THE CHARGING OF SPACECRAFT SURFACES › Handbook_of_Geophysics_1985 › Chptr07.pdfChapter 7 THE...

Chapter 7

THE CHARGING OF SPACECRAFT SURFACESH.B. Garrett

The buildup of static charge on satellite surfaces is an analysis is applicable to current spacecraft charging prob-important issue in the utilization of satellite systems. The lems. This is true as in a very real sense the space vehicleanalysis of this spacecraft environmental interaction has re- itself can be considered as a "floating probe." This theme,quired important advances in basic charging theory and the of the vehicle as a probe, will form the basis of much ofdevelopment of complex codes to evaluate the plasma sheaths this chapter.that surround satellites. The results of these theories and Probe theory has developed into an important subfieldcalculations have wide application in space physics in the of plasma physics in its own right, see review by Chendesign of systems and in the interpretation of low energy [1965]. It has only been with the advent of rockets andplasma measurements. ultimately satellites that the charging of objects in space has

In this chapter, those aspects of charge buildup on sat- become a major separate area of concern. The first periodellite surfaces relevant to the space physics community are of charging studies, in fact, was concerned with the potentialsummarized. The types of charging processes, models of of interstellar dust grains. One of the earliest studies, thatcharge buildup, satellite sheath theories, and charging ob- of Jung [1937], found that photoemission and electron ac-servations are described with emphasis on basic concepts. cumulation were probably the dominant processes in inter-

As many books and monographs on specific aspects of stellar space. This subject was extended and put on a firmthe charging of bodies in space have appeared in the last physical footing by Spitzer [1941; 1948], Spitzer and Sav-two decades, it is difficult to cover all areas in detail in a edoff [1950], and others [Cernuschi, 1947; Opik, 1956].chapter of this nature. Rather, the chapter is limited to the Depending on the assumed "sticking" probability of thecharging of spacecraft surfaces in the near-earth magneto- electrons, the photoemission yield, and the ambient envi-sphere. Rocket measurements are only briefly treated. The ronment, the estimate satellite to space potentials for thesereader is referred to books by Singer [1965], Grard [1973a]; early studies ranged between - 3 and + 10 V.Rosen [1976], Pike and Lovell [1977], and Finke and Pike With the advent of rocket-borne sensors in the early[1979] that contain papers on the charging of natural bodies 1950s, spacecraft charging emerged as a discipline. Perhapssuch as the moon [Manka, 1973; Freeman et al., 1973], the first example of a spacecraft charging effect is in a paperdust particles [Feuerbacher et al., 1973] and other planetary by Johnson and Meadows [ 1955]. They theorized that shiftsbodies [Shawhan et al., 1973]. A brief historical review of in the ion peaks measured by their RF mass spectrometerspacecraft charging is followed by a discussion of obser- above 124 km could be explained by a negative rocketvations. Following a description of the major charging potential of -20 V. The first treatment of the charging ofmechanisms, specific spacecraft charging models are ex- a macroscopic object was published the next year by Lehnertamined with emphasis on basic concepts. A substorm, worst [1956] who estimated satellite to space potentials of -0.7case environment is included. The chapter concludes with to - 1.0 V when ion ram effects were included.a discussion of spacecraft charge mitigation techniques. A Not only did 1957 see the launch of Sputnik, but itmore detailed version of this chapter can be found in Garrett ushered in a second phase in spacecraft charging studies.[1981]. Gringauz and Zelikman [1958] discussed the distribution of

charge (or sheath) around a space vehicle in the ionosphereand the influence of photoemission and satellite velocity.

7.1 SPACECRAFT CHARGING Jastrow and Pearse [1957], while neglecting photoemissionHISTORICAL PERSPECTIVE but including ram effects, computed the drag on a satellite

caused by charged particles in the ionosphere. Their studyThe historical roots of spacecraft charging analysis can for the ionosphere assumed TE >> TI so that the estimated

be traced to the early electrostatic probe work of Langmuir potentials were between - 10 V (night) and - 60 V (day),[Langmuir, 1924; Mott-Smith and Langmuir, 1926]. Not values which are too high as TE > TI is the actual caseonly is the Langmuir probe still an important space plasma [Brundin, 1963]. Another basic assumption of their study,instrument, but as will be discussed, much of Langmuir's as in the related study of Chang and Smith [1960], is that

7-1

CHAPTER 7

the ion density is little changed in the immediate vicinity effects (-0. 14 V). During this period more believable po-of the vehicle. tential measurements were also reported for rocket probes

Zonov [1959] and Beard and Johnson [1960] analyzed as exemplified by Sagalyn et al. [1963] who found potentialsthe effects of electric fields induced by the movement of a of -0.4 V (150 km) to - 1.7 V (450 km).satellite across the earth's magnetic field; these fields can In a 1961 paper, Kurt and Moroz [1961] predicted po-be quite important for large structures. Beard and Johnson tentials of -3.2 to 4 V outside the radiation belts. They[1961] also discussed the effects of emitting charged par- also predicted potentials as high as - 20 kV in the radiationticles from a vehicle and the limitations on vehicle potential belts. Although only crude estimates, their predictions an-in the ionosphere, another issue which is still of concern ticipated the - 20 kV potentials observed in eclipse on the(see Section 7.4.1). In the same period, the first satellite geosynchronous ATS 6 satellite in the 1970s. These andpotential measurements were made by Sputnik 3. Krassov- other results were compared in an excellent review of thesky [1959] found a potential of - 6.4 V and TE = 15 000 effects of charged particles on a satellite by Brundin [1963].K at 795 km. Another good review from this period, in which the validity

The first review of spacecraft charging appeared in 1961 of various ionospheric measurements were discussed, is that[Chopra, 1961]. Despite difficulties with this review (Cho- of Bourdeau [1963]. The most complete works of this pe-pra predicted high positive potentials since the photoelectron riod, however, are in the first book concerned with space-flux he assumed was too high), it can be used as a convenient craft charging [Singer, 1965] and the thesis of Whipplemarker for the end of the second phase of the study of [1965]. Whipple's thesis brings together most of the pre-spacecraft charging. By 1961 most of the elements of current ceding results in an analysis of the roles that secondaryspacecraft charging theory were in place. Preliminary ob- emission, backscatter, photoemission, and magnetic fieldservations by rockets and satellites had confirmed that charg- effects have in spacecraft charging. As such, it completesing existed and, in agreement with some theories, was on the third period of spacecraft charge analysis-a period markedthe order of a volt (typically negative) in the ionosphere. by a realization of the importance of spacecraft chargingPhotoemission and the ambient electron flux were recog- for plasma measurements and of the importance of self-nized as dominant sources and v x B effects had also been consistent calculations. Quantitative measurements also be-considered. On the negative side, secondary emission and came available for the first time. The period 1965 to thebackscatter had not really been adequately considered present has been primarily one of refinement and extension[Whipple, 1965], charged particle drag (which was ulti- of these 1961-1965 results to higher altitude regimes andmately shown to be of less importance than errors in the more complex geometric situations. It represents the "fourthneutral drag coefficient (see reviews by Brundin [1963] and period" of spacecraft charging and is the concern of thisdeLeeuw [1967])) was still of primary concern, and self- chapter.consistent solutions of the particle trajectories and fields hadnot been carried out. Only monoenergetic or Maxwelliandistributions were being considered. 7.2 SPACECRAFT CHARGING

The new phase of studies in spacecraft charging actually OBSERVATIONSstarted somewhat earlier than 1961 with Bernstein and Ra-binowitz's probe study. Bernstein and Rabinowitz [1959]introduced a means of calculating particle trajectories in the 7.2.1 Rocket Measurementsvicinity of a probe for the case where collisions could beignored. The importance of their study (see Section 7.4.4) Rocket measurements of the ionospheric plasma havewas that their method allowed a self-consistent solution of been routine since the early 1950s. The first observationsthe time-independent Vlasov equation and Poisson's equa- of spacecraft potentials were probably the RF spectrometertion. Their work was later adapted to spacecraft by a number measurements on a rocket by Johnson and Meadows [1955].of investigators. Davis and Harris [1961], by a more sim- They made use of the differences in the energy shifts ofplified method, calculated the shielding of a rapidly moving different ionized species to estimate a vehicle potential ofsphere in the ionosphere by estimating ion trajectories in a - 20 V above 120 km. Sagalyn et al. 11963], employing 2fixed electron sheath. Their results concerning the distri- spherical electrostatic analyzers mounted on a Thor rocket,bution of ions in the wake, despite their neglecting the ion found much lower potentials of -0.4 V (150 km) to - 1.7thermal velocity, are consistent with Explorer 8 measure- V (450 km). Their measurements are in good agreementments reported in the same year [Bourdeau et al., 1961]. with subsequent satellite measurements in the same region.These latter results are probably the first accurate spacecraft Narcisi et al. [1968] also found rocket potentials of aboutpotential measurements between 425 km and 2300 km. The -0.5 V in the D and E regions although their results mayion current, which varied strongly as a function of angle have been affected by the potential distribution near therelative to the satellite velocity vector, was found to agree rocket [Parker and Whipple, 1970]. As discussed by Parkerwith Whipple's [1959] theory (see Equation (7.23)). A sat- and Whipple [1970], however, there are for these and similarellite potential of - 0.15 V was observed along with v x B satellite measurements difficulties in interpreting the results

7-2

CHARGING OF SPACECRAFT SURFACES

since the detailed particle trajectories must be considered in ELECTRON DENSITY (electrons/cm 3)

determining the actual instrument responses. Further, as 270 3 104 105 106probably happened to Johnson and Meadows [1955], the 260

electric fields near the rockets may be perturbed by exposed 250 Electron Density

potential surfaces. See, for example, the results of the recent 240

"tethered payload" experiment of Williamson et al. 11980], 230in which a potential of + 10 V on the main payload induced 220

a potential of -5 V on the secondary payload 40 m away. 210

Olsen [1980] (see also Winckler [19801) has described 200

potential measurements from a number of rocket beam ex-180 THERMAL EMISSIVE PROBE

periments. These ranged from the Aerobee flight [Hess, BIPOLAR VOLTMETER

1969] through the Echo series [Hendrickson, 1972; Winck- 160 ROCKET UPLEG

ler, 1976] down to the recent ARAKS [Cambou et al., 150

1978], Precede, and Excede [O'Neil et al., 1978a, and b]. 140

Although extensive literature exists on many of these flights, 130

the majority is concerned with the beam aspects. Potentials, 120

when observed, were typically a few tens of volts positive 110

or negative relative to the ambient plasma (Jacobsen and 100 10 2 10Maynard [1980], however, have reported potentials of POTENTIAL DIFFERENCE (volts)

hundreds of volts on the POLAR 5 rocket experiment). Asan example, voltages of + 4 V (108 km) to + 28 V (122 Figure 7-1. Vehicle-to-ambient potential difference and electron densitykm) were observed by Precede (electron beam voltage: ~2.5 (modeled) as a function of altitude [Cohen et al., 1979].

kV; current: ~0. 8A O'Neil et al., [1978a]).An exception to the rocket beam flights just mentioned km (OGO 4); Sagalyn and Burke [19771, - 1.5 V to 4 V

was the "Spacecraft Charging Sounding Rocket Payload" in the plasma trough and -0.5 to - 1 V in the polar cap[Cohen et al., 1979; Mizera et al., 1979]. This flight tested at 2500 km (INJUN 5); and Samir et al. [1979 a, b], - 0.1prototypes of the positive and negative charge ejection sys- to - 1.3 between 275 to 600 km (AE-C). The highest valuestems, the transient pulse monitor, and the rocket surface observed at low altitudes were by Hanson et al. [1964; 1970]potential monitor subsequently flown on the P78-2 SCA- who estimated potentials of -6 V at 240 km to - 16 V atTHA satellite. Additionally, a thermal emissive probe, a 540 km and Knudsen and Sharp [1967] who recorded - 15bipolar-intersegment voltmeter, and a retarding potential V at 516 km. Even higher values of -40 V were observedanalyzer were also flown. The unneutralized beams repeat- by Sagalyn and Burke [19771 at 2500 km on INJUN 5.edly varied the rocket ground potential between - 600 V These latter values are probably valid as they were observedand + 100 V (Figure 7-1, Cohen et al. [1979]). Potentials in the auroral zone during impulsive precipitation eventsas high as + 1100 V were observed on conducting surfaces and at night. Although most of these results were for eclipseand +400 V on insulators [Mizera et al., 1979] relative to conditions, there was no unambiguous effect due to pho-spacecraft ground. The variations in the vehicle to space toelectrons at these altitudes (this is not true for higherpotential correlated well with the ambient plasma density. altitudes).

Higher voltage variations, particularly in sunlight, areseen in the plasmasphere proper at altitudes above 2500 km.

7.2.2 Satellite Measurements On OGO .5, Norman and Freeman [1973] found potentialsof -7 to - 10 V at 1.1 RE. Between 2 to 6 RE, as the

Satellite measurements at low earth orbit have been made satellite crossed the plasmapause, the voltage varied fromprimarily by retarding potential analyzers and similar current - 5 to + 5 V. At 8 RE the potential reached + 20 V (notecollection probes. The earliest satellite observations of that in eclipse the potential fell below -3.5 V). Ahmedspacecraft charging were by the ion trap experiment on and Sagalyn [1972], employing spherical electrostatic ana-Sputnik 3 which measured potentials in the -2 V to - 7 lyzers on OGO 1, calculated potentials of - 3 to -6 VV range [Krassovsky, 1959]; however, Whipple [1959] es- beyond the plasmapause and -11 to -8 V in the plas-timated -3.9 V. As has been discussed, the first well doc- masphere. On the same satellite, Taylor et al. [1965], em-umented measurements of satellite potential at low altitudes ploying an RF spectrometer, estimated - 15 V at low al-were by the Explorer 8 where potentials of - 0.15 V were titudes (1500-2700 km) to ~0 V at 30 000 km. As discussed,observed between 425 and 2300 km [Bourdeau et al., 19611. however, this potential variation may have resulted fromSuch low negative values are typical of this region: Reddy the interaction of the exposed positive electrodes on theet al. [1967], -0.5 V at 640 km on TIROS 7; Samir [1973], spacecraft solar cells with the environment. Whipple et al.-0.71 V to -0.91 V between 600 and 900 km (Explorer [19741 reported potentials between 0 and -5.4 V in the31); Goldan et al. [1973], -0.7 V between 400 and 650 plasmasphere on OGO 3 in sunlight. Montgomery et al.

7-3

CHAPTER 7

[1973] observed potentials of + 100 V in the high latitude satellites in the plasmasheet (TE ~ 10 keV). The best doc-magnetotail at 18.5 RE on Vela 6. (As there were apparently umented and most extensive set of such observations comeno ion measurements at the time of these estimates, there from the University of California at San Diego (UCSD)may be some uncertainty in the method used as a result of particle experiments on the geosynchronous satellites ATSpossible differential charging [see Whipple, 1976b, or Grard 5 and ATS 6. The large potentials observed by these sat-et al., 1977].) During eclipse in the same region, they es- ellites were first reported and explained by DeForest [1972;timated the potential to be + 15 V. 1973], and provided a major impetus to the discipline of

As the satellite potential in eclipse is proportional to the spacecraft charging. A typical example of a - 10 000 Velectron temperature, it is not surprising that the most spec- eclipse charging event in spectrogram format for day 59,tacular potential variations have been for geosynchronous 1976, for ATS 6 is presented in Figure 7-2a. In this type

200 2. 3 DBP=1.4 DBS= .070 SIPE= 3 PSN= 2 NS= 1.0 PA(-360, 360) COM= 20512014 SA= -6LNG= 3590

100 0

BEZ

-90

-50 02/28/76

10

UCSD, ATS-6 DAY 59 OF 1976

Figure 7-2a. Spectrogram of the UCSD particle detectors on ATS 6 for day 59, 1976 showing a 10-kV charging event between 2140 and 2200 UT.

7-47-4


later are the ATS 5 and ATS 6 beam experiments [Goldstein10 °

ELECTRONS 10 5 PROTONS and DeForest, 1976; Olsen, 1980; and Purvis and Bartlett,1980]. These studies presented evidence that while electron

emission reduced satellite charging, neutral plasma emission10 4 was necesssary to achieve zero satellite to space potentials.

ECLIPSE Limited observations are availiable in the solar wind and

in the vicinity of the other planets. The Vela satellites typ-ically experienced potentials of +3 to +5 V in the solarwind [Montgomery et al., 1973]. Whipple and Parker [1969a]computed potentials of + 2.2 V and + 10 V for OGO 1 andIMP 2, respectively, in the solar wind. The Voyager space-craft observed potentials of + I V to + 10 V [Scudder et

0 10 20 30 40 50 60 0 10 20 30 40 50 60 70ENERGY (KeV) ENERGY (KeV) al., 1981]. Although preliminary, similar potentials were

apparently measured by the Voyager in Jupiter's outer mag-Figure 7-2b. Electron and ion distribution functions versus energy for day netosphere while slightly negative potentials occurred inside

59, 1976. (Dashed lines represent the spectra before and the denser, cooler regions of Io's plasma torus [Scudder etafter eclipse; solid lines represent eclipse spectra.) al., 1981; see also comments in Grard et al., 1977].

The most complete spacecraft charging measurementsare those being made currently by the P78-2 SCATHA sat-

of plot [DeForest and McIlwain, 1971] the Y axis is particle ellite (Figure 7-6). P78-2 SCATHA was launched in Januaryenergy, the X axis is time, and the Z axis (shading) is particle of 1979 into a near-synchronous orbit (5 x 7 RE). Thecount rates. The figure is interpreted as follows. When the satellite is specifically designed to study spacecraft chargingsatellite entered eclipse (-2140 UT), the photoelectron flux as is evidenced by the extensive list of scientific and en-went to zero shifting the already (100 V) negative potential gineering instruments (Table 7-1). P78-2 SCATHA has con-even more negative. This negative satellite potential Vs ac- firmed current ideas concerning the charging process. Atcelerated the positive ions as they approached the satellite, the same time, information on the sheaths surrounding aadding energy qVs to each particle. Zero energy positive satellite has been obtained. An abbreviated list of obser-ions thus appear as a bright band between 2140 and 2200 vations follows:UT at an energy (10 keV) equal to q times the potential Vs. 1. Arcs were observed under different potential con-Electrons, in contrast, were decelerated giving the dropout ditions (eclipse, sunlight, beam operations, etc.in the electron spectra between 2140 and 2200 UT. The [Koons, 1980]).spectra for before and after eclipse are presented in Figure 2. The satellite surface potential monitor (SSPM)7-2b demonstrating this 10 keV shift. Potentials as high as has determined the response of a number of ma-- 2000 V [Reasoner et al., 1976] in sunlight and - 20 000 terials to both natural and artificial charging eventsV in eclipse have been observed on ATS 6 [S.E. DeForest, [Mizera, 1980]. Sample potentials of over - 10001978, private communication]. V have been observed relative to spacecraft ground

Another effect of potential variations, differential charg- (see Figure 7-26b).ing, is also visible in the ATS 5 and ATS 6 spectrograms. 3. Natural charging events of - 1000 V or greaterIn Figure 7-3, a spectrogram from day 334, 1969, for ATS have been observed with one event in excess of5 is presented for the detector looking parallel to the satellite - 8000 V.spin axis. Between 0500 and 1100 UT a feathered pattern These observations are the first to include simultaneousis visible in the ions and a dropout in the electrons below data on the plasmas, magnetic and electric fields, surface750 eV is observed. These patterns are not visible in the potentials of dielectrics and other surface materials, arcing,detectors looking perpendicular to the satellite spin axis. and surface contaminants.The explanation [DeForest, 1972; 1973] is that a satellite The SCATHA data set has been of particular value insurface near the detectors has become differentially charged defining a "worst case" charging environment for the geo-relative to the detectors resulting in a preferential focusing synchronous orbit. In Table 7-2 are listed two "worst case"of the ion fluxes and a deficiency in the electron fluxes to examples from SCATHA as adapted from Mullen et al.the parallel detectors. [1981] and Mullen and Gussenhoven [1982]. For compar-

The frequency of occurrence of the ATS 5 and ATS 6 ison with earlier estimates, a "worst case" example fromcharging events in eclipse are presented in Figure 7-4 [Gar- ATS 6 has also been included [Deutsch, 1981]. The plasmarett et al., 1978]. The daylight charging events on ATS 6 moments and single maxwellian temperatures [described inhave been found by Reasoner et al. [1976] (see also Johnson Garrett, 1979] are averaged over all angles while for SCA-et al. [1978]) to be anticorrelated with encounters with the THA the 2-maxwellian values are for components parallelplasmapause. The level of charging has, however, been and perpendicular to the magnetic field. The SCATHA ex-found to correlate with Kp (Figure 7-5). To be discussed ample on Day 114 (24 April 1979, 0650 UT, 2311 MLT)

7-5

CHAPTER 7

Figure 7-3. Day 334, 1969, spectrogram from ATS 5 [DeForest, 1973]. The feathered pattern in the ions between 0700 and 1100 UT and the correspondingloss of low energy electrons is real and the result of differential charging.

was particularly well documented. For this example, it was The average ratio of oxygen ions to hydrogen ions was 0.4found that the vehicle frame potential closely followed the during the event.electron current between 33 keV and 335 keV. It is thiscurrent that apparently caused the observed high negativevehicle potentials ( - 340 V in sunlight; estimated to be - 16 7.2.3 The Effects of Spacecraft ChargingkV in eclipse). Maximum surface material charging levelsfor this event were: -3.8 kV on quartz fabric, -6.4 kV Aside from direct measurements of spacecraft charging,on silvered Teflon, and - 1.5 kV on aluminized Kapton. indirect indicators that reflect the effects of spacecraft charg-

7-6


50ATS-5/ATS-6 ECLIPSE POTENTIALS

ATS-5 (1969-1972) -KT8 (AVG). Ln (j8 0 / 10 j 10)---- ATS-6 (1976) O-KT8 (RMS).Ln(j80/10j10)40

o o 2 MAXWELLIAN 3

- 5000

30

-4000 0

z20 -3000

-1000

.2 .4 1.0 2 4 10 20

VOLTAGE (keV)

Figure 7-4. Occurrence frequency of ATS 5 (1969-1972) and ATS 6 00 10 2 0 03 04 05 6 0 70 80 90(1976) eclipse potentials (10-min intervals). kp

ing also exist. Typical is the plot of satellite operational Figure 7-5. Statistical occuence frequency of observed variationsofATS5 and ATS 6 eclipse potentials as a function of Kp (solid dots)anomalies as a function of local time at geosynchronous and various theoretical predictions [Garrett et al., 19791.

orbit presented in Figure 7-7 [McPherson and Schober, 1976].The cause of this clustering near local midnight is believedto be spacecraft charging-intense fluxes of energetic elec- defined power laws: peak current scales as the 0.50 powertrons associated with injection events are encountered near of the area, released charge as 1.00, energy dissipation aslocal midnight which lead to charge buildup and arcing and 1.50, and pulse duration as 0.53. Although still preliminary,hence to control circuit upsets and operational anomalies. various attempts are also underway to theoretically model

Given that differential charging can take place, whether these arcing phenomena [Muelenberg, 1976; Beers et al.,through potential differences on adjoining surfaces or through 1979].charge deposition in dielectrics, arcing can occur. Arcing, Another result for surface arcs [Stevens, 1980; Naneviczdefined as the rapid (~nanosecond) rearrangement of charge and Adamo, 1980] in the laboratory is that the breakdownby punchthrough (breakdown from dielectric to substrate), potential on a negative surface varies from - 100 V at lowby flashover (propagating subsurface discharge), blowoff earth orbit to - 10 000 V at geosynchronous orbit implying(arc to surface), between surfaces, or between surfaces and that arcing should not be a common occurrence. In Figurespace, is not well understood. A typical arc discharge pulse 7-9 [Shaw et al., 1976] the arcing rate on a geosynchronous[Balmain et al., 1977] is plotted in Figure 7-8. Balmain satellite shows a steady increase with the daily geomagnetic[1980] finds that surface discharges display characteristics index ap. As arcing is common even at low levels of geo-that scale with variations in specimen area according to well magnetic activity, a discrepancy exists between laboratory

SC6-1P78-2

Figure 7-6. The P78-2 SCATHA satellite. The dimensions are approximately 1.3 m wide by 1.5 m high.

7-7

CHAPTER 7

Table 7-1. Principal investigators/sponsors for P78-2 SCATHA

Experiment Principal Investigator/Number Title Sponsor Address

SC1 Engineering Dr. H.C. Koons/ The Aerospace CorporationExperiments USAF/AFSC/SD P.O. Box 92957

Los Angeles, CA 90009

SC2 Spacecraft Dr. J.F. Fennell/ The Aerospace CorporationSheath USAF/AFSC/SD P.O. Box 92957Electric Fields Los Angeles, CA 90009

SC3 High Energy Dr. J.B. Reagan/ Lockheed Palo Alto Rsch LabParticle Office of Naval 3251 Hanover StreetSpectrometer Research Palo Alto, CA 94304

SC4 Satellite H.A. Cohen/ AFGL/PHGElectron and USAF/AFSC/AFGL Hanscom AFB, MA 01731Positive IonBeam System

SC5 Rapid Scan Capt. D. Hardy/ AFGL/PHGParticle USAF/AFSC/AFGL Hanscom AFB, MA 01731

SC6 Thermal R.C. Sagalyn/ AFGL/PHPlasma USAF/AFSC/AFGL Hanscom AFB, MA 01731Analyzer

SC7 Light Ion Dr. D.L. Reasoner/ NASA Marshall Space FlightMass Office of Naval Center, Code BS-23Spectrometer Research Huntsville, AL 35815

SC8 Energetic Ion Dr. R.G. Johnson/ Lockheed Palo Alto Rsch LabComposition Office of Naval 3251 Hanover StreetExperiment Research Palo Alto, CA 94304

SC9 UCSD Dr. E.C. Whipple/ University of CaliforniaCharged Office of Naval B019 Dept. of PhysicsParticle Research/USAF/AFSC/ La Jolla, CA 92093Experiment SD

SC10 Electric Field Dr. T.L. Aggson/ NASA Goddard Space FlightDetector Office of Naval Center, Code 625

Research Greenbelt, MD 20771

SC11 Magnetic Dr. B.G. Ledley/ NASA Goddard Space FlightField Office of Naval Center, Code 625Monitor Research Greenbelt, MD 20771

ML12 Spacecraft Dr. D.F. Hall/ The Aerospace CorporationContamination USAF/AFSC/AFML P.O. Box 92957

Los Angeles, CA 90009

TPM Transient Dr. J.E. Nanevicz/ SRIPulse USAF/AFSC/SD Menlo Park, CAMonitor

7-8


Table 7-2. "Worst" case geosynchronous environments. The moments, TAVG, and TRMS are averaged over all angles. The SCATHA 2-Maxwellianparameters are for fluxes parallel and perpendicular to the magnetic field. ATS 6 2-Maxwellian parameters are averaged over all directions.

SOURCE DEUTSCH [1981] MULLEN ET AL. MULLEN AND[1981] GUSSENHOVEN [1982]

DATE DAY 178, 1974 DAY 114, 1979ATS 6 SCATHA SCATHA

ELECTRONS IONS ELECTRONS IONS ELECTRONS IONS(ND) (cm-3 ) 0.112E + 01 0.245E + 00 0.900E + 00 0.230E + 01 0.300E + 01 0.300E + 01(J) (nA cm- 2) 0.410E + 00 0.252E - 01 0.187E + 00 0.795E - 02 0.501E + 00 0.159E - 01

(ED) (eV cm-3 ) 0.293E + 05 0.104E + 05 0.960E + 04 0.190E + 05 0.240E + 05 0.370E + 05

(EF) (eV cm-2 s-1 sr-1) 0.264E + 14 0.298E + 12 0.668E + 13 0.430E + 13 0.151E + 14 0.748E + 12

N1 (cm-3 ) parallel - 0.882E - 02 0.200E + 00 0.160E + 01 0.100E + 01 0.110E + 01perpendicular - - 0.200E + 00 0.110E + 01 0.800E + 00 0.900E + 00

T1 (eV) parallel - 0.111E + 03 0.400E + 03 0.300E + 03 0.600E + 03 0.400E + 03

perpendicular - - 0.400E + 03 0.300E + 03 0.600E + 03 0.300E + 03

N2 (cm-3) parallel 0.122E + 01 0.236E + 00 0.600E + 00 0.600E + 00 0.140E + 01 0.170E + 01perpendicular 0.230E + 01 0.130E + 01 0.190E + 01 0.160E + 01

T2 (eV) parallel 0.160E + 05 0.295E + 05 0.240E + 05 0.260E + 05 0.251E + 05 0.247E + 05perpendicular 0.248E + 05 0.282E + 05 0.261E + 05 0.256E + 05

TAVG (eV) 0.160E + 05 0.284E + 05 0.770E + 04 0.550E + 04 0.533E + 04 0.822E + 04TRMS (eV) 0.161E + 05 0.295E + 05 0.900E + 04 0.140E + 05 0.733E + 04 0.118E + 05

and in situ measurements which underscores the need for IEEE Conference on Nuclear and Space Radiation Effects,further analysis. 1979). Balmain [1980] and Nanevicz and Adamo [1980]

The effects of arcing are somewhat better understood have analyzed the effects of arc discharges on material sur-than the process itself. The current pulse (Figure 7-8) gen- faces. Balmain [1980] gives numerous examples of holeserates an electrical pulse in spacecraft systems either by and channels of micron size in dielectric surfaces. Naneviczdirect current injection or by induced currents due to the and Adamo [1980] find additional, large scale physical dam-associated electromagnetic wave (see Proceedings of the age to solar cells such as fracturing of the cover glass.

Of more immediate concern to the space physics com-munity than arcs, however, are the effects of spacecraft

LOCAL TIME DEPENDENCE OF ANOMALIES charging on plasma measurements. There are numerous waysthat charging can complicate the interpretation of low energy

15 14 13 12 11 10 9 plasma measurements. These can be loosely defined as shift-16 8 ing of the spectra in energy, preferential focusing or exclu-

ARC CURRENT

18 6

195

26

DSP LOGIC UPSETS 0

DSCS II RGA UPSETS 22 0 100 200 300 400y INTELSAT IV 10 INTELSAT III T (nsec)

Figure 7-7. Local time plot of satellite operations anomalies; radial dis- Figure 7-8. Oscilloscope tracing of discharge currents into a conductortance has no meaning [McPherson and Schober, 1977]. supporting a mylar specimen [Balmain et al., 1977].

7-9

CHAPTER 7

12 JANUARY 1974-02 FEBRUARY 1974 4

70 INCREASINGGEOMAGNETIC

INCREASING ACTIVITY60 GEOMAGNETIC

ACTIVITY

50 AT/At

40LEAST MEAN

30 SQUARES FIT30 SQUARES FIT

20 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20

DST10

0 Figure 7-10. Heating rate per day divided by the average heating rate for0 5 10 15 20 25 30 35 40 45 50 the entire time period as a function of the daily Dst index

ap [Nanevicz and Adamo, 1980].

Figure 7-9. Number of arcs per hour as a function of daily ap for a Contaminant ions, due to thrusters (ionic or chemical)geosynchronous satellite [Shaw et al., 1976]. or outgassing of satellite materials, can be trapped within

the satellite sheath and preferentially deposited on nega-

tively charged spacecraft surfaces. Cauffman [1973] (seesion of particles of a particular energy or direction, andcontamination of measurements by secondaries, backscat- also Jemiola [1978; 1980]) has estimated that as much as

50 A of material can be deposited on charged optical sur-tered electrons, and photoelectrons. Each of these effects faces in as little as 100 days. In Figure 7-10 [Nanevicz andbriefly described below.

As described earlier in reference to the ATS 6 obser- Adamo, 1980] the heating rate of sensors on a geosynchron-ous satellite apparently rose with geomagnetic activity. This

vations (Figure 7-2), a potential difference between the ye- is believed to be due to increased contaminant depositionhide and the ambient plasma can raise or lower the energyof the incoming particles. In the case of differential flux during peiods of geomagnetic activity and therefore, in-

measurements such as the ATS 6 electrostatic analyzers, creased charging (Figure 7-5). Such deposition may alsoalter secondary emission and photoelectron properties.

the shift in energy is easily detected in the attracted species Another effect related to charging observed in the lab-

(Figure 7-2). For devices that measure the total current (such oratory is parasitic power loss. This is anticipated to be

as a Langmuir probe) more subtle techniques must be em- important at low orbital altitudes due to interactions between

ployed which involve intimate knowledge of the current- the ambient plasma and exposed high voltage surfaces such

voltage characteristic. as solar cells. McCoy et al. [19801 and Stevens [1980] haveThe most difficult effects to correct are due to particle

focusing or exclusion. As demonstrated in Figure 7-3, dif- estimated this effect both theortically and by laboratory

ferential charging of surfaces near a detector can result in experiments in large vacuum chambers to result in a 10%focusing or defocusing at specific energies. Just as the ge- power loss for voltages in excess of 5000 V at low earth

orbit. They also find that arcing begins at low earth orbitometry of the vehicle can shadow the field of view of a

at - 100 V and is a significant problem for potentials ofdetector, the potential gradients near the detector can distort

the particle trajectories. Methods for estimating particle fluxes -1000 V at geosynchronous orbit. Apparently, the powerloss and damage due to such arcing is much more serious

in the vicinity of such charged surfaces are discussed inon high voltage arrays than parasitic power loss.

Section 7.4.Secondary electrons, backscattered electrons, and pho-

toelectrons are emitted by spacecraft surfaces. If the vehicle

is positively charged, these low energy particles can be 7.3 CURRENT MECHANISMSreattracted to the vehicle. They constitute an extra and un-

desirable current source that can confuse ambient electron The spacecraft charging effects reported in the previous

measurements. Even in the case of negative potentials, dif- section result from current balance, that is, all the various

ferential potentials or space charge potential minima can currents of charged particles to and from the satellite surface

result in significant secondary and backscattered electrons must balance. Such current balance is valid for a uniform,

and photoelectron currents into the detector. This current is conducting satellite surface or for a non-conducting surface

easily misinterpreted as a positive potential effect if only in the limit of a point. Unless otherwise stated, the former

electron measurements are available. case (for a uniform conducting satellite) will be assumed (if

7-10


a non-uniform satellite surface is considered, then the cur- s. These time scales imply at least three different ranges forrent balance for each isolated surface and the resistive, ca- the validity of current balance. Except for the highest fre-pacitive, and inductive currents between surfaces must also quency ambient electron variations, for plasma frequencybe considered). The calculation of the satellite surface po- variations at low altitudes, and arcing, satellite to spacetential consists of 2 steps. First, the currents to the satellite current balance can be realized. Thin dielectrics can respondsurface are determined as functions of ambient conditions, to typical environmental variations (note this includes am-satellite geometry, and potential. Second, a satellite poten- bient variations due to satellite spin modulations, which aretial is found so that current balance is achieved. The cal- usually a few seconds to a minute). Current balance of largeculation of the currents to the satellite surface is very de- surfaces relative to each other may, however, not be achievedpendent on the fields in the vicinity of the space vehicle. (this behavior is illustrated in Figure 7-25b). Thus, currentThese not only depend on the geometry of the vehicle but balance is expected to be valid in a number of interestingalso on the sheath or the cloud of charged particles trapped cases although care must be exercised in the vicinity of thenear the satellite. The formulas for calculating the current plasma frequency and, in the other extreme, of large isolatedsources, given the incident particle distribution at each sat- dielectric surfaces.ellite surface, will be described in this section.

7.3.2 Incident Particle Fluxes7.3.1 Time Scales

The major natural source of potentials of 10 kV or higherIn determining the validity of the assumption of current on satellite surfaces is the ambient space plasma. Although

balance, an important issue to consider is the time scales space plasma is seldom representable in terms of a singlefor which it is applicable. Basic electrostatic considerations temperature and density, the Maxwell-Boltzmann distri-give order of magnitude estimates of these time scales. As bution function is a useful starting point for describing thean example, assume the satellite is a conducting sphere of ambient plasma conditions that generate these large poten-radius r and has a capacitance of Cx (ocr). The time scale tials. Given the distribution function f for an isotropic Max-Ts-s for the charging of a conducting sphere relative to space well-Boltzmann plasmain the earth's magnetosphere is then [Katz et al., 1977]

Cx V (v i) =ni( m mnv2e2kTi (7.3)Ts-s 4 J 2 x 10-3s (7.1) ( 2 k exp 2kTi)

~ where ni = number density of species i, mi = mass ofwhere r - 1 m, V is the satellite potential relative to space species i, Ti = temperature of species i, vi = velocity of(~1 kV), and J is the ambient flux (-0.5nA cm-2). species i, k = Boltzmann constant, and f = distribution

Unfortunately satellites normally are covered with ther- function.mal blankets that consist of thin dielectrics deposited over The current flux to a surface in the absense of an electricconducting substrates. The capacitance of a given dielectric field isarea A of thickness s can be estimated by CD (oc A/4rrs) sothat the time scale TD is [Katz et al., 1977] Jio = qi vi n fd3V. (7.4a)

CD VTD 1.6S (7.2)

AJ Assuming isotropy,

~where s - 0.1 cm, V 1 kV, and J 0.5nA cm-2 . = (qini) (2kT (7.4b/2

Other important time scales are the charging time of io 2 milarge, isolated surfaces relative to each other (from secondsto perhaps hours, depending on surface details), the plasma where Jio is the current density per unit area for 0 potential,frequency (104-107 Hz), and the gyrofrequency (103-106 n is the unit normal to surface, qi is the charge on speciesHz for electrons and 10-103 for H+); lower values are i, and d3V is the volume element in velocity space.representative of geosynchronous orbit where n ~1 cm -3 As will be shown in Section 7.4, when the effects ofand B ~ 100nT, and the higher values for the ionosphere, the spacecraft potential, sheath or plasma anisotropies, andwhere n ~ 106 cm -3 and B ~ 3 x 104nT. Typically envi- deviations of the ambient plasma from a Maxwellian dis-ronmental changes take place in minutes or longer, although tribution are considered, the simple distribution function oftime scales on the order of the plasma frequency and gy- Equation (7.3) is no longer valid and the integration ofrofrequency are observed. Arcing durations are 10 -9-10-8 Equation (7.4) becomes difficult. Even so, Equation (7.4)

7-11

CHAPTER 7

or a modification of it, is accurate for many practical pur- photoelectron yield H(E) (= W(E)S(E)) as functions of en-poses. Approximate values of T and n for various space ergy for aluminum oxide [Grard, 1973b]. The total currentplasmas are tabulated in Table 7-3. density for zero or negative satellite potential and normal

incidence, as derived by Grard, is

7.3.3 Photoelectron Currents JPHO = W(E) S(E) dE = H(E) dE. (7.5)

The photoelectron current from a surface is a functionof satellite material, solar flux, solar incidence angle, and JPHO for a variety of materials is tabulated in Table 7-4satellite potential (see review by Lucas, [1973]). In Figure [Grard, 1973b].7-11 adapted from Grard [1973b] are plots of the 4 functions If the satellite is positively charged, the ambient pho-necessary to describe the photoelectron current. In Figure toelectron current is attracted to the surface. As this return7-11 the solar flux S is plotted as a function of energy E current is a function of potential and geometry, the energy(or wavelength). The details of the spectrum change with spectrum of the electrons for a given incident monochro-solar activity and can vary greatly if the sunlight reaching matic photon must be known to calculate it accurately. Grardthe spacecraft is attenuated by the atmosphere [Garrett and [1973b] has carried out these calculations for several ma-DeForest, 1979]. Also shown in Figure 7-11 are the electron terials and different probe geometries (see also Whipple,yield per photon for normal incidence, W (E), and the total [1965]).

Table 7-3. Estimated plasma parameters for various environments. Most values are rough estimates. See appendix.

Charac-

teristic

Energy (eV) XD(m) Potential (V)**

Sunlight Eclipse

Region Altitude No (cm- 3) Ions I + E- I + E- V(km/s) (nA-cm -2) I-D RAM 3-D I-D RAM 3-D

Venus200km 105 O+,O2 + 0.05 0.3 0.005 0.01 8 8 -1.2 1.0 -0.83 - 1.8 - 1.2 -0.881500km 102 O

+ 0.2 1 0.33 0.74 8 8 6.0 6.0 2.4 -5.6 -4.4 -2.9

Earth

150km 105D* O+

,O2+ ,NO+

0.1 0.2 0.007 0.01 8 2 -1.1 -0.7 0.55 - -

103N NO 0.05 0.1 0.05 0.07 8 2 - - -0.58 0.33 0.37

1000km 104D O

+0.3 0.4 0.04 0.05 8 2 -1.3 -1.2 - 1.2 - - -

104N H+ 0.2 0.2 0.03 0.03 8 2 - - - -0.75 -0.73 -0.52

3.5RE 103 H+ 1

1 0.23 0.23 3.7 2 1.6 -1.6 -1.4 -3.8 -5.2 -2.5

Geosyn- 5.62RE 2 H+ 5000 2500 370 260 3 2 2.0 1.9 2.0 - 8500 -23000 6500

chronous

High - 0.1 H+ 200 200 330 330 800 2 15. 15. 15. -750 -490 500

Latitude

Jupiter

Cold Torus 3.5Rj- 50 S+ ,O+,O+ +

0.5 0.5 0.74 0.74 44 0.08 -. 75 .59 -. 72 - 2.3 -1.2 1.6

5.5Rj 1000 2 1 0.33 0.23 69 0.08 -3.8 -2.2 -3.1 -4.2 -2.3 -3.3

Hot Torus 6.0Rj- 1000 S+,O + + 40 10 1.5 0.74 75 0.08 -37 -34 -33 -39 -34 -33

8.0Rj- 100 80 20 6.6 3.3 100 0.08 - 65 - 60 - 60 - 78 - 70 - 65

Plasma 8.0Rj- 12 H+,S + 50 50 15 15 150 0.08 -110 -110 -94 -190 -170 -130

Sheet 15Rj

Outer - 0.01 H 1000 1000 2300 2300 250 0.08 9.6 9.5 -9.5 -3800 -4400 -2500

Magnetosphere

Solar Wind0.3AU 50 H+ 40 65 6.6 8.5 500 20 4.6 4.9 4.4 -260 -150 - 160

1.0AU 2 H+ 10 50 17 37 450 2 7.8 8.0 7.3 -230 120 - 110

5.2AU 0.2 H 1 10 17 53 400 0.08 7.4 8.0 6.0 -50 18 -21

*D = Day, N = Night**See Appendix for description of computations and captions

Underlined values are "preferred" estimates


01022 8

10 10 102 103 104 105 106 107PRIMARY ENERGY (eV)10

0 ner, 1973, Chung and Everhart, 1974; Baragiola et al.,10 5 10 15 20 25 1979]. Each of the three has a characteristic emission spec-

E (eV) trum.The equation for the current density due to secondary

Figure 7-11. Composite plot of W(E)the electron yield per photon;S(E), emission, assuming an isotropic flux and ignoring otherthe solar flux; and their product, H(E), the total photoelectron angular variations is (see, however, Whipple, [1965]):yield, as function of energy E for aluminum oxide [Grard,1973]. J 2 = 2qi dE (E' E) B(E)E fi(E) dE (7.6)

7.3.4 Backscattered and Secondary Electrons where Jsi = secondary electron flux due to incident speciesi (usually assumed to be electrons, e-, or protons, H+),

The impact of ambient electrons and ions on a spacecraft gi = emission spectrum of secondary electrons due to in-surface generates backscattered and secondary electrons- cident species i of energy E , = secondary electron yieldbackscattered and secondary ion fluxes being insignificant. due to incident species i of energy E, E' = secondary elec-These fluxes, though often neglected in charging calcula- tron energy, and fi = distribution function of incident par-tions can exceed the incident fluxes under some circum- tides at surface.

backscattered electrons is not always possible, backscattered minum from Whipple [1965] are plotted in Figure 7-12aelectrons are those ambient electrons reflected back from and 7-12b (see also Sternglass [1957], Willis and Skinnerthe surface with some loss of energy [Sternglass, 1954] (see [1973], Chung and Everhart [1974], and Baragiola et al.also reviews by Dekker [1958], Hachenberg and Brauer [1979]). The function gi is assumed to be independent of[1959], Gibbons [1966], and Lucas [1973].) Secondary incident energy and incident particle species. The normal-

Table 7-4. Photoelectron emission characteristics of various spacecraft materials.

Photoelectron Saturation Flux Saturation CurrentMaterial Work Function (eV) (10 12ne/s-m2 ) Density ( u A/m2 )

Aluminum 3.9 260 42OxideIndium 4.8 190 30OxideGold 4.8 180 29Stainless 4.4 120 20SteelAquadog 4.6 110 18LiF on Au 4.4 90 15Vitreous 4.8 80 13CarbonGraphite 4.7 25 4

7-13

CHAPTER 7

10.0 0.510.0 0.5

H+ ON ALUMINUM

0.4

1.01.0

0.3O Consini et al[] Ghosh and Khare

0.1 A Hill et alV Ghosh and Khard* Aarset et al

0.013 104 105 0.1

PRIMARY ENERGY (eV)

Figure 7-12b. Secondary electron yield 8I due to incident ions of energyE impacting on aluminum [Whipple, 1965].

0 0.5 1.0E'/E

ized curve [Whipple, 1965] for aluminum is plotted in Fig-ure 7-12c. Figure 7-13. Graph of G (E'/E) as a function of (E'/E) where G is ap-

proximately the percentage of electrons scattered at a givenFor backscattered electrons, the current density is given energy E' as a result of an incident particle of energy E

by DeForest [1972] [Sternglass, 1954].

JBSE = 2rrqE dE' B(E',E) E fE(E) dE, (7.7) tual values are dependent on angle of incidence which hasm2E ° E' been ignored in the preceding discussion. Further, the sec-

ondary and backscatter properties of actual satellite surfaceswhere which are invariably oxidized or contaminated are not well

known. Currently the lack of knowledge in this area is one

B (E', E) = G (E) 1E of the major deficiencies in spacecraft charging theory.

and G is the percentage of electrons scattered at fraction E'/ 7.3.5 Magnetic Field -Induced CurrentE of the incident energy E. Distortions

Sternglass [1954] has published experimental measure-ments of backscatter parameters for different materials. An A problem in low earth orbit often encountered by elec-estimate of G for Al from his data is plotted in Figure 7- tric field experiments employ long (~10 m or longer) an-13. For negative potentials, the backscatter flux is roughly tennas or booms is the induced electric field due to the20% of the incident flux. satellite crossing the earth's magnetic field lines. Briefly, a

For both secondary and backscattered currents, the ac- satellite moving relative to a plasma (assumed to have azero electric field with velocity vs will see an electric fieldE in its rest frame given by

80 E = Vs x B = 10-8 (vs x B) V/cm (7.8)C

60where E is in V/cm, vs is in cm/s, B is in G, and C is the

40 speed of light.

An earth-orbiting satellite will see a maximum induced20 v x B field at low altitudes on the order of -0.3 V/m. The

local fields and current flows in the vicinity of the vehicle0 2 4 6 8 10 12 14 16 18 20 will be distorted by this effect.

SECONDARY ELECTRON ENERGY (eV)Besides the v x B current, the magnetic field also in-

Figure 7-12c. Emission spectrum of secondary electrons due to incident duces anisotropies in the particle fluxes. Ambient fluxes,electrons or ions impacting on aluminum [Whipple, 1965]. secondaries, beam fluxes, and charged particle wakes are

7-14


all controlled to a greater or lesser extent by the magneticfield. Whipple [1965] and Parker and Murphy [1967] have j(8)/joanalyzed some of the effects of these magnetic field-induced h=550-640anisotropies on spacecraft charging (see also reviews by 0.1 520-720

Brundin [1963] and Guverich et al. [1970]) and find thatthe electron flux can be reduced by as much as a factor of2, but as a rule these are ignored in spacecraft charging 0.01calculations. McCoy et al. [1980] has suggested that this

0 60 120180 240300360 0 60 120 180 240 300 360constraint of electrons to field lines may become of real to) 8 (b) 8concern for very large structures which are much larger than j (8)/joa gyroradius.

h=720-820

7.3.6 Motion-Induced Effects nH+=0.45 2.82

In low earth orbit, the velocity of a satellite is 7.5 km/s.Within the plasmasphere, where particle energies are 1 eV 0 60 120 180 240 300 360 0 60 120 180 240 300 360

or less, the ion thermal velocity is 10 km/s or less. Thisimplies that a plasma wake would be formed around the j(8)/jovehicle. Chang et al. [1979] have estimated that motion-induced effects on the satellite potential due to such a wakeare important for ion ram to thermal velocity ratios as lowas 0.1. These motion-induced effects would be present even 0.1

for neutral particles and result in there being large asym- 0 60 120 180 240 300 360

metries in the flow between the leading surfaces of the (e)satellite and the rear for even small objects such as booms.The motion of the satellite can also induce space charge Figure 7-14. Normalized electron current versus angular position of the

plasma probe on Explorer 31 [Samir and Wrenn, 1969];variations in the vicinity of the vehicle [Parker, 1977]. The 180 would correspond to the center of the wake (that is,depletion of electrons and ions in the satellite wake can opposite the direction of movement). Also shown are the-

distort the flow of the particles to the vehicle. A typical oretical fits. The altitude h and ambient density n are indi-cated [Gurevich et al., 1970].

observation is presented in Figure 7-14 in terms of the nor-malized electron fluxes in the wake of the Explorer 31 sat-ellite [Samir and Wrenn, 1969]. Although simple modelsof this phenomena will be discussed below, reviews by 3Brundin [1963], Kasha [1969], Liu [1969], and Al'Pert[1976] and papers by Gurevich et al. [1970] and Kunemann[1978] should be consulted for details. 2

7.3.7 Charge Deposition 1by Energetic Particles

The deposition of charge in dielectrics by high energy 0particles is a well known phenomena in nuclear physics (see, 400 seconds

for example, Gross and Nablo [1967]; Evdokimov and Tub-alov [1974]; and Frederickson [1979]) and has been proposed -1as a source of satellite charging [Meulenberg, 1976]. As anexample [Frederickson, 1980], electrons between 10 keV and100 keV lose energy at a rate of R = 106to5 x 10 eVg-1 cm2

-2depending on energy and the material involved (R · p, wherep is the density of the material, gives the energy loss rate per

2 3 4 5 6cm). Electrons of I MeV will typically penetrate several mil- DEPTH ( mm )

limeters into a solid. Fields of the order of M V/mm are nec-essary to retard such incident fluxes. Fields of this magnitude

Figure 7-15. The electric field in 6 mm PVC sample as a function ofare more than adequate to cause electrical breakdown in a die- exposure time to a 4.66 x 10 -10 A/cm2 , I MeV electron

lectric. Figure 7-15 is a theoretical plot of the potential in a PCV beam [Frederickson, 1980].

7-15

CHAPTER 7

sample exposed to 1-MeV electrons as a function of time to a much larger beam spread marked by an increase in the[Frederickson, 1980]. local plasma density. The critical current Ic when this occurs

As satellites in the earth's radiation belts or the hostile is proportional to the beam energy, VB, such that IcVB 3/2,environment of Jupiter can experience high dosages of en- an equation resembling Equation (7.14). The NASA Lewisergetic particles, this effect becomes important if long mis- studies are part of a coordinated effort to validate the NAS-sion lifetimes are desired. Recent evidence [Treadway et CAP code (see Section 7.4.6) and have included testing ofal., 1979] indicates that the effects of charging and arcing the P78-2 SCATHA experiments [Stevens et al., 1980a].may be substantially altered by the buildup of charge indielectrics. As yet, this process has not been included inspacecraft charge modeling. Its inclusion, however, will be 7.4 SPACECRAFT CHARGING THEORYcritical to a complete understanding of the charging/arcing

process. The basic equation expressing current balance for a givensurface in an equilibrium situation is, in terms of the current:

7.3.8 Artificial Charging Mechanisms IE (V) - [II(V) + ISE (V) + ISI(V) + IBSE (V)

+ IPH (V) + IB (V)] = IT (7.9)Artificial mechanisms that effect spacecraft charging are

numerous and include electron and ion beams and exposed, where V = satellite potential, IE = incident electron cur-high potential surfaces such as the junctions between solar cells rent on satellite surface, I = incident ion current on sat-[Stevens, 1980]. Recently, beam sources have been actively ellite surface, ISE = secondary electron current due to IE,exploited both as probes of the satellite sheath and as a means ISI = secondary electron current due toof controlling the spacecraft potential [Goldstein and De-

IBSE = backscattered electrons due to IE, IPH = photoelectronForest, 1976; Olsen, 1980; Purvis and Bartlett, 1980; Cohen current, I = active current sources such as charged particleet al., 19791. Voltages in the KV range and currents between total current to satellitebeams or ion thrusters, and I, = total current to satellitemA and A are typical of these systems [Winkler, 19801. The (st equlibrum, IT =0)Excede 2 test [O'Neil et al., 1978b], in fact, ejected 3 kV In this section methods of solving Equation (7.9) for Velectrons at 10 A. An example of a theoretical beam calcula- so that IT = O will be described. The basic problem is thetion will be given in Section 7.4 as an illustration of the com- solution of Equation (7.9) subject to the constraints of Pois-plexities involved in analyzing such experiments. son's equation:

Parker [1979, 1980], Stevens [ 1980], McCoy et al. [1980],and Rieff et al. 11980] have carried out calculations of thecurrents to exposed potential surfaces for large, high voltagestructures. They find that a major effect is to induce largevoltage gradients in the satellite sheath that must be con-sidered in the proper design and use of such systems. Thepotentials can lead to multipacting and preferential depo-sition of ion contaminants. Another possible difficulty as- v Vf i- qi V V (r) Vv fi = 0, (7.11)sociated with very high positive potentials is the "pinhole" mieffect. As discussed in Kennerud [1974], the insulation onsuch surfaces can become punctured. Even microscopic holes where nE = local electron density, n, = local ion density,can result in exceptionally high focusing of electrons-in ns = surface-emitted electron density, V, and Vv = gradientsome cases the pinhole can completely defeat the insulation. operators with respect to position and velocity space re-

Finally, a number of experiments have been conducted spectively.in vacuum chambers. Currently, the most extensive pro-grams are those at NASA Johnson [McCoy et al., 1980]and NASA Lewis [Stevens, 1980; Purvis et al., 1977; and 7.4.1 Analytic Probe Theorytheir colleagues]. The NASA Johnson chamber tests have General Considerationsinvolved testing of high potential surfaces and of rocketbeam sources prior to flight [Konradi, private communi- The most important concept in probe theory is that ofcation, 1980] in an environment resembling the ionosphere. the Debye length XD, the distance over which a probe orAs discussed in Bernstein et al. 11978; 1979], these latter satellite significantly perturbs the ambient medium. (Notetests have concentrated on the analysis of the so-called "beam- that this is only one definition of the satellite sheath. Theplasma discharge" (BPD) in electron beam experiments. sheath thickness is not only dependent on satellite potentialThey have found that the electron beam at a critical current and charge, but through the so-called "presheath", influ-transitions from one well defined by single particle dynamics ences the plasma up to the order of the satellite radius

7-16


[Parker, 1980]. More precisely, electrons and ions form a In order to solve these equations, it is assumed that V andcloud around any charged surface that is a function of the dV(Y)/dY are 0 at some distance Y = S which determinesparticles' energies and densities and the potential on the the sheath thickness (called the "space-charge limited" as-surface. As an illustration, the solution to Poisson's equation sumption). The solution becomesfor spherical symmetry is

(7.14)e-r/D 9 m S2V(r) = q e (7.12)

rThis is the "space-charge limited diode model" solution or

where XD = (KT/4 q2 no)1/2 and no = ambient charge Child-Langmuir model for a plane. If J is replaced by Jo = K*density. This is the classical Debye length for the assumption qno (kT/m)1/2 (where (2 ) -1/2 < K* < 1, the lower limitof "linearized space charge." The "linearized space charge" corresponds to Equation (7.4b); the upper limit is for aapproximation can be extended to spherical and other multi- monoenergetic flow of energy E 1/2 kT) then the sheathdimensional geometries; an analytical fit for the spherical thickness can be estimated:case is discussed by Parker [1980]. Values for D are listedin Table 7-3. S = 1 ( 2 1/4 3/4 (1 (7.15)

The terminology "thick" sheath and "thin" sheath de- 3 qKT) n K*rives from the assumption that the region over which thesatellite affects the ambient plasma or is screened from the This sheath thickness determines the region over which chargeambient plasma is either larger or smaller than the char- is collected and is important in determining the maximumacteristic dimensions of the spacecraft. Usually this reduces current that can flow to a probe for a given V.to determining whether XD is long (thick sheath) or short Although seldom utilized in spacecraft charging calcu-(thin sheath) compared to the spacecraft radius. From Table lations, a form of Equation (7.14) was employed by Beard7-3, for a 1 m radius spacecraft with no exposed potential and Johnson [1961] to obtain the potential to which a vehiclesurfaces in low earth orbit, the term thin sheath is appro- can be charged by an electron emitter in the ionosphere.priate. For geosynchronous orbit, unless the satellite is 10 This calculation placed an upper limit on the current thatm or larger, the thick sheath approximation is appropriate. could be drawn at a given potential ignoring magnetic fieldIf active surfaces (that is, exposed potentials driven by the shielding effects. When included [Parker and Murphy, 1967],satellite systems) or a substantial photoelectron population the maximum current was reduced by as much as a factorare present, these limiting criteria will change, but even so of 10. Linson [1969], including turbulence, found valuesfor most satellite studies they are very useful (Opik [1965] between these limits, however. These studies imply that ahas carefully considered this issue of the appropriate screen- I m sphere emitting a 0.5A electron beam at shuttle altitudesing criteria for the general case of an arbitrary central force). would have a potential of 104 -106 V, depending on the mag-

As a first example, consider a large structure such that netic field [Liemohn, 1977], thereby seriously inhibiting athe characteristic scale of the sheath is significantly smaller 10-100 keV beam. Recently, Parker [1980] (see also Ken-than rs, the radius of the surface (the thin sheath assump- nerud [1974], McCoy et al. [1980], and Parks and Katztion). Assuming at the surface (X = rs) the potential is Vo [1981]), in order to estimate the sheaths around large spaceand that the surface is nearly planar relative to the sheath structures, have developed an analytic expansion for thedimensions, at distance Y( = X - rs) from the surface (only thin sheath approximation to a sphere. He has investigatedthe attracted species is considered) the applicability of this estimate of the sheath to extremely

high applied potentials in the ionosphere by comparing itto the results of a self-consistent numerical calculation (see

Poisson's Equation d2V(Y) -4 q n(Y) (7.13a) Section 7.4.2). Although his rigorous computations (for adY2 Debye length to satellite radius ratio of 1 to 100) deviate at

low potential values (qV/kT < 10) from the space chargeCurrent continuity limited model, the results approach each other for very high

J = q n(Y) v(Y) = constant (7.13b) potentials (qV/kT ~ 400 000).The preceding theory concerning the thin sheath assumes

The particles are assumed to have E = 0 in the ambient that sheath effects dominate the current flow to the satellite.space: This places emphasis on Poisson's equation and the space

charge around the satellite. In the opposite extreme, thesheath and space charge are ignored so that, to first order,

Energy conservation Laplace's equation holds. In practical terms this translates1 mv(Y)2 + q V(Y) = 0. (7.13c) into the assumption that D>> rs. For spherical symmetry,2 conservation of energy and angular momentum imply that

7-17

CHAPTER 7

for an attracted particle approaching the satellite from in- and for the repelled species Ji = Jio e Qis wherefinity

v2 = m v (rs)2 + q V(rs) (7.16a) Qis (+ for electrons, - for ions) (7.21)2 o =2 kTi2

m RIvo = m rsv (rs) (7.16b)The current-voltage characteristics implied by Equations

where vo is the velocity in ambient medium, R is the impact (7.20) and (7.21) for the three geometries are plotted inparameter, and RI is the R for a grazing trajectory for a Figure 7-16. Several important conclusions can be drawnvehicle of radius rs. from Equations (7.20) and (7.21) and Figure 7-16. First

Solving for the impact parameter RI (only particles hav- Prokopenko and Laframboise's results for a sphere are iden-ing R < RI will reach rs): tical to Equation (7.18) (with 1/2 mv2 replaced by kTi) foro2 2

RI=rs(1 -2qV(rs) (7.17) current

(infinite(RI - rs) is equivalent to the sheath thickness S defined for sheath)

a thin sheath as it also is the size of the region from whichparticles can be drawn.

The total current density striking the satellite surface for (infinite sheath)

a monoenergetic beam is infinite plane

J(V) =1 -2qV(rs) (7.18) Maxwellian4 r2 mvy 2mono

s energeticwhere I is the total current to spherical satellite equal to the repulsive voltage 0 attractive voltageambient current that would pass through an area 4 rr R2Iand depends on independent (approximately) of

Jo is the ambient current density outside the sheath equal to velocity distribution velocity distribution

I/4 RI2. This is the so-called "thick sheath, orbit-limited" independent of geometry depends on geometry

current relation.The thick sheath results are readily extended to more com- Figure 7-16. Qualitative behavior of Equations (7.20) and (7.21) for a

plex distributions. For most spacecraft charging problems, Langmuir probe [Parker and Whipple, 1967]. (Reprinted

Boltzmann's equation [Equation (7.11)] in the absence of with permission of Academic Press © 1967)

collisions reduces to Liouville's theorem. For a complexdistribution function, F, Liouville's theorem states that: a thick sheath. It should also be readily apparent that the

planar solution is conceptually equivalent to a thin sheath.

F (v) = F' (v') (7.19) Thus, Equation (7.20) additionally gives a qualitative pic-ture of how the probe characteristics change as the ratio ofthe Debye length to satellite radius is varied from smallwhere F' and v' are the distribution function and velocity

at the surface of the spacecraft. F and v are the ambient values (thin sheath or planar) to large values (thick sheathor spherical). This was done explicitly by Whipple et al.distribution and velocity at the end of the particle trajectory y by Whipple et al.[1974] and Whipple [1977] for the ratio of the Debye lengthconnected to the satellite surface where F' and v' are meas-

ured. Prokopenko and Lafromboise [ 1 977, 1980] have de- to satellite radius and is closely related to the parametrization

rived (based on Equation (7.19)). in more general terms the method of Cauffman and Maynard [1974].current density to a sphere, infinite cylinder, and infiniteplane (that is, three-, two-, and one-dimensions) for a Max-well-Boltzmann distribution for the orbit-limited solution. 7.4.2. Analytic Probe TheoryTheir results (see original derivation in Mott-Smith and Thick Sheath ModelsLangmuir [19261) for the attracted species are

At this point a complete analytic theory for the case of

[(1 + Qis) Sphere a thick sheath, spherical probe has been developed. Sub-Ji = Jio * [2(Qis/,'r) 2 + eQ+ i erfc (QisQ/2)] Cylinder stituting into Equation (7.10) and assuming that the sec-

L(1) Plane ondary and backscatter terms can be parametrized, for an(7.20) ambient Maxwellian plasma

7-18


AE JEO [1 - SE (V,TE,nE) - BSE (V,TEnE)]

exp(qV/kTE) 12 ([])

(7.22)- AI JIo [1 + SI(V,TI,nI)] ( (7.22) 10

- APH JPHO f(Xm) = IT=0 V < 0 8

where6

JEO = ambient electron current density 4[Equation (7.4)] To (AVG) To(RMS)

ATS -5JIo = ambient ion current density [Equation 2 ATS - 6

(7.4)]

AE = electron collection area (4 r2s for a 00 -2 -4 -6 -8 -10 -12

SATELLITE POTENTIAL (kV) IN ECLIPSEAI = ion collection area (4 r r2s for a sphere)

ApH = photoelectron emission area ( r2s for a Figure 7-17. Observed temperature of ambient electrons versus satellitepotential in eclipse. To(AVG) is two thirds of energy density/sphere) number density: To(RMS) is one half of energy flux/number

flux.SE, SI, BSE = parametrization functions for secondary

emission due to electrons and ionsand backscatter threshold temperature below which charging does not occurJPHO = saturation photoelectron flux (Table 7-4) is real and is due to the fact that at an intermediate energy

(usually a few hundred eV), the secondary yield is greaterf(Xm) = percent of attenuated solar flux as a than 1 [Rubin et al., 1978]. The electron temperature must

function of altitude Xm of center of sun be several times greater than this threshold energy beforeabove the surface of the earth as seen charge buildup occurs.by satellite. The agreement can be significantly improved for Figure

7-17 if the actual ambient spectra are utilized in the inte-Equation (7.22) is appropriate for a small (<10 m), uni- gration of Equations (7.4), (7.6), and (7.7) instead of aformly conducting satellite at geosynchronous orbit in the Maxwellian in computing the currents. This method of usingabsence of magnetic field effects. To solve the equation, V the actual particle spectra to estimate the currents has beenis varied until IT = 0. A number of examples of this pro- extensively employed by DeForest [1972], Knott [1972],cedure, assuming SI = SE = BSE = 0, are tabulated in Garrett and DeForest [1979], and Prokopenko and Lafram-Table 7-3 for various plasma regions. boise [1977, 1980] in the calculation of satellite to space

If it is assumed that SI, SE, and BSE are constants (that potentials for geosynchronous spacecraft. The potentials ofis, -3., -0.4, and -0.2 for Al), then Equation (7.2) Figure 7-17 are recalculated in this manner and plotted inpredicts [Garrett and Rubin, 1978] that in eclipse, the po- Figure 7-18a [Garrett and DeForest, 1979]. Results are pre-tential between the satellite and space is sented both for particle spectra immediately before entry or

~ immediately after exit from eclipse ("sunlit") and for eclipseV ~ -TE (7.23) ("eclipsed"); differences are attributed to the digitization of

the spectra. As the exact secondary response of the satelliteThe satellite to space potentials observed by UCSD elec- surface was not known, SE, SI, and BSE were assumed to

trostatic detectors for twenty-one ATS 5 and four ATS 6 follow the Al curves of Figures 7-12 and 7-13. Their ab-eclipses are plotted in Figure 7-17 versus the electron tem- solute amplitudes were then varied until the observationsperature. As the geosynchronous plasma is not necessarily were fit in a least squares sense [Garrett and DeForest,Maxwellian, two different "temperatures," To (AVG) 1979].(=2/3 energy density/number density) and To (RMS) Given the validity of the calibration method, the effects(= 1/2 energy flux/number flux), are presented (these would of a varying photoelectron flux on the satellite to spacebe equal if the plasma was actually Maxwellian). The agree- potential can be studied during eclipse passage. If the sat-ment is good considering that the range of potentials is ellite position is known, the photon flux reaching the satellitebetween - 300 V and - 10 000 V. The existence of a can be calculated from first principles [Garrett and Forbes,

7-19

CHAPTER 7

1981]. If the satellite surface materials were known, thenthe photoelectron current, JPHO . f(Xm), could also be cal-culated from first principles. Although the exact surfaceresponse is in actuality not known, adequate approximations

-10 ATS-5 ATS-6 can be derived [Garrett and DeForest, 1979; Garrett andSUNLIT Forbes, 1981]. JPHO in Equation (7.22) is then varied to fit

-8 ECLIPSED observations. Estimates of the varying potential on ATS 6during eclipse entry and exit by this technique are compared

-6 with actual observations in Figure 7-18b [Garrett andDeForest, 1979]. This eclipse model has proven valuable

-4 in estimating photoelectron flux and potential variations forATS 5, ATS 6, Injun 5, and P78-2 SCATHA.

-2 The results of Prokopenko and Laframboise [1977, 1980],using the spectra suggested by Knott [1972], are particularly

0 -2 -4 -6 -8 -10 -12 -14 important because they established the existence of muiltipleOBSERVED POTENTIAL (kV) roots for Equation (7.22) (see also Sanders and Inouye [1979]).

Multiple roots imply that a satellite can undergo rapid volt-Figure 7-18a. Predicted and observed potentials in eclipse for ATS 5 and age variations in response to small environmental pertur-

ATS 6. Solid symbols are for calculations using the spectra bations and that adjacent surfaces can come to radicallyin eclipse. Open symbols are for calculations using the different potentials for the same conditions. To obtain their

result, they solved an equation equivalent to Equation (7.22)(that is, local current balance) for the spherical, the cylin-drical, and planar assumptions of Equations (7.20) and (7.21)and for eclipse conditions. They found that the potential ismarkedly increased for a planar probe relative to a spherical

-104 probe.DAY 66, DAY 59,

1976 1976

ATS-6 7.4.3 Analytical Probe TheoryThin Sheath and Related Models

Analytic probe theory can also be utilized to estimate-103 satellite to space potentials in the 250-700 km range. As

discussed in Brundin [1963], in the absence of magneticforces, photoelectrons, and secondaries, Equation (7.9) re-duces to

J AE JEO CE. eqV/kTE- AI JIR CI = 0 (V < 0) (7.24)

where

JEO = ambient electron current density (Equation (7.4)),

JIR = ion ram current density (ignoring ion thermalo OBSERVED

velocity)o PREDICTED

= qI nI Vs,

-10 11284 1285 1286 1319 1320 1321 1322 vs = satellite velocity,

UT (min.) AE = electron collection area (4 rs2 for a sphere),

Figure 7-1 8b. Observed and predicted potentials for the entry into eclipse AI = ion collection area ( rs2 for a sphere),of ATS 6 on day 66, 1966. and for eclipse exit on day 59,1976. rs = satellite radius

7-20


CE = electron shielding factor (= 1, no electron wake 16

assumed; 1/2, wakeon rear half),

CI = ion shielding factor {(= 1, complete shielding ofambient ions or thin sheath;

= I mv2), no shielding or thick sheath,

(Equation (7.18)).

Samir [1973] and Samir et al. [1979b], assuming no -l80 -135 -90 -45 0 45 90 135 180

electron wake and no ion shielding (note that this is a thick ANGLE WITH VELOCITY VECTOR (DEGREES)

sheath assumption which is usually inappropriate in thisregion), have compared the predictions of Equation (7.24) Figure 7-19. Variations in the positive ion current density with angle

relative to the satellite velocity vector. The data and figurewith observations. In spite of the simplicity of Equation are from Bourdeau et al. [1961]. The fitted line is given by(7.24) and the assumption of a thick sheath, they predict Equation (7.29) with a assumed to be 3.6 km/s; the satellite

the satellite to space eclipse potential (typically - - 0.75V) potential is assumed to be 0.

for a large range of ambient conditions to a factor of 2.5or better. rs > XD, the Debye length in the ionosphere being much

A simple approximation for estimating the current to an smaller than the satellite's characteristic dimensions. Thisisolated point on a planar satellite surface in the ionosphere allows the neglect of the effects of the satellite potentialas a function of the surface normal relative to the velocityas a function of the surface normal relative to the velocity except very close to the satellite surface. The left hand sidevector is that of Whipple [19591 and Bourdeau et al. [1961] of Equation (7.10) can then be ignored, so that it becomes:(see also Tsien [1946] and Chang et al. [1979]):

nE - nI 0 (7.10*)

Ii = aqniAi vs cos 0 (1/2 This is the so-called "quasi-neutrality" assumption [for ex-+ 1/2 erf (x)) + -- (7.25) ample, Gurevich et al., 1966, 1968, 1973; Grebowski and

]2 VIT, Fischer, 1975; Gurevich and Dimant, 1975; Gurevich andPitaveskii, 1975]. Equation (7.11) for the ions can be re-

where duced by making use of the "hypersonic" character of the

motion of a body in the ionosphere (that is, M, the square=vs cos (qV)1/2 root of the ratio of the ion kinetic energy to electron thermal

a (kTi / energy, is much greater than 1). First, this implies that the0 = angle between sensor normal and velocity vector, gradient of the potential perpendicular to the flow direction

Ai = collection area, is much greater than the gradient along the flow directiona = grid transparency function, so that this latter term can be ignored. Second, the thermala = most probable ion thermal velocity. velocity of the ions in the direction along the flow direction

can be neglected relative to the satellite velocity vs in theThis equation, the so-called "planar approximation", is good ionosphere. Based on these assumptions, Equation (7.11)for short Debye lengths but becomes inaccurate for long for ions can be rewritten asDebye lengths [Parker and Whipple, 1970] and more com-plicated orbital trajectory calculations must be carried out. f+ v afI - q aV afIEven so, Bourdeau et al. [1961] found it to be a good s ar mI ar av

approximation to the ion current relative to the velocityvector measured by the ion planar probe on Explorer 8 where r and v correspond to components normal to the(425-2300 km altitude). Their results for V = 0 are plotted direction of motion and z is in the vs direction.in Figure 7-19 (note that there is some question as to the For the electrons, a Boltzmann distributionbest value for a, see Bourdeau et al. [1961]). (nE = nEO ' exp (qV/KTE)) is usually assumed. The re-

A simple analytic theory closely related to thin sheath sulting system of equations for the ions does not containprobe methodology and capable, within limits, of explaining the ion thermal velocity along the direction of motion andthe satellite wake structure in the ionosphere has also been can be put into a dimensionless, self-similar form [Al'pertdeveloped. It (see reviews in Gurevich et al. [1970] and et al., 1965; Gurevich et al., 1970] that resembles classicalAl'pert [1976]) is based on the thin sheath assumption, hypersonic aerodynamic equations. Depending on the char-

7-21

CHAPTER 7

acteristics of the assumed plasma conditions, the wake vari- that dielectric surfaces can charge in tens of minutes butations for a number of simple geometries can be analytically may take hours to discharge. Further, charge up can be asolved. These range from the extreme assumption of a true long term (days) process and be dependent on the timeneutral flow as reviewed in Gurevich et al. [1970] and Al'pert history.[1976]-charged particle variations in the wake mirroringthe neutral variations-to plasma flows around infinite half-planes, wedges, plates, cylinders, and discs. The predictionsfor one such analytic solution [Gurevich et al., 1970] are 7.4.4 General Probe Theorycompared with Explorer 31 observations in Figure 7-14 fromSamir and Wrenn [1969] for various distances r/rs from the Whereas analytic probe theory is applicable to a numbersatellite. The theory is not considered reliable at angles of practical problems, it does not allow for the complexgreater than ~ 120° as the electron density can differ greatly geometric and space charge effects of the satellite sheathfrom the ion density in this region of maximum rarefaction on particle trajectories. As a consequence, it is severely[Gurevich et al., 1970]. limited in its quantitative accuracy (the parametrization method

Although severe constraints (primarily rs >> XD and ne- of Cauffman [1973]; Cauffman and Maynard [1974], is oneglect of the ion thermal velocity) have been placed on the qualitative means of studying these effects using analyticrealm of applicability of this "hypersonic," quasi-neutral probe theory). In order to include the effects of the sheaththeory, it does allow the analytic study of the effects of on particle trajectories, it is necessary to seek simultaneous,geometry, magnetic field, and, of more importance, ionic self-consistent solutions of Equations (7.10) and (7.11).composition on the wake. As discussed in Gurevich et al. Typically, this is not analytically possible and an iterative[1970, 1973] and Samir et al. [1980], variations in ion procedure must be employed. First, V (r) is assumed socomposition play a critical role in the details of the expan- that fi (r,v) can be computed subject to Equation (7.10).sion of the ion population into the rarefied wake region The number densities, ni, are then found frombehind the satellite. Although these results are useful, inmost practical situations a finite Debye length is a necessary ni (r)= f fi (r,v) d3V. (7.26)assumption. This greatly complicates any theoretical com-putation and requires the advanced probe theory of Section7.4.4. Given the ni (r), V (r) is computed according to Equation

An application of analytic probe theory based on local (7.10). The process is iterated until a consistent set of valuecurrent balance is in the so-called circuit models. The single of ni(r), V(r), and fi (r,v) at grid points surrounding theprobe theory introduced so far does not explicitly consider surface are found. Then the Ji's at the surface rs are foundthe problem that satellites consist of a variety of surfaces, from the generalized form of Equation (7.4)including dielectrics, and that each surface can charge to adifferent potential if isolated from the others. In order to Ji (rs) = qi v . n fi(rs,v) d3V (7.27)explicitly model this differential charging effect, the cou-pling currents between surfaces must be included in Equa-tion (7.9). Circuit models [Robinson and Holman, 1977; The theories to be discussed assume the time-indepen-Inouye, 1976; Massaro et al., 1977], as this class of models dent form of the Vlasov equation. Equation (7.10) is thenis termed, consist of many "probes," each representing a just a restatement of Liouville's theorem, namely, thatparticular point or surface on the satellite (a dielectric sur- fi (r,v) is constant along a particle trajectory in a potentialface, for example, would be approximated by one or more V(r). To determine fi (rp,v) at a point rp for a particle of aindividual points). Besides the ambient, secondary, back- given energy, all that is required is to find the intersectionscattered, and photoelectron currents considered in the sin- of that particle's trajectory with a surface where fi is known.gle probe model, the coupling currents to each point, JRLC, The trajectory may either be traced from the point backwardsare included in J to estimate the currents between surfaces. to the surface (the inside-out procedure) or from a surfaceTime variations are explicitly handled by including induc- to the point (outside-in procedure). According to Parkertive and capacitive elements which have finite charging times [1976a], the inside-out trajectory tracing method is pref-(local current balance with space is assumed at each instant erable in that the points at which the density is calculatedin time) making these models applicable to a wider range can be picked at random and is suitable for both electronsof problems than the single probe models. Inouye [1976] and ions. It has the disadvantage that the trajectory infor-and Massaro et al. [1977] have utilized such models to assess mation computed for a given point is lost in moving to thethe effects of geomagnetic storm variation, varying solar next, increasing the computer time. The outside-in methodangle, isotropic fluxes, etc., on individual satellite surfaces can be readily adapted to time-dependent simulations butas a function of time. Their results, although subject to the introduces difficulties in choosing trajectories so that thedifficulties associated with simple probe analysis, indicate density at an arbitrary point can be determined. As a result

7-22


many time-consuming trajectory calculations are required. r- 1. For various values of L we find that U has the shapesThe computation can be greatly reduced, however, by using plotted in Figure 7-20a. Looking at the contour Lp, fourthe "flux tube" method. As Parker [1976a] notes, this ad- types oforbits can be defined relative to point r = rs. Adopt-aptation of the outside-in method, in which all the particle ing the terminology of Parker [1973, 1980], they are (Figuretrajectories between two reference trajectories are assumed 7-20b) as follows:to be similar, ignores the possibility of orbit crossings or Type 1: The particle has sufficient kinetic energy andreversals and is only suitable for axisymmetric bodies and small enough angular momentum to reach rs from infinitycold ion beams [Davis and Harris,1961]. Unless otherwise or to reach infinity from point rs. These orbits would con-stated Parker's inside-out method is assumed in the follow- tribute only once to a density integral at rs.ing. The integration of Equation (7.26) then reduces to Type 2: The particle starts at infinity but never reachesdetermining the limits on the trajectories that intersect rp as rs, being repelled at some minimum distance. If the mini-these will be the limits on the integral. mum distance is inside the region being integrated over, it

The precise method of determining the trajectories that contributes twice as it goes both in and out [Parker, 1980]intersect rp differentiates the various probe calculations [Par- and zero if it is outside the region of interest.ker, 1978b, 1980]. Common to all, however, is the so- Type 3: The particle starts at rs, but is reflected at somecalled orbit classification scheme. Consider the following distance back to rs. These particles contribute twice to thearguments from classical mechanics (see for example, Gold- integral if rs lies outside the turning point.stein [1965], Bernstein and Rabinowitz [1959], Whipple Type 4: Type 4 orbits are trapped orbits that circulate[1976a], Parker [1977, 1980]). The equation for energy around the satellite. These are normally ignored as the orbitsconservation in a spherically symmetric potential V(r) is can only be populated by collisions that are assumed zero

in most satellite studies. As Parker [1980] notes, this as-L2 1 sumption has never been justified rigorously.

E = qi V(r) + + m vr (7.28) As a specific example of these calculations, we willreview the spherically symmetric models of Parker [1973,1975, 1976b, 1980]. These models have been successfully

where E is total energy, L is m var = angular momentum, compared to the "Equivalent Potential Formulation" [Par-va is total tangential velocity, and vr is radial velocity. ker, 1975] and the particle-pushing code of Rothwell et al.

The two terms in brackets are called the "equivalent (or [1976] (Figure 7-23a). The typical proceedure follows. As-effective) potential" U(r,L) [Goldstein, 1965]. For illustra- suming spherical symmetry, Equations (7.26) and (7.27)tion assume the potential V(r) is attractive and of the form can be reduced to two-dimensional integrals. It isalso more

TYPE

Figure 7-20a. The "equivalent potential" U (r,L) as a function of r for Figure 7-20b. Same as a, only for the Lp contour illustrating the fourvarious values of L. classes of orbits.

7-23

CHAPTER 7

convenient to work in terms of E and L2 so that the equationsbecome L2

fi(E,L2) dE dL2 TYPE (2)

ni (r) = m2r2 (2m [E - q V(r)] - L2 /r2)1/2 L2C

(7.29a) TYPE(1)

Ji (r)= m3 r2 fi (E,L2) dE dL2. (7.29b) Figure 7-21. Turning-point formulation of Parker [1980]. Example illus-trating domains of four types of orbits in (R, LK2) space.Four in this plot is in units of rs.

The integrations are now over the allowable ranges of Eand L2. computed. V(r) is found by numerical integration from Pois-

There are two common ways of defining the allowable son's equation given the ni(r) at grid points around the sur-range of integration in the (E,L2) space. The first scheme face. The process is then iterated until a consistent solutionmakes use of the fact that the energy E must be greater than is found. Recently, Parker (1979,1980) employed the spher-U(r) if the trajectories are to exist: ically symmetric model to calculate the sheath of a body of

radius 100 Debye lengths and for a voltage of 400 000 kT/q,the most extreme combination of size and voltage solved

E > qi V(r) + 2mr2 = U(r). (7.30) rigorously to date.More general geometric situations require actual nu-

merical trajectory tracing and are discussed in Parker [1973;The maxima are found in U(r). This is the "Effective Po- 1977; 1978a, b; 1979], Parker and Whipple [1967, 1970],tential Formulation" [Parker, 1980] and has been utilized Whipple [1977], and Whipple and Parker [1969a, b]. Whileby Bernstein and Rabinowitz [1959], Laframboise [1966], the above procedure for spherical symmetry is qualitativelyand Chang and Bienkowski [1970]. representative of the calculations represented by these pa-

The other approach is to define a function: pers, numerical particle tracing is required if more realisticgeometries such as for the truncated cylinder or "pillbox"

L2 illustrated in Figure 7-22 are to be studied. The final po-g = r2 [E - qiV(r)] > - (7.31) tential contours, in this case for a directed plasma flow

2m showing the effects of a wake [Parker, 1978a], arrived atby the iteration process are plotted in Figure 7-22.

where g is called the turning point function [Parker, 1980]. The preceding theoretical studies of Parker, Whipple,To classify the orbits, the minima in g are found. This and others have been particularly useful in studying thetechnique is termed the "Turning-Point Formulation" and effects of differential charging and space-charge potentialhas been utilized by Bohm et al. 11949], Allen et al. [1957], minima. Differential charging, as distinct from space-chargeMedicus [1961], and Parker [1973, 1975, 1976b]. Although potential minima, has been demonstrated by these and sim-the two methods are equivalent, Parker [1975] indicates that ilar efforts to result from wake effects [Parker, 1967a, 1978a,the Turning-Point Formulation is simpler and more efficient. b], from asymmetric photoelectron emission (see, for ex-

After obtaining equations of the form of Equations (7.29a) ample, Grard et al. [1973]; Fahleson [1973]; Whipple [1976b];and (7.29b), solutions are found at a given point in space Prokopenko and Laframboise [1977b, 1980]; Besse andassuming V(r) is known. That is, Equations (7.29a) and Rubin, [1980]), and from exposed potentials (Reiff et al.(7.29b) are broken up into integrals corresponding to the [1980]; Stevens 11980]). The effects of the space-chargedifferent orbit types (note that type 4 orbits are normally potential minimum produced by emitted-electron space chargeignored). fi (E,L2 ) is assumed known at the probe surface has been investigated by Soop [1972, 1973], Schroder [1973],(0 for no emission or the appropriate values for secondary Parker [1976b], Whipple [1976a], and Rothwell et al. [1977]or photoelectron emission) and, typically, assumed to be a [see also Guernsey and Fu, 1970; Grard and Tunaley, 1971;Maxwellian in the ambient medium. and Grard et al., 1973]. Whipple [1976b] and Parker [1976a]

The next step is to determine the integral bounds on E found that such barriers, which are typically a few volts,and L2. A typical example in terms of the Turning-Point are inadequate to account for the ATS 6 observations ofFormulation is presented in Figure 7-21 [Parker, 1980] and trapped photoelectrons and secondaries, and that a differ-should be compared with Figure 7-20. For a given value of ential charging barrier must be invoked. Such charging bar-r and E the limits on L2 are determined. Once the integral riers can significantly affect observations and their existenceranges of E and L2 are known for r, ni(r) and Ji(r) are must be considered in designing satellite instrumentation.

7-24


incremented in time using this net potential. The next groupis then moved based on the other particles. The process is

AXIS iterated in time with the computer keeping track of surfaceinteractions (backscattered and secondary electrons, pho-toelectrons, and the outer boundary) and interactions be-tween the satellite fields and the particles. Although plasmasimulation codes of this type have been extensively em-

WAKE ployed in plasma physics, they are just beginning to be usedREGION for the plasma probe problem.

Although still limited by computer capacity to relativelysimple spherical and cylindrical geometries, these modelshave been invaluable in studying the detailed effects of space

-3.0 -2.0 charge and the time-history of the plasma sheath. ResultsNON - for a spherical model of this type from Rothwell et al. [1976,CONDUCTING 1977] are presented in Figures 7-23a and b. Of considerableSURFACEES interest are comparisons in Figure 7-23a between the code

and a steady state solution for the case of strong electronemission [the "PARKSSG" code of Parker, 1976b]. Theprobe in this case was biased at +2 V and the electrons

FRONT emitted at an energy of leV, the other parameters are asindicated (secondary emission has been ignored). The re-

SADDLE sults are meant to resemble isotropic photoemission andPOINT show very good agreement between the two very differentBARRIER types of codes. Figure 7-23b illustrates the important ability

that such codes have in simulating the time-dependent be-havior of satellite charging following the turn-on of pho-toemission as a function of different ambient conditions.

Figure 7-22. Differential charging of nonconducting spacecraft by di- The rapid (2-10us) rise time of the probe in response torected plasma flow (equipotential contours are in units ofkT/q) [Parker, 1978a].

STRONG EMISSION COMPARISON OF STEADY STATE (PARKSSG)WITH TIME SIMULATION (AFGL-SHEATH)

7.4.5 Numerical Simulation Techniques Ro=1mEMISSION CURRENT = 10-

5 amp/m

2

EMISSION ENERGY = leV (monoenergetic electrons)Although general probe theory can be applied to a num- EMISSION DENSITY =211/cm3

ber of interesting and important cases, it has not been ex- AMBIENT TEMPERATURE = 5eV(Maxwellian)

tended much beyond spherical or cylindrical geometries nor AMBIENT DENSITY = 1/cm3o =+2V=Sphere Potential (quasi-equilibrium)does it take into consideration time variations in the sheath. vs. +1Vequilibrium

Numerical techniques have been developed that, though 2.0 TIME -SIMULATION POTENTIAL 500

retaining many of the basic concepts of probe theory, allow TIME-SIMULATION(ISOTROPIC)AVG OF 100 ITERATIONSexplicit inclusion of time dependency or geometry. These t 12us 400

models are capable of handling time variations on the order (PARKSSG - ISOTROPIC)

of the plasma frequency or complex shapes such as the (volts) (cm-3)

shuttle or the P78-2 SCATHA satellite.The most straightforward numerical techniques concep- 1.0

tually, though perhaps the most demanding computation- 200ally, are the so-called "particle pushing" codes. As origi-nally presented by Albers [1973] and Rothwell et al. [1976, (PARKSSG) 100

1977] for a spherical geometry and by Soop [1972, 1973]and Mazzella et al. [1979] for cylindrical geometry, many 0individual or groups of similar particles are followed si- 1.42

r/R omultaneously by computer as they move through the satellitesheath. At each time step the potential on a given particleor set of particles due to all the other particles is computed Figure 7-23a. Comparison of steady state sheath potential and density for

2 models: the steady state PARKSSG code and the AFGL-by a fast Poisson equation solver. The particle group is SHEATH code [Rothwell et al., 1977].

7-25

CHAPTER 7

SATELLITE POTENTIAL FOR A STRONG PHOTOEMISSIONAND VARIOUS AMBIENT PLASMA DENSITIES

Te =0.5eV Ephot =6eV(MAXWELLIAN) a = iphot / ie,AMB14 212 iphot = 1 X 10 -5 AMP/m2

NO SECONDARIES10 a 527 ne = 1/cc

8

6 a 52.7n, 10/cc

4 a = 5.27ne =10 2 /cc

2 a=0.53 ne =103/cc

-2

I0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

t (us)

Figure 7-23b. Spacecraft voltage transients following the "turn-on" of the plasma at t = 0. The results are for a sphere (no secondary emission). a is theratio of photoelectron to ambient electron temperature, and EPhot is the mean energy of the photoelectrons assumed to be Maxwellian[Rothwell et al., 1977].

the turn-on of photoemission could be significant in causingsatellite transients as only -2 V are necessary to triggermany circuits.

The cylindrical, particle pushing code AFSIM (Air ForceSatellite Interactions Model) [Mazzella et al., 1979] has beenemployed to follow the effects of an electron beam emittedby a satellite. A 300 eV beam at 200 uA was emitted intoa vacuum from a satellite initially at 0 potential. The com-putations showed that the satellite potential rose to + 300V at 36 us, at which point a portion of the beam was trappedin the sheath and began to orbit the satellite. A space-chargepotential formed four spacecraft radii away with most ofthe beam being reflected back to the satellite. Figure 7-24shows the configuration 65 us after turn on. The circlerepresents the satellite and the beam is visible as a collimatedsource while the comet-like structure to the right is the cloudof previously trapped beam electrons orbiting the satellite.

7.4.6 NASCAP

Particle pushing codes are very useful in studying thedetailed behavior of particles in time and in the sheathssurrounding a probe. They are still, however, limited torelatively simple geometries because of computer limitationsand are subject to numerical instabilities. Recently an al-ternative model has become available that explicitly treatsthe effects of geometry. This is the NASCAP (NASA Charg- Figure 7-24. Sheath simulation using the ASIM code [Mazzella et al.,1970] at 65 us after turn-on of a 30 eV, 200 uA electroning Analyzer Program) computer code [Katz el al., 1977, beam.

7-26


1979; Schnuelle et al., 1979; Roche and Purvis, 1979; Rubin -1et al., 1980] for the thick sheath limit (the model is currentlybeing extended to thin sheaths). This code combines a so-lution of the Poisson equation and a probe charging modelalong with a complex graphics package to compute the -2detailed time behavior of charge deposition on spacecraftsurfaces. An approximate circuit model of the satellite isused to estimate voltage changes during time steps for animplicit potential solver. The propagation of particle beams -4through the satellite sheath is computed by orbit tracing in BOOMthe sheath field. The code has several options availableranging from a less-detailed code capable of calculating thedifferential potential on a simple laboratory material sample -7to a detailed code capable of modeling individual booms REFERENCE BANDand sensor surfaces on a complex satellite such as the P78- 10-3 10-2 1002 SCATHA satellite [Rubin et al., 1980]. The primary intent TIME (SEC)

of the model is to compute the effects of satellite geometryon the satellite photosheath, sheath field, and surface ma-terial potentials. Figure 7-25b. NASCAP computer simulation time-dependence of poten-

tial for two surfaces on the P78-2 SCATHA satelliteThe first step in the NASCAP model is to insert the [Schnuelle et al., 1979].

satellite geometry and material content. Using simple3-dimensional building blocks, the code has provisions formodeling surfaces ranging from cubes and planes to com-plete satellites with their booms and solar panels (Figure the circuit element model, the inside-out technique, and7-25a). In the second stage the currents to the satellite sur- Langmuir probe theory in one model along with the addedfaces are computed by treating each surface element as a advantage of detailed graphical results. Unfortunately, withcurrent-collecting probe. The inside-out technique may then this gain in capability, the code has become large and re-be used to model the charge distribution in the photosheath. quires hours of computing time for the more detailed models.The program is stepped forward in time, local current bal- Two steps have been taken to alleviate these problems. First,ance being assumed at each time step. Time-dependency efficient versions have been developed for specific com-and variations in differential potential can thus be modeledas demonstrated in Figure 7-25b. The analysis is carried outon successively larger, coarser nested grids [Katz et al.,1977], allowing the trajectories of particles emitted fromthe satellite to be traced in the space surrounding the satellite(Figure 7-25c). 50

0The NASCAP program combines the best elements of

-50SCATHA MODEL -50 0 50

Zone Size= 11.5 cm.

Figure 7-25c. Particle trajectories from an electron emitter as computedFigure 7-25a. NASCAP computer simulation of the P78-2 SCATHA sat- by the NASCAP code in the presence of a magnetic field

ellite [Schnuelle et al., 1979]. Compare with Figure 7-6. [Rubin et al., 1980]

7-27

CHAPTER 7

TIME IN SECONDS TIME, sec60000 60500 65000 61500 62000 62500 0 50 100 150 200 250

SPACECRAFT-.5 POTENTIAL

-5 FLIGHT DATA-6 NASCAP SIMULATED SCATHA CHARGING

RESPONSE FOR DAY 87 ECLIPSENASCAP

-7 PREDICTIONNASCAP RESPONSE

------ OBSERVED RESPONSE

Figure 7-26b. Observed potential difference measured by the P78-2 SCA-THA satellite surface potential monitor experiment betweena Kapton sample and the satellite ground. Also shown are

Figure 7-26a. Observed satellite to space potential (P78-2 SCATHA) be- NASCAP predictions from same period [Stevens et al.,tween 1630 and 1730 UT on day 87, 1979. Also shown 1980a].are NASCAP predictions for the same period [Schnuelle etal., 1981].

the potential between the Kapton and the satellite groundat the spin frequency of the satellite. Second, it illustrates

putational tasks such as the SCATHA version discussed in the power of NASCAP in predicting such rapid variationsRubin et al. [1980]. Secondly, in conjunction with a number (the slight time-lag between the data and theory is due toof laboratory and in situ satellite experiments, an attempt the actual satellite spin period being slightly faster than theis being made to verify all aspects of the code and determine assumed 1 rpm). This agreement is, in part, much betterwhat are the critical input parameters [Purvis et al., 1977; than the prediction of the satellite to space potential as theRoche and Purvis, 1979; Stevens et al., 1980a]. The model Kapton sample properties were obtained prior to flight inhas been applied to many satellite charging problems such ground test simulations-an important consideration in fu-as large cavities, exposed potentials, and arbitrary geome- ture studies.tries not considered previously [Purvis, 1980; Stevens, 1980;Stevens and Purvis, 1980].

Preliminary results of comparisons between the P78-2 7.5 PREVENTION OFSCATHA measurements and NASCAP have recently be- SPACECRAFT CHARGINGcome available. Some of these results are plotted in Figures7-26a and 7-26b. In Figure 7-26a [Schnuelle et al., 1981], Although varying the satellite to space potential allowsthe observed satellite to space potential between 1630 and the measurement of very low energy plasma, charge buildup1730 UT on day 87, 1979 is plotted. The data, consisting on satellite surfaces is not in general a desired phenomenon.of potential and plasma measurements during an eclipse, In order to eliminate or at least limit the worst effects ofwere input into the NASCAP "one-grid" model (as the name spacecraft charging, several techniques have been devel-implies, this computation makes use of only the inner most oped. Although the obvious solution is to develop systemsNASCAP computational grid-Figure 7-25c) at ~1 minute that can withstand the worst effects, this is not always a(1 spin period) intervals. Although the NASCAP simulation feasible or desirable method. Alternatives to this "brutemisses the two minor jumps in potential, it reproduces the force" method will be described in this section.two major ones and is in excellent quantitative agreement The simplest method for preventing spacecraft chargingwith the data considering the uncertainties in material prop- effects is to employ sound design techniques-use con-erties. NASCAP also responds more slowly to environ- ducting materials where possible and proper grounding tech-mental changes than the actual data. As Schnuelle et al. niques. These techniques are detailed in a design guideline[1981] note, this is due to the 1 minute time steps imposed handbook recently completed at NASA Lewis [Purvis et al.,on NASCAP by the data whereas the real environment is 1984]. Although a large satellite to space potential can oc-changing continuously. cur, differential charging, the major spacecraft charging

Figure 7-26b [Stevens et al., 1980c], comparing the problem, is significantly reduced by these procedures. Sev-NASCAP predictions with the surface potential of a Kapton eral different methods have been developed to assure ansample (SC -2-see Table 7-1) on P78-2-SCATHA, is in- adequately conducting surface. As an example, non-con-teresting for two reasons. First, it illustrates kV changes in ducting surfaces on the GEOS series of geosynchronous

7-28


satellites were coated with indium oxide. As solar cells are dielectric materials may be altered by the arcing process inthe primary non-conducting surfaces on GEOS and as in- a manner which greatly reduces future arcing [A.R. Fred-dium oxide is sufficiently transparent to sunlight so that it erickson, private communication, 1980]. It is currentlydoes not degrade their operation, this technique has been thought, however, that the techniques described above arequite successful [G.L. Wrenn, private communication, 1980] adequate in reducing charging. Basically, spacecraft chargeat keeping satellite differential potentials near zero and, prevention is a matter of good design technique-groundbecause of the secondary emission properties of indium well, avoid cavities in which charge can be deposited, andoxide, the satellite to space potential between zero and - 1000 avoid exposed potentials.V even in eclipse. Such coating techniques, however, canbe expensive and difficult if large surfaces are involved.Furthermore, they do not reduce the hazards associated with 7.6 CONCLUSIONScharge deposition in dielectrics and, in the case of "pinholes"(Section 7.3.8), may be ineffective. Before concluding this chapter, a brief summary of the

Another technique that may be applicable to large sur- major accomplishments of this fourth period of chargingfaces involves the use of electron and ion emitters. Grard analysis is in order. Probably the major step forward has[1977] and Gonfalone et al. [1979] discussed the application been the growing realization by the space physics com-of such systems to actual satellite systems. The latter paper munity of the role of spacecraft charging. Before the geo-described the successful application of a low current (mA) synchronous observations of 10(kV)and higher potentials,electron emitter on the ISEE-1 satellite. The ISEE-1 is in a spacecraft charging was considered to be a nuisance. Sincehighly elliptical (300 km to 23 RE) orbit so that it spends a that time, however, spacecraft charging analysis has becomelong time in the solar wind. The ISEE-1 results indicated an important adjunct to plasma experiments and to satellitethat the electron cloud emitted by the satellite gun success- design. On the negative side, however, there is still apparentfully clamped the potential of the satellite at a few volts confusion on the part of some experimentalists as to howpositive to the ambient solar wind plasma. Purvis and Bar- to correct low energy measurements and an unwillingnesstlett [1980] reported results from ion and electron emitters on the part of satellite designers to spend the necessary timeon the geosynchronous ATS 5 and ATS 6 satellites. These in properly designing their satellites. Both of these problemsresults indicated that whereas electron emission alone re- have proven hard to solve.duced the satellite to space potential to -0, it did not sig- In the area of plasma measurements, the spacecraftnificantly reduce the charge on dielectrics. Use of an ion charging theory necessary for their interpretation can be saidemitter and neutralizer together not only clamped the sat- on the basis of this review to be quite sophisticated. Theellite to space potential at 0, but also, through the cloud of simple probe theory of Langmuir and his successors hasions, neutralized the negative charge on the dielectrics. Sim- been shown to give adequate order of magnitude estimatesilar success was demonstrated by the beam experiments on of the gross effects of spacecraft charging. The introductionthe P78-2 SCATHA satellite [H.A. Cohen, private com- of various sophistications such as the satellite velocity ormunication, 1980]. There may be some difficulties, how- the satellite sheath [Cauffman and Maynard, 1974, for ex-ever, with these techniques as reducing the surface charge ample] have made this theory applicable to many practicalmay enhance dielectric breakdown [A.R. Frederickson, pri- cases. The development of finite element models has al-vate communication, 1980] between the deposited charge lowed fairly sophisticated engineering studies. The originaland the surface. Also there is the possibility of contami- methods of Bernstein and Rabinowitz have grown into thenation of the satellite environment by the beam ions. intricate, advanced trajectory codes of Parker, Whipple, and

Careful selection of satellite materials can reduce space- others. In combination with various simplifications thesecraft charging. Although thermal control surfaces which are techniques have yielded straightforward methods of cor-necessary on many satellites generally consist of dielectric recting Langmuir probe data. Even secondary emission,materials, careful selection of the materials according to photoelectron emission, and velocity effects can be mod-their secondary emission properties and bulk conductivity eled.can reduce charge buildup. Rubin et al. [1978] have dem- With the advent of electrostatic analyzers and their abil-onstrated that for materials with a secondary emission greater ity to provide both detailed spectral information and massthan 1, the plasma temperature must be several times the discrimination, experimental information on charging ef-energy at which this occurs if a satellite is to charge up. fects has increased enormously. As a result, active studiesAgain, however, the increased secondary electron popula- of the sheath population and fields in the vicinity of a space-tion could contaminate low energy (E < 10 eV) plasma craft under a variety of ambient conditions have becomeobservation. ~ feasible. These have been carried out in detail on the GEOS

Several other techniques have been proposed (for ex- and P78-2 SCATHA satellites for the geosynchronous orbit.ample, see Beattie and Goldstein [1977] for methods of Similar experiments are planned for the early shuttle pay-protecting the Jupiter probe) and recent results indicate that loads. Theoretical models of the sheaths and fields around

7-29

CHAPTER 7

typical geosynchronous satellites are available, ranging from where:the simple thick sheath probe models to the NASCAP code qnEO 2TI 1/2

which is capable of handling complex geometries. Ad- IEO 4r2s 2vanced wake and sheath models are also available for shuttlestudies. Rapid time variations on the order of the plasma 2 4r2s qnIO 2TI 1/2frequency have even been modeled. 2 = mI 2

In the area of engineering design, finite element modelshave been applied in the design of a number of geosyn- V >0chronous and interplanetary missions. NASCAP has been r2s JPHO V < 0applied to several systems and proven useful in designingvehicles so as to avoid the worst effects of charging. On rs = satellite radiusthe practical side, effort is beginning to be expended indeveloping charge-reducing materials and techniques. More For the "RAM" case and assuming a thin sheath for theimportantly, the techniques learned on small spacecraft are electrons:beginning to be applied in the design of the next generationof large, high voltage vehicles. V = -TE IEO V < 0

Despite this impressive growth of spacecraft charging q I'IO+ IPH

technology since 1965, there are still a number of areas inneed of study. These can be grouped under the headings ofmaterial properties, geometry, magnetic fields, wakes, arcs, V = 1- IEO-IPH 1/2 mIVs2q-1 V > 0large size/high potential, and charge deposition in dielec- I'IO V> 0trics. Although work is under way in each of these areas,much still remains to be accomplished. Even so, more thanenough has been accomplished in this fourth stage of space- Where: IIO = rs2 qnIovscraft charging analysis so that, as a scientific discipline,spacecraft charging can be said to have come of age. vs = satellite velocity

APPENDIX-Table 7-3 Explanation This assumes, for ion repulsion, that the ion ram current,IIO, is reduced by a factor (1 - qV/1/2mIv 2s) and that the

ions have ~ 0 thermal velocity (see Whipple [1965], p. 28).The simple probe models of Section 7.4.1 . can give first

order estimates of the satellite to space potential under a The assumed environmental parameters have been adoptedfrom many sources. They should be treated at best as rough

variety of conditions. Given the plasma parameters listedin Table 7-3, this potential has been estimated using ap- approximations as the actual environments can vary by fac-

tors of x 10 to x 100. The Jupiter data are from Scudderproximations to Equations (7.22) and (7.24). As only a first

et al. [1981] and J. Sullivan [private communication]. Theorder estimate is desired, a conducting spherical satellite solar wind data for less than 1 AU are from Schwenn et al.( ~1 m in diameter) has been assumed. Secondary and [1977]. Values greater than 1 AU are estimated.

backscatter terms are ignored (these would tend to make thepotential more positive). For the planar, thin sheath as-sumption (I-D in Table 7-3): [T is in eV.] ACKNOWLEDGMENTS

V = -T Ln ( IEO V <q IIO + IPH This work represents the conclusion of 5 years of workqTI IEO -IPH at the Air Force Geophysics Laboratory. During that time,

V = - Ln V > 0 my main source of advice and direction was C.P. Pike.q IIO ) Grateful appreciation is also extended to A. Rubin, P. Roth-

For the spherical, thick sheath assumption (3-D in Table well, L.W. Parker, and N. Saflekos, who helped me learn7-3): the intricacies of spacecraft charging. N.J. Stevens and C.

Purvis have provided much practical assistance and advice.V = Ln IEO V < 0 T. Gindorf, P. Robinson, E.C. Whipple, Jr., and P. Leung

q IIO (1 -q) + IPH helped in the final revision. M. Spanos and B. Short pre-TI pared the transcript. Finally, K. Garrett provided much needed

physical support through the long hours expended in pro-IPH ducing the manuscript. The work described in this chapter

V =-TI Ln 1+ TE V >0 was carried out in part at the Jet Propulsion Laboratory,V TI Ln V > 0

q Ln California Institute of Technology, under NASA contractNAS7- 100.

7-30


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