Modelacion Electroestatica de Polvo Lunar

8/17/2019 Modelacion Electroestatica de Polvo Lunar

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IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 36, NO. 5, OCTOBER 2008 2459

Modeling Electrostatic Levitation of Dust Particles on Lunar Surface

Joseph Wang, Xiaoming He, and Yong Cao

Abstract—This paper presents a simulation model on electro-static levitation of lunar dust particles in the lunar terminatorregion. Full-particle particle-in-cell simulations are carried outusing real ion to electron mass ratio to obtain plasma sheath,surface charging, and the transition point of surface electric field.Test particle simulations are carried out to simulate the levitationof dust particles from lunar surface. Results show that the dust lev-itation condition in the terminator region is sensitively influencedby the ambient plasma condition and surface charging, and thelevitation altitude varies significantly even for small changes of thesun elevation angle.

Index Terms—Electrostatic levitation of dust particles, full-

particle particle-in-cell (PIC), lunar dust charging, lunar surfacecharging.

I. INTRODUCTION

DUST CLOUDS suspended above the lunar surface were

first observed as horizon glow by the Surveyor spacecrafts

[1] and later by the Apollo astronauts [2]. Dust “storms”

were observed by the Lunar Ejecta and Meteorite experiment

deployed during the Apollo 17 mission [3]. Dust “streamers”

reaching from tens to hundreds of kilometers above the lunar

surface were also observed by Apollo 17 astronauts from the

lunar orbit [4]. It is well documented that lunar dust can cause

significant problems for spacecraft and/or astronauts on extra-vehicular activities, ranging from vision obscuration, false

instrument reading, clogging of equipment, seal failures, con-

tamination of surface leading to thermal control problems, and

abrasion of space suits to breathing problems and potential

long-term respiratory problems for astronauts on the moon [2].

The dust environment near lunar surface is determined by

the dynamic processes that levitate and transport dust particles.

While micrometeoroid impacts and/or disturbances by human

activities can also contribute to the liftoff of dust grains from

the lunar surface, electrostatic levitation is generally accepted

as the primary mechanism (see, for example, [5]–[8] and

references therein). The lunar surface is electrically charged

due to the impingement of the ambient plasma, the emission

of photoelectrons under sunlight and secondary electrons, and

the collection of backscattered electrons. For lunar surface

Manuscript received February 9, 2008; revised June 23, 2008. First publishedOctober 31, 2008; current version published November 14, 2008. This work was supported in part by the Jet Propulsion Laboratory (JPL) and in partby NASA Marshall Space Flight Center (MSFC). The work of X. He wassupported in part by an NSF Grant DMS-0713763.

J. Wang and X. He are with Virginia Polytechnic Institute and State Univer-sity, Blacksburg, VA 24061-0203 USA (e-mail: [email protected]).

Y. Cao is with Harbin Institute of Technology, Harbin 150001, China.Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TPS.2008.2003016

material, the contributions of the secondary and backscattered

currents to surface charging are much less than that from the

ambient plasma and photoelectron currents [9], [10]. Hence, the

local surface potential Φs is determined by the following localzero net current condition:

I sw,i(Φs)− I sw,e(Φs)− I pe(Φs) = 0 (1)

where I sw,i, I sw,e, and I pe are the ambient ion current andelectron current, and the photoelectron current emitted by lunar

surface, respectively. A dust particle resting on the charged

lunar surface can also become charged by several mechanisms,such as induced charging due to surface electric field, charging

by contact potential difference, triboelectrification, and charg-

ing by ambient plasma and photoelectron emission. Dust grains

will be levitated if the dust and surface are like-charged and

the repulsive electrostatic force between dust and surface is

sufficiently large to overcome the gravitational force F g and thesurface adhesive force F c on the dust grain

QdE s ≥ F g + F c (2)

where Qd is the dust charge and E s is the local surface electricfield.

This paper presents a modeling study of electrostatic levita-tion of dust particles initially resting on lunar surface. As the

day-side region near the lunar terminator is currently consid-

ered a potential area to establish lunar landing sites and lunar

outposts, the results presented in this paper will specifically

focus on dust levitation in that region.

Electrostatic levitation of dust particles is closely related to

the problem of lunar surface charging, as the electric field and

the plasma sheath near lunar surface largely determine whether

electrostatic levitation would occur and how high the dust

particle would be elevated. The condition for electrostatic dust

levitation (2) is expected to be particularly sensitive to surface

charging in the day-side region near the lunar terminator wherethe transition from sunlight-driven positive surface potential

to the plasma-charged negative surface potential occurs. The

transition from photoelectron sheath to plasma sheath and the

ambient plasma flow will result in a complicated electric field

near the lunar surface, which may vary significantly even for

small changes in the sun elevation angle. Hence, an accurate

solution of the electric field and sheath near the surface is

critical in determining the dust levitation condition.

Several modeling studies have considered lunar surface

charging [11] and electrostatic levitation of dust particles on the

moon and on asteroids [12]–[16]. All of these studies applied

the standard analytical charging calculation [17], where the

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2460 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 36, NO. 5, OCTOBER 2008

Fig. 1. Model setup.

charging currents I sw,i, I sw,e, and I ph are expressed as analyti-cal functions of Φs by assuming that the ambient electrons andions, and the photoelectrons remain in Maxwellian distribution

near the surface, and so, the lunar surface potential Φs can be

solved directly from (1). The limitations of such an analyticalapproach are well known. For instance, this approach is typ-

ically not sufficient for solving plasma interactions involving

high-voltage surface, current-emitting surface, or high-speed

plasma flow. The analytical approach also cannot be easily

extended to more realistic problems with complex boundary

conditions.

In this paper, a full-particle particle-in-cell (PIC) simula-

tion model is developed for lunar surface charging. In this

model, all plasma species (ambient proton and electron, and

photoelectron) are modeled as macroparticles. PIC simulations

are carried out using the correct ion to electron mass ratio to

preserve the correct mesothermal velocity ratio in plasma flow.The electric field, space charge, charged particle trajectories,

and lunar surface charging are solved self-consistently. The

electric field obtained from full-particle PIC simulation is then

used in a test particle model for dust grains to study dust

levitation. Section II discusses the problem setup and the sim-

ulation models for lunar surface charging and dust levitation.

Section III presents simulation results. Section IV contains a

summary and conclusions.

II. FORMULATION AND A PPROACH

The problem setup is shown in Fig. 1. We consider lunar dust

particles initially at rest on lunar surface under typical solarwind plasma conditions. The solar wind plasma impinges the

lunar surface at a small sun elevation angle α with respect tothe surface. The sunlight direction is taken to be the same as

the solar wind flow direction. This problem is simulated using

a two-step approach. First, a full-particle PIC code is applied

to solve the plasma sheath and lunar surface charging. Second,

a test particle model is applied to simulate single dust particle

dynamics. This section discusses the interaction characteristics

and the simulation models.

A. Modeling Lunar Surface Charging

We first consider the plasma interaction between lunar sur-face and the solar wind. The solar wind is a tenuous relatively

hot plasma which flows radially outward from the sun. Its

parameters may undergo substantial variation, but the mean

observed values of plasma parameters which are relevant to this

study at 1 AU are as follows [18]: solar wind flux nswV sw 3.8× 108/cm2 · s1, solar wind density nsw 8.7 cm

−3, solar

wind flow speed V sw 468 km/s, solar wind ion temperature

T i 10 eV, solar wind electron temperature T e 12 eV, andsolar wind magnetic field magnitude Bo 6.2 nT. From theseparameters, we find that the plasma flow on lunar surface is

mesothermal, vti V sw vte, where vti and vte are the solarwind ion and electron thermal velocity, respectively. The effect

of the magnetic field on solar wind flow may be ignored for

modeling local charging problem because the gyro-radius of

both the ions and electrons is larger than the typical scale length

considered here.

For lunar surface under sunlight, the number density of the

emitted photoelectrons at lunar surface can be estimated from

[14] npe0 = 2I ph0 sin(α)/(evt,pe), where I ph0 4.5 µA/m2

is the photoelectron emission current at lunar surface [10]

and vt,pe is the photoelectron thermal velocity. The averagephotoelectron temperature is T ph 2.2 eV [10]. Assuming aMaxwellian distribution for photoelectrons, the number density

associated with the photoelectrons emitted at lunar surface is

npe0 64 sin(α)/cm3. (3)

Hence, the Debye length associated with the emitted photoelec-

tron is λD,ph 1.37/

sin(α) m. As the sun elevation angle αdecreases, the plasma sheath transitions from the photoelectron

sheath to that dominated by the solar wind plasma when the

Debye length associated with the emitted photoelectrons be-

comes larger than the solar wind Debye length λD,sw. Underthe mean solar wind density, λD,sw 8.7 m, and thus, λD,ph >λD,sw for α


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WANG et al.: MODELING ELECTROSTATIC LEVITATION OF DUST PARTICLES ON LUNAR SURFACE 2461

TABLE ITYPICAL SOLAR WIN D CONDITIONS

the lunar surface at each PIC step as a one-sided stationaryMaxwellian distribution. As the lunar soil is a dielectric ma-

terial, when an ion or electron impinges the lunar surface, its

charge is deposited to the surface at the impact location. When

a photoelectron is emitted from the lunar surface, a positive

charge corresponding to the photoelectron is also deposited to

the surface.

The electric field is solved self-consistently with the space

charge of the particles from the Poisson’s equation

∇ · (0∇Φ) = −e(ni − ne − nph) (4)

where ni, ne, and nph are the number densities of solar windion, solar electron, and photoelectron, respectively, and aredetermined from particle trajectories. The trajectory of each

charged particle is determined from the self-consistent electric

field and the Newton’s second law

d

dt(mv) = F = q E, v =

dx

dt . (5)

The potential of the lunar surface Φs is updated at each PIC stepfrom the charge deposited at lunar surface ρs

∇ · (d∇Φs) = −ρs (6)

where d is the dielectric constant of the lunar soil. The linearsystem from the finite-difference implementation of (4) and (6)

is solved using the preconditioned conjugate gradient method.

When the PIC cycle reaches the steady state, the lunar surface

potential calculated from (6) and the collection calculated from

macroparticle deposition satisfy the local current balance con-

dition (1).

B. Modeling Dust Particle Levitation

We next consider the levitation of dust grains which are

initially at rest on the lunar surface. The dust grains are assumed

to be spherical particle with radius rd, and the dust mass densityis taken to be the same as that of the lunar soil ρd 2.65 g/cm

3.

A test particle model is developed to simulate dust dynamics

using Newton’s second law

F = M ddv

dt = QdE−M dg (7)

where M d and Qd are the dust charge and mass, respectively,and g = 1.67 m/s2 is the gravitation constant of the moon.The simulation domain and mesh are the same as that of

the PIC model for lunar surface charging. The electric field

E is obtained from the output of the PIC simulation and is

interpolated to the dust position from the PIC mesh points usingthe same PIC interpolation scheme. Note that this approach is

valid only for the dust-in-plasma condition, where a dust grainis mostly isolated from its neighboring dust grains because

the effects from charged dust particles on the sheath and the

coupling between charged dust particles are not included. As

the PIC simulation domain is taken to be sufficiently large to

contain the plasma sheath, E 0 in the region outside of thedomain boundary. Hence, when a dust particle moves out of the

PIC simulation domain boundary, subsequent dust dynamics is

calculated analytically from dv/dt = −g.Various charging mechanisms, such as induced charging by

surface electric field, charging by contact potential difference,

and charging by ambient plasma and photoelectron emission,

will contribute to the charging of a dust grain on lunar surface.

No theoretical or empirical models currently exist that can be

directly applied to model all of these charging mechanisms. For

instance, existing models of induced charging due to electric

field and charging due to contact potential difference only apply

to metallic particle resting upon a metal surface. The commonly

used plasma charging model for a single dust grain based on

the orbital motion limited (OML) theory for spherical probe is

also not directly applicable for a dust-on-surface or for closely

packed dusts. Many laboratory experiments have been carried

out to study the charging properties of lunar dust simulant

[5]–[9]. However, existing data are mostly for relative large-

size dust grains with rd in the range of 10−102 µm. The

development of a charging model for dust-on-surface which canaccount for all the charging mechanisms leading to the initial

charging is clearly beyond the scope of this paper.

Regardless of the detailed initial charging process for a

dust-on-surface, electrostatic levitation will occur once a dust

particle has accumulated sufficient charge to satisfy the dust

levitation condition [see (2)]. For simplicity, we shall ignore the

surface adhesive force F c. Hence, the dust charge that satisfies(2) is given by

Qd ≥ Qd,min = M dg

E s(8)

where E s is the electric field on lunar surface. Note that Qd,mindiffers for different sun elevation angles and different solarwind conditions.

In this paper, we shall consider two simplified models for

dust charging. As dust levitation will occur as soon as a dust

has accumulated sufficient charge such that the electrostatic

force balances the gravitational force, the first model assumes

that the initial charge for a dust-on-surface is given by Qd,minin (8). Hence, in the first model, the initial dust charge Qd ismodeled as

Qd = (1 + δ )Qd,min = (1 + δ )M dg

E s(9)

where δ 1 provides the initial dust acceleration. As a dustgrain in contact with the lunar surface will most likely have the


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same potential as the lunar surface, the second model assumes

that the dust grain is completely charged and the dust grain

potential Φd is the same as the local lunar surface potential,Φd = Φs. Such an assumption is also used in [16]. Hence, inthe second model, the initial dust charge is given by

Qd = C Φd = 4πordΦs. (10)

Both of these models will be applied in dust levitation simula-

tions in the next section. Once a dust is levitated from the sur-

face, subsequent dust charging may be calculated from current

collection by dust. A commonly used approach is to assume

single dust grain charging and that the current collection by dust

can be calculated by the OML theory. We found that the single

dust grain charging model does not change the dust charge sig-

nificantly during the initial dust levitation process, and hence,

we shall ignore the changes on dust charge in this paper.

III. RESULTS AND D ISCUSSIONS

A. Plasma Sheath and Lunar Surface Charging

This section presents PIC simulations of lunar surface charg-

ing under typical solar wind conditions. The solar wind plasma

parameters used in the simulation, shown in Table I, are taken

from the range of the observed values listed in [18]. In Table I,

the first set parameters are the mean observed values of the solar

wind parameters in [18] and will be referred to as the “mean

flux density” condition. For comparison, in the second set, both

the solar wind flux density and number density are taken to be

at the 5% range of the observed values in [18]. The second set

will be referred to as the “5% flux density” condition. Modest

variations in these parameters should not lead to qualitativechanges in lunar surface charging.

Full-particle PIC simulations were performed for sun eleva-

tion angles in the range of 0◦ ≤ α ≤ 10◦. The simulation isrun until the lunar surface potential reaches the steady state.

In order to resolve the plasma sheath correctly, the cell size

needs to be sufficiently small so the Debye length associated

with the higher density photoelectrons near the lunar surface

can be resolved and the domain size needs to be sufficiently

large so the plasma at the simulation boundary representing

the infinity is undisturbed. We choose the cell size to be the

same as the photoelectron Debye length at the subsolar point,

λD,ph(90

◦

)

1.37 m. Note that the cell size is significantlysmaller than the photoelectron Debye length for small sun ele-vation angles. The domain size is determined through test runs

to ensure that the results are not affected by domain boundary.

In order to preserve the correct mesothermal velocity ratio in

the solar wind plasma flow, PIC simulations were carried out

using the real proton to electron mass ratio (mi/me = 1836).Simulations were performed typically using ∼100 particles/cell

for each species, and the total number of macroparticles is about

6–7 million. For the results presented here, each simulation run

typically requires about 20–36 CPU hours on a desktop PC with

dual AMD Opteron 2.4-GHz processor.

For the problem setup shown in Fig. 1, where we consider a

solar wind plasma flow at a fixed α, the potential and plasmadensity vary only along the z-direction. Fig. 2 shows the poten-

Fig. 2. Potential profile versus distance from lunar surface. (a) Mean flux solarwind condition. (b) 5% flux solar wind condition.

tial profiles versus z for α = 0◦, 5◦, and 10◦, respectively. Wenote the qualitative difference in the potential profile between

the “mean flux density” and the “5% flux density” cases on

the α = 5◦ and α = 10◦ curves. A nonmonotonic potentialprofile develops when the excessive charge from photoelectron

emissions cannot be neutralized sufficiently by the ambient

solar wind plasma. Due to their low energy, some of the

photoelectrons emitted are reflected back to the lunar surface

by the nonmonotonic potential profile. Fig. 3 shows the steady-

state velocity phase space plot (vz versus z) for all the threespecies. The reflection of photoelectrons by the nonmonotonicpotential profile near the lunar surface (z ∼ 0), as shown bythe “red” particles with negative vz , is evident in the phasespace plot for the “5% flux density” case. Fig. 4 shows the lunar

surface potential Φs obtained from simulation as a function of the sun elevation angle α for both the “mean flux density” andthe “5% flux density” conditions. Table II further shows the

values of Φs and the surface electric field, E s = E z(z = 0).The location on lunar surface where the surface electric field

E s = 0, or the “transition” point, is of special interest to dustlevitation. As E s switches its direction across the transitionpoint, only positively charged dust particles satisfy the dust lev-

itation condition (8) on one side and negatively charged dustssatisfy (8) on the other side. Moreover, only those dusts with a


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Fig. 3. Phasevelocity plot for photoelectrons (darkgray), solar wind electrons(black), and solar wind protons (light gray). Sun elevation angle: 5◦. (a) Meanflux solar wind condition. (b) 5% flux solar wind condition.

Fig. 4. Lunar surface potential versus sun elevation angle.

very large Qd can satisfy (8) near the transition point becauseE s ∼ 0. Under the “mean flux density” condition, we find that

the direction of E s switches from −z to +z near α ∼ 10◦ whilethe surface potential Φs remains negative. Under the “5% flux

TABLE IISURFACE POTENTIAL AND SURFACE ELECTRIC FIELD

Fig. 5. Electric field profile versus distance from lunar surface for sunelevation angles near the transition point. (a) Mean flux solar wind condition.

(b) 5% flux solar wind condition.

density” condition, the direction of E s switches from −z to +zbetween 2◦ and 4◦ while Φs becomes positive at α ≥ 8◦. Acrossthe transition point from the night side to the day side, the

potential profile also changes from monotonic to nonmonotonic

due to enhanced photoelectron emission. The E (z) profilearound the transition point is compared in Fig. 5. Its implication

on dust levitation will be further discussed in the next section.

B. Dust Levitation

Test particle simulations were performed to simulate the

dynamics of charged dust particles which are initially at reston lunar surface. We first simulate dust levitation using the first


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Fig. 6. Dust levitation height versus time for selected sun elevation angle fordusts with the minimum required charge for elevation. (a) Mean flux solar windcondition. (b) 5% flux solar wind condition.

dust charging model [see (9)]. Under this assumption, the dust

dynamics equation (7) is rewritten as

dvzdt

= d2z

dt2 =

(1 + δ )

E (z)

E s− 1

g. (11)

Fig. 6 shows the orbits of charged dust particles (levitation

height versus time) from the test particle simulations for several

sun elevation angles. It shows that a dust grain with an initial

charge given by (9) will be levitated and remain suspended

above the surface. As the electric field changes significantly

within the sheath, the dust particles oscillate around an equilib-

rium height. In this simulation, we take the dust grain charge

to be Qd = 1.05Qd,min. Table III shows the maximum dustlevitation height as a function of sun elevation angle α. Underthe assumption of (8), the levitated dust trajectory is only

dependent upon the electric field profile and is independent

of dust grain size because Qd is linearly proportional to M d.

Hence, the results shown in Table III and Fig. 6 apply to all sizedust grains.

TABLE IIIDUS T ELEVATION HEIGHT: Qd = 1.05Qd,min

An important conclusion from Fig. 6 and Table III is that thedust levitation height changes drastically around the transition

point where the surface electric field E s ∼ 0. This drasticchange is due to both the surface electric field Es and the

electric field profile E(z). For instance, let us compare dustlevitation heights for α = 0◦, 2◦, and 4◦ under the “5% fluxdensity” condition, which are 2.3, 55, and 0.3 m, respectively.

For α = 0◦ and α = 2◦, E(z) is negative throughout the entiredomain, and only negatively charged dusts satisfy (8). As the

magnitude of E s(2◦) is much smaller than that of E s(0

◦), amuch larger Qd,min is required for levitation at α = 2

◦. This

results in a much larger levitation height at α = 2◦. On theother hand, at α = 4◦, E(z) changes from positive at surfaceto negative at z 4 m above the surface. As only positivelycharged dust particles can satisfy (8), dust acceleration is

confined within the region where E(z) is positive. The drasticchange in elevation height observed around α = 8◦ for the“mean flux density” condition is due to the same reason. Hence,

if dust levitation occurs as soon as dust charge reaches Qd,minin (8), one would observe a drastic increase in dust levitation

height from the terminator to the transition point. The maxi-

mum dust levitation height would occur to negatively charged

dusts on the immediate night side of the transition point.

We next simulate dust levitation using the second dust charg-

ing model [see (10)]. From (8) and (10), only those dusts with

a radius

rd ≤ rd,max =

3oΦsE s

ρdg (12)

can satisfy the necessary condition for levitation. Table IV

shows rd,max as a function of α. For the two solar windconditions considered in this paper, dust levitation would occur

only for submicrometer-sized dusts. Moreover, in order for (12)

to be valid, Φs and E s must have the same sign. From PICsimulation results in Table II, we find that no dust size can

satisfy (12) on the immediate day-side region of the transition

point because Φs is negative and E s is positive.Table IV shows the dust levitation for two dust radii rd =

0.01 µm and rd = 0.1 µm. The dust charge Qd calculated from(10) is also shown. The results show that, for a fixed size dust

particle, the dust levitation height is also sensitively influenced

by the surface electric field. For instance, under the “mean flux

density” condition, the levitation height for an rd = 0.01 µmdust ranges from altitudes of tens of kilometers for α ≤ 2◦ tohundreds of meters at α ∼ 8◦.

IV. SUMMARY AND C ONCLUSION

In summary, a simulation model based on full-particle

PIC simulations of lunar surface charging and test particlesimulations of charged dust particle dynamics is developed


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TABLE IVDUS T ELEVATION HEIGHT: Qd = 4πoΦs

to investigate electrostatic levitation of dust grains on lunar

surface. Full-particle PIC simulations are carried out using the

real ion to electron mass ratio to obtain the plasma sheath and

surface charging self-consistently. The simulations show that,

under typical solar wind conditions, the lunar surface potential

ranges from about Φs ∼ 30 V negative with respect to the ambi-ent at the sun elevation angle α = 0 to near zero or slightly pos-itive at α ∼ 10◦. The transition point, where the surface electricfield E s ∼ 0, does not occur at the same location where Φs ∼ 0.Due to photoelectron emissions, the transition point takes place

closer to the terminator than the location of Φs ∼ 0 does. Thepotential profile above the lunar surface is nonmonotonic on

the day side of the transition point. PIC simulation results are

incorporated into the test particle simulation model to simulate

the levitation of dust grains which are initially at rest on lunar

surface. We find that dust levitation in the terminator region is

sensitively influenced by the ambient plasma and surface charg-

ing condition and varies significantly even for small changes of

the sun elevation angle. For instance, assuming that dust levita-

tion occurs as soon as a dust grain has acquired the minimum

required charge for levitation, the dust levitation height will

increase drastically from the terminator to the transition point.

Negatively charged dust grains will reach the maximum levita-

tion height on the immediate night side of the transition point.

This paper applies two simplified models to calculate charging

for a dust-on-surface. More sophisticated dust charging models

will need to be developed in future studies.

ACKNOWLEDGMENT

The authors would like to thank D. Brinza, H. Garrett, andI. Jun of JPL and also J. Minow and D. Ferguson of NASA

MSFC for the many useful discussions.

REFERENCES

[1] J. Rennilson and D. Criswell, “Surveyor observations of lunar horizon-glow,” Moon, vol. 10, no. 2, pp. 121–142, Jun. 1973.

[2] J. Gaier, “The effects of lunar dust on EVA systems during the Apollomissions,” NASA, John H. Glenn Res. Center, Cleveland, OH, NASATM-2005-213610, 2005.

[3] O. Berg, H. Wolf, and J. Rhee, “Lunar soil movement registered by theApollo 17 cosmic dust experiment,” in Interplanetary Dust and Zodiacal

Light , H. Elsasser and H. Fechtig, Eds. New York: Springer-Verlag,1976, pp. 233–237.

[4] J. McCoy and D. Criswell, “Evidence for a high altitude distribution of lunar dust,” in Proc. 5th Lunar Sci. Conf., Geochim. Cosmochim. Acta,1974, vol. 3, pp. 2991–3005. Suppl. 5.

[5] M. Horanyi, B. Walch, S. Robertson, and D. Alexander, “Electrostaticcharging properties of Apollo 17 lunar dust,” J. Geophys. Res., vol. 103,no. E4, pp. 8575–8580, 1998.

[6] A. Sickafoose, J. Colwell, M. Horanyi, and S. Robertson, “Experimen-tal investigations on photoelectric and triboelectric charging of dust,”

J. Geophys. Res., vol. 106, no. A5, pp. 8343–8356, 2001.[7] A. Sickafoose, J. Colwell, M. Horanyi, and S. Robertson, “Experimental

levitation of dust grains in a plasma sheath,” J. Geophys. Res., vol. 107,no. A11, p. 1408, 2002.

[8] Z. Sternovsky, S. Robertson, A. Sickafoose, J. Colwell, and M. Horanyi,“Contact charging of lunar and martian dust simulants,” J. Geophys. Res.,vol. 107, no. E11, p. 5105, 2002.

[9] M. Abbas, D. Tankosic, P. Craven, R. Hoover, L. Taylor, J. Spann,A. LeClair, and E. West, “Photoelectric emission measurements onApollo 17 lunar dust grains,” in Proc. 37th Lunar Planetary Sci. Conf. ,South Shore Harbor, TX, Mar. 13–17, 2006.

[10] R. Willis, M. Anderegg, B. Feuerbacher, and B. Fitton, “Photoemis-sion and secondary electron emission from lunar surface material,” inPhoton and Particle Interactions with Surfaces in Space, R. Grard, Ed.Dordrecht, The Netherlands: Reidel, 1973, pp. 369–387.

[11] R. Manka, “Plasma and Potential at the Lunar Surface,” in Photon and Particle Interactions with Surfaces in Space, R. Grard, Ed. Dordrecht,The Netherlands: Reidel, 1973, pp. 347–361.

[12] T. Nitter, O. Havnes, and F. Melandso, “Levitation and dynamics of charged dust in the photoelectron sheath above surfaces in space,” J. Geophys. Res., vol. 103, no. A4, pp. 6605–6620, 1998.

[13] P. Lee, “Dust levitation on asteroids,” Icarus, vol. 124, no. 1, pp. 181–194,Nov. 1998.

[14] J. Colwell, A. Gulbis, M. Horanyi, and S. Robertson, “Dust transport inphotoelectron layers and the formation of dust ponds on Eros,” Icarus,vol. 175, no. 1, pp. 159–169, May 2005.

[15] T. Stubbs, R. Vondrak, and W. Farrell, “A dynamic fountain model forlunar dust,” Adv. Space Sci., vol. 37, no. 1, pp. 59–66, 2006.

[16] W. Farrell, T. Stubbs, R. Vondrak, G. Delory, and J. Halekas, “Complexelectric fields near the lunar terminator: The near-surface wake and ac-celerated dust,” Geophys. Res. Lett., vol. 34, no. 14, pp. 14 201–14 206,2007.

[17] H. Garet, “The charging of spacecraft surfaces,” Rev. Geophys., vol. 19,no. 4, pp. 577–616, 1981.

[18] J. Gosling, “The solar wind,” in Encyclopedia of the Solar System.

San Diego, CA: Academic, 1999.[19] J. Fu, “Surface potential of a photoelectron emitting plane,” J. Geophys.

Res., vol. 76, pp. 2506–2509, 1971.

Joseph Wang received the B.Eng. degree inengineering mechanics from Tsinghua University,Beijing, China, in 1985, and the S.M. degree inaeronautics and astronautics and the Ph.D. degreein plasma physics from Massachusetts Instituteof Technology, Cambridge, in 1988 and 1991respectively

From 1991 to 2001, he was a Staff Member withJet Propulsion Laboratory. Since 2001, he has beenwith the Aerospace and Ocean Engineering Faculty,Virginia Polytechnic Institute and State University,

Blacksburg. His research interests include spacecraft plasma interactions, spaceplasma physics, electric propulsion, and plasma simulation algorithms.Dr. Wang is an Associate Fellow of AIAA.


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Xiaoming He received the B.S. and M.S. degreesin computational mathematics from Sichuan Univer-sity, Chengdu, China, in 2002 and 2005, respectively,and the M.S. degree in mathematics from VirginiaPolytechnic Institute and State University (VirginiaTech), Blacksburg, in 2007. He is currently workingtoward the Ph.D. degree in mathematics at VirginiaTech.

His ongoing research involves the developmentof the immersed finite elements and extrapolationalgorithms for plasma simulation applications.

Yong Cao received the B.Eng. degree in thermalengineering from Tsinghua University, Beijing,China, in 1993, the M.S. degree in fluid mechanicsfrom the Institute of Mechanics, Chinese Academyof Sciences, Beijing, China, in 1998, and the Ph.D.degree in mechanical engineering from CarnegieMellon University, Pittsburgh, PA, in 2003.

From 2003 to 2006, he was a Postdoctoral

Fellow with Virginia Polytechnic Institute and StateUniversity, Blacksburg. He is currently an AssociateProfessor of mechanical engineering with Harbin

Institute of Technology, Harbin, China.

Modelacion Electroestatica de Polvo Lunar

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