impacts of solar storm events and ion beam emission on ... · impacts of solar storm events and ion...

Abstract # 133

Impacts of Solar Storm Events and Ion BeamEmission on Electrostatic Tractor Performance

Erik A. Hogan and Hanspeter Schaub

Abstract—A recent proposed technique for GEO debris mit-igation is the electrostatic tractor. The tug vehicle approachesa debris object within 5-10 craft radii and emits a focusedelectron beam onto it. This results in a negative charge onthe debris, and a positive charge on the tug vehicle. Used inconjunction with low thrust, the electrostatic force is used totow a debris object into a disposal orbit. In this study, theimpacts of geomagnetic storm activity on the charging of tug anddebris are considered. The influence of electrons emitted fromthe deputy (photo- and secondary electrons) on tug chargingare also considered. Both of these phenomena yield improvedelectrostatic tractor performance. The simultaneous emission ofan electron and ion beam by the tug is also considered to improvetractor performance and enable charge transfer for scenarioswhere it fails when only an electron beam is used. The theoreticalmaximum electrostatic force that is possible with simultaneousemission is computed, and the results indicate that emitting bothan electron and ion beam enables smaller tug vehicles to towlarger objects that could not otherwise be towed with only anelectron beam.

Index Terms—Electrostatic tractor, spacecraft charge control,geomagnetic storm impacts on charging

I. INTRODUCTION

The high value of the geostationary ring (GEO), coupledwith the increasing number of orbital debris, highlights theneed for active debris removal methods.[1], [2], [3] Whenspacecraft reach end-of-life in GEO, international guidelinescall for reorbiting into a disposal orbit typically 200-300 kmabove GEO.[4], [5] For debris objects that do not possess theability for reorbiting, an external method is needed to reachthe disposal orbit. Originally proposed as a means for asteroiddeflection,[6] the electrostatic tractor has been suggested asa means for GEO debris remediation.[7] The concept relieson a combination of an attractive electrostatic force betweentwo craft and low thrusting capability on one of the craft, asillustrated in Figure 1. The attractive force acts as a virtualtether between the two objects, and a low thrust maneuver isused to tow the noncooperative, possibly tumbling large debrisobject into a new orbit.[8] GEO debris can be tumbling up to10’s of degrees per second,[9] making any physical dockingmethods particularly challenging.[10] The electrostatic tractormethod allows the tumbling object to be reorbited without firsthaving to despin it. Considering non-symmetrical spacecraftgeometries, the charging also gives rise to torques on thecraft.[11], [12], [13] Through careful manipulation of thecharging histories, these torques can be applied in a manner

E. A. Hogan and H. Schaub are with the Colorado Center for AstrodynamicsResearch, University of Colorado, Boulder, CO 80309-0431, USA (e-mail:[email protected], [email protected])

Fig. 1. Illustration of electrostatic tractor concept.

sufficient to despin a noncooperative object remotely.[12] Thislatter ability greatly simplifies any orbital servicing missionwhere great efforts are required to first despin objects spinningat 1 degree per second or greater.[14], [10]

For the electrostatic tractor application, a method of activecharge control is needed. Charged particle beams are the mostideal candidates for this purpose. Emitting a high-energy beam(10s of keV) at sufficient current levels enables the tug toreach high potentials. Either an ion or electron beam maybe used, though an electron beam is preferred due to itssimpler implementation and reduced momentum transfer.[12]Directing the beam onto the deputy provides a current thatwill affect the deputy charging, much like the natural chargingthat occurs due to the plasma environment. The vast major-ity of prior work with Coulomb formations merely assumeeither a charge or a potential on the different spacecraft inthe formation, without actually modeling the mechanism forand environmental influences on achieving the charging.[15],[16], [17], [18], [12], [8], [19], [20] The electrostatic tractorperformance is dependent on the charging that is achievedwith electron or ion beam emission, and it is importantto characterize the charge transfer process. Reference [12]presents a first-order charging model to compute potentials ontug and deputy as a function of various environmental currentsources, applied to the electrostatic tractor problem. Assumingan electron beam is used for charge control, one particulartug and deputy configuration is considered, and the resultingelectrostatic forces are computed for specific space weatherconditions. The work does not consider the impact of solarstorm events on tractor performance, or the simultaneous useof electron and ion beam emission for improved performance.This first-order charging model provides the tools needed to

1

Spacecraft Charging Technology Conference 2014 - Poster 133

Abstract # 133

analyze the general charging trends that may be encounteredfor the electrostatic tractor application, and is used extensivelyin the current study.

The charging of a spacecraft is dependent on the spaceplasma environment.[21], [22] Because of the potential threatsto mission viability caused by charging events, much workhas been done to characterize the space weather environmentboth in LEO and GEO.[23], [24] The plasma environmentis typically characterized by two parameters: density andtemperature. The LEO plasma environment is much colderand denser than in GEO, with typical LEO densities rangingfrom 104 − 106 particles/cm−3 and corresponding tempera-tures below 1 eV. In GEO, the plasma densities are ordersof magnitude smaller, ranging from .1 − 10 particles/cm−3.Depending on geomagnetic storm activity, ion temperaturesmay range from below 100 eV to 20 keV or more. Electrontemperatures are typically above 1 keV, and may reach tensof keV depending on storm activity.

The severity of geomagnetic storms is classified using thekp index, which is based on the observed variation in thedegree of irregular magnetic activity throughout each day,observed at various ground stations.[25] The kp index utilizesan integer scale ranging from 0-9, and values of 5 and upindicate that a geomagnetic storm is occurring. The NationalOceanic and Atmospheric Administration (NOAA) has alsodeveloped a scale for classifying the severity of geomagneticstorms.[26] The scale ranges from G-1 minor storms (kp = 5)to G-5 extreme storms (kp = 9). The NOAA scale providesinformation about expected impacts to spacecraft for differentstorm levels. In a minor storm (G-1, kp = 5), minimal impactsto spacecraft operations can be expected. At the other endof the spectrum, an extreme storm (G-5, kp = 9) may causeextensive surface charging, loss of attitude, and problems withcommunications and satellite tracking. Fortunately, strongerstorms only occur a few times per eleven year solar cycle. Thefrequency of occurrence for the various storm conditions in atypical solar cycle is shown in Figure 2. The vast majority ofthe time (> 85%), there is either no storm activity or a minorstorm occurrence.

In prior work considering environmental impacts on electro-static tractor performance, quiet storm conditions are used.[27]Further, only electron beam emission is considered as a meansfor charge control.[12], [27] Reference [28] illustrates thatwhen the deputy sizes are roughly the same as or largerthan the tug, it becomes very difficult for charge transfer tooccur when only an electron beam is used. In the currentstudy, several novel results are presented. First, the impacts ofgeomagnetic storm events on the charge transfer process areconsidered. These storm events lead to changes in the plasmaenvironment in GEO, and change the charging behavior ofthe tug and deputy. To mitigate some of the relative sizingissues, simultaneous emission of an electron beam (onto thedeputy) and an ion beam (into space) is considered as ameans to improve charge transfer performance by providing anadditional control variable for charge control. During charging,electrons are emitted from the deputy surface. In the vicinity

G-2 Moderate (kp = 6)9.0%

G-3 Strong (kp = 7)3.2%

G-4 Severe (kp = 8)1.5%

G-5 Extreme (kp = 9)0.10%

G-1 Minor (kp = 5)22.4%

No Storm Activity (kp < 5)63.8%

Fig. 2. Percent of days in an 11 year solar cycle for which variousgeomagnetic storm levels occur. Data adapted from [26].

University of ColoradoBoulder

International High Power Laser Ablation and Beamed Energy Propulsion Conference, Santa Fe, NM, April 21-25, 2014 8

Charging Model

- -- -

-

- Photoelectron Current

- -- --

--

-

+

---

--

-

Plasma Electron and Ion Currents

EB Current

Secondary Electron Emission

++++

++

The potential achieved satisfiesX

i

Ii(�) = 0Fig. 3. Illustration of various current sources that affect spacecraft charging.

of the positively charged tug, some of these electrons will berecaptured. This back-flux has thus far not been investigated.In the current study, the impacts of this electron back-flux ontothe tug on tractor performance are investigated, as well.

The paper is structured as follows. First, an overview ofthe charging and electrostatic force models is presented. Next,the influence of geomagnetic storm conditions on charging ispresented and compared with quiet storm conditions. Then,the effects of the electron back-flux from deputy to tug ontractor performance are investigated. Lastly, the simultaneousemission of an electron and ion beam is considered, and theperformance benefits that result are characterized.

II. BACKGROUND

A. Charge Transfer Model

The electrostatic tugging force used for towing is dependenton the charging that occurs on both the tug and deputy.Several factors influence this charging process. Naturally oc-curring ion and electron plasma currents are collected by thespacecraft, and photoelectrons may be emitted depending onthe spacecraft potential and presence of sunlight. Focusedelectron beam emission by the tug is used for charge control.When the electron beam is absorbed by the deputy, secondaryelectron emission occurs as the incoming beam electronsexcite and release electrons from the deputy surface material.The potential levels achieved by the tug and deputy result from

2


Abstract # 133

a balance of these various current sources, which are illustratedin Figure 3. To compute these potentials, the charging modeldeveloped in [29] is applied.

A photoelectron current occurs whenever the spacecraft arein sunlight. This current is modeled by[21]

Iph(φ) = jph,0A⊥e−φ/Tph φ > 0 (1a)

= jph,0A⊥ φ ≤ 0 (1b)

where φ is the spacecraft potential, Tph = 2 eV is thetemperature of the emitted photoelectrons, jph,0 = 20 µA/m2

is the photoelectron flux, and A⊥ is the cross-sectional area ex-posed to sunlight. For the spherical geometries assumed here,A⊥ = πr2. For high positive potentials, the photoelectroncurrent is effectively zero because all of the emitted electronsare recaptured.

The plasma electron current is modeled by[30]

Ie(φ) = −Aqnewe4

eφ/Te φ < 0 (2a)

= −Aqnewe4

(1 +

φ

Te

)φ ≥ 0, (2b)

where A is the surface area exposed to the plasma envi-ronment, Te is the plasma electron temperature, ne is theplasma electron density, q is the elementary charge, andwe =

√8Te/πme is the thermal velocity of the electrons.

The electron mass is represented by me. Note that for largenegative potentials, Ie is very small. This is due to the factthat electrons are repelled by the negatively charged spacecraft.Similarly, the plasma ion current is computed using[30]

Ii(φ) =Aqniwi

4e−φ/Ti φ > 0 (3a)

=Aqniwi

4

(1 − φ

Ti

)φ ≤ 0, (3b)

where wi =√

8Ti/πmi. Note that the variable quantitiesrepresent the same parameters as before, except the subscripti is used to denote they represent ions. In the space weathermodel for the GEO environment utilized here, the ion speciesconsists solely of protons. For high positive potentials, theion current is very small because the ions are repelled by thepositively charged spacecraft.

Charge control is achieved using an electron emitted fromthe tug onto the deputy. A portion of the beam current will beabsorbed by the debris, depending on tug pointing accuracyand the charge levels of both tug and debris. This current ismodeled as

ID(φD) = −αIt qφT − qφD < EEB (4a)= 0 qφT − qφD ≥ EEB , (4b)

where It is the beam current emitted by the tug, EEB is theelectron beam energy, and the subscripts T and D representthe tug and deputy, respectively. The parameter α representsthe efficiency of the charge transfer process; it is the fractionof the beam current emitted by the tug that reaches the deputy.In general, this is a function of beam pointing accuracy and

-15000 -10000 -5000 0

-400

-200

0

200

400

Debris Potential HVL

CurrentHmAL ISEE

Ii

IeIph

ID

ITot

Fig. 4. Currents acting on the deputy for a range of deputy potentials. Deputyachieves a potential that results in ITot=0.

the width of the beam at the deputy location. It can alsobe impacted by the tug and debris potentials, in addition tothe beam energy. In the current paper a value of α = 1is used, which maintains the value established in [29]. Thisassumes a well focused and accurately pointed beam. Betterquantification of the α parameter is beyond the scope of thispaper, and is left for future work. Once φT − φD = EEB ,it is impossible for additional beam current to make it to thedeputy. The emitted beam electrons do not have enough energyto cross the potential difference between tug and deputy.

When the electron beam impacts the deputy object, the in-coming electrons result in the emission of secondary electrons.Because of the large negative potential of the debris object (kVlevel), these electrons will escape. This represents a significantcurrent source that must be accounted for. Secondary electronemission is modeled by[31]

ISEE(φD) = −4YMID(φD)κ φD < 0 (5a)= 0 φD ≥ 0, (5b)

where

κ =Eeff/Emax

(1 + Eeff/Emax)2

and Eeff = EEB − qφT + qφD. YM is the maximum yield ofsecondary electron production, and Emax is the impact energyat which this maximum occurs. In this paper, the values ofYM = 2 and Emax = 300 eV are used.

For the tug, the charging is dominated by the plasmaelectron current and electron beam emission. The tug settles toa potential that satisfies the current balance Ie(φT ) + It = 0.This is solved analytically as

φT =

(4It

Aqnewe− 1

)Te, (6)

which assumes a positive tug potential. This will be the caseprovided the beam current is sufficient. The current balanceon the deputy object contains a few more contributions, andan analytical solution does not exist. The deputy will achieve

3


Abstract # 133

-15000 -10000 -5000 0

-400

-200

0

200

400

Debris Potential HVL

CurrentHmAL ISEE

Ii

IeIph

ID

ITot

200 300 400 500 600 700-20

-10

0

10

20

30

Beam Current HmAL

PotentialHkV

L�T

�D

Fig. 5. Tug and deputy potentials as a function of beam current.

a potential that satisfies

ITot = Ie(φD) + Ii(φD) + ISEE(φD)

+ Iph(φD) + ID(φD) = 0. (7)

The presence of the photoelectron current implies the deputyis in the sunlight. When in the Earth’s shadow, the currentbalance contains all of the same terms except for Iph. Anumerical root finder is used to solve for φD in Eq. (7).

An example charging scenario is presented in Figure 4.Shown are the various currents impacting deputy charging forspace weather conditions of ne = 0.6 cm−3, ni = 9.5 cm−3,Ti = 50 eV, and Te = 1250 eV. The results assume a beamenergy of EEB =40 keV and a beam current of It=520 µA.The tug and deputy are treated as spheres, with radii ofrT = 2 m and rD = 0.935 m. With these conditions, thetug achieves a potential of φT = 21.5 kV and the deputyreaches a potential of φD = −15.3 kV. As seen in Figure 4,the deputy potential results in a net zero current balance, i.e.ITot = 0. While the plasma electron current is included inthe current balance, for the deputy it provides an insignificantcontribution to charging at the high potential levels achieved.The tug and deputy potentials as a function of beam currentare shown in Figure 5. The tug potential increases linearlywith beam current, while the deputy potential has its largestvalue around It = 350 µA.

There are two electron beam parameters that may be used toinfluence charging: the beam energy and potential. Generally,a higher beam energy will result in higher deputy charging.This is due to the reduced secondary electron emission thatstems from the higher energy of the incoming beam electrons.As the energy of an absorbed electron increases, fewer sec-ondary electrons are emitted. Because the secondary electronsessentially result in the loss of some fraction of the incomingbeam current, reducing the number of secondary electronsemitted will improve deputy charging. Depending on the spaceweather conditions, increasing or decreasing the beam currentcan improve or worsen deputy charging, as shown in Figure 5.However, the tug will always charge to higher potentials as thebeam current is increased, up to the level of the beam energy

(qφT ≤ EEB).

B. Electrostatic Force Model

The performance of the electrostatic tug is dependent onthe electrostatic force in place between the tug and deputy.To allow for analytic expressions, the tug and deputy objectare treated geometrically as spheres, and are assumed to beperfectly conducting. The potential on the tug object is a resultof its own charge and the potential due to the charged deputyobject as[18]

φT = kcqTrT

+ kcqDρ, (8)

where kc = 8.99×109 Nm2/C2 is the Coulomb constant, ρ isthe distance between tug and deputy, qT is the charge on thetug, qD is the charge on the deputy, and rT is the radius ofthe tug craft. Similarly, the potential on the deputy object iscomputed as

φD = kcqDrD

+ kcqTρ, (9)

where rD is the radius of the deputy object.If the potentials on the tug and deputy are controlled,

then the above relationships may be rearranged to solve forcharge,[18][qTqD

]=

ρ

kc(ρ2 − rT rD)

[rT ρ −rT rD

−rT rD rDρ

] [φTφD

]. (10)

After computing the charges, the electrostatic force betweentug and deputy is computed using

Fc = kcqT qDρ2

. (11)

Due to the space weather environment, some shielding of thiselectrostatic force will occur. The distance over which thisshielding is prevalent is described by the Debye length of thelocal plasma.[32] The space weather conditions considered inthis study yield Debye lengths that are on the order of tens ofmeters. However, because of the high potential levels obtainedby tug and deputy, the Debye shielding effect will be severaltimes smaller than predicted by the standard Debye lengthcalculation. As discussed in [6] and [33], objects charged totens of kiloVolts in the space environment experience effectiveDebye lengths several times larger. Looking specifically at thisphenomenon as it pertains to charging in quiet GEO spaceweather conditions, the effective Debye lengths are predictedto be roughly 5 times larger than the classic Debye shieldingmodel predicts.[33] The shortest Debye lengths consideredhere are on the order of 15 meters or more, leading to effectiveDebye lengths over 75 meters. This means that the spaceweather environment will not contribute significant shieldingof the electrostatic force below distances of 75 meters. Becausethe separation distances considered here are less than 20meters, the impacts of Debye shielding are insignificant andwill not be included in the force model.

The ultimate goal of the electrostatic tractor is to raise thedeputy orbit enough to reach a disposal orbit. The size ofthe deputy orbit is characterized by its semi-major axis, andreaching a disposal orbit requires an increase in the deputy

4


Abstract # 133

semi-major axis of 200-300 km. Assuming a circular deputyorbit, the semi-major axis increase in the deputy orbit overone day is[7]

∆a ≈ 4π

n2FcmD

, (12)

where n is the mean motion of the deputy orbit and mD thedeputy mass. A GEO orbit radius of 42,164 km is assumedfor this analysis. The deputy mass is required to computethe semi-major axis change. Considering publicly availabledata on GEO satellites, [18] provides a relationship betweenspacecraft mass and an approximate sphere radius. The simplelinear expression

rD(mD) = 1.152 m + 0.00066350mkgmD (13)

provides a deputy radius for use in the charging model. Whilecertainly not perfect, this linear relationship does capture thegeneral trend of increased mass for larger objects and is basedon actual data for GEO objects.

III. IMPACT OF GEOMAGNETIC STORM EVENTS ONTRACTOR PERFORMANCE

In [27] electrostatic tractor performance is analyzed forquiet (kp = 1.5) geomagnetic storm conditions. Here theeffects of geomagnetic storm events are considered. When ageomagnetic storm occurs, the population of lower energy ions(1-100 eV) in the period following local midnight is lost, witha higher energy population of slightly lower density (1 cm−3)remaining.[24], [34] Solar storm events also provide a higherenergy population of electrons, with energies as high as a fewtens of keV. This phenomenon was experienced by the ATS-5satellite and recorded in GEO space weather measurementstaken by the magnetospheric plasma analyzer (MPA) instru-ments flown by Los Alamos National Laboratory.[35] When aspacecraft enters into eclipse during a storm event it may natu-rally charge to potential levels in excess of -10 kV, dependingon the severity of the geomagnetic storm. During storm eventsexperienced by ATS-5, typical potentials achieved in shadowwere 3-4 kV (negative polarity), with lows of 70-100 V andhighs in above 10 kV.[34] Note that a spacecraft experienceseclipse for under an hour each day in the 3-4 weeks beforeand after an equinox. Over an electrostatic tractor reorbitingscenario with a deorbit time of several months, this representsa very small portion of the total operating time. When aspacecraft is in sunlight, the photoelectron current precludesthese very high natural charging levels. ATS-5 observed amaximum potential of -300 V in the sunlight, and reachedpotentials of between -50 and -300 V several times. All ofthese charging events occurred during periods of very highsolar activity, and occurred between local midnight and dawn.The SCATHA satellite was also used to study natural chargingin sunlight, and recorded potentials as high as -740 V.[36]Charging events in excess of -100 V only occurred for kpindices of 2 or greater.

The NOAA space weather scale classifies the severity andfrequency of geomagnetic storms, with a scale ranging from

TABLE IPLASMA PARAMETERS USED FOR GEOMAGNETIC STORM ANALYSIS

Storm Level ne (cm−3) Te (keV) ni (cm−3) Ti (keV)Moderate (kp = 6) 1 4.7 1 15Severe (kp = 8 − 9) 1 20 1 20Quiet (kp = 1.5) 0.925 2.64 3.05 0.05

G-1 (minor, kp = 5) to G-5 (extreme, kp = 9).[26] Inan 11 year solar cycle, minor storm activity is expectedfor roughly 900 days, with extreme storm events occurringmuch less frequently, only about 4 times. For the analysisof storm activity, two storm conditions are considered: amoderate geomagnetic storm, G-2 on the NOAA scale, withkp = 6 and a worst-case severe storm event. Only the effectson the charge transfer process are considered. Severe solaractivity can be harmful to spacecraft subsystems, causingelectrical failures and differential charge driven arcing events,but consideration of these phenomena is beyond the scope ofthe current work. For the moderate storm condition (kp = 6),data from [24] are used to determine plasma temperatures anddensities. The data are taken at a local time of 3:00, whichcorresponds to the post-midnight period where high naturalcharging is observed. For the severe storm condition, theplasma parameters corresponding to a severe storm in [37] areused. The ion and electron densities for both storm conditionsare presented in Table I, along with the quiet (kp = 1.5)conditions computed for 3:00 local time using the data in [24].

To determine the effects of these storm conditions, the tugand deputy potentials are computed as a function of electronbeam current, for EEB = 40 keV, rT = 2 m, and rD = 0.935m. The electrostatic force is also computed, assuming a sep-aration distance of 12.5 m. The potentials and forces are alsocomputed for the quiet solar conditions (kp = 1.5) to serve asa baseline for comparison. For the moderate solar storm event(kp = 6), the results are illustrated in Figure 6. Also shownare potentials computed using the quiet conditions. The stormconditions result in the tug charging to higher potentials fora given electron beam current. For the deputy, the maximumpotential occurs at a lower beam current level, and the potentialdecreases at a faster rate as the beam current is increased.The tug reaches its maximum potential (qφT = EEB) at alower current level than for quiet space weather conditions.Considering the electrostatic forces that result, a slightly highermaximum force occurs for the storm condition and it occursat a lower beam current level. The potentials and forces arealso computed for the severe storm conditions, and are shownin Figure 7. The same effects are observed that are seen formoderate storm conditions, but to a higher degree. The tugpotential increases more rapidly as beam current is increased,and the deputy potential decreases in a similar fashion. Forthe severe storm condition, the tug reaches its maximumpotential for a beam current of about 575 µA, while in themoderate storm condition the tug potential is at its maximumfor a beam current of almost 900 µA. As the storm severityincreases, less current is required to maximally charge thetug. Looking at the electrostatic forces for the severe storm

5


Abstract # 133

�T = 20 kV�D = 0 kV

�D = �10 kV �T = 10 kV �T = 20 kV�D = �20 kV

✓ = 20� ✓ = 20�

450 500 550 600 650 700-10

0

10

20

30

It HmAL

fHkVL

450 500 550 600 650 7000.0

0.2

0.4

0.6

0.8

1.0

It HmAL

F cHmNL

�T

�D

No Back-Flux

No Back-Flux

With Back-Flux With Back-Flux

TugDeputy

- -

- -- -

- ---

-- +-

+

+++

++

- -

--

--

✓, angle of recapture region

Recaptured photo- andsecondary electrons

�T

�D

kp = 1.5k p

=6

kp = 6

200 400 600 8000.00.10.20.30.40.50.60.7

It HmAL

F cHmNL

kp =

1.5

200 400 600 800-40

-20

0

20

40

It HmAL

fHkVL

kp = 1.5

250 300 350 400 450 500 550 600-60

-40

-20

0

20

40

60

It HmAL

fHkVL

Severe Storm Conditions

�D

�T

250 300 350 400 450 500 550 6000.00.10.20.30.40.50.60.7

It HmAL

F cHmNL


kp = 1.5

(a) Potentials

�T = 20 kV�D = 0 kV

�D = �10 kV �T = 10 kV �T = 20 kV�D = �20 kV

✓ = 20� ✓ = 20�

450 500 550 600 650 700-10

0

10

20

30

It HmAL

fHkVL

450 500 550 600 650 7000.0

0.2

0.4

0.6

0.8

1.0

It HmAL

F cHmNL

�T

�D

No Back-Flux

No Back-Flux


TugDeputy

- -

- -- -

- ---

-- +-

+

+++

++

- -

--

--



�T

�D

kp = 1.5

k p=

6

kp = 6

200 400 600 8000.00.10.20.30.40.50.60.7

It HmAL

F cHmNL

kp =

1.5

200 400 600 800-40

-20

0

20

40

It HmAL

fHkVL

kp = 1.5

250 300 350 400 450 500 550 600-60

-40

-20

0

20

40

60

It HmAL

fHkVL


�D

�T

250 300 350 400 450 500 550 6000.00.10.20.30.40.50.60.7

It HmAL

F cHmNL


kp = 1.5

(b) E-Force

Fig. 6. a) Potentials and b) electrostatic force as a function of electronbeam current for moderate solar storm event (solid) and quiet solar conditions(dashed). Results assume rT = 2 m, rD = 0.935 m, and EEB = 40 keV.

condition, the maximum is once again slightly above that ofthe quiet condition, but occurs at much less current.

Clearly, geomagnetic storm events do not prevent chargetransfer for the electrostatic tractor. In fact, they are actuallysomewhat helpful. A slightly higher electrostatic force is pos-sible, and less current is required to achieve it. Current modi-fication is required to compensate for the onset of these stormevents, however. When considering the nominal GEO spaceweather conditions for quiet periods of activity, the maximumelectrostatic force occurs for a beam current of nearly 600µA. If a severe solar storm event occurs and the beam currentis not modified to compensate, Figure 7 shows that the tugwill reach its maximum potential (qφT = EEB), preventingcharge transfer and significantly impacting performance. Thus,to account for solar storm events the beam current shouldbe controllable, which is likely to be the case anyway. Theanalysis of solar storm events on tractor performance revealsthat the worst-case scenario from a performance perspective isactually the nominal, quiet space weather conditions. For thisreason, quiet storm conditions are assumed for further studies.

IV. TUG ELECTRON BACK-FLUX

Two deputy current sources are due to emission of electronsfrom the deputy surface: photoelectron and secondary electronemission. Because the deputy is charged negatively, these elec-

�T = 20 kV�D = 0 kV

�D = �10 kV �T = 10 kV �T = 20 kV�D = �20 kV

✓ = 20� ✓ = 20�

450 500 550 600 650 700-10

0

10

20

30

It HmAL

fHkVL

450 500 550 600 650 7000.0

0.2

0.4

0.6

0.8

1.0

It HmAL

F cHmNL

�T

�D

No Back-Flux

No Back-Flux


TugDeputy

- -

- -- -

- ---

-- +-

+

+++

++

- -

--

--



�T

�D

kp = 1.5

k p=

6

kp = 6

200 400 600 8000.00.10.20.30.40.50.60.7

It HmAL

F cHmNL

kp =

1.5

200 400 600 800-40

-20

0

20

40

It HmAL

fHkVL

kp = 1.5

250 300 350 400 450 500 550 600-60

-40

-20

0

20

40

60

It HmAL

fHkVL


�D

�T

250 300 350 400 450 500 550 6000.00.10.20.30.40.50.60.7

It HmALF cHmNL


kp = 1.5

(a) Potentials

�T = 20 kV�D = 0 kV

�D = �10 kV �T = 10 kV �T = 20 kV�D = �20 kV

✓ = 20� ✓ = 20�

450 500 550 600 650 700-10

0

10

20

30

It HmAL

fHkVL

450 500 550 600 650 7000.0

0.2

0.4

0.6

0.8

1.0

It HmAL

F cHmNL

�T

�D

No Back-Flux

No Back-Flux


TugDeputy

- -

- -- -

- ---

-- +-

+

+++

++

- -

--

--



�T

�D

kp = 1.5

k p=

6

kp = 6

200 400 600 8000.00.10.20.30.40.50.60.7

It HmAL

F cHmNL

kp =

1.5

200 400 600 800-40

-20

0

20

40

It HmAL

fHkVL

kp = 1.5

250 300 350 400 450 500 550 600-60

-40

-20

0

20

40

60

It HmAL

fHkVL


�D

�T

250 300 350 400 450 500 550 6000.00.10.20.30.40.50.60.7

It HmALF cHmNL


kp = 1.5

(b) E-Force

Fig. 7. a) Potentials and b) electrostatic force as a function of electronbeam current for severe solar storm event (solid) and quiet solar conditions(dashed). Results assume rT = 2 m, rD = 0.935 m, and EEB = 40 keV.

�T = 20 kV�D = 0 kV

�D = �10 kV �T = 10 kV �T = 20 kV�D = �20 kV

✓ = 20� ✓ = 20�

450 500 550 600 650 700-10

0

10

20

30

It HmAL

fHkVL

450 500 550 600 650 7000.0

0.2

0.4

0.6

0.8

1.0

It HmAL

F cHmNL

�T

�D

No Back-Flux

No Back-Flux


TugDeputy

- -

- -- -

- ---

-- +-

+

+++

++

- -

--

--



Fig. 8. Electron back-flux from the deputy to the tug.

trons are lost. The nearby tug, however, recaptures a portion ofthese emitted electrons, as depicted in Figure 8, owing to highpositive potential. This serves as an additional current sourceon the deputy object which will impact its charging. Thus, it isimportant to study this effect, and obtain a rough estimate forhow significantly these current sources affect tug charging. Thescope of this analysis is not meant to be comprehensive, butrather to provide some insight into how much this back-fluxmight affect electrostatic tractor performance. A two meter

6


Abstract # 133

�T = 20 kV�D = 0 kV

�D = �10 kV �T = 10 kV �T = 20 kV�D = �20 kV

✓ = 20� ✓ = 20�

450 500 550 600 650 700-10

0

10

20

30

It HmAL

fHkVL

450 500 550 600 650 7000.0

0.2

0.4

0.6

0.8

1.0

It HmAL

F cHmNL

�T

�D

No Back-Flux

No Back-Flux


(a) φT = −φD = 10 kV

�T = 20 kV�D = 0 kV

�D = �10 kV �T = 10 kV �T = 20 kV�D = �20 kV

✓ = 20� ✓ = 20�

450 500 550 600 650 700-10

0

10

20

30

It HmAL

fHkVL

450 500 550 600 650 7000.0

0.2

0.4

0.6

0.8

1.0

It HmAL

F cHmNL

�T

�D

No Back-Flux

No Back-Flux


(b) φT = −φD = 20 kV

Fig. 9. Electron back-flux trajectories computed by NASCAP-2K for a)φT = −φD = 10 kV and b) φT = −φD = 20 kV. Results assume spheresof two-meter radius separated by a distance of 12 meters.

radius is assumed for both tug and deputy and the quiet spaceweather conditions at 17:30 local time are used, correspondingto ne = 0.47 cm−3, Te = 1180 eV, ni = 11 cm−3, Ti = 50eV.[24] These values are chosen to represent the worst-casecharge transfer performance conditions, as observed in [27].

To identify the angle of the recapture region, θ,the NASCAP-2K spacecraft charging analysis software isused.[38] Developed by NASA and the Air Force ResearchLab, NASCAP-2K is capable of simulating charging behaviorof 3-D spacecraft models, computing potentials in space,and tracking particle trajectories. To identify the region ofrecapture, potentials are prescribed onto two spherical objects(each with two-meter radius) separated by a distance of 12meters. NASCAP-2K is then used to compute the potentialsin space around the objects. Following this computation,electrons are distributed around the deputy object with atemperature of 2 eV. These electrons may represent eithersecondary or photoelectrons, as both are emitted at low energy.The electron trajectories are then computed to determine ifthey are recaptured by the tug vehicle. Two particular casesare considered: φT = −φD = 20 kV and φT = −φD = 10kV.

The resulting electron trajectories are shown in Figure 9.The region of recapture for the 10 and 20 kV equal potential

5 10 15 20 25 30 35 400.00

0.02

0.04

0.06

0.08

fT HkVL

I ph,rêI e

Fig. 10. Ratio of recaptured photoelectron current and tug plasma electroncurrent for two meter tug and deputy radii.

cases is nearly identical, with θ = 20◦. Any electrons emittedwithin this region will be recollected by the tug, constitutingan additional current source that will affect tug charging. If theelectron beam is directed along the line of sight from tug todeputy and is sufficiently narrow when it reaches the deputy, avery large portion of the resulting secondary electrons may berecaptured by the tug. Depending on the potential levels of tugand deputy, the secondary electron current can be a significantfraction of the beam current. In order to avoid the recapture ofthese electrons, a very narrow electron beam may not be thebest choice. Alternately, the electron beam could be focusedonto an area outside the region of recapture.

The back-flux of photoelectrons is an additional currentsource onto the tug. Assuming a worst-case scenario where thesun shines directly onto the region of recapture, the maximumcross sectional area for which emitted photoelectrons arerecaptured is

A⊥ = πr2D sin2

(θ

2

). (14)

This is a higher area than could physically be exposed tosunlight because the tug would shadow at least some portionof the deputy. Assuming the tug is at potential levels of at leasta few kiloVolts, the magnitude of this recaptured photoelectroncurrent is insensitive to further increases in electron beamcurrent. The recaptured photoelectron current is expressed as

Iph,r = −πjphr2D sin2

(θ

2

). (15)

To provide insight into how significant this current is onthe tug, it is compared with the collected plasma electroncurrent (Ie). Using the value of θ = 20◦ determined from theNASCAP-2K simulations, the ratio of recaptured photoelec-tron current to plasma electron current is shown in Figure 10.For the tug potentials considered for the electrostatic tractorapplication, the recaptured photoelectron current is a verysmall fraction (5% or less) of the incoming plasma electroncurrent. Thus, this effect will not significantly impact the

7


Abstract # 133

�T = 20 kV�D = 0 kV

�D = �10 kV �T = 10 kV �T = 20 kV�D = �20 kV

✓ = 20� ✓ = 20�

450 500 550 600 650 700-10

0

10

20

30

It HmAL

fHkVL

450 500 550 600 650 7000.0

0.2

0.4

0.6

0.8

1.0

It HmAL

F cHmNL

�T

�D

No Back-Flux

No Back-Flux


(a) Potentials

�T = 20 kV�D = 0 kV

�D = �10 kV �T = 10 kV �T = 20 kV�D = �20 kV

✓ = 20� ✓ = 20�

450 500 550 600 650 700-10

0

10

20

30

It HmAL

fHkVL

450 500 550 600 650 7000.0

0.2

0.4

0.6

0.8

1.0

It HmAL

F cHmNL

�T

�D

No Back-Flux

No Back-Flux


(b) Electrostatic Force

Fig. 11. a) Tug and deputy potentials with and without electron back-fluxonto the tug and b) resulting electrostatic forces.

charging of the tug. The tug vehicle can simply emit slightlymore current to offset these recaptured photoelectrons.

Assessing the impacts of recaptured secondary electrons issomewhat more complicated, because the recaptured SEE cur-rent depends on how well focused the beam is and how muchbeam current is absorbed by the deputy. Assuming a worstcase scenario where all secondary electrons are recaptured bythe tug, the potentials φT and φD are found by solving

It + Ie(φT ) − ISEE(φT , φD) + Iph,r = 0 (16a)ID(φT , φD) + Ie(φD) + Ii(φD) + ISEE(φT , φD)

+ Iph = 0. (16b)

In the absence of back-flux, the tug potential is not a functionof the deputy potential and can be solved directly. With back-flux, however, the tug potential is a function of the deputypotential due to the recaptured secondary electrons and thesetwo current balance equations must be solved simultaneouslyfor φT and φD. Considering the same 2 meter radius tugand deputy objects, at a separation distance of 12 meters, thepotentials as a function of electron beam current are computedand shown in Figure 11. Also shown for comparison are thecharging results if back-flux is neglected (or nonexistent).With back-flux, the tug and deputy potentials both increaseas the electron beam is increased. Without back-flux, the tugpotential increases linearly; the deputy potential increases upto a certain point and then begins to decrease. The presence of

back-flux results in potential changes of several kiloVolts. Thetug potential is lower than without back-flux, while the deputypotential is higher. The resulting electrostatic forces are alsoshown in Figure 11. For lower current values, the electrostaticforce is reduced by the back-flux. However, there is a certaincurrent level beyond which the electrostatic force is higherwith back-flux than without it.

The recaptured electrons reduce the tug potential for agiven electron beam current. This allows for more current tobe sent to the deputy at a higher energy level. The beamelectrons lose less energy because the potential differencebetween tug and deputy is reduced by the back-flux. Becausethey arrive with more energy, the beam electrons induce fewersecondary electrons. This allows for the deputy to reach ahigher potential, which can improve tractor performance atthe cost of higher electron beam current. This phenomenonis driven primarily by the recaptured secondary electrons,because this current source is significantly larger than the smallportion of photoelectrons that are recaptured. Of course, thisanalysis assumes a worst case scenario where all secondaryelectrons emitted by the deputy are recaptured by the tug,which depends on how well-focused the beam is and where itis absorbed on the deputy. As a smaller portion of electronsare recaptured, the charging results approach those with noback-flux.

V. SIMULTANEOUS ELECTRON/ION BEAM EMISSION

Deputy charging is limited by the amount of current that canbe delivered to it by the tug. As the tug emits more electronbeam current, it will charge itself to higher potentials. Thisresults in the beam electrons having lower energy when theyreach the deputy, generally causing a higher secondary electronyield. Thus, the deputy charging can actually decrease even forhigher beam currents, as illustrated in Figure 5. Furthermore,the plasma electron conditions can cause the tug to charge upto relatively high values and limit the deputy potential. Thiscan cause significant deviations from the ideal potential split,leading to reduced performance. These performance losses areencountered in the analysis of space weather variations ontugging performance studied in [27]. A dip in electron densityafter local noon results in a higher tug potential for a givenbeam current, which in turn results in a lower deputy potential.

It would be very beneficial if the tug could change theamount of current delivered to the deputy without affecting itsown potential. If a tug vehicle could maintain, for example,a 20 kV potential while emitting a broad range of electronbeam currents, deputy charging could be improved and the tugvehicle would be able to perform charge transfer onto a widervariety of deputy sizes. With only electron beam emission, ofcourse, this is impossible. However, consider a scenario wherethe tug is equipped not only with an electron gun, but also anion beam. Assuming the ion beam is directed away from thedeputy object in a manner that does not result in an additionalcurrent source on the deputy, the deputy charging dynamicswould be the same as in Eq. (7). Assuming there is sufficientlymore electron beam current than ion beam current so that the

8


Abstract # 133

tug charges to a high positive potential, the tug current balancetakes on the slightly modified form

It − Ib + Ie(φT ) = 0, (17)

where Ib is the ion beam current. Note that electron back-fluxis ignored here. This may be accomplished with a defocusedelectron beam, or by focusing the electron beam away fromthe region of recapture. The tug potential, then, is a functionof the net emitted current ∆IB = It − Ib:

φT =

(4∆IBAqnewe

− 1

)Te (18)

The tug vehicle, being charged positive, will not recapture thebeam ions in any significant capacity.

With the ion beam, a tug vehicle can theoretically emit anyamount of electron beam current while maintaing a specificpotential. For example, if the tug is desired to maintain apotential of 20 kV with a ∆IB of 500 µA, any amount ofelectron beam current above 500 µA may be delivered to thedeputy. If 1000 µA of electron beam current is emitted, then500 µA of ion beam current must also be emitted to maintainthe necessary ∆IB .

The ion beam emission allows for performance improve-ment in a variety of ways. Revisiting the issue of tug/deputysize limitations, a tug would be able to achieve charge transferonto objects larger than itself. With only an electron beam, theamount of beam current that the tug can emit is limited by thetug size. As the tug emits more current, it charges to a higherpotential. The beam electrons that reach the deputy have alower effective energy when they arrive, resulting in furtherperformance losses due to higher secondary electron emission.With an ion beam included, however, the tug can now deliverthe necessary amount of electron beam current for deputycharging. Emitting higher levels of electron beam current doesnot necessarily result in higher tug potentials, because ionbeam current can be increased to maintain a constant tugpotential. More current can be delivered to the deputy athigher energies, inhibiting losses due to secondary electronemission. Considering the space weather driven performancelosses encountered in [27], the increase in tug potential inthe afternoon period can be eliminated by compensation withthe ion beam. Keeping the tug potential from increasing alsoprevents the deputy potential from decreasing. The end resultis that both potentials remain close to the ideal split, wherebest performance occurs.

Naturally, simultaneous beam emission raises the questionof what current emission strategy will yield the best perfor-mance for the electrostatic tractor. To provide insight into theeffects of increasing electron and ion beam currents on theresulting electrostatic force, a numerical optimization is used.Considering a range of emitted ion beam currents, the max-imum possible electrostatic force and its associated electronbeam current are computed. The quiet GEO space weatherconditions at 17:30 are, again, used. Both tug and debris areassumed to have radii of two meters, and the electron beamenergy is assumed to be 40 keV. The ion beam current is

0 2 4 6 8 10

0.6

0.8

1.0

1.2

1.4

1.6

Ib HmAL

MaxF cHmNL

(a) Maximum E-Force

0 2 4 6 8 100.3

0.4

0.5

0.6

0.7

0.8

Ib HmALIdealDI BHmAL

(b) Ideal ∆IB

Fig. 12. a) Maximum possible electrostatic force and b) ∆IB required toobtain the maximum force for simultaneous electron and ion beam emission.Dashed lines are the limiting values for the case of very large current emission.The results are computed with rT = rD = 2 m and EEB = 40 keV.

swept across a range of values, and the maximum possibleelectrostatic force is computed, along with the ∆IB need toachieve the max force. The results are shown in Figure 12. Asthe ion and, correspondingly, electron beam currents are in-creased, the maximum electrostatic force increases. However,there is a limit on the increase, regardless of how much currentis emitted. This reflects the fact that for a given beam energy,the maximum potential difference between tug and deputy isfinite. Furthermore, as the current is increased the ideal ∆IBalso converges towards a distinct value. Here, the inclusion ofan ion beam allows for a significant boost in the electrostaticforce magnitude. With only electron beam emission (Ib =0), the maximum electrostatic force that can be generated isjust under 0.8 mN. As the ion and, correspondingly, electronbeam currents are increased, the maximum electrostatic forceincreases towards a limit of slightly less than 1.5 mN. This isan an increase of 87%, which would nearly cut the reorbitingtime required in half.

These results imply that for the case of simultaneous elec-tron and ion beam emission, delivering ever higher amounts ofcurrent to the deputy will yield the best tractor performance.Clearly, though, there is a limit to how large of an electrostaticforce may be generated, even for very high current levels. Theonly non-beam deputy current source that increases directly

9


Abstract # 133

as a function of the electron beam current is the secondaryelectron current. As the beam current is increased to very highvalues, the ion and photoelectron currents become insignifi-cant relative to the secondary electron and beam absorptioncurrents. Thus, the deputy will reach a potential that satisfies

ID − 4YMIDκ = 0. (19)

The deputy potential that satisfies this current balance is

φD = φT − EEB + Emax (2YM − 1)

+ 2Emax√YM (YM − 1). (20)

The maximum secondary electron yield YM must be greaterthan one for a real solution to exist. If the max yield werebelow 1, the secondary electrons would be unable to balancewith the incoming beam current and the deputy would settleto a potential difference such that qφT − qφD = EEB .With simultaneous electron and ion beam emission, the largesttheoretical difference that is possible between tug and deputyis EEB−Emax (2YM − 1)+2Emax

√YM (YM − 1). The losses

in efficiency due to secondary electron emission are apparent.To compute the maximum possible force with electron/ion

beam emission, the cost function

J = (rDφD − ρφT )(ρφD − rTφT ) (21)

is used. This comes directly from the electrostatic force ex-pression, and the electrostatic force is at its largest magnitudewhen J is maximized. After substituting in Eq. (20) for φD,and setting ∂J/∂φT = 0, the tug potential that will yield thatmaximum force is found to be

φ∗T =EEB − Emax

(2YM − 1 + 2

√YM (YM − 1)

)

2×

ρ2 − 2ρrD + rDrT(ρ− rD)(ρ− rT )

. (22)

Similarly, the deputy potential at the maximum force conditionis

φ∗D = −EEB − Emax

(2YM − 1 + 2

√YM (YM − 1)

)

2×

ρ2 − 2ρrT + rDrT(ρ− rD)(ρ− rT )

. (23)

The ∆IB required to provide the necessary φ∗T is

∆I∗B =Aqnewe

4

(1 +

φ∗TTe

). (24)

This limit is plotted in Figure 12 for the scenario consid-ered therein, and reflects the asymptote that the numericallycomputed result is approaching. The theoretical maximumforce that can be generated with both ion and electron beamemission is

Fc = − rDrT4kc(ρ− rD)(ρ− rT )

(EEB + Emax(1 − 2YM )

− 2Emax√YM (YM − 1)

)2

. (25)

0.2

0.6

11.2

1.622.4

2.83.2

3.6

45

6

500 1000 1500 2000 2500 3000 3500 4000400

600

800

1000

1200

1400

1600

Deputy Mass HkgL

BeamCurrentHmAL

Charge Transfer

No ChargeTransfer

0.2

0.6

11.2

1.622.4

2.83.2

3.6

45

6

500 1000 1500 2000 2500 3000 3500 4000400

600

800

1000

1200

1400

1600

Deputy Mass HkgL

Beam

CurrentHm

AL

20 30 40 50 60 700

1000

2000

3000

4000

EEB HkVL

MaxTowableMassHkgL

rT=

1 m

rT=

2m

r T=

3m

0.5 1.0 1.5 2.0 2.5 3.0

4

6

8

10

12

rD HmL

E EBHkVL

rT = 1 m

rT = 2 m

rT = 3 m

EEB = 20 kV

EEB= 40 kV

EEB= 60

kV

dA=2.5,1 km:20 30 40 50 60 700

1000

2000

3000

4000

EEB HkVL

MaxTowableMassHkgL

rT=

1 m

r T=

2m

r T=

3m

0.5 1.0 1.5 2.0 2.5 3.00

10

20

30

40

rD HmL

I crHmAL

500 1000 1500 2000 2500 3000 3500 400012345678

Deputy Mass HkgL

DaHkmêdayL

rT = 1 m

rT = 2 m

rT = 3 m

Fig. 13. Theoretical maximum semi-major axis increase per day for a rangeof tug and deputy masses with simultaneous electron and ion beam emission.Results assume EEB = 40keV .

This limit is also plotted in Figure 12, and the numericallycomputed maximum forces approach it as the currents areincreased.

Of course, emitting arbitrarily large currents is not phys-ically possible for a number of reasons. In addition to veryhigh power requirements, the maximum current is limited bythe space charge effect. If the charge density in a beam ishigh enough, the mutual repulsion between similarly chargedparticles reduces the beam velocity and limits the currentflow.[21] These results should not be interpreted as implyingthat arbitrarily large currents can be emitted for the electro-static tractor application. Rather, they serve to provide anupper limit on the performance improvement that may begained by including ion beam emission in addition to electronbeam emission. Further, Figure 12 shows that, for the vehiclesizes considered here, the achievable electrostatic forces withmilliamp level currents approach the theoretical maximum towithin 10%. Electron beam currents in excess of 10 milliampshave been demonstrated in flight, and the SCATHA missionis one such example.[39]

The semi-major axis increases per day for a one, two,and three meter radius tug as a function of deputy massare computed using the ideal electrostatic force expression inEq. (25), assuming an electron beam energy of 40 keV andquiet space weather conditions at 17:30. The results are shownin Figure 13. The largest, three meter radius tug provides thebest performance, towing objects of 4000 kg with a semi-major axis increase of more than 3 km/day. For the one metertug, even simultaneous electron and ion beam emission is notenough to tow larger deputy objects at a rate of ∆a = 1km/day.

Considering the dual beam scenario, we address the ques-tion of the maximum towable deputy mass. To compute themaximum towable mass, the linear mass-radius relationship inEq. (13) is employed. Using the best-case electrostatic forcepredicted by Eq. (25) in conjunction with the approximatesemi-major axis increase per day from Eq. (12) allows for a

10


Abstract # 133

0.2

0.6

11.2

1.622.4

2.83.2

3.6

45

6

500 1000 1500 2000 2500 3000 3500 4000400

600

800

1000

1200

1400

1600

Deputy Mass HkgL

BeamCurrentHmAL

Charge Transfer

No ChargeTransfer

0.2

0.6

11.2

1.622.4

2.83.2

3.6

45

6

500 1000 1500 2000 2500 3000 3500 4000400

600

800

1000

1200

1400

1600

Deputy Mass HkgL

Beam

CurrentHm

AL

1 2 3 4 5 6 70.9

1.0

1.1

1.2

1.3

1.4

1.5

Ib HmAL

MaxF cHmNL

1 2 3 4 5 6 70.0

0.1

0.2

0.3

0.4

0.5

0.6

Ib HmAL

IdealDI BHmAL

20 30 40 50 60 700

1000

2000

3000

4000

EEB HkVL

MaxTowableMassHkgL

rT=

1 m

rT=

2m

r T=

3m

500 1000 1500 2000 2500 3000 3500 40000

5

10

15

20

Deputy Mass HkgL

I crHmAL

EEB = 20 kV

EEB = 40 kV

EEB= 60 kV

0.5 1.0 1.5 2.0 2.5 3.0

4

6

8

10

12

rD HmL

E EBHkVL

rT = 1 m

rT = 2 m

rT = 3 m

0.5 1.0 1.5 2.0 2.5 3.00

5

10

15

rD HmL

I crHmAL

EEB = 20 kV

EEB= 40 kV

EEB= 60

kV

dA=2.5,1 km:20 30 40 50 60 700

1000

2000

3000

4000

EEB HkVL

MaxTowableMassHkgL

rT=

1 m

r T=

2m

r T=

3m

(a) ∆a =1 km/day

0.2

0.6

11.2

1.622.4

2.83.2

3.6

45

6

500 1000 1500 2000 2500 3000 3500 4000400

600

800

1000

1200

1400

1600

Deputy Mass HkgL

Beam

CurrentHm

AL

Charge Transfer

No ChargeTransfer

0.2

0.6

11.2

1.622.4

2.83.2

3.6

45

6

500 1000 1500 2000 2500 3000 3500 4000400

600

800

1000

1200

1400

1600

Deputy Mass HkgL

Beam

CurrentHm

AL

1 2 3 4 5 6 70.9

1.0

1.1

1.2

1.3

1.4

1.5

Ib HmAL

MaxF cHmNL

1 2 3 4 5 6 70.0

0.1

0.2

0.3

0.4

0.5

0.6

Ib HmAL

IdealDI BHmAL

20 30 40 50 60 700

1000

2000

3000

4000

EEB HkVL

MaxTowableMassHkgL

rT=

1 m

rT=

2m

r T=

3m

500 1000 1500 2000 2500 3000 3500 40000

5

10

15

20

Deputy Mass HkgL

I crHmAL

EEB = 20 kV

EEB = 40 kV

EEB= 60 kV

0.5 1.0 1.5 2.0 2.5 3.0

4

6

8

10

12

rD HmL

E EBHkVL

rT = 1 m

rT = 2 m

rT = 3 m

0.5 1.0 1.5 2.0 2.5 3.00

5

10

15

rD HmL

I crHmAL

EEB = 20 kV

EEB= 40 kV

EEB= 60

kV

dA=2.5,1 km:20 30 40 50 60 700

1000

2000

3000

4000

EEB HkVL

MaxTowableMassHkgL

rT=

1 m

r T=

2m

r T=

3m

(b) ∆a =2.5 km/day

Fig. 14. Maximum towable mass using simultaneous electron and ion beamemission to meet performance criteria of a) ∆a = 1 km/day and b) ∆a =2.5km/day.

numerical solution of the deputy mass that will yield a desired∆a given a particular tug radius, separation distance, andelectron beam energy. Two performance thresholds are used:∆a =1 km and ∆a =2.5 km. The ∆a =1 km performancelevel is somewhat lower than typically assumed, and for thedebris reorbiting scenario would require a maneuver durationof roughly 7-10 months. The higher performance level of∆a =2.5 km is more typical of what has been assumed inprior electrostatic tractor research.[7]

The maximum towable masses as a function of electronbeam energy are shown in Figure 14 for tug sizes of rT =1,2, and 3 meters. The improved performance for larger tugvehicles is apparent. Significantly less beam energy is neededto achieve the same level of performance for the three metertug radius than for the one meter tug radius. By incorporatingion beam emission, a tug with a one meter radius can towobjects as large as 4000 kg at a rate of ∆a =2.5 km/day withan electron beam energy of 65 keV. To achieve a ∆a of 2.5km/day, the three meter radius tug needs only 35 keV.

Ion beam emission, owing to the higher mass of ionsrelative to electrons, can impart a significant thrust force ontothe tug vehicle. In fact, low-thrust propulsion systems havebeen designed around continuous ion emission.[40], [41], [42]Further, the ion-beam shepherd concept considers the use of

0.2

0.6

11.2

1.622.4

2.83.2

3.6

45

6

500 1000 1500 2000 2500 3000 3500 4000400

600

800

1000

1200

1400

1600

Deputy Mass HkgL

BeamCurrentHm

AL

Charge Transfer

No ChargeTransfer

0.2

0.6

11.2

1.622.4

2.83.2

3.6

45

6

500 1000 1500 2000 2500 3000 3500 4000400

600

800

1000

1200

1400

1600

Deputy Mass HkgL

Beam

CurrentHm

AL

20 30 40 50 60 700

1000

2000

3000

4000

EEB HkVL

MaxTowableMassHkgL

rT=

1 m

rT=

2m

r T=

3m

0.5 1.0 1.5 2.0 2.5 3.0

4

6

8

10

12

rD HmL

E EBHkVL

rT = 1 m

rT = 2 m

rT = 3 m

EEB = 20 kV

EEB= 40 kV

EEB= 60

kV

dA=2.5,1 km:20 30 40 50 60 700

1000

2000

3000

4000

EEB HkVL

MaxTowableMassHkgL

rT=

1 m

r T=

2m

r T=

3m

0.5 1.0 1.5 2.0 2.5 3.00

10

20

30

40

rD HmL

I crHmAL

Fig. 15. Ion beam current for which Fth is equal to the maximum possibleelectrostatic force for simultaneous electron and ion beam emission.

a collimated ion beam to impart a small force onto a debrisobject due to the impact of the incoming ions on the debrisobject, which is used for deorbiting purposes.[43] For the caseof simultaneous ion and electron beam emission, performanceimproves as more beam current is emitted. Because the ionthrust force increases as more current is emitted, there willbe a point beyond which the thrust force is higher than theelectrostatic force. Because the tug vehicle is charged to ahigh positive potential ions that are emitted will be repelled,so there is no need for a high energy ion beam. It is assumedthat the ions are emitted in a direction that will not lead totheir capture by the negatively charged deputy.

The thrust force on the tug due to the ion beam emission is

Fth =Ibqmbv∞(φT ) (26)

where mb is the mass of the ions and

v∞(φT ) =

√2qφTmb

(27)

is the velocity of the ions at infinity, after they have beenaccelerated out of the tug potential well. This formulationassumes that the ions are emitted with low energy, and thatall of their v∞ is due to acceleration by the tug’s electricfield. The ion species is assumed to be Argon (Ar+), with anassociated mass of mb = 6.63 × 10−26 kg. The thrust forcematches the performance limit for dual beam emission when

Ibqmbv∞(φ∗T ) = − rDrT

4kc(ρ− rD)(ρ− rT )

(EEB

+ Emax(1 − 2YM ) − 2Emax√YM (YM − 1)

)2

. (28)

Solving this equation for Ib yields the critical beam current,Icr, for which more force is generated by the ion beamemission than is possible for the electrostatic attraction. Con-sidering the case of a two meter tug radius, this critical currentlevel is computed for electron beam energies of 20, 40, and60 keV and presented in Figure 15. Higher beam energiesallow for higher potentials on tug and deputy, resulting in a

11


Abstract # 133

0 2 4 6 8 100

20

40

60

80

100

120

Ib HmAL

mFHgL

Fig. 16. Fuel required for continuous ion beam emission over the course ofone year.

larger electrostatic force. Thus, it takes more ion beam currentto generate equivalent levels of thrust. As rD is increased,more charge accumulates on the deputy for the same potentiallevel. This also results in a larger electrostatic force and ahigher Icr level. Depending on EEB and the deputy size,only a few milliamps of current are required for the ion beamthrust to equal the maximum electrostatic force. As seen inFigure 12, it may take several milliamps of current before theelectrostatic force magnitude begins to closely approach thetheoretical maximum. This implies that actually achieving thepotential increases that are possible with dual beam emissionmay result in a scenario where the ion beam thrust is onthe same order of the electrostatic force. Considering againthe scenario depicted in Figure 12, with a two meter tugand deputy radius, the electrostatic forces begin to closelyapproach the theoretical maximum around an ion beam currentof 5-6 milliamps. Considering Figure 15, the amount of ionbeam current required to reach the level of these electrostaticforces is 12 millamps. For this particular scenario, whereroughly 5-6 milliamps of ion beam current are required toachieve maximum performance, the thrust due to the resultingion beam emission is roughly half of the electrostatic forcemagnitude.

Operating the ion beam requires a consumable source offuel for ion generation. The reorbiting times of several monthsmeans that the ion beam will have to be emitted continuouslyfor a long duration. Thus, it is of interest to investigate roughlyhow much fuel is required for ion beam operation. The massflow rate of fuel due to the ion beam is computed as

mF =Ibqmi. (29)

Considering a continuous operating time of one year, the totalfuel consumption for a range of ion beam currents is shownin Figure 16. For current levels of several milliamps, the totalfuel consumption is about 130 g. Considering the sizes of thetug and deputy objects, this is a negligible increase in totalsystem mass and not a significant hindrance for adding ionbeam emission.

The decision to equip a tug vehicle with both an ion andelectron beam depends on several factors. Really maximizingthe benefits that are possible with simultaneous emissionrequires a large increase in the emitted beam current levels.This has a direct impact on the resulting power require-ments. For a two meter tug with only an electron beam,the maximum power required for beam operation is drivingthe tug to its maximum potential (qφT = EEB), and isabout 30 W. Maximizing performance benefits with an ionbeam requires at least several milliamps of current. Estimatingpower requirements as P = ItEEB , emitting 6 milliampsof electron beam current with an energy of 40 keV requires240 W. This is an increase of 700%, and does not eveninclude additional power consumption due to the ion beamemission. Still, power generation in excess of 10 kW hasbeen achieved in operating GEO satellites,[44] so this issueof increased power consumption is not likely to pose anysignificant technical hurdles.

Another practical concern is the additional complexity ofadding a second current source (the ion beam). While itcan greatly improve the performance for smaller tug vehicleswhere electron beam only charge transfer onto large deputyobjects fails, this must be weighed against the decision tosimply build a larger tug vehicle with only an electron beam.Increasing the size of the tug does not necessarily necessitateincreased vehicle mass and higher launch costs. There are norequirements on tug density, so it could be built like a hollowshell, keeping the mass increases manageable for larger tugvehicles.

Lastly, the ion beam emission introduces a significant thrustforce. While this does not preclude any functionality of theelectrostatic tractor it is something that the relative motioncontrol system will have to compensate for, increasing therequired thrust for station keeping. If the ions are emitteddirectly away from the deputy object, a ion-beam thrust onthe same order as the electrostatic will double the station-keeping thrust requirements. This will, in turn, double fuelrequirements. It may be possible, however, to mitigate theseeffects somewhat by emitting the ions such that they providesome portion of the required station-keeping thrust. Doingso, however, would require emission in the direction of thedeputy object. This could lead to recollection of the ions by thedeputy, which would reduce deputy charging and hurt tractorperformance. A full analysis of this phenomenon is beyondthe scope of this study.

VI. CONCLUSION

The impacts of geomagnetic storm activity on charge trans-fer for the electrostatic tractor application are considered.While the variations in the plasma environment resulting fromthese storm events do affect the charging of tug and deputy,they can actually improve tractor performance. The tug mustbe able to compensate, however, by modifying electron beamcurrent for the onset of such storms or performance will suffer.Both photoelectrons and secondary electrons are emitted fromthe deputy in the near vicinity of the positively charged tug.

12


Abstract # 133

Some of the electrons are recaptured by the tug, resulting inan additional current source. This back-flux also somewhatimproves tractor performance by allowing the tug to delivermore current at a slightly higher energy to the deputy. Chargetransfer performance can be improved by incorporating an ionbeam onto a tug vehicle equipped with an electron beam.Simultaneous electron and ion beam emission allows the tugto deliver more electron current to the deputy while keeping itsown potential from increasing. This allows the deputy to reacha higher potential and the tractor force may be significantlyimproved, especially for smaller tug vehicles where chargetransfer fails with only an electron beam. Of course, thiscomes at the cost of higher power requirements and the addedcomplexity of dual beam emission.

ACKNOWLEDGMENT

The authors would like to thank Zoltan Sternovsky for hisinput on the charging dynamics.

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[6] N. Murdoch, D. Izzo, C. Bombardelli, I. Carnelli, A. Hilgers, andD. Rodgers, “Electrostatic tractor for near earth object deflection,” in59th International Astronautical Congress, Glasgow, Scotland, vol. 29,2008.

[7] H. Schaub and D. F. Moorer, “Geosynchronous large debris reorbiter:Challenges and prospects,” The Journal of the Astronautical Sciences,vol. 59, no. 1&2, pp. 165–180, 2012.

[8] E. Hogan and H. Schaub, “Relative motion control for two-spacecraftelectrostatic orbit corrections,” AIAA Journal of Guidance, Control, andDynamics, vol. 36, no. 1, pp. 240–249, Jan. – Feb. 2013.

[9] Y. S. Karavaev, R. M. Kopyatkevich, M. N. Mishina, G. S. Mishin,P. G. Papushev, and P. N. Shaburov, “The dynamic properties of rotationand optical characteristics of space debris at geostationary orbit,” inAdvances in the Astronautical Sciences, vol. 119, 2004, pp. 1457–1466,Paper No. AAS-04-192.

[10] P. Couzin, F. Teti, and R. Rembala, “Active removal of large debris:Rendezvous and robotic capture issues,” in 2nd European Workshop onActive Debris Removal, Paris, France, 2013, paper No. 7.5.

[11] L. B. King, G. G. Parker, S. Deshmukh, and J.-H. Chong, “Space-craft formation-flying using inter-vehicle coulomb forces,” NASA/NIAC,http://www.niac.usra.edu, Tech. Rep., January 2002.

[12] H. Schaub and D. Stevenson, “Prospects of relative attitude controlusing coulomb actuation,” in Jer-Nan Juang Astrodynamics Symposium,College Station, TX, June 25–26 2012, Paper AAS 12–607.

[13] D. Stevenson and H. Schaub, “Multi-sphere method for modelingelectrostatic forces and torques,” Advances in Space Research, vol. 51,no. 1, pp. 10–20, Jan. 2013.

[14] P. Couzin, F. Teti, and R. Rembala, “Active removal of large debris:System approach of deorbiting concepts and technological issues,” in6th European Conference on Space Debris, Darmstadt, Germany, April22–25 2013, paper No. 6a.P-17.

[15] A. Natarajan and H. Schaub, “Linear dynamics and stability analysisof a coulomb tether formation,” Journal of Guidance, Control, andDynamics, vol. 29, no. 4, pp. 831–839, July–Aug. 2006.

[16] I. I. Hussein and H. Schaub, “Invariant shape solutions of the spinningthree craft coulomb tether problem,” Journal of Celestial Mechanics andDynamical Astronomy, vol. 96, no. 2, pp. 137–157, 2006.

[17] S. Wang and H. Schaub, “Nonlinear charge control for a collinear fixedshape three-craft equilibrium,” AIAA Journal of Guidance, Control, andDynamics, vol. 34, no. 2, pp. 359–366, Mar.–Apr. 2011.

[18] H. Schaub and L. E. Z. Jasper, “Orbit boosting maneuvers for two-craft coulomb formations,” AIAA Journal of Guidance, Control, andDynamics, vol. 36, no. 1, pp. 74–82, Jan. – Feb. 2013.

[19] U. Yamamoto and H. Yamakawa, “Two-craft coulomb-force formationdynamics and stability analysis with debye length characteristics,” inAIAA/AAS Astrodynamics Specialist Conference and Exhibit, Honolulu,Hawaii, Aug. 18–21 2008, paper No. AIAA 2008-7361.

[20] L. Felicetti and G. B. Palmerini, “Evaluation of control strategies forspacecraft electrostatic formation keeping,” in IEEE Aerospace Confer-ence, Big Sky, MO, Mar. 1–8 2014, paper No. 2.0904.

[21] S. T. Lai, Fundamentals of Spacecraft Charging. Princeton UniversityPress, 2012.

[22] T. Nakagawa, T. Ishii, K. Tsuruda, H. Hayakawa, and T. Mukai, “Netcurrent density of photoelectrons emitted from the surface of the geotailspacecraft,” EARTH PLANETS AND SPACE, vol. 52, no. 4, pp. 283–292,2000.

[23] M. C. Kelley, The Earth’s Ionosphere: Plasma Physics & Electrody-namics. Academic press, 2009, vol. 96.

[24] M. H. Denton, M. F. Thomsen, H. Korth, S. Lynch, J. C. Zhang, andM. W. Liemohn, “Bulk plasma properties at geosynchronous orbit,”Journal of Geophysical Research, vol. 110, no. A7, 2005.

[25] J. Bartels, N. H. Heck, and H. F. Johnston, “The three-hour-rangeindex measuring geomagnetic activity,” Terrestrial Magnetism andAtmospheric Electricity, vol. 44, no. 4, pp. 411–454, 1939. [Online].Available: http://dx.doi.org/10.1029/TE044i004p00411

[26] N. Oceanic and A. Administration, “Noaa space weather scales,”http://www.swpc.noaa.gov/NOAAscales, Tech. Rep., March 2005.

[27] E. Hogan and H. Schaub, “Space weather influence on relative motioncontrol using the touchless electrostatic tractor,” in AAS/AIAA SpaceflightMechanics Meeting, Santa Fe, New Mexico, Jan. 26–30 2014, PaperAAS 14-425.

[28] E. A. Hogan and H. Schaub, “Impacts of tug and debris sizes onelectrostatic tractor charging performance,” in International High PowerLaser Ablation and Beamed Energy Propulsion, Santa Fe, New Mexico,April 21–25 2014.

[29] H. Schaub and Z. Sternovsky, “Active space debris charging for contact-less electrostatic disposal maneuvers,” in 6th European Conference onSpace Debris. Darmstadt, Germany: ESOC, April 22–25 2013, paperNo. 6b.O-5.

[30] S. Pfau and M. Tichy, Low Temperature Plasma Physics: FundamentalAspects and Applications. Berlin: Wiley, 2001.

[31] B. T. Draine and E. E. Salpeter, “On the physics of dust grains in hotgas,” Astrophysical Journal, vol. 231, no. 1, pp. 77–94, 1979.

[32] J. Bittencourt, Fundamentals of Plasma Physics. Springer-Verlag NewYork, Inc, 2004.

[33] L. A. Stiles, C. R. Seubert, and H. Schaub, “Effective coulomb forcemodeling in a space environment,” in AAS Spaceflight MechanicsMeeting, Charleston, South Carolina, Jan. 29 – Feb. 2 2012, PaperAAS 12.

[34] S. E. DeForest, “Spacecraft charging at synchronous orbit,” Journal ofGeophysical Research, vol. 77, no. 4, pp. 651–659, 1972. [Online].Available: http://dx.doi.org/10.1029/JA077i004p00651

[35] S. Bame, D. McComas, M. Thomsen, B. Barraclough, R. Elphic,J. Glore, J. Gosling, J. Chavez, E. Evans, and F. Wymer, “Magne-tospheric plasma analyzer for spacecraft with constrained resources,”Review of scientific instruments, vol. 64, no. 4, pp. 1026–1033, 1993.

[36] E. G. Mullen, M. S. Gussenhoven, and D. A. Hardy, “Scatha survey ofhigh-voltage spacecraft charging in sunlight,” Journal of the GeophysicalSciences, vol. 91, pp. 1074–1090, 1986.

[37] M. J. Mandell, I. Katz, G. W. Schnuelle, P. G. Steen, and J. C.Roche, “The decrease in effective photocurrents due to saddle pointsin electrostatic potentials near differentially charged spacecraft,” IEEETransactions on Nuclear Science, vol. 25, no. 6, pp. 1313–1317, 1978.

13


http://www.sciencedirect.com/science/article/pii/S0273117713000410

http://www.sciencedirect.com/science/article/pii/S0273117713000410

http://dx.doi.org/10.1029/TE044i004p00411

http://dx.doi.org/10.1029/JA077i004p00651

Abstract # 133

[38] M. J. Mandell, V. A. Davis, D. L. Cooke, A. T. Wheelock, and C. Roth,“Nascap-2k spacecraft charging code overview,” Plasma Science, IEEETransactions on, vol. 34, no. 5, pp. 2084–2093, 2006.

[39] S. T. Lai, “An overview of electron and ion beam effects in chargingand discharging of spacecraft,” IEEE Transactions on Nuclear Science,vol. 36, no. 6, pp. 2027–2032, 1989.

[40] D. M. Goebel and I. Katz, Fundamentals of electric propulsion: ion andHall thrusters. John Wiley & Sons, 2008, vol. 1.

[41] J. R. Beattie, “Electrostatic ion thruster with improved thrust modula-tion,” Jun. 13 1989, uS Patent 4,838,021.

[42] P. J. Wilbur, V. K. Rawlin, and J. Beattie, “Ion thruster developmenttrends and status in the united states,” Journal of Propulsion and Power,vol. 14, no. 5, pp. 708–715, 1998.

[43] C. Bombardelli and J. Pelaez, “Ion beam shepherd for contactless spacedebris removal,” AIAA Journal of Guidance, Control, and Dynamics,vol. 34, no. 3, pp. 916–920, May–June 2011.

[44] C. Hoeber, E. A. Robertson, I. Katz, V. Davis, and D. Snyder, “Solararray augmented electrostatic discharge in geo,” in 17th AIAA Inter-national Communications Satellite Systems Conference and Exhibit,Yokohama, Japan, Feb 23-27 1998, Paper AIAA 98–1401.

14


AVS LabAVS LabAutonomous Vehicle Systems Laboratory

University of Colorado Boulder

University of Colorado BoulderIdentity Standards

January 2011

Impacts of Solar Storm Events and Ion Beam Emission on

Electrostatic Tractor PerformanceErik A. Hogan, Graduate Research Assistantand Hanspeter Schaub, Professor!!

13th Spacecraft Charging Technology Conference (SCTC), Pasadena, CA, June 23–27, 2014

1

Spacecraft Charging Technology Confernece 2014 - Viewgraph 133



Introduction

• Electrostatic Tug Overview

• Solar Storm Impacts

• Electron Backflux Considerations

• Ion and Electron Emission

• Conclusions

2

Electron beam emission onto deputy Low-thrust used to tow

deputy

Electrostatic force results from craft charges

++

+

++ +

+

+

+

++

--

---

------

---




Early Work: Charged Actuation in GEO Space Environment

3

Cover, J. H., Knauer, W., and Maurer, H. A., “Lightweight Reflecting Structures Utilizing Electrostatic Inflation,” US Patent 3,546,706, October 1966.


13th Spacecraft Charging Technology Conference (SCTC), Pasadena, CA, June 23–27, 2014 4University of ColoradoBoulder

Non-Contact Debris Remediation to Disposal Orbit



13th Spacecraft Charging Technology Conference (SCTC), Pasadena, CA, June 23–27, 2014 4

Electrostatic Tractor Force

• No physical contact required with the debris!• Robust debris actuation!• Simplified relative navigation!• Gently tug the entire debris object!• Extremely fuel efficient method!• Multi-year missions feasible

Continuous Charge Emission



Moorer, D. F. and Schaub, H., “Electrostatic Spacecraft Reorbiter,” US Patent 8,205,838 B2, Feb. 17 2011.

Moorer, D. F. and Schaub, H., “Hybrid Electrostatic Space Tug,” US Patent 0036951-A1, Feb. 17 2011.




• No physical contact required with the debris!• Robust debris actuation!• Simplified relative navigation!• Gently tug the entire debris object!• Extremely fuel efficient method!• Multi-year missions feasible

Low-Thrust Inertial Propulsion to deorbit debris



Moorer, D. F. and Schaub, H., “Electrostatic Spacecraft Reorbiter,” US Patent 8,205,838 B2, Feb. 17 2011.

Moorer, D. F. and Schaub, H., “Hybrid Electrostatic Space Tug,” US Patent 0036951-A1, Feb. 17 2011.




Equilibrium charge/potential is calculated as INet = 0

Servicer: IPH + Ie + Ii + ITrans + IAux = 0

Debris: IPH + Ie + Ii - ITrans + ISEE= 0

Photo-electron emission Ion and electron collection from plasma

Charge transfer (electrons or ions)

Ion and electron collection from

plasma

Photo-electron emission

Debris

Servicing Vehicle

Secondary electron emission (SEE)Auxiliary charge emission


Electrostatic Tractor





Prior Work: Charging Model

6

Iph(�) = jph,0A?e��/Tph � > 0

= jph,0A? � 0

Photo-Electron Current:

Ie(�) = �Aqnewe/4 e�/Te � < 0

= �Aqnewe/4

✓1 +

�

Te

◆� � 0

Plasma electron Current:

ID(�D) = �↵IT,0 �T � �D < EEB

= 0 �T � �D � EEB

Plasma Ion Current:

ISEE

(�D) = 4YMID(�D)E

e↵

/Emax

(1 + Ee↵

/Emax

)2�D < 0

= 0 �D � 0

Ee↵ = EEB � �T + �D

Secondary Electron Emission Current:

Assumes a well-focused electron beam where all charge hits the debris.

H. S

chau

b an

d Z.

Ste

rnov

ksy,

“Act

ive S

pace

Deb

ris C

harg

ing f

or

Cont

actle

ss

Elec

trost

atic

Disp

osal

Man

euve

rs,”

Adva

nces

in

Spac

e Re

sear

ch, V

ol. 5

3, N

o. 1

, 201

4, p

p. 1

10–1

18.




Prior Work: Insensitive to Nominal GEO Space Weather Variations

7

0.42

0.42

0.45

0.45

0.45

0.48

0.480.51

0.51

0.54

0.54

0.570.57

0.6

0.6

0 5 10 15 20300

400

500

600

700

Local Time HhL

CurrentHmAL

0 5 10 15 200.50

0.55

0.60

0.65

0.70

Local Time HhL

ElectrostaticForceHmNL

0 5 10 15 20

480500520540560580600

Local Time HhL

CurrentHmAL

Optimal Current

Constant Current

Constant Current

Optimal Current

Optimal Current

Constant Current

E. H

ogan

and

H. S

chau

b, “S

pace

Wea

ther

Influ

ence

on

Relat

ive M

otio

n Co

ntro

l usin

g th

e To

uchle

ss E

lectro

stat

ic Tr

acto

r,” A

AS/A

IAA

Spac

eflig

ht

Mec

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s M

eetin

g, S

anta

Fe,

New

Mex

ico, J

anua

ry 2

6–30

, 201

4




G-2 Moderate (kp = 6)

9.0%

G-3 Strong (kp = 7)

3.2%

G-4 Severe (kp = 8)1.5%

G-5 Extreme (kp = 9)

0.10%

G-1 Minor (kp = 5)

22.4%

No Storm Activity (kp < 5)

63.8%

Solar Storm Events

8


International High Power Laser Ablation and Beamed Energy Propulsion Conference, Santa Fe, NM, April 21-25, 2014 8

Charging Model

- -- -

-

- Photoelectron Current

- -- --

--

-

+

---

--

-

Plasma Electron and Ion Currents

EB Current

Secondary Electron Emission

++++

++

The potential achieved satisfiesX

i

Ii(�) = 0

Abstract # 133

semi-major axis of 200-300 km. Assuming a circular deputyorbit, the semi-major axis increase in the deputy orbit overone day is[7]

�a ⇡ 4⇡

n2

Fc

mD

, (12)

where n is the mean motion of the deputy orbit and mD

thedeputy mass. A GEO orbit radius of 42,164 km is assumedfor this analysis. The deputy mass is required to computethe semi-major axis change. Considering publicly availabledata on GEO satellites, [18] provides a relationship betweenspacecraft mass and an approximate sphere radius. The simplelinear expression

rD

(mD

) = 1.152 m + 0.00066350mkg

mD

(13)

provides a deputy radius for use in the charging model. Whilecertainly not perfect, this linear relationship does capture thegeneral trend of increased mass for larger objects and is basedon actual data for GEO objects.

III. IMPACT OF GEOMAGNETIC STORM EVENTS ONTRACTOR PERFORMANCE

In [27] electrostatic tractor performance is analyzed forquiet (k

p

= 1.5) geomagnetic storm conditions. Here theeffects of geomagnetic storm events are considered. When ageomagnetic storm occurs, the population of lower energy ions(1-100 eV) in the period following local midnight is lost, witha higher energy population of slightly lower density (1 cm�3)remaining.[24], [34] Solar storm events also provide a higherenergy population of electrons, with energies as high as a fewtens of keV. This phenomenon was experienced by the ATS-5satellite and recorded in GEO space weather measurementstaken by the magnetospheric plasma analyzer (MPA) instru-ments flown by Los Alamos National Laboratory.[35] When aspacecraft enters into eclipse during a storm event it may natu-rally charge to potential levels in excess of -10 kV, dependingon the severity of the geomagnetic storm. During storm eventsexperienced by ATS-5, typical potentials achieved in shadowwere 3-4 kV (negative polarity), with lows of 70-100 V andhighs in above 10 kV.[34] Note that a spacecraft experienceseclipse for under an hour each day in the 3-4 weeks beforeand after an equinox. Over an electrostatic tractor reorbitingscenario with a deorbit time of several months, this representsa very small portion of the total operating time. When aspacecraft is in sunlight, the photoelectron current precludesthese very high natural charging levels. ATS-5 observed amaximum potential of -300 V in the sunlight, and reachedpotentials of between -50 and -300 V several times. All ofthese charging events occurred during periods of very highsolar activity, and occurred between local midnight and dawn.The SCATHA satellite was also used to study natural chargingin sunlight, and recorded potentials as high as -740 V.[36]Charging events in excess of -100 V only occurred for k

p

indices of 2 or greater.The NOAA space weather scale classifies the severity and

frequency of geomagnetic storms, with a scale ranging from

TABLE IPLASMA PARAMETERS USED FOR GEOMAGNETIC STORM ANALYSIS

Storm Level ne (cm�3) Te (keV) ni (cm�3) Ti (keV)Moderate (kp = 6) 1 4.7 1 15Severe (kp = 8� 9) 1 20 1 20Quiet (kp = 1.5) 0.925 2.64 3.05 0.05

G-1 (minor, kp

= 5) to G-5 (extreme, kp

= 9).[26] Inan 11 year solar cycle, minor storm activity is expectedfor roughly 900 days, with extreme storm events occurringmuch less frequently, only about 4 times. For the analysisof storm activity, two storm conditions are considered: amoderate geomagnetic storm, G-2 on the NOAA scale, withk

p

= 6 and a worst-case severe storm event. Only the effectson the charge transfer process are considered. Severe solaractivity can be harmful to spacecraft subsystems, causingelectrical failures and differential charge driven arcing events,but consideration of these phenomena is beyond the scope ofthe current work. For the moderate storm condition (k

p

= 6),data from [24] are used to determine plasma temperatures anddensities. The data are taken at a local time of 3:00, whichcorresponds to the post-midnight period where high naturalcharging is observed. For the severe storm condition, theplasma parameters corresponding to a severe storm in [37] areused. The ion and electron densities for both storm conditionsare presented in Table I, along with the quiet (k

p

= 1.5)conditions computed for 3:00 local time using the data in [24].

To determine the effects of these storm conditions, the tugand deputy potentials are computed as a function of electronbeam current, for E

EB

= 40 keV, rT

= 2 m, and rD

= 0.935m. The electrostatic force is also computed, assuming a sep-aration distance of 12.5 m. The potentials and forces are alsocomputed for the quiet solar conditions (k

p

= 1.5) to serve asa baseline for comparison. For the moderate solar storm event(k

p

= 6), the results are illustrated in Figure 6. Also shownare potentials computed using the quiet conditions. The stormconditions result in the tug charging to higher potentials fora given electron beam current. For the deputy, the maximumpotential occurs at a lower beam current level, and the potentialdecreases at a faster rate as the beam current is increased.The tug reaches its maximum potential (q�

T

= EEB

) at alower current level than for quiet space weather conditions.Considering the electrostatic forces that result, a slightly highermaximum force occurs for the storm condition and it occursat a lower beam current level. The potentials and forces arealso computed for the severe storm conditions, and are shownin Figure 7. The same effects are observed that are seen formoderate storm conditions, but to a higher degree. The tugpotential increases more rapidly as beam current is increased,and the deputy potential decreases in a similar fashion. Forthe severe storm condition, the tug reaches its maximumpotential for a beam current of about 575 µA, while in themoderate storm condition the tug potential is at its maximumfor a beam current of almost 900 µA. As the storm severityincreases, less current is required to maximally charge thetug. Looking at the electrostatic forces for the severe storm

5




Solar Storm Impact on E-Tractor

9

Abstract # 133

�T

= 20 kV�D

= 0 kV

�D

= �10 kV �T

= 10 kV �T

= 20 kV�D

= �20 kV

✓ = 20� ✓ = 20�

450 500 550 600 650 700-10

0

10

20

30

It HmAL

fHkVL

450 500 550 600 650 7000.0

0.2

0.4

0.6

0.8

1.0

It HmAL

F cHmNL

�T

�D

No Back-Flux

No Back-Flux


TugDeputy

- -

- -- -

- ---

-- +-

+

+++

++

- -

--

--



�T

�D

kp

= 1.5

k p

=6

kp

= 6

200 400 600 8000.00.10.20.30.40.50.60.7

It HmAL

F cHmNL

kp = 1.5

200 400 600 800-40

-20

0

20

40

It HmAL

fHkVL

kp

= 1.5

250 300 350 400 450 500 550 600-60

-40

-20

0

20

40

60

It HmAL

fHkVL


�D

�T

250 300 350 400 450 500 550 6000.00.10.20.30.40.50.60.7

It HmAL

F cHmNL


kp

= 1.5

(a) Potentials

�T

= 20 kV�D

= 0 kV

�D

= �10 kV �T

= 10 kV �T

= 20 kV�D

= �20 kV

✓ = 20� ✓ = 20�

450 500 550 600 650 700-10

0

10

20

30

It HmAL

fHkVL

450 500 550 600 650 7000.0

0.2

0.4

0.6

0.8

1.0

It HmAL

F cHmNL

�T

�D

No Back-Flux

No Back-Flux


TugDeputy

- -

- -- -

- ---

-- +-

+

+++

++

- -

--

--



�T

�D

kp

= 1.5

k p

=6

kp

= 6

200 400 600 8000.00.10.20.30.40.50.60.7

It HmAL

F cHmNL

kp = 1.5

200 400 600 800-40

-20

0

20

40

It HmAL

fHkVL

kp

= 1.5

250 300 350 400 450 500 550 600-60

-40

-20

0

20

40

60

It HmAL

fHkVL


�D

�T

250 300 350 400 450 500 550 6000.00.10.20.30.40.50.60.7

It HmAL

F cHmNL


kp

= 1.5

(b) E-Force

Fig. 6. a) Potentials and b) electrostatic force as a function of electronbeam current for moderate solar storm event (solid) and quiet solar conditions(dashed). Results assume rT = 2 m, rD = 0.935 m, and EEB = 40 keV.

condition, the maximum is once again slightly above that ofthe quiet condition, but occurs at much less current.

Clearly, geomagnetic storm events do not prevent chargetransfer for the electrostatic tractor. In fact, they are actuallysomewhat helpful. A slightly higher electrostatic force is pos-sible, and less current is required to achieve it. Current modi-fication is required to compensate for the onset of these stormevents, however. When considering the nominal GEO spaceweather conditions for quiet periods of activity, the maximumelectrostatic force occurs for a beam current of nearly 600µA. If a severe solar storm event occurs and the beam currentis not modified to compensate, Figure 7 shows that the tugwill reach its maximum potential (q�

T

= EEB

), preventingcharge transfer and significantly impacting performance. Thus,to account for solar storm events the beam current shouldbe controllable, which is likely to be the case anyway. Theanalysis of solar storm events on tractor performance revealsthat the worst-case scenario from a performance perspective isactually the nominal, quiet space weather conditions. For thisreason, quiet storm conditions are assumed for further studies.

IV. TUG ELECTRON BACK-FLUX

Two deputy current sources are due to emission of electronsfrom the deputy surface: photoelectron and secondary electronemission. Because the deputy is charged negatively, these elec-

�T

= 20 kV�D

= 0 kV

�D

= �10 kV �T

= 10 kV �T

= 20 kV�D

= �20 kV

✓ = 20� ✓ = 20�

450 500 550 600 650 700-10

0

10

20

30

It HmAL

fHkVL

450 500 550 600 650 7000.0

0.2

0.4

0.6

0.8

1.0

It HmAL

F cHmNL

�T

�D

No Back-Flux

No Back-Flux


TugDeputy

- -

- -- -

- ---

-- +-

+

+++

++

- -

--

--



�T

�D

kp

= 1.5

k p

=6

kp

= 6

200 400 600 8000.00.10.20.30.40.50.60.7

It HmAL

F cHmNL

kp = 1.5

200 400 600 800-40

-20

0

20

40

It HmAL

fHkVL

kp

= 1.5

250 300 350 400 450 500 550 600-60

-40

-20

0

20

40

60

It HmAL

fHkVL


�D

�T

250 300 350 400 450 500 550 6000.00.10.20.30.40.50.60.7

It HmAL

F cHmNL


kp

= 1.5

(a) Potentials

�T

= 20 kV�D

= 0 kV

�D

= �10 kV �T

= 10 kV �T

= 20 kV�D

= �20 kV

✓ = 20� ✓ = 20�

450 500 550 600 650 700-10

0

10

20

30

It HmAL

fHkVL

450 500 550 600 650 7000.0

0.2

0.4

0.6

0.8

1.0

It HmAL

F cHmNL

�T

�D

No Back-Flux

No Back-Flux


TugDeputy

- -

- -- -

- ---

-- +-

+

+++

++

- -

--

--



�T

�D

kp

= 1.5

k p

=6

kp

= 6

200 400 600 8000.00.10.20.30.40.50.60.7

It HmAL

F cHmNL

kp = 1.5

200 400 600 800-40

-20

0

20

40

It HmAL

fHkVL

kp

= 1.5

250 300 350 400 450 500 550 600-60

-40

-20

0

20

40

60

It HmAL

fHkVL


�D

�T

250 300 350 400 450 500 550 6000.00.10.20.30.40.50.60.7

It HmAL

F cHmNL


kp

= 1.5

(b) E-Force

Fig. 7. a) Potentials and b) electrostatic force as a function of electronbeam current for severe solar storm event (solid) and quiet solar conditions(dashed). Results assume rT = 2 m, rD = 0.935 m, and EEB = 40 keV.

�T

= 20 kV�D

= 0 kV

�D

= �10 kV �T

= 10 kV �T

= 20 kV�D

= �20 kV

✓ = 20� ✓ = 20�

450 500 550 600 650 700-10

0

10

20

30

It HmAL

fHkVL

450 500 550 600 650 7000.0

0.2

0.4

0.6

0.8

1.0

It HmAL

F cHmNL

�T

�D

No Back-Flux

No Back-Flux


TugDeputy

- -

- -- -

- ---

-- +-

+

+++

++

- -

--

--



Fig. 8. Electron back-flux from the deputy to the tug.

trons are lost. The nearby tug, however, recaptures a portion ofthese emitted electrons, as depicted in Figure 8, owing to highpositive potential. This serves as an additional current sourceon the deputy object which will impact its charging. Thus, it isimportant to study this effect, and obtain a rough estimate forhow significantly these current sources affect tug charging. Thescope of this analysis is not meant to be comprehensive, butrather to provide some insight into how much this back-fluxmight affect electrostatic tractor performance. A two meter

6

40keV Electron Gun rT=2 m, rD=0.935 m

12m separation

Mod

erat

e So

lar S

torm

Seve

re S

olar

Sto

rm

40keV Electron Gun rT=2 m, rD=0.935 m

12m separation




Electron Back-Flux

10

�T = 20 kV�D = 0 kV

�D = �10 kV �T = 10 kV �T = 20 kV�D = �20 kV

✓ = 20� ✓ = 20�

450 500 550 600 650 700-10

0

10

20

30

It HmALfHkVL

450 500 550 600 650 7000.0

0.2

0.4

0.6

0.8

1.0

It HmAL

F cHmNL

�T

�D

No Back-Flux

No Back-Flux

With Back-Flux

With Back-Flux

TugDeputy

- -

- -- -

- ---

-- +-

+

+++

++

- -

--

--


Recaptured photo- and

secondary electrons

�T = 20 kV�D = 0 kV

�D = �10 kV �T = 10 kV �T = 20 kV�D = �20 kV

✓ = 20� ✓ = 20�

450 500 550 600 650 700-10

0

10

20

30

It HmAL

fHkVL

450 500 550 600 650 7000.0

0.2

0.4

0.6

0.8

1.0

It HmAL

F cHmNL

�T

�D

No Back-Flux

No Back-Flux

With Back-Flux

With Back-Flux

NASCAP-2K Simulation

�T = 20 kV�D = 0 kV

�D = �10 kV �T = 10 kV �T = 20 kV�D = �20 kV

✓ = 20� ✓ = 20�

450 500 550 600 650 700-10

0

10

20

30

It HmAL

fHkVL

450 500 550 600 650 7000.0

0.2

0.4

0.6

0.8

1.0

It HmAL

F cHmNL

�T

�D

No Back-Flux

No Back-Flux

With Back-Flux

With Back-Flux

�T = 20 kV�D = 0 kV

�D = �10 kV �T = 10 kV �T = 20 kV�D = �20 kV

✓ = 20� ✓ = 20�

450 500 550 600 650 700-10

0

10

20

30

It HmAL

fHkVL

450 500 550 600 650 7000.0

0.2

0.4

0.6

0.8

1.0

It HmAL

F cHmNL

�T

�D

No Back-Flux

No Back-Flux

With Back-Flux

With Back-Flux




Electron/Ion Emission

11

0 2 4 6 8 10

0.6

0.8

1.0

1.2

1.4

1.6

Ib HmAL

MaxF cHmNL

0 2 4 6 8 100.3

0.4

0.5

0.6

0.7

0.8

Ib HmALIdealDI BHmAL

Maximum Achievable E-Tractor Force assuming nominal GEO space weather

Difference in Electron and Ion Beam Currents to achieve Negative Debris

and Positive Tug Potentials

40keV Electron Gun rT=2 m, rD=2 m 12m separation




Best-Case Performance

12

0th-O

rder

Spher

eR

adiu

s[m

]

GEO Space Object Mass [kg]

1000 2000 3000 4000 5000 6000

2

3

4

5

6nominal trend

Figure 7. Illustration of the nominal size to mass trend of Geosynchronous RSOs

Using a public NASA web site⇤ discussing geostationary satellite data, the approximate massand satellite dimensions were obtained. Figure 7 illustrates the resulting mass to 0th-order effectiveradius for a range of GEO Resident Space Objects (RSO). This data yields a mean mass to radiusrelationship of

r2(m2) = 1.152m + 0.00066350mkg

m2 (16)

where r2 is in units of meters, and m2 is in units of kilograms. Please note that this relationship ofthe NASA site provides the launch masses of each satellite. Thus, Eq. (16) illustrates the worst casemass to area ratio you could have. For many older geostationary satellite designs, the fuel stored fororbit corrections is a significant fraction of the total mass. Thus, if a satellite is moved which hasexpelled its fuel, its mass could be considerably smaller while maintaining the same surface area(capacitance).

SMA Changes With Initial Launch Mass: First, let us consider what SMA changes are feasibleper geosynchronous orbit (24 hours) using the �a approximation in Eq. (15) and the GEO RSOmean mass to radius relationship in Eq. (16). The Coulomb craft with inertial thrusters is ahead ofthe towed Coulomb vehicle in a pulling configuration.

Figure 8 sweeps the towed mass from 500-5000kg, and the voltages from 0-40kV. This studyassumes V1 = �V2. Four scenarios are shown where with the center-to-center separation distances25, 20, 15, and 10 meters. Given the larger outer dimensions of many GEO satellites, separationdistances shorter than 10 meters result in significant collision risks. The Coulomb vehicle withinertial thruster is assumed to have a radius of 3 meters for all these numerical sweeps.

The ATS-6 mission has shown that natural charging during solar storm activities can reach 18kV.Thus, achieving potential levels of 20kV and larger are feasible. Furthger, if the towed object hasa mass of 1000kg, a separation distance of 20 meters, then a 20kV potential would result in SMAchanges of about 2 km/day. A 10km correction could be accomplished using a low-thrust spiralingtrajectory over only 5 days. If a larger object of 2000kg mass is considered, the SMA changesreduce to about 1.5 km/day. Note that the SMA change performance does not scale with the massof the towed object because larger objects also act as larger capacitors.

⇤http://nssdc.gsfc.nasa.gov/nmc/SpacecraftQuery.jsp

10

0.2

0.6

11.2

1.622.4

2.83.2

3.6

45

6

500 1000 1500 2000 2500 3000 3500 4000400

600

800

1000

1200

1400

1600

Deputy Mass HkgL

Beam

CurrentHm

AL

Charge Transfer

No Charge

Transfer

0.2

0.6

11.2

1.622.4

2.83.2

3.6

45

6

500 1000 1500 2000 2500 3000 3500 4000400

600

800

1000

1200

1400

1600

Deputy Mass HkgL

Beam

CurrentHm

AL

20 30 40 50 60 700

1000

2000

3000

4000

EEB HkVL

MaxTowableMassHkgL

rT= 1 m

rT=2m

r T=3m

0.5 1.0 1.5 2.0 2.5 3.0

4

6

8

10

12

rD HmL

E EBHkVL

rT = 1 m

rT = 2 m

rT = 3 m

EEB = 20 kV

EEB= 40 kV

EEB= 60

kV

dA=2.5,1 km:20 30 40 50 60 700

1000

2000

3000

4000

EEB HkVL

MaxTowableMassHkgL

rT=1 mr T

=2m

r T=

3m

0.5 1.0 1.5 2.0 2.5 3.00

10

20

30

40

rD HmL

I crHmAL

500 1000 1500 2000 2500 3000 3500 400012345678

Deputy Mass HkgL

DaHkmêdayL

rT = 1 m

rT = 2 m

rT = 3 m

0.2

0.6

11.2

1.622.4

2.83.2

3.6

45

6

500 1000 1500 2000 2500 3000 3500 4000400

600

800

1000

1200

1400

1600

Deputy Mass HkgL

BeamCurrentHmAL

Charge Transfer

No Charge

Transfer

0.2

0.6

11.2

1.622.4

2.83.2

3.6

45

6

500 1000 1500 2000 2500 3000 3500 4000400

600

800

1000

1200

1400

1600

Deputy Mass HkgL

BeamCurrentHmAL

1 2 3 4 5 6 70.9

1.0

1.1

1.2

1.3

1.4

1.5

Ib HmAL

MaxF cHmNL

1 2 3 4 5 6 70.0

0.1

0.2

0.3

0.4

0.5

0.6

Ib HmAL

IdealDI BHmAL

20 30 40 50 60 700

1000

2000

3000

4000

EEB HkVL

MaxTowableMassHkgL

rT= 1 m

rT=2m

r T=3m

500 1000 1500 2000 2500 3000 3500 40000

5

10

15

20

Deputy Mass HkgL

I crHmAL

EEB = 20 kV

EEB = 40 kV

EEB= 60 kV

0.5 1.0 1.5 2.0 2.5 3.0

4

6

8

10

12

rD HmL

E EBHkVL

rT = 1 m

rT = 2 m

rT = 3 m

0.5 1.0 1.5 2.0 2.5 3.00

5

10

15

rD HmL

I crHmAL

EEB = 20 kV

EEB= 40 kV

EEB= 60

kV

dA=2.5,1 km:20 30 40 50 60 700

1000

2000

3000

4000

EEB HkVL

MaxTowableMassHkgL

rT=1 mr T

=2m

r T=

3m




Conclusions

• Solar storm events facilitate tug charging, require a lower e-beam current to get maximum force

• Use of nominal, constant current emission can lead to significantly lower E-Force levels during storms

• Electron back-flux can lead to slightly larger E-forces, but the benefit is minimal

• Ion emission can improve E-forces, particular for smaller tug vehicles

13

Electron beam emission onto deputy Low-thrust used to tow

deputy

Electrostatic force results from craft charges

++

+

++ +

+

+

+

++

--

---

------

---


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