I
I ANALYSIS OF THRUSTER REQUIREMENTS AND CAPABILITIES FOR LOCAL SATELLITE CLUSTERS
G. I. Yashkot, D.E. Hastingstt I Massachusetts Institute of Technology Cambridge, Massachusetts I Abstract This paper examines the propulsive requirements necessary to maintain the relative positions of satellites orbiting in a local cluster. Formation of these large baseline arrays could allow high resolution imaging of terrestrial or I astronomical targets using techniques similar to those used for decades in radio interferometry. A key factor in the image quality is the relative positions of the individual apertures in the sparse array. The relative positions of satellites in a cluster are altered by "tidal" accelerations which are a function of the cluster baseline and orbit altitude. These accelerations must be counteracted by continuous thrusting to maintain the relative positions of the satellites. I Analysis of propulsive system requirements, limited by spacecraft power, volume, and mass constraints, indicates that specific impulses and efficiencies typical of ion engines or Hall thrusters (SPT's) are necessary to maintain large cluster baselines. In addition, required thrust to spacecraft mass ratios for reasonable size clusters are approximately I 15J..LNlkg. Finally, the ability of a proposed linear ion microthruster to meet these requirements is examined. A variation of Brophy's method is used to show that primary electron containment lengths on the order of 10 mm are I necessary to achieve those thruster characteristics. Preliminary sizing of the linear ion microthruster is given. Nomenclature IDtot = total thruster mass flow rate, kg/s 2 Ac = thruster chamber area, m2 Nc = thruster chamber width, m N = number of lifetime impulsive thruster firings b = filled aperture characteristic dimension f 3 I B = sparse aperture baseline no = chamber neutral atom density, kg/m BDV = electric field breakdown voltage, V Pin = required thruster power input, W Co = primary electron utilization factor, A-I Pslc = available spacecraft power, W da = accelerator grid spacing, m ra = along-track resolution I DtaIlk = propellant tank diameter, m R = reference satellite distance from Earth center Dslc = spacecraft diameter, m Rs = slant range e = electric charge, 1.6x10-19 C S = synthetic aperture dimension I fB = fraction of ions extracted Vo = neutral atom velocity, m1s fc = fraction of ion current produced that goes VrY!;t = net voltage across deceleration grid, V to cathode potential surfaces, m VfIJt = total voltage across acceleration grid, V Ftot = total thrust, N VD = discharge voltage, V I go = gravitational acceleration, 9.8 m1s2 Wc = thruster chamber width, m h = orbit altitude x = Displacement of cluster satellite in x y Displacement of cluster satellite in ~ = thruster chamber height, m = y IB = Impulse bit, N s z = Displacement of cluster satellite in z I Isp = spacecraft mass, s flsIc = spacecraft specific power, W/kg IB = ion beam current, A
1. Backaround I 1.2 Interferometry I Sparse Arrays Interferometry has been used for ~ to produce images of astronomical objects in radio Another method to increase resolution is wavelengths with resolutions rivaling that of ground interferometry. Interferometers use separate apertures I based optical systems. I This technique, when spaced some distance apart to create a sparse aperture deployed across a cluster of satellites, may be used to as sketched in Figure 1. produce high resolution remote sensing images of I terrestrial targets from space or provide a platform above the atmosphere for space-based viewing of astronomical objects. I 1.1 Synthetic APertures
The diffraction limited ground resolution of I typical filled apertures is given by2 AR I r =_'3 (1) a b' Figure 1. Ground-based Radio Interferometer Equation (1) indicates that increasing the aperture size I improves the resolving power of the instrument. Interferometers were originally used in radio Aperture size is limited, however, by size and weight astronomy to distinguish discrete radio sources from constraints of the launch vehicles which place the the diffuse background. Synthesis is obtained by satellites in orbit. Synthetic Apertw'e Radar (SAR) observing separately all the interferometer pairs that I can improve resolution at RF wavelengths from Low exist within a large aperture. A chessboard with only Earth Orbit (LEO) by utilizing the Doppler shifting two chess pieces may be used as an analogy. All of signals to "synthesize" an aperture much larger combinations of the pieces on the board must be I than the satellites filled aperture. Resolutions of sampled to recreate a uniform aperture. To SAR systems are given by2 accomplish this, the receiving elements are designed to be mobile across the so-called u-v plane. As b I Ta=- (2) baselines increased, the rotation of the earth was used 2 to sweep a range of spacings with fixed antennae. Very large baselines composed of widely separated where b is again a characteristic dimension of the antennae soon made sampling the entire u-v plane I filled aperture. Although contrary to intuition, impractical. Computer calibration techniques are now . 3 equation (2) indicates that reducing the filled aperture commonly used for sparse aperture syn th eslS. size improves the resolving power of the radar. At I some point, however, aperture temperature, power The position and spacing of the elements is key to output, and gain limitations preclude the use of the quality of the image produced. The paths traced smaller apertures. Table 1 lists allowable resolutions out by the electro-magnetic waves must be carefully for a typical 10m filled aperture sensing in the controlled so that the signals may be coherently I optical, infrared (IR), or radio frequency (RF) combined. This tolerance is typically ')J20. In the wavelengths at several altitudes. case of the Space Telescope's primary mirror, this margin is a few hundredths of a micron.4 For a I Table 1. Current Achievable Resolution regularly spaced array, a pOSitional error of a few with 10m Aperture. wavelengths can cause significant sidelobes, even if Optical Infrared (IR) Radio (RF) the faulty positions are known exactly so that each I Altitude A=O.5!-l A.=10 !-lm A.=3cm element can be correctly phased.5 In cases where the m relative pOSitions of the element are not known (such tOOO kID 5cm 1m 5 m (SAR) as with random arrays), calibrations can be carried out I 10,000 kID 50cm 10m 30km to improve the quality of the images providing the 35.768 kIn 1.8 m 18 m 107km I 2 I I
I relative positions do not change from one image to the next.
The achievable angular resolution is diffraction I limited in accordance with the Rayleigh criteria. The size of the aperture, however, is the maximum linear distance between the individual elements. This I distance is known as the baseline, B, so thae I (3) Table 2 lists the angular resolution versus Fig. 2a. Cluster Formation Normal to sampled wavelengths for numerous existing Reference Orbit Plane I interferometers along with the baseline of each system. Although aperture synthesis is well established in the radio spectrum, imaging of I astronomical sources with multi-aperture interferometers is just beginning with the construction of the Infrared-Optical Telescope Array (IOTA) at the F .L. Whipple Observatory on Mount I Hopkins, AZ.6
Table 2. Angular resolution of existing I interferometers
Int ... J~e A Ang. Resol. I VLBI 8,500 kIn 1cm-1m le-4" to le-2" VLA 35 kIn 1cm-5m 0.1" to 20" W esterbrook 3.2km 10cm-1m 5" to 100" I Merlin 135 kIn 10cm-lm 0.1" to 1" non-inertial orbit Source: Wohllenben 7 ,Pg 17 Figure 2b. Cluster Formation in Plane of Reference Orbit I 1.3 Local Satellite Clusters By coherently adding the signals received by Forming space-based sparse apertures, analogous several satellites, the cluster would, in effect, create a to the ones discussed in section 1.2, could be sparse aperture many times the size of a real aperture. I accomplished through the use of a local satellite The sparse aperture's large size could vastly increase cluster. Satellites in a local cluster orbit in the level of resolution possible. There are several formations such as those shown in Figures 2a and 2b. possible advantages of creating a sparse array cluster. I Although one or more reference satellites will be in For example: standard Keplerian (ie. inertial) orbits, maintaining 1) Extensive earth coverage could be achieved at the formation will require the other satellites to orbit GEO with a resolution similar to that of current I in planes parallel to the reference orbits. These non satellites in LEO. inertial orbits are characterized by either a focus which 2) By turning satellites within the cluster "on and is not located at the Earth's center of mass (Fig 2a), off' it may be possible to alter the dimensions of or orbital velocities which do not provide the proper the sparse aperture and thus zoom in on a target I centripetal acceleration to offset gravity at that detected in a broad, coarse field of view. altitude (Fig 2b). As expected, the Earth's gravitation will act to move these satellites into Keplerian orbits. The gravitational forces which act on the satellites in I It will be shown in Section 2 that continuous low non-inertial orbits will now be examined in more level thrusting is required to maintain each satellites detail. position.
'. 3 I I I 2. Orbital Dynamics Of Satellite Clusters (5) 2.1 Tidal Forces I Figure 3 shows the coordinate system for a simple two satellite cluster. Satellite 1 is in an inertial reference orbit at an distance, R from the center of I the Earth. Satellite 2's position relative to satellite 1 Section 3 identifies the maximum displacements from is r. the reference orbit that are feasible due spacecraft mass, power, and volume constraints. For those size I clusters, this extra r z term is negligible.
Equation (4), when multiplied by the Illgc' describes I the required on-board thrusting necessary to produce desired accelerations and velocities relative to some reference satellite in an inertial orbit. Notice that for x=y=z=i=y i=x=y=z=O, (4) reduces to I the case of a satellite in a inertial orbit where no thrusting is necessary to maintain its orbit under two body orbit assumptions. I
Even with x = Y= t = x = y = z= 0, y and z displacements create "tidal" forces which will tend to I move the satellite into an inertial orbit as described by Janson.9 These tidal forces need to be counteracted by thrusting in order to maintain the I cluster. Tidal forces arise from displacements along Figure 3. Satellite Cluster Coordinate System. z because the cluster satellite is constrained to orbit with the same velocity as the reference satellite yet at a different altitude. Thus, unlike the reference I The motion satellite 2 with respect to 1 can be found satellite, the gravitational attraction of the Earth is using the linearized equations of relative motion for a not exactly offset by the centripetal acceleration d.'cE circular reference orbit. These equations, known as the to the satellite's circular motion. Displacements Clohessey-Wiltshire equations, ares I along y force the satellite to orbit in a plane rx =i+2nt parallel to reference satellite. In that case, only a component of the gravity vector lies in the plane of I ry= y+n2y (4) the orbit. Once again, the centripetal acceleration is r = z+2lli-3n2z not offset by Earth's gravity. A displacement along z x can be considered a displacement along z occurring at a point further ahead in the reference I where n=~f.l/ R3. orbit. Tidal accelerations, which must be counteracted I with thrusting, are shown in Figures 4 and 5 for One would intuitively expect a rz term due to displacements along y. It is eliminated by the displacements normal to the reference orbit plane ( y) linearization process in the derivation of (4), and radially within the reference orbit plane ( z ). I although it does appear in the full length equations. I I 4 I I
around the reference orbit completing one oscillation I 1 E-02 every orbit. In essence, it would be in an inertial orbit inclined with respect to the reference orbit. This 1 E-03 :1:::r::::::]::r:::1-:: coo GIl motion relative to the reference orbit would move the I E satellite beyond the allowed tolerance for elements of ri 1 E-04 a sparse array. Therefore, the thruster will need to c , ------+-·---1-- y J ... m ~ fire an impulse bit which keeps the satellite within «I I ~ 1E-05 the tolerance region. Gi u U «I
iii 1E-OS -~ ~~~fv-~~~~u/-. ; 250 m ~ tolerance / I 0.8 zone ; 1E-07 ------:------1------:------i ./ 25 m ::: ---- \~:::::---':~---- I 1 E -0 S t---t---t-----...1f-----i---+----t-----r- lHRUST 0.2 5000 10000 15000 2000025000 3000035000 C'CCl.f5 " x Altitude (km) Figure. 4. Tidal accelerations along y for I satellite displaced a distance y. \ -':r-0.4 ~\ 1- \ ~ \ I . .' '. FEFEREN:E ::>RBIT PLANE 1 E-02 -O.S t \. I -0.8
-1 1 E-03
z :2500 m I Figure 6. Impulsive Thrusting Procedure 1 E-04 ri c ~ At time t=O, halfway between impulse firings, II I ~ 1 E-05 x = z = i = z= i = z= rx = ry = rz = O. Equation ...u U (4) II then reduces to
~ 1E-OS I (6) N
1 E-07 9 I :::::::::::::::~::::I::::::::t::::::--r------,----!-- ~ m This undamped linear oscillator has the solution yet) = Yo cos(nt) (7) 1 E-osl I I I 5000 10000 15000 20000 25000 30000 35000 yet) = -YoQsin(nt) (8) Altitude (km) yet) = _yoQ2 cos(ru). (9) I Figure_ 5. Tidal accelerations along z for satellite displaced a distance z. Then, from (7), the time at which the satellite would I drift beyond the tolerance limit is 2.3 Impulsiye ys Continuous Ihrustin~ t=-cos1 -1( Yo - tOI] (10) To remain within the allowable relative position Q Yo I tolerances discussed briefly in Section 1.3, the cluster of satellites could use either a series of impulsive Figure 7 shows the plot of equation (10) at several thruster firings at regular intervals or apply a lower, altitudes. It can be seen from the figure that, at all I continuous thrust. altitudes, as the required relative position tolerance decreases the time the satellite is able to drift before Consider the case of a satellite displaced along y as frring an impulse decreases. The largest value of I shown in Figure 6. If no thrust were applied in the tolerance/displacement will be for RF sensing sparse y direction, the displaced satellite would oscillate apertures in LEO. For an RF cluster satellite sensing I 5 I I at A=.05m, tolerances will be on the order of 2.5 impulsive thrusts. As the tolerances tighten (and I mm. At 1000 kIn altitude and displaced 25m, this the time between impulsive thrusts shortens), the ~ V tolerance/displacement is 1e-4. Figure 7 indicates expended for a impulsive thrust approaches that that the satellite could drift for 14 seconds. In the expended by continuous thrusting. optical region, however, allowable drift time is I approximately 0.05 seconds. 783.00 : 100T-----~------~~--~ I 782.95 ~ 90 .. +... '" "0 GI \ Gontinuous "0 80 GI 782.90 GI ,ThrUSting C) 70 )( .- I UJ km 782.85 .! 60 ! > GI
Assuming that the satellite's y velocity after the The previous analysis would indicated that, at the impulse is exactly negative that before the impulse, broadest relative position tolerance levels, the I and that the tidal forces and impulse thrust are maximum time between required impulsive thrusts is constant during the time the impulse is applied, then on the order of seconds. For optical and infrared wavelengths, this time is on the order of tenths of a second. Further, at these short thrusting intervals, I only minimal amounts of propellant savings result from impulsive thrusting. Therefore, continuous thrusting will be assumed for the rest of this analysis. I where t is found from (10) and ~ t is the thruster firing time. 2.3 DynamiC Clusters The total impulsive firings during the mission life is I then For the situation where satellite positions are fixed (12) relative to each other, the total ~ V expended during the satellite's mission life is I
Calculating the total impulsive ~ V expended over the mission life, (14) I where is the acceleration produced continuously by (13) r an on-board propulsive system to counteract tidal forces. Equation (4) indicates that the required thrust I per unit of spacecraft mass is larger for a satellite Figure 8 compares the ~ V expended for continuous stationed at a greater distance from the reference orbit. thrusting to that of impulse thrusting. The figure From equation (14), for a given mission life, a shows that for a given displacement, as the tolerance I satellite stationed far from the reference orbit will region in which the satellite can drift increases, only consume more fuel than a satellite stationed closer. It negligible amounts of ~V can be saved by using I 6 I I
I may be desirable, therefore, to rotate the positions of that expended by a satellite at the far edge of a static, the satellites during their life as a means of non-rotating cluster. distributing the fuel consumption amongst all the I satellites in the cluster. Consider the case, illustrated in Figure 9, where the satellites in a cluster continually rotate in a circular I pattern relative to the reference satellite. Figure 9 shows only two of the many satellites comprising the cluster. This is one of many possible methods by which satellites in a cluster change position, but it I serves well as an example of a "dynamic cluster".
y I O. 1 -t",~.w"'.:''ow~",~.·,;:u.,.w"",;.• w''''·'''·'~:·'W'~''h~''w'W"'';';''NU.'W'~'.''UN··1 ..... --. 0.0 -Jo-...... - ...... ---+--"----I-'"""""""~ o 2 3 4 I Number of Rotations During Mission Life x Figure 10. Reduction in Cluster Maintenance AV
Vomit I .., , .. .. As the number of rotations about the reference .. . satellite increases beyond about 1/3, the AV ratio REFERENCE ' ...... CRBIT - ... ~ •• begins to increase again because the satellite is I spending more time displaced further from the reference orbit along -y. At a rate of 1 rotation Figure 9. Dynamic Cluster Formation during the mission, the A V expended is about 65% I that of the worst case satellite in a static cluster. The AV ratio levels off at this value for more than 5 For this si tuati on, rotations during the mission. Although not shown in x = rsin(O) Figure 10, as the rotation rate is increase further, the I Y= rcos(O) (15) AV required just to maintain the circular motion z=o around the reference satellite begins to dominate. At rate of a few hundred rotations during the mission, the I By substituting the relations from (15), equation (4) AV ratio increases above unity indicating it no longer becomes beneficial to rotate the cluster satellites.
'2 I rx =-rO sinO It should be stated that a sparse aperture might be formed using a constellation of satellites rather than a 2 ry = -r cos 0(0 +~F) (16) local cluster, depending on whether the positional tolerance problem could be solved. For that = 2r(cosO)OO I rz situation, all satellites would orbit in inertial orbits and the sparse aperture would be formed using where 0= ~J..l1 R3 , whatever satellites are available as they fly over the I region of interest. The AV for maintaining that It can be seen from (16) that the required thrust levels "sparse aperture" would be zero. The analysis of a satellite in a dynamic cluster are a function of the throughout the rest of this paper, however, is focused I cluster radius, r, the cluster's reference altitude, the only on the requirements of maintaining a local static position of the satellite, a, as well as the rate at cluster. which the satellite rotates about the reference satellite, iJ. Figure 10 shows A V expended by all satellites I in the example dynamic cluster can be as low as 54% I I 7 I I 3. Propulsion System Reguirements 3.2 Methodology Based on the acceleration levels presented in section 2, the propulsion system requirements to maintain a In determining the feasible range of thruster Isp and 11 I local satellite cluster can be calculated. The feasible necessary to maintain a local satellite cluster, the range of specific impulse and efficiency, constrained following assumptions were made: spacecraft mass, volume and power considerations, is • The satellites operate as a static cluster I the primary characteristic to be determined. maintaining a fixed displacement normal to the reference orbit. 3.1 Current Thruster Characteristics • Isp and 11 are the same for all thrusters used in I cluster maintenance and station-keeping Two classes of propulsion, chemical and electric, • Thrust levels of each thruster are constant during are currently used as station-keeping thrusters on the life of the mission. board spacecraft. Tables 3 and 4 list several types of • Any cluster maintenance and station-keeping I thrusters falling within those two classes along with maneuvers are performed continuously. ranges of specific impulse and efficiency. These • The spacecraft and propellant tanks are spherical. ranges can be displayed graphically as shown in • Spacecraft total mass is constant throughout the I Figure 11. This format will be used as a template for life of the mission. a comparison of current thruster capabilities to those • An additional SOmis of propellant per year is required for maintaining cluster formations. It is allocated for traditional station keeping I important to point out that Figure 11 simply shows requirements. the range of Isp vs. 11. If a local cluster formation requires a combination of Isp and 11 which falls A spacecraft displaced a gi ven distance from the within the shaded box, there is no guarantee a reference orbit using a thruster operating at a given 11 I thruster with those characteristics exists. However, if and Isp must satisfy the following three design the cluster satellite needs a combination of Isp and 11 constraints. which does not fall within a shaded box, then it can < I be said that no current thruster exists which is able to • Dtank (Dtank) meet those requirements. Dslc Dslc max
• mp+mpp < (mp+mpp ) (17) I mslc mslc max I 5000
4000 +- ...... ~ ...... The values for the maximum ratios allow margin for I the satellite to accomplish tasks other than simply CD :: 3000 +-...... ; ...... : operating the thrusters. Specifically, the three .! statements gauge whether or not there is, once I station-keeping requirements have been met, 2000 + ...... :...... : sufficient volume, mass, and power available on board the satellite to perform mission operations such as payload, communications, etc. If the answer to I 1000 one or more of these criteria is no, then it is concluded that a satellite of mass, ms/ ' and propellant --+-...... c O+--I---I--+--+-ol---+-...... mass fraction, nyffistc is unable to adequately o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 I maintain its position, f, from the reference orbit at Efficiency an altitude, h, for a mission time, life, using a Figure 1 L Current Thruster Capabilities thrusters with specific impulse, Isp and efficiency 11. I I 8 I I
I Table 3 Current Chemical Thruster Characteristics SYSTEM PROPELLANT Isp (s) THRUST (N)
COLD GAS Nz. NHp Freon, 50-75 0.05-200 Helium I SOLID MOTOR 280-300 50 - 5xl06 LIQUID * MONOPROPEI.LANT fI:z~,Nz~ 150-225 0.05 0.5 I MONOPROPHLANT Nz~ 200-230 0.03 - 100 6 BIPROPELLANT ~ andRP-l 350 5 - 5xl0 6 ~ and Hz 450 5 - 5xl0 6 I Nz~ andMMH 300-340 5 - 5xl0 (N,fL, UDMH) F, andN,Rt 425 5 - 5xl06 6 OF2 and B2H.- 430 5 - 5xl0 I 6 C1F5,Nz~ 350 5 - 5xl0 WA1ER fl:z0? H2 + O2 340-380 50 - 500 ELECrROLYSIS • HYBRID O 250 - 3.5xl06 I 2 and rubber 255 SOURCES: *Organic polymers + ammonium percholorate + powdered aluminium • Larson & Wertz2 I lO ··Sutton
I Table 4. Current Electric Propulsion Characteristics SYSTEM PROPELLANT Isp (s) EFFICIENCY THRUST (N) ELECTROTHERMAL I 6 RESISTOJEI' Nz, NH3 , Nz~. Hz 150 - 700 5xl0- - 0.5 RESISTOJET NH3,Nz~,H2 200 - 300 65 - 90 0.002 - 0.1 ARCJET NH3.N2~.H2 450 - 1500 0.5 - 5 I ARCJET·... ~,N2~,Hz,N2 40 - 50 0.002 - 0.7 ELECTROSTATIC IONENGlNES Hg/AlXe/Cs 2000 - 6000 5xl0·6 0.5 I ION CONTACT Cs, Hg 1500 - 5000 60 - 80 lxl0·6 - 0.1 ION BOMBARDMENT Xe, Hg, Ar,Kr 1500 - 5000 60 - 80 lxl0·5 - 0.2 COllOID Glycerine 1200 5xl0·6 - 0.5 I ELECTROMAGNETIC SPI'(HAlL) Xe 800 - 3000 37 - 71 0.015 - 0.26 MPD Argon 2000 25 - 200 I MPDARCJET 30 - 50 lxlO-6 - 2 HA1L EFFECT MPD Cs, Bi, Ar, Nz, 30 - 50 lxl0-s - 2 Xe,H, 6 PPI' Teflon 1500 5xlO- - 0.005 I s SOlID PUlSED Teflon 1000 - 2000 20 - 30 5xl0' - 0.01 PLASMA•• PUlSED INDUCTIVE Nz~ 2500 2-200 I SOURCES: • Larson & Wertz2 •• 10 Sutton *** 11 I G. Malyshev et al. I I 9 I
The values for the three constraints listed above can I be found as follows:
1. For a given cluster size and altitude, the Table 5 lists the maximum values chosen for these I accelerations along y can be found by evaluating constraints as well as other input parameters. equation (4). T a bl e 5 . B aseI" me parameters 2. The corresponding thrust to counteract those I 1 10Wlkg accelerations is given by cx"p Cl.sic 2 Wlkg Pp 500 kg/m3 I 3 Pslc 79 kg/m 3. Knowing the acceleration and assuming life 5 yrs continuous thrusting, the total Ll V required is I ~/ms/c .1 IDsIc 100 kg (~/~c)max 0.1 I 4. The total propellant used during the life of the (Pin IP slc)um. 0.20 mission is simply (Dr.am.ID slc)um. 0.33 mp - (1 -e-.6V/I"g(l) ms/c [(Mp +MpP)/MslC]um. 0.30 I
5. The diameter of the spacecraft is 1 I Ds/c = (~ ms/c]"3 3.3 Analysis of Cluster Missions 1& Ps/c The methodology developed in section 3.2 can I 6. Using mp' the diameter of the propellant tank is now be used to determine the range of thruster 1 specific impulse and efficiency which can maintain Dtank = (~ mp J3 the relative positions of a satellite in a cluster I 1& Pp without exceeding the satellite design ratios.
7. The total power available to the spacecraft is Figures 12 through 14 illustrate the feasible regions of thruster specific impulse vs. efficiency for I clusters orbiting at various altitudes. At specific impulses below the feasible regions, the required 8. For electric propulsion, a power plant is required propellant to maintain the cluster during the five year I on-board the satellite to provide power to the mission life exceeds the assumed 10% maximum thruster. Therefore, the maximum required input initial propellant mass fraction. In actuality, the power to the thrusters, using the current value of thruster must operate at an ~p above this lower limit I Isp being evaluated and thrust levels from step 2 since propellant utilization, 'flu=l, is assumed in this is initial analysis. Combinations of specific impulse and efficiency above and to the left of the feasible regions result in thruster power requirements greater I (18) than the allowable 20% of spacecraft power. Because the thruster power is determined by equation (18), an increase in thruster efficiency allows for higher 9. The mass of the power plant can be found using I specific impulses without exceeding the power input power calculated in step 8 along with the limitations. specific power of the power plant I I 10 I I
I As shown in Figure 12, a satellite in a cluster orbiting at 1000 km altitude with a 25 m baseline requires thrusters operating at a minimum specific impulse and efficiency of 2000s and 40% 5000 I respectively. SPT's and ion engine technology can currently achieve these ranges. If the baseline is 4000 increase to 35 m, thruster requirements increase to I 2700s specific impulse and 80% efficiency. ~ c.. 3000 .!! Similar effects can be seen for clusters orbiting at I 10,000 km (Fig. 13) and at GEO (Fig. 14), At 10,000 km, cluster baselines in the hundreds of meters can be achieved using SPT or ion engine 1 000 t'-:.Jtl.=~:.:.;,;,;,;,~ technologies. These baselines increase to 4000-6000 I m for clusters stationed at GEO. An important point oh&Ji~~~~ to notice is that at no altitude can chemical o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 propulsion maintain cluster formations for the 5 year Efficiency lifetime. I Figure 13. Feasible Isp vs. TI at 10,000 kID The achievable resolutions from the sparse aperture baselines shown in Figures 12 through 14 are listed 6000~~--~------~----~~ I in Tables 5 and 6. I 5000 4000
5000 ~ a. 3000 I II,) 4000 2000 I ~ c.. 3000 .!! I 2000 o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1000 Efficiency I Figure 14. Feasible Isp vs. TI at GEO o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Efficiency Table 5. Feasible S)parse A~perture Gr oun dReso l' ution ALmtrDE I Figure 12. Feasible Isp vs. 11 at 1,000 Ian BASEUNECW~J~ ., " ) (~~) 1000 km 25 m 20 mm 40cm 2km I Moving a cluster to higher orbits dramatically 35 m 14mm 29cm 1.5 km increases the allowable baselines for sparse apertures. 10,000 km 25 m 200mm 400cm 20km However, due to the increased range to target from 100 m 50mm 100cm 5km I GEO. ground resolutions increase by only about a 200m 25mm 50cm 2.5 km factor of 5 (see Table 5). 400m 13 mm· 25cm 1.3 Ian 35768 km 25 m 710mm 15 m 72 km 2000m 9mm l 18cm 900m I 5000m 4mm 7cm 350m I 7000m 3mm 5cm 250 m I 11 I I For mission where angular resolution is the main concern (such as for imaging of astronomical objects), Table 6 shows that angular resolution can I be increased by a factor of order 1000 if the cluster is positioned in GEO rather than LEO. These values can be compared with the angular resolutions given I for terrestrial interferometers in Table 2. I Table 6. Achievable Sparse Aperture An ular Resolutions 1000 km CLUSTER AL1IIUDE VT~IBl.E IR RF I I (.5J.1lIl.) (lOJ.Ull) (5cm) x y z 3 300 m 1000 km 25 m 4x10- " 82x10"3 " 412" diameter ::Iiameter 3 35 m 3x10- " 59x10"3 " 294" Figure 15. Thrust/mass Levels 3 3 I 10,000 km 25m 4xl0- " 82xlO- " 412" 3 3 100m 1x10- " 2Oxl0· " 103" 3 250m 412xl0-6 " 8xl0- " 40" 6 3 I 400m 258x10- " 5x10- " 25" 3 35768 km 25m 4x10- " 82x10"3 " 412" 6 3 2000m 51x10- " 1xl0· " 5" 6 6 I 5000m 2Ox10- " 415x10- " 2" > 7000m 15x10-6 " 294x10"6 " 1.5" Figure 15 shows the thrust levels per unit of spacecraft mass required by a satellite displaced from I the reference orbit by 15m, 150m, and 2750m (30 m, 300m, 5500m cluster baselines respectively). These values were found using the full length equation (5). Combinations of cluster baselines and altitudes which Figure 16. Required AV I can be achieved with moderate propulsive requirements (Figs. 12 through 14) are all seen from 4. Desian of Candidate Thruster Figure 15 to require thrust levels on the order of 15J.1N per kg of spacecraft mass along y. Although any type of thruster can support a '. Thrust/mass along z is approximately 5 orders of small cluster formation for a short time period, the magnitude smaller, justifying the use of the linearized analysis of Section 3 demonstrates that to maintain I equation (4). In addition, thrust levels along i equal reasonable cluster baselines at a given altitude for a zero. five year mission requires continuous thrusting by a propulsive system operating at approximately 2200- This is also apparent in Figure 16 which shows the 3200s specific impulse, 50-70% efficiency, and at I required AV for a five year mission. The AV expended thrust-to-spacecraft mass ratios on the order of in z is negligible compared to that expended in y. 15J.1N/kg. Thus, a 100 kg satellite would require approximately 1.5 mN of thrust to maintain its I position at the far edge of the cluster. As an extension of this analysis, the ability of a proposed Linear Ion Microthruster to meet these requirements is evaluated. I I 12 I I 4.1 Linear Ion Microthruster I 1) Ions from ambient plasma charge the top surface of the solar array dielectric resulting in a strong The linear ion microthruster, shown in Figure electric field at the triple junction. 17, is a concept for a micro-machined ion propulsion 2) The electric field causes electrons to be emitted I system proposed by members of the Jet Propulsion from the conductor provided there existed an Laboratory .12 The thruster consists of several linear enhanced field electron emission site on the discharge chambers situated parallel to each other. conductor surface. Some electrons hit the Each discharge chamber has dimensions of I dielectric side surface releasing secondary approximately l00f..lII1 x 300Jlm x 10 cm. The walls electrons on impact thereby fwther enhancing the separating the discharge chambers are built up from electric field. alternating layers of conducting and insulating 3) The intense electron current incident to the I materials. dielectric causes a dense. localized neutral cloud to form over the dielectric side surface due to Two methods to produce ions are proposed by electron stimulated desorption. The positive I JPL. The first is the use of radio frequency discharge. space charge resulting from the electron Contained within the walls is the ion accelerator collisional ionization in the neutral cloud further system which includes the RF "ionizing coil". the enhances the electric field at the conductor ion accelerator grid. and the ion decelerator grid. The I surface, leading to a discharge from the neutral second concept is based on a direct-current (DC) cloud. Results show the arc emits a plasma discharge utilizing doped diamond films as cold cloud which also discharges the surfaces in the cathode emitters. I neighborhood of the arc. 4. The charging of the dielectric surface then I repeats. ARCING IN SOLAR ARRAYS I AMBIENT IONS CHARGEFRONf SURFACE. E SCREEN GRID FIEID SET -UP RF"con:.."--.liiiil I ~~-4"~L-~~ __~~ DISCHARGE PLASMA CHAMBER ....1 0.1 mm E FIElD INDUCES e' Figure 17. Linear Ion Microthruster CURRENT. nO GAS I DESORBED. no DENSITY The scale and geometry of the linear ion microthruster INCREASES. I is very similar to that of solar array cells. These IONIZATION DUE TO e-_no COWSIONS solar cells, when operating at high negative voltages in the ionospheric plasma. have experienced arcing in I the regions near the cell interconnectors. This DISCHARGE. mechanism may be exploited as an alternative method E-FIEID GONE. to produce ionization within the linear ion nO GAS GONE. PROCESS REPEATS. I microthruster discharge chamber. 4.2 Possible Alternate Ionization Mechanism Figure 18. Solar Array Arcing Mechanism I Figures 18 and 19 illustrate the analogy between the solar array arcing mechanism and its use as the ionization mechanism of the microthruster. I Accordin¥: to the theory developed Cho and Hastings 3, the arcing in a solar array occurs as I follows: 13 I I J.1-THRUSTER OPERA nON Other than the fact that the PIC code predicted the I flight experiment arcing rate very well, one should APPLIED E FIELD notice that a "turn on" voltage for the arcing is SET-UP present at about 200 V. This will become a factor in the section 4.2 when we discuss the Brophy Model I analysis of the linear ion microthruster. SECONDARY ELECTRON MULTIPUCATION E FIELD INDUCES 4.2 Brophy Model Analysis I CURRENT. nOGAS SUPPLIED The perfomlance of an ion thruster is gauged by the power required to produce, but not accelerate, an nOAT PROPER I DENSITY. ion which eventually becomes part of the beam. The IONIZATION average energy cost to produce a single beam ion, ED' OCCURS DUE TO e 0 is a key parameter in the measure of the thrusters -n COLLISIONS perfomlance. To produce a more efficient thruster it is I necessary to reduce the value of ED while maintaining DISCHARGE. E-FIELD REMAINS. a high propellant utilization. The model developed 1S nO GAS RESUPPLIED. by Brophy and Wilbur for predicting ED in ring and I PROCESS CONTINUES. line cusp ion thrusters can be modified to facilitate the design of the linear ion microthruster. Figure 19. Alternate J.1Thruster Ionization Mechanism I The average beam ion energy cost is given as A possible advantage of this mechanism is the "hopping" of the electron up dielectric sidewall as it moves within the electric field. This trajectory acts I to keep the electron within the chamber longer, making it a more effective ionizer. where the Co = 4aolel~voAg ED (Total Power - Useful Power)/J (20) I = D +-.. ···· ...... ··· ..~ .. ······· .. ········:ii'!:·....l.···:: .. ·.I-:~t~~:: f::::~~~ . - ~: ."._...... ; i where useful power=JD (VD+ V net) and total power=Pin . 100 200 300 400 500 I Bias Voltage, ·v Substituting Pin from equation (20), the efficiency, T), of the thruster can then be related as: Figure 20. Solar Array arcing rates (flight Pbeam 1]=-- I data and PIC code simulation) Rzn I 14 I I I Therefore, if one desires a thruster to operate at a certain Isp and 11. Figure 21 specifies what the average ion energy cost per beam ion needs to be (21) subject to some combination of m, l1u' and Ie to be I determined in section 4.3. Figure 21 shows efficiencies plotted versus specific 4.3 Minimum Required Confinement Length. Ie I impulse as calculate using equation (21) for several values of £B' For a given thruster configuration The stated goal to this point has been to (constant VD, £p*, fe, fB ) , equation (19) says that £B maximize the value of the primary electron confinement length, Ie' for the purpose of increasing I is a function of propellant utilization, l1u ' and mass flow rate. m. Intuitively. the curves in Figure 21 the efficiency of the thruster. We now reverse this can be interpreted as follows: analysis and ask what is the minimum value of Ie for I Along a constant £B line, which a thruster could operate at a given Isp' 11, and If Isp i , then Vnet i. total thrust, Ftot ? For constant thrust, if Vnet i, then Vtot .1. I If Vtot .1, then "'-i .1. Solving equation (19) for Ie yields For constant l1u ' if "'-i .1 then m .1. If m.1 then no .1 since I (23) (22) where fhtot is the total propellant mass flow rate for I => With a lower no' Co (Le. Ie) must i to all chambers in kg/so maintain constant £B • Alternatively. for constant m,if "'-i .1 then l1u .1. Assuming 1-D space charge limited ion mass flow I Ifl1u.1, then no i by (22) rate, then => Co (i.e. Ie) must .1 to maintain constant I £B' (24) CCNSTANTiii 1.00 ." ...... " ...... ,,'''' ".,," ..... " DECRE.AS1NG llu where "'-itot is in kg/so I ..... DECRE..6SING Ie 0.90 CCNSTANT llu ...---"": £s (eV) DECRE..6SING m : 0.80 For a given thrust level -a-100 1~~~~I.~~~···.·····.oJIIIj,...... ~- . F tot (25) 0.70 ...__200 1n;tot=Jg I sp 0 ...... 300 ~0.60 c CD Therefore, the LHS of (24) is a constant. Thruster U 0.50 I design iterations which change Vtot' da• Ac. or Nc -iii 0.40 must do so in accordance with (24) in order to 0.30 maintain a constant Ftot . I 0.20 vd~IU Using the fact that "'-itot = fhtotllu and substituting 0.10 ...... mj = 2~18e-25 kg ": (24) and (25) into (23) gives I 0.00 0 1000 2000 3000 4000 Isp (26) I FIGURE 21. 11 vs. Isp at Several £B I I 15 I Equation (26) says that for a linear ion microthruster 5. The minimum average beam ion energy cost I operating at a given eB (i.e. Isp and 11 from Fig. 21), must be greater than 200 eV. This requirement the required primary electron containment length can stems from results of the SAMPlE flight be minimized by decreasing 11u or decreasing the experiment data and Cho PIC codes simulation I quantity A~c' By equation (24) decreasing ~c is (Figure 20) that indicate a minimum bias voltage 2 of 200 V is needed to initiate the arcing equivilent to increasing Vtot 312 I da • mechanism. 1.E-02 ,...... -__~_~_~ ...... _6E·08 I The amount by which 11u and A~c can be reduced are limited by several constraints .. ep'=SOeV 1.E-02 .... L.. ee=300eV SE·08 1. The amount of propellant required can not exceed : -4 j Ftot = 1x10 N the initial propellant mass fraction of 10%, i.e., I 8.E-03 ~ isp=2000 s 4E-08 : AeNc =1.Sx10·3 m2 • mion l' g 6.E-03 3E·08 1;, -71- ife< (mp-- Jmsl c (27) .lI: M ..!I I mslc 4.E-03 t .. ···~··· .. ·;····~······:···· .. ········:···.. · .. ····,.·;·········· ... 2E·08 Ii 2. At very low thrust levels, it would be possible to 2.E-03 +..... ; ...... :...... , ...... ,.,...... "' ...... ,...... of- 1 E·08 reduce Ie by operating the linear ion micro thruster I at very low values of 11u and still remain below o 0.1 0.20.30.40.50.6 0.70.8 0_9 1 10% propellant mass fraction. Although it could accomplish the mission, such a thruster would 1lu I require a lot of propellant for little thrust Figure 22. Mass flow rate and containment length provided. Therefore, a minimum operating 11u VS·11u will be assumed. Figure 22 shows the additional I reduction in Ie possible by continuing to reduce Table 7 list addition assumptions used in 11u' An "elbow" in the curve appears around 0.6. determination of the minimum allowable primary For m , the elbow occurs at l1u =0.3. Splitting electron confinement length. the difference the minimum operating is I T abl e 7 BrOpJ1Y h M o d e I As sumptlOn s 11u > 0.45. (28) eD 50eV V 30V I D 3. The electric field across the accelerator "grid" can fR 0.95 not exceed the breakdown limit, i.e, fc 0.05 m· 2.18x10·2!) kg I "tot < BDL =1 0 6 ~ (29) d m Tn 450K a 20 2 0'0 2.18xl0' m I 2 CPo 1 The exponents in the ratio Vtot 312 I da indicate that, to minimize Ie' da should be made as small as possible (within manufacturability limits) Figures 23, 24, and 25 show the minimum required even though equation (29) will force Vrot to be primary electron containment length, Ie' versus I reduced. efficiency at several values of specific impulse for thrust to mass ratios (ie. required accelerations) equal 6 6 6 4. The voltage across the accelerator grids must be to, 0.lx10· , 1xl0· , and 15xl0' respectively. I greater than the net voltage across the • For a given thrust to spacecraft mass ratio and 11, deceleration grid to prevent backstreaming of an increase in Isp reduces required Ie because, from electrons into the chamber A high value of Figure 21, the average beam ion energy costs eB I V net N rot is desired so that da can be reduced. is allowed to increase. Therefore, • For a given thrust to spacecraft mass ratio and Isp, an increase in 11 increases required Ie because, I Vtot = Vnet I 0.8 again from Figure 21, eB is decreasing. For this situation, an upper limit on allowable 11 exists I 16 I I I due to the constraint that EB is greater than 200 e V. A lower limit on allowable 11 exists due to ISp 2000s Isp = 2500s spacecraft power limitations of equation (17). 1111 =0.80 11u=0.64 • For a given Isp and 11, as the thrust to spacecraft lE-02 I .: ::"! ~ mass ratio increases, Ie increases because a larger E ~: ~ fraction of the propellant must be utilized to i produce thrust (Le. l1u t). At any thrust to E 1E-03 rn :::J I spacecraft mass ratio less than 0.1xl0·6 (Fig. E i: ·······.·········'·~~:·~\····i.' : 23), no further reduction in Ie is possible without i .: Isp = 3500s : sp 3000s ...... 11u 0.46 lE-04 = = violating the minimum operating l1u given by : fill 0.54 I equation (28). Also as the thrust to mass ratio 6 increases, the minimum Isp which the thruster Fto{ m$/C = 10X1O- N/kg operates increases due to initial propellant mass 0.1 0.2 0.3 0.4 O.S 0.6 0.7 0.8 0.9 1 I fraction constraints. efficiency, 'I Operating at l1u lower than that listed with I 6 • Figure 24. Minimum Ie for F /II1stc = 10xl0- Nlkg along side each curve in Figures 23 through 2~ to I would violate the initial propellant mass fraction constraints. Operating at higher l1u would result in a larger required value of Ie' lE-01 T"""'~.- ..... ~.-...,.-~. --~-...... ---- .: Isp = 2500S:-;---:../ : : 'Iu = 0.97 ~ :r I : : 1E-01 r---~-:---~------lE-02 ...... :· .. isp:;;·3~OOS··~· .... ·.. :·· .. m~ ...... : •••••• E ~ 'Iu = 0.80 ',/ Isp = 2500s i I 1E-02 '';'''Iu = 0.45 E lE-03 E fT E= : Isp = 3500s ~ i: i i ~ 'Iu = 0.69 E 1E-03 I :::J 1.. ·· .... : .. · .. · ...... lE-04 E ··· .. ·:··· .. ···:·· .. ···; .... ·.. +...... ·: ...... ··· .... i: i 1E-04 I 1 E-OS -f-w~...... j.....o.....J--+-....j,...n...... ;..-+-.....j....-j.....o.-f o 0.1 0.2 0.3 0.4 O.S 0.6 0.7 0.8 0.9 efficiency, 'I Figure 25. Minimum Ie for F /II1stc = 15xl0-6 Nlkg I 0.1 0.2 0.3 0.4 O.S 0.6 0.7 0.8 0.9 1 to effiCiency, 'I 6 Figure 23. Minimum Ie for Fto/II1stc = lxl0- Nlkg I 4.4 PreHroimuy Desi~ns It was concluded in Section 3.3 that a reasonable cluster baseline would need thrust to spacecraft mass The values of V tot' d , and 11u which led to ratios of approximately 15J..LNlkg. A thruster a I minimization of Ie at each combination of Isp and 11 operating at this acceleration level and at ~=2500 can now be used to generate preliminary designs of would, from Fig. 25, need a primary electron the linear ion microthruster. confinement length, Ie' equal to a few centimeters. I Increasing the specific impulse at which the thruster 2 The quantity V tot 3/2 I d specifies AcNe by equation operates to 3000 s reduces Ie to a few millimeters a (24). To produced an approximately square thruster, which is more on the scale of the linear ion I microthruster. Additionally, the l1u=O.8 corresponding to Isp=3000 s is more realistic. where the factor of 2 assumes the walls separating the I chambers have the same width as the chambers. I I 17 I The width of the chamber can be found from ion microthruster. The code implements the Brophy I model using a value of primary electron confinement We= (AcNe) length determined by a Monte Carlo simulation of LeNe primary electron motion within the discharge where Ne is chosen to produce a reasonable value of chamber. Based on experience gained in I implementing the Arakawa code, the Particle-in-Cell W c' Finally, with Ne chosen, the quantity A~e and (PIC) code developed at MIT to predict the solar array be solved for Ac' arcing phenomenon, will also be adapted to the I microthruster's geometry and scale. Modification of The height of the chamber can be, to fIrst order, the PIC code for the linear ion microthruster will chosen arbitrarily without altering the minimum Ie' allow prediction of energy cost per beam ion, the This is due to the fact that the neutral density in the propellant utilization factor, and the fraction of ions I chamber (equation 22) is a function only of the extracted into the beam. chamber exit area if m is constant. More intuitively, increasing He initially decreases neutral density I because the chamber volume increases. However, the rate at which neutrals are lost from the chamber also . IS decreases by th e same amount smce I I Therefore, if m is constant, no and no and will increase back to their Original levels. If the neutral density is not affected by a change in chamber height, I then the probability that the primary electron will have a collision, 1-exp[-oonole], also remains unchanged. IS The bottom line is that the primary I electrons are just as effective as ionizers and no additional energy per beam ion needs to be expended. Figure 26. Preliminary sizing of Linear Ion Microthrusters A linear ion microthruster producing 1.S mN of I thrust on-board a 100 kg satellite (lSJ.1N per kg of 6. Summary and Conclusions spacecraft) could, from Figure 2S, operate at Isp=3000s, 11=.6S, 11u=0.80. Total voltage across the This paper has examined the propulsion system I acceleration region is 736 V although there is no requirements for maintaining a local satellite cluster actual grid through which the ions accelerate. The formation in Earth's orbit for the purpose of forming minimum allowable primary electron confinement sparse aperture arrays. Near continuous thrusting by I length is apprOximately, Ie = 6 mm. To produce the propulsive system was found necessary to square thruster, chamber length, Le, equals 2 mm. maintain the relative positions of the satellites within Choosing a 10 chamber configuration results in a allowable tolerances. Satellite mass, volume, and I chamber width of 0.1 mm. The chamber height, Hc' power constraints limit reasonable cluster baselines to is chosen to equal 1 mm. Therefore, the normalized approximately 30 m, 300 m, and SOOO m at 1000 primary electron confinement length, liRc= 6. These kID, 10,000 kID, and GEO altitudes respectively. To preliminary dimensions are shown in Figure 26. maintain these cluster baselines, the propulsive I system must operate at minimum Isp and efficiency 5. Future Work equal to approximately 3000s and 6S% respectively with a thrust/spacecraft mass ratio of approximately I Continuation of this work will focus on analysis lSJ.1Nlkg. A linear ion micro thruster of this type of linear ion microthruster designs. A code developed could have dimensions 2mm x 2mm x 1mm, with 10 l7 by Arakawa which predicts the perfonnance of discharge chambers each 0.1 mm wide. The resulting I cusped ion thrusters will be modified for the scale, primary electron confinement length would then be 6 geometry and confinement mechanism of the linear times the chamber height. I 18 I I I References 12. Brophy, J.R. et al. "Ion Thruster-On-A Chip for Microspacecraft" unpublished white paper. Jet I 1. Swift, C. T. "Terrestrial Sensing with Propulsion Lab. April 26, 1995. Synthetic Aperture Radiometers." IEEE MIT-S International Microwave 13. Cho, M .. "Arcing in High Voltage Solar Arrays Symposium Digest, vol. 1, p. 387-388, in Low Earth Orbit: Theory and Computer I Boston MA, June 10-14, 1991. Particle Simulation", Ph.D. Thesis, MIT, 1992. 2. Larson, W. J., Wertz, J. R. (editors), S:wG 14. Perez de la Cruz, C. "Arc Rate Predictions and Right Data Analysis, for the Solar Array Module I Mission Desi~n and Analysis 2nd ed pp. Kluwer Academic Publishers, Boston, 1992. Plasma Interactions Experiment (SAMPIE)", S.M Thesis, MIT, 1995. 3. Wall, J.V., Modern Technol02Y and It5 Influence I 15. Brophy, J.R., Wilbur, P.J., "Simple on Astronomy. Cambridge University Press, Perfromance Model for Ring and Line Cusp Ion Cambridge, 1990. Thrusters" AIAA J oumal pp. 1731-1736, 23 No. 11, November 1985. I 4. Stachnik, R., Labeyrie, A. "Astronomy from Satellite Clusters." Sky and Telescope, pp 205- 16. Martinez-Sanchez, M., Course Handout: 16.522 209, March 1984. I Space Propulsion, Fall 1995, MIT. 5. Heimiller, R.C., Belyea, J.E., Tomlinson, 17. Arakawa, y" Ishihara, K., "A Numerical Code P.G., "Distributed Array Radar." IEEE for Cusped Ion Thrusters," IEPC-91-118, 22nd Transactions on Aerospace and Electronic I International Electric Propulsion Conference, Systems vol. AES-19, No.6, November 1983. 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