Modeling Dust Clouds on the Moon - University of Colorado Boulderlasp.colorado.edu/media/projects/ccldas/ldap_2012/pdf/... · 2012. 12. 12. · ley, one moving apparently toward the

MotivationModel

ResultsConclusion

Modeling Dust Clouds on the Moon

Jamey SzalayMihaly Horanyi

CCLDASUniversity of Colorado at Boulder

DAP 2012

Jamey Szalay Mihaly Horanyi Modeling Dust Clouds on the Moon

MotivationModel

ResultsConclusion

Surveyor ImagesLEAM

MotivationSurveyor ImagesLEAM

ModelSheathGrain ChargingDusty Sheath

ResultsExperimental ComparisonLunar

ConclusionJamey Szalay Mihaly Horanyi Modeling Dust Clouds on the Moon

MotivationModel

ResultsConclusion

Surveyor ImagesLEAM

Surveyor 7 Horizon Glow

d

McCoy 1974


MotivationModel

ResultsConclusion

Surveyor ImagesLEAM

LEAM Terminator Measurements

Berg 1976


MotivationModel

ResultsConclusion

SheathGrain ChargingDusty Sheath

Two Fluid Plasma Sheath

∂2ϕ

∂x2=

en0

ε0eeϕ/kTe︸︷︷︸

electrons

− en0

ε0

(1− 2eϕ

miv2i ,dr

)−1/2

︸︷︷︸ions


MotivationModel

ResultsConclusion


Grain Charging


MotivationModel

ResultsConclusion


Dusty Plasma Sheath

∂2ϕ

∂x2=

en0

ε0eeϕ/kTe︸︷︷︸

electrons

− en0

ε0

(1− 2eϕ

miv2i ,dr

)−1/2

︸︷︷︸ions

− ρd(x)

ε0︸︷︷︸dust


MotivationModel

ResultsConclusion

Experimental ComparisonLunar

Arnas et al.

Simulation Parameters

I Te = 1.8 eV

I Argon Plasma

I Glass spheres with radiia = 22 µm

High negative charge of a dust particle in a hot cathode discharge

C. Arnas, M. Mikikian, and F. DoveilEquipe Turbulence Plasma, Laboratoire de Physique des Interactions Ioniques et Moleculaires, UMR 6633 du CNRS/Universitede Provence, Centre de Saint Jerome, case 321, Avenue Escadrille Normandie Niemen, 13397 Marseille Cedex 20, France

!Received 29 April 1999"

Dust particle levitation experiments in a plasma produced by a hot filament discharge, operating at low argonpressure, are presented. The basic characteristics of a dust grain trapped in a plate sheath edge in theseexperimental conditions are reported. Taking into account the sheath potential profiles measured with a dif-ferential emissive probe diagnostic, the forces applied to an isolated dust grain can be determined. Twodifferent experimental methods yield approximately the same value for the dust charge. The observed highnegative charge is mainly due to the contribution of the primary electrons emitted by the filaments as predictedby a simple model. #S1063-651X!99"14611-7$

PACS number!s": 52.40.Hf, 52.25.!b, 94.10.Nh

I. INTRODUCTION

Dust particles trapped in a laboratory plasma can acquirefrom a few to several thousand electron charges dependingon their size and on plasma conditions. In the case of highdust concentration !rf discharge for plasma processing or indc glow discharge" several plasma properties can be drasti-cally modified: the charge equilibrium #1,2$, the plasma par-ticles collective behavior #3–8$, and the plasma particlestransport #9,10$. Moreover, crystallization #11–17$ of dustgrains can be observed #18–25$. In symmetrical parallel-plate rf discharges, dust particles of small size !"0.1 %m"can accumulate in the center of the electropositive plasma#26,27$, in local maxima of the plasma potential #28$, in theplasma-sheath transition of the upper electrode #29$ or of thelower electrode #30$. Large dust particles are usually trappedat the sheath edge of the lower electrode #18–24$. In general,their location is determined by the relative strength of theforces applied to them due to gravity, electric fields, ion andgas drag, and in certain conditions, thermophoresis effects#31,32$.We report experiments on dust particle levitation in the

sheath edge of a conducting horizontal disc plate embeddedin a continuous argon discharge plasma. Permanent magnetsfixed on the outside device wall !magnetic box" enable us tooperate at low argon pressure: Par#10!3 mbar !collisionlessplasma". The ionization sources are two heated tungsten fila-ments emitting energetic primary electrons. This populationis correctly represented by an isotropic drifting Maxwelliandistribution. In these conditions, using the orbital-motion-limited !OML" model #33$, we show that the main contribu-tion to the high negative charge of an isolated dust particle isdue to the primary electrons.Using a differential emissive probe diagnostic, we mea-

sure the sheath-presheath profile of the disc plate, for differ-ent negative plate biases. Taking into account the shape ofthe obtained potential distributions and the dust charge givenby the OML model, we can evaluate the strength of theforces applied to a dust grain. Because we use dust particleswith relatively large radius, only the gravitation and the elec-tric forces play a significant role.The dust charge is evaluated experimentally by two meth-

ods. The first one consists in measuring the levitation heighth. When the negative plate voltage is increased, h increasestoo. For any plate bias, the equilibrium height corresponds tothe same sheath potential !and the same electric field" wherethe balance between the electric and the gravitation forces isachieved. The second one is provided by natural vertical os-cillations exhibited by a dust particle around its equilibriumposition, in the measured potential profile. The chargesfound in both ways are compared to the value predicted bythe OML model.

II. EXPERIMENTAL SETUP

A. Apparatus

The experiments are performed in a multipolar stainless-steel cylinder, 40 cm long and 30 cm in diameter very simi-lar to the one presented in Ref. #34$. The ionization sourcesare two heated tungsten filaments !shaped like springs with20 cm length" situated at the bottom of the device assketched on Fig. 1. Each filament is heated by a currentdelivered by a current regulated power supply. The primaryelectrons emitted by the hot filaments are accelerated to-wards the grounded wall by the negative discharge voltageVD#!40V, provided by a voltage regulated power supply,the plasma discharge appearing at VD0#!35V. The dis-

FIG. 1. Multipolar device in series with the continuous dis-charge circuit. A conducting disc plate over which dust particleslevitate is set in the center of the chamber.

PHYSICAL REVIEW E DECEMBER 1999VOLUME 60, NUMBER 6

PRE 601063-651X/99/60!6"/7420!6"/$15.00 7420 © 1999 The American Physical Society

Arnas 1999


MotivationModel

ResultsConclusion


Arnas et al.


I Te = 1.8 eV

I Argon Plasma

I Glass spheres with radiia = 22 µm


MotivationModel

ResultsConclusion


Lunar Inputs


I Te = 10 eV

I vsw = 400 km/s

I a = 0.16 µm


MotivationModel

ResultsConclusion


Lunar Sheath


MotivationModel

ResultsConclusion


Comparison to Surveyor 7

Surveyor 7

I a = 6 µm

I nd = 106 m−3

Model

I a = 0.16 µm

I nd = 103 m−3


MotivationModel

ResultsConclusion


Charging

NASA/GSFC, UCB/SSL


MotivationModel

ResultsConclusion


Terminator

378

Fig. 1. Segment of terminator configuration showing zig-zag line and associated sunlit islands on shadow side and dark valleys in sunlit side.

plained by the presence of a sub-micron-thick layer of lunar soil sufficiently thick to shield crater formation, but not to significantly dilute the formation o f tracks [6].

Although observational evidence of electrostatic transport is very strong, theoreticians, engaged in ap- plying those observations to a lunar model accommo- dating electrostatic transport , struggle with: (1) measured surface potentials on the sunlit side which are inadequate to initiate electrostatic transport; and (2) only derived potentials on the dark side which vary widely from - 1 0 0 V [7] to several kilovolts negative [8], and depend critically upon the existing sets of conditions in a very complex solar particles and fields ensemble. The fact that theoreticians cannot agree on a lunar surface model that reasonably accommodates electrostatic soil transport should not in any way cast doubt on the evidence! The absence of a model in the presence of all the existing evidence merely means that in the complex jig-saw puzzle portrai t of the lunar surface many pieces are still missing and some are possibly incorrectly oriented. This paper proposes

a "must be the case" configurational model for the terminators which plausibly provides high electric fields adequate to initiate and sustain electrostatic transport.

There is a natural tendency to consider lunar surface field effects and particle movements in the region o f the terminator as if the terminator were a well-defined line, whereas in reality it is a diffuse, zig- zag line as suggested in Fig. 1. The configurational excursions vary from millimeters to many kilometers depending upon the local terrain (mountain, valley, crater, etc.). In the Taurus-Littrow area (Apollo 17), as an example, the excursions become extremely long and complex, and each of the passing terminators un- doubtedly exhibits a double line as it crosses the valley, one moving apparently toward the sun and one moving apparently away from the sun. In this zig-zag terminator region, myriads of positively charged sunlit "islands" are formed and momentari ly exist in the dark, negatively-charged side of the morning * terminator, as shown. Conversely, on the sunlit side of the morning terminator, miniature dark "valleys" composed of negatively charged lunar fines, momen- tarily linger in the sunlit side of the morning terminator, as shown. For simplicity in submitting this terminator configuration, it is assumed that the same line which is defined by the sunlit/dark surface of the moon, is also generally the line between the positively and negatively charged lunar surface. I f the terminator surface zone is negative, as suggested [7], the pro- posed effects will still be valid, but modified, as de- scribed later.

Fig. 2 is an enlarged cross-sectional diagram of a typical sunlit island shown as element A in Fig. 1, and demonstrates some of the quasi-violent activity which may occur momentari ly in the vicinity of a typical sunlit island. Dimensions are relatively unimportant for the presentation of this terminator concept except to state that the vertical magnitudes of the

* The primary purpose of this paper is to suggest a more realistic configuration for the terminators. The paper there- fore tends to be limited to the morning terminator, as an example. In the evening terminator the appearance of the islands and the valleys will be reversed, i.e. the sunlit islands will "linger" and the dark valleys will be "formed". Obvi- ously there are more subtle and complex differences associated with the solar wind and geomagnetic tail which are too extensive for this paper.

Berg 1978

1972LPSC....3.2671C

Criswell 1972


MotivationModel

ResultsConclusion

Next Steps

I Photoemission

I Multi-size grain distributions

I 2D/3D

I Complex Geometries

1000 DE AND CRISWELL: ELECTRIC CHARGING IN LUNAR SUNSET TERMINATOR, I

sunlit areas. Consequently, the sunlit areas charge up to a potential that would cause all the subsequently emitted electrons to return to these areas. Our purpose here has been to estimate this potential by using a numerical simulation method.

In the model used, emission of monoenergetic photoelectrons was considered. This is because while the introduction of an electron energy spectrum affects the time taken by a sunlit area to charge to its steady potential, the value of this potential is the same as if the monoenergetic electrons considered were effectively the highest-energy electrons in the spectrum. We shall discuss the charging time scale in a later section. We have ignored in our model any effects that hinder the growth of the potential (i.e., discharging effects). Such effects will also be discussed in a later section.

In order to facilitate computations the realistic situation (such as is sketched in Figure la) was reduced to a simplified model (Figure lb) in which one hemisphere of a spherical rock sitting on a dark plane was illuminated by the sun. Equal probabilities of photoelectron emission were assigned to equal elemental areas of the sunlit surface projected on a plane perpendicular to the solar direction. A large number (4000) of sequential ejection events were considered. The ejection sites were selected randomly, as were the ejection directions; the latter, however, were weighted by a cosinelike factor which made near-normal ejection directions more probable than far- normal directions. Since the actual number of electron ejec- tions to be considered in order to achieve the high potentials is very large (so as to leave behind a surface charge density of • 109 electrons cm -•' in the case of our model), a large number (10 e) of ejected electrons were bunched together and considered as a single ejection event. As one of these 'particles' was ejected, its trajectory was computed. The trajectory was termi- nated when one of the following situations was encountered: (1) the particle hit the dark plane, (2) the particle hit the dark hemisphere, (3) the particle traveled beyond a predefined cutoff distance (which, for the reason we shall see later, we need

BEYOND 'CUTOFF' DISTANCE

z(t6•*SuH)

(b) IDEALIZED MODEL

Fig. l. The realistic situation and the idealized model used for computations. Deep shadowing may be produced by a western ridge. The ejected photoelectrons can hit the dark plane or the dark hemisphere, escape beyond a 'cutoff' distance, or return to the sunlit area.

not define physically; it could, for instance, be the .solar wind Debye length), or (4) the particle returned to the sunlit hemisphere. In cases 1,2,• and 3 the charge of the sunlit hemisphere was increased by one particle charge. In cases I and 2 the final locations of the particles were noted, and their presence in these locations was recognized in all subsequent calculations. The computations were carried on until about 95% of the ejected electrons were returning to the sunlit hemisphere.

CHARGE DISTRIBUTION ON THE SUNLIT AREA

The lunar soil and rocks are made up of highly resistive dielectric material. On this basis, one would expect that different points on the sunlit area would acquire different potentials.

In our calculations, however, we have assumed that the sunlit portion of the surface behaves like a conductor to the extent that it does not permit the buildup of any electric field components tangential to the surface. This is because the relatively large flux of low-energy photoelectrons that continue to return to the surface (and comprise most of the photoelectron sheath) during the development of the high potential redistributes the surface charges in such a way as to annul any electric field components parallel to the surface. We present below a semiquantitative argument to support this view.

Suppose that the sunlit hemisphere of a rock of radius R (see Figure lb) has acquired at the time in question a positive potential ½• and the potential is continuing to increase. This means that the electrons emitted with energies •<e½•/2 (e is the electronic charge; the factor 2 will be justified later) all return to the sunlit surface. Let N(e½) be the emission flux of electrons with energy e½. Assuming that the electron collision time in the classical expression for conductivity is the 'hopping' time of the returning electrons in our case, we estimate the

.

conductivity parallel to the surface due to the hopping electrons to be

8e all = •-•$o N(e½) d(e½) (l) where E, is the electric field component normal to the surface. The field component E• parallel to the surface causes a transport of photoelectrons in the direction antiparallel to E• at a rate

a,,E,. _ 8( E,, ) fo htl- e • N(e½) d(e½) (2) As a reasonable example, let E•/E, = 10 -• and ½• = 50 V.

Then a lower limit to the integral in (2) can be estimated from various sources, observational and theoretical [Reasoner and Burke, 1973; Willis et al., 1973], to be of the order of 5 X 109

ß

electrons cm -• s -•, so that .ti• • 4 X 11Y electrons cm -• s -•. This is to be compared with the escaping flux t•, of electrons having energies higher than eCx/2. Parallel electric field components [ E•[ •< 10-•[ Ex[ can exist only if ti• << d•_. In the same way as in the case of ti• we estimate ti• •< 11Y electrons cm -• s -•. This shows that the sunlit surface responds even to very small parallel electric field components and quickly annuls such components. We may thus reasonably assume that the sunlit surface behaves as a conductor with regard to the charge distribution on this surface. The above analysis assumes that the effective hopping height of the returning electrons is •<R, a reasonable assumption in most conceivable situations.

For a spherical conducting bowl of angle I•o (see Figure lb) that is freely electrified, the surface density of charge for any angle I• < I•o is given by [e.g., Jeans, 1925]

De and Criswell 1977


MotivationModel

ResultsConclusion

Scope

Other airless bodies

I Mercury

I 433 Eros & other asteroids

I Phobos/Deimos

I Many more


MotivationModel

ResultsConclusion

Acknowledgements

I Colorado Center for Lunar Dust and Atmospheric Studies

I CU Boulder


MotivationModel

ResultsConclusion

Questions?


Appendix Lunar Simulation

a = 0.16 µm



a = 0.15 µm



Size Comparison


Documents

Modeling Dust Clouds on the Moon - University of Colorado Boulderlasp.colorado.edu/media/projects/ccldas/ldap_2012/pdf/... · 2012. 12. 12. · ley, one moving apparently toward the