ04 1.20E-05 3.34Eþ09
0.02 2.86Eþ15 6.44Eþ03 1.20E-05 5.34Eþ08 Anyone who has aligned a pulsed laser beam using
0.015 1.61Eþ15 3.62Eþ03 1.20E-05 3.01Eþ08 apiece of black photo paper has heard and felt the “pop”
due to laser momentum transfer. This is one of the few
Note:Thisisa9MpixelgateableUVdetectorarrayarray(3000x3000
examplesofactionwithoutreactiononthesource.
pixels,12cmdia.)
The figure of merit for pulsed laser ablation is the
mechanical coupling coefficient C , which relates the
m
Table8 impulse delivered to the target by the laser ablation jet
Active Acquisition: Spacebased S/B (W¼1J, λ¼355nm, 900km range) tothelaserpulseenergyrequiredtoproducethejetonits
[Iλ¼540Wm(cid:5)2sr(cid:5)1μm(cid:5)1, Bλ¼1.5μWm(cid:5)2sr(cid:5)1μm(cid:5)1Rdiff¼0.25, Db¼ surface:
1.5m,Δt¼Δz/c¼2ms,pixelFOV¼2mrad,dsp¼1.8m,arrayFOV1¼6mrad,
Δλ¼0.2nm]. C ¼pτ=Φ¼p=IN=W: ð4Þ
m
Debris Laser Signal Background S/B In Eq. (4), p is the ablation pressure delivered to the
d(m) photons photons photonsafter targetbyalaserpulsewithintensityIanddurationτ,and
ontarget/ received/ filter,splitter, laserfluenceΦ(J/m2)¼Iτ.C valuesforlaserablationare
pulse pulse rangegate m
well-known for many materials (Table 10, [21–26]), and
1 5.52Eþ17 9.58Eþ04 2.89E-05 3.31Eþ09 are about four orders of magnitude larger than the weak
0.5 1.38Eþ17 2.39Eþ04 2.89E-05 8.28Eþ08 effectoflightmomentum(Cmhν¼2/c¼6.7mN/MW).
0.2 2.21Eþ16 3.83Eþ03 2.89E-05 1.33Eþ08 Short-pulse laserablation creates hotvaporor plasma
0.1 5.52Eþ15 9.58Eþ02 2.89E-05 3.31Eþ07
bytheinteraction,notnewdebris.
0.05 1.38Eþ15 2.39Eþ02 2.89E-05 8.28Eþ06
0.02 2.21Eþ14 3.83Eþ01 2.89E-05 1.33Eþ06
0.015 1.24Eþ14 2.16Eþ01 2.89E-05 7.45Eþ05 4.1. Variationwithlaserparameters
Note:Thisisa9MpixelUVgateabledetectorarrayarray(3000x3000
AsincidentpulsedlaserintensityIincreasesinvacuum,
pixels,12cmdia.)
vaporisformedandC risesrapidlytoapeakwhenlaser-
m
producedplasmaisformedonthesurface,thengradually
decreases(Fig.7,[22])accordingto
obtained adequate [but much smaller] S/B ratio using C ¼C =ðIλ√tÞ1=4 ð5Þ
range gating and filtering with a groundbased station, m mo
against a daylight sky background, with about the same becausemoreenergyisgoingintoreradiation,ionization,
laserpulseenergyperunitofpixelFOV.Here,wecanusea andbondbreakingthantopropulsion.
μ
verysmallpixelFOV(2 rad)becauseourwavelengthis3 The parameter C is primarily a function of the
mo
times smaller, and because of the absence of scintillation average atomic mass A and charge state Z in the laser
inspace.Table9givesthereactionwheelcapacityneces- producedplasmaabovethesurface[21],ratherthanofthe
sarytocounterthetorquecausedbysteeringthe1000kg surfaceopticalreflectivityatthelaserwavelength.Thisis
250 C.R.Phipps/ActaAstronautica104(2014)243–255
Wehave
Φ (cid:6)B√τJ=m2 ð6Þ
opt
for1ms4τ4100ps.Datashowsthereisnoadvantageto
usingshorterpulses[21].Forexample,withan8nspulse,
Φ ffi75kJ/m2, while, for a 100ps pulse, Φ ffi8.5kJ/
opt opt
m2.Peakcouplingoccursbecauseofcompetitionbetween
the vapor and plasma regimes. Exact prediction of the
intensity where C will be maximized is complicated,
m
dependingonthecompetitionbetweenvaporandplasma
formation [6,27]. However, we can find the approximate
intensity I for optimum (peak) impulse coupling using
Fig.6. Surfacecouplingathighlaserintensity. Eq.(6)intohpet formI √τ ¼Φ /√τ ¼8.5E8W/m2s1/2so
opt opt
that
ðIλ√τÞopt¼850λμmWm(cid:5)1s1=2: ð7Þ
There is no reason to operate elsewhere than at the
peak, because this parameterdirectlyaffects laserenergy
andsystemcost.
Finally,wecansubstituteEq.(7)intoEq.(5)toobtain
Cm(cid:6)0:19Cmo=λμm1=4N=W ð8Þ
4.2. Shortpulsesandwavelengths
Foraparticulartargetmaterialandchargestate,Eq.(8)
showsanadvantageforshortwavelengths.
μ
Just going to 100ps pulse duration at 1.06 m should
give C ¼106N/MW instead of 75N/MW (Table 10). In
m
fact, Fournier [29] recently measured C ¼155N/MW at
m
Fig.7. Whatoptimumcouplingmeans(typicaldata).Optimumimpulse 200ps,1.06μm.Eq.(3)alsotellsusthatΦoptffi8.5kJ/m2.
couplingintensitydependsonthewavelengthandthepulseduration. If we also go to λ¼355nm, the 3rd harmonic of Nd,
Plasmaregimemodelisthedashedline.
Eq. (8) tells us that we expect C : 100N/MW at
m
Iλ√τ¼300W-s1/2/m,ouroperatingpoint[AppendixA].
because the plasma mediates energy transfer from the
μ
lasertothesurface.Fora1.06 m,ns-pulselaserincident
4.3. PulsedVs.CW
onatarget,thecenterwavelengthreachingthesurfacecan
wellbeinthehardultraviolet.Thisisbecausetheplasma
Table 11 ([7,28,30]), in which the continuous wave
is a blackbody radiator, and its temperature in the Fig. 6
(CW) values are based on our calculations using proce-
exampleis55,000K,correspondingtoabout50nmwave-
duresin[6],showsalargecouplingandefficiencyadvan-
length at peak emission. For constant A and Z, C is a
mo
constant. For a singly ionized plasma [Z¼1] at 1.06μm tageforpulsedlasersvs.CWlasersforimpulsegeneration
ontargets.
wavelength,C variesfrom75to200N/MWasthetarget
mo
materialchangesfromhydrocarbonwithAE6toironore, These calculations are important because, to our
from45 to120Ν/W for Z¼3. Foraluminum under these knowledge, no published results exist for CW impulse
conditions, CmoE420N/MW. An approximate relation- coupling on targets in vacuum. Table 11 shows about a
shipfortheoptimumfluenceΦ ¼I τwherethispeak factor of 10 improvement in maximum Cm for pulsed vs.
opt opt
CW lasers. The table shows an unreasonable power
occurs,forarangeofmetallicandnonmetallicmaterials,is
given by Eq. (6) with a value B¼8.5E8J/m2 for robust
Table11
couplingacrossallmaterials(abouttwicethevalueinRefs.
ComparingCWandImpulsiveMomentumCoupling.
[7,20–22]).
As these examples show, the target material matters CW 100ps
only to second order. For example, consider optical glass pulse(thiswork)
damage(Fig.6).Onthistransparentmaterial,with100ps
Cmopt(N/MW) 10 100
pulses,surfacedefectsinitiateahot,highpressureplasma BeamParameteronTarget 10MW/m2 8.5kJ/m2,32Hz
layer in less than 50ps. The plasma is self-regulating so MinimumLaserPowerRequired 1.45MW 40kW
that most of the light is absorbed or reflected. Yet, ThrustDelivered(N) 100 4.0
Relativeeffectiveness 1 10
howeverhotorreflective,theplasmalayerstillgenerates
impulse which [22] predicts. Thermal transport to the
Commonparametersforthisexample:Target:aluminum;Wavelength:
interiorofthesubstrateoccursafterthelaserpulse. 1.06μm;Range:500km;Illuminationspotdiameteratrange:0.43m.
C.R.Phipps/ActaAstronautica104(2014)243–255 251
(1.5MW) for a CW laser to illuminate a 43cm spot with includesthecombinedeffectsofimproperthrustdirection
sufficient intensity to generate good impulse coupling. on the target, target shape effects, tumbling, etc. in
Looked at another way, CW lasers cannot reach the reducing the laser pulse efficiency in producing the
required intensity for efficient coupling to targets at the desired vector velocity change antiparallel to the target
ranges involved without a very small illumination spot track. For large debris, we use the same formulation, but
size, requiring an unacceptably large mirror. Other dis- artificially increase μ to get the desired mass – which is
advantagesofCWtargetheatingarethatslowheatingand always1000kgforouranalysis,andrequirethatthetarget
decayoftumblingdebriswillnormallygiveanablationjet isalwayslargerthanthebeamatitslocation.
whose average momentum contribution cancels itself as Forsmalldebris,wechooseμ¼1kg/m2astypical[32].
the target rotates. CW heating also causes messy melt Some pieces are heavier and will take longer to re-enter
ejection (as with a welding torch) rather than clean jet thanthetypicalcase,andsomearelighter.
formation, adding to the debris problem, contrary to the
behaviorofpulsedablation.
5. Systemperformance
4.4. Relationshipamonglaserparametersforoptimum
impulseontarget
5.1. Systemoperation
Inordertocalculatedeliverable(Iλ√τ) onatargetat
opt
Pulse duration is constant. Pulse energy can easily be
range z, we first need to consider beam spread due to
variedfromjust1Jforlocatingtargetsto(cid:1)1kJforcreating
diffraction. If beam quality is held constant, short wave-
plasma,andenergy(hightolow)andrepetitionrate(low
lengths focus better, proportionally to wavelength and
to high) is varied as the target approaches, keeping
range but inversely with effective aperture diameter D ,
eff
averagepowerroughlyconstant(Fig.8).
because of diffraction. The product of the effective
A1–2minretargetingintervalletsthelasercooloffin
launched beam diameter D and beam spot diameter d
eff s
heat capacity mode, although we may still use 1J pulses
atthetargetis
foractiveacquisitionwhileitiscooling(Tables12,13).The
dsDeff¼aM2λz; ð9Þ passivesystemdetectstargetsat500or900kmrangeand
whereM2isthebeamqualityfactor(1isperfect)andD tells the active system where to change its pointing
eff
directionduringtheretargetinginterval.Forsmalltargets,
istheeffectiveilluminatedbeamdiameterassociatedwith
we can detect as many as 80/min at 500km range, and
the laser station output aperture with diameter D for
b
5/min for the large ones at 900km because of the larger
calculatingdiffraction,anddependsonbeamradialprofile.
samplevolume–sowecanletalotofthemgoby.Then,
For example, if we use a 6th-order hypergaussian radial
intensityprofileI(r)/I ¼exp((cid:5)r/r )6,withcorrectedbeam we pick an optimum target when the laser is cool and
o o
quality M2¼2.0 (Strehl ratio S¼1/M2¼0.25), we find shoot it. More than likely, there are 1 to 3 of them just
D /D¼0.9anda¼1.7[31]. locatedintheboxwherewewantthem[250þ/(cid:5)75kmor
eff 600þ/(cid:5)300km] at the moment we 'are ready to shoot
The constant a regulates diffraction: for the classical
Airypattern,a¼2.44. (Tables3,4),andthecomputerwillhavestabilizedpoint-
TheproductWD2 requiredtodeliverfluenceΦtothe ingbythattime.
eff
targetisgivenby[7]
pffiffiffi
πM4a2λ2z2Φ πM4a2λ2z2B τ
WD2 ¼ ð10Þ
eff 4T 4T
eff eff
InEq.(10),Wislaserpulseenergy(J)onthetargetand
the effective transmission from the L'ADROITaperture to
thetargetT istheproductofallsystemlosses,including
eff
apodization,obscurationandatmospherictransmission.
Eq. (10) shows that the required pulse energy W
increaseslessthanlinearlywithpulsedurationandquad-
ratically with range in this case. Inverting Eq. (10), the
deliveredfluencegiventheotherparametersis
4WD2 T
Φ¼ eff eff ð11Þ
πM4a2λ2z2
Eq.(12)givesvelocitychangeperlaserpulse.
Δvjj¼ηcCmΦ=μ: ð12Þ
Thisformulationisimportant.Itallowsustocalculate
velocity change along the track for one or many small
μ
debris of a given , of whatever size, if they are in the
beam and smaller than the beam at their location. In
Fig. 8. As pulse energy and repetition frequency vary for large target
η
Eq. (12), c is an impulse transfer efficiency factor which reentry,powerduringthelaserburstisconstant.
252 C.R.Phipps/ActaAstronautica104(2014)243–255
Table12
SmallTargetRe-entry,355nmStationinPolarOrbit[GenericTarget].
Targetandstationparameters Opticalsystemparameters
TotalNumberin560–960kmAltitudeBand 100k TypicalPulseEnergy(J) 380
Mass[nonspecifictarget](kg) o0.038 PulseRepetitionFrequency(Hz) 56
Rangez(km) 250775 Laseroutputpower(burst,kW) 21
OperatingFraction[day/night](%) 50 Wavelengthλ(nm) 355
NumberofPassesforsmalldebrisRe-entry 1 PulseLengthτ(ns) 0.1
TimetoRe-enteronedebris(Head-on,s) 10 SpotSizeonTargetdsp(m) 0.22
Recovery/Retargetinginterval(s) 120 FluenceonTarget(kJ/m2) 8.5
PrimaryMirrorDiameter(m) 1.5 BeamQualityFactor 2.0
PushEfficiencyηc 0.50 TargetTypicalCrossfieldRate(mrad/s) 30
MomentumCouplingCoefficient(N-s/MJ) 99 DetectionRate(/min) 15
TimetoRemoveAllTargets(mo.) 4.6 TimeAverageLaserPower(kW) 1.8
CostpersmallObjectRemoved($) 310 TargetRemovalRate(/operatinghour) 30
CostperkgRemoved($)a 8 AcquisitionFieldofView(degrees) 60
Launchcostfraction(%) 31
aCostisproratedtotimepertarget.CostmodelisapproximateandproprietarytoPhotonicAssociates,LLC,basedon[11].
Table13
LargeTargetRaise/Lower40km,355nmStationinPolarOrbit[GenericTarget].
Targetandstationparameters Opticalsystemparameters
TotalNumberin560–960kmAltitudeBand 2kmk TypicalPulseEnergy(J) 1950
Mass[nonspecifictarget](kg) 1000 PulseRepetitionFrequency(Hz) 21
Rangez(km) 6007300 Laseroutputpower(burst,kW) 40
OperatingFraction[day/night](%) 100 Wavelengthλ(nm) 355
NumberofPassesforRaising/Lowering 625 PulseLengthτ(ns) 0.1
ShineTimeperInteraction(s) 40 SpotSizeonTargetdsp(m) 0.50
Recovery/RetargetingInterval(s) 60 FluenceonTarget(kJ/m2) 8.5
PrimaryMirrorDiameter(m) 1.5 BeamQualityFactor 2.0
PushEfficiencyηc 1.0 TargetTypicalCrossfieldRate(mrad/s) 12
MomentumCouplingCoefficient(N-s/MJ) 99 DetectionRate(/min)[muchlargertestvol.] 5
Timetoremovealltargets(yrs) 4 Timeaveragelaserpower(kW) 16
Costpertargetlowered/raised(k$) 280 TargetΔv||/pass(cm/s) 8.3
Costperkgremoved($)a 280 Acquisitionfieldofview(degrees) 60
Launchcostfraction(%) 18
aCostisproratedtotimepertarget.CostmodelisapproximateandproprietarytoPhotonicAssociates,LLC,basedon[11].
InFig.4,onlythebeamprojectionCassegraintelescope sufficient for re-entry. It is interesting that this task can
is steered. In order to avoid aberration, this requires a becompletedfor100ktargetsinalittleoverfourmonths,
periscopearrangementoftwoflatmirrorsinsidethelaser almostimmediatelyremovingtheobjectswhichcommu-
system to rotate and tilt the laser beam along with the nicate the breakup instability. In small target mode, the
telescope. The reaction wheel and steering components duty factor is 50% because we need daylight to locate
μ
will cause vibration onboard the spacecraft. The 0.5 rad targets.
pointingaccuracyimpliedbyTables3and4isachievedby
precisionpiezoelectrictransducerstiltingthefirstofthese 5.3. Largetargetraising/lowering
μ
mirrors overa rad range against a combination of fixed
star and angular accelerometer references with a 1kHz For large targets (cid:1)1000kg, we can only make small
feedbackloopbandwidth. velocity changes in one interaction [Table 13], so we
assume groundbased tracking assistance to relocate a
5.2. Smalltargetre-entry specific object afteran interaction and give us 100% duty
factor. Typical Δv per interaction is 8.3cm/s, so 625
Table 12 shows performance for an optimized space- interactions are requiredtoprovide 43m/s Δv necessary
basedUVlasersysteminproducingsmalltargetre-entry. toraiseorlowerthe1000kgobjectby40km(seeSection
Here, our goal is single interaction re-entry, because 3.2) It will take about 4 years to complete this operation
post-shottrackingofthesmallobjectsisdifficult.Forthis on 2000 one-ton objects, so we consider the majority of
reason, we provide bursts of laser power sufficient tore- systemcosttobebornebythisapplication.Wenotethat
entermostofthesmalltargetsinatensecondinteraction. bothjobscanbedonewitha2–15kWaveragepowerlaser
In one interaction, we provide 236m/s Δv, which is capableof20–40kWburstslasting10–40s.