Modeling Dust Clouds on the Moon J. Szalay1 and M. Horányi1

1Colorado Center for Lunar Dust and Atmospheric Studies, Laboratory for Atmospheric and Space Physics, and Department of Physics,

University of Colorado at Boulder, USA

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Summary •  Surveyors 5, 6, and 7 observed forward scattered light after sunset

•  Explained by a dust cloud levitated in the plasma sheath •  1D hybrid code with fluid plasma and particle dust grains is developed

•  Agrees with theoretical and experimental results from [1, 2] •  Estimates on characteristic grain size and optical depth are calculated for various airless bodies

Horizon Glow: Surveyors 5, 6, and 7 captured the first evidence of dust transport on airless bodies with their television cameras (Figure 2). Just after sunset, a horizon glow was observed above the western horizon. This was interpreted to be forward scattered light from a cloud of dust particles with radii ~5 μm, vertical dimension ~3-30 cm, and horizontal dimension ~14 m [3].

[1] Nitter, T., et al., IEEE Trans. Plasma Sci., 22, 1994 [2] Arnas, C., et al, Phys. Plas., 7, 4418-4422 [3] J. Rennilson and D. Criswell, The Moon, 10, 1973 [4] Criswell, D.R. Proc. Lunar Sci. Conf., 3rd, 1972

[5] Nitter, T., et al., Earth, Moon and Planets, 56, 1992 [6] Havnes, O., et al, J. Geophys. Res. 2, 2281-2287 [7] Sun, M., et al., Adv. Sp. Res. 38, 2575-2580 Figure 2. Surveyor 7 compilation images showing horizon glow just

after local sunset [3,4].

port depend also on the mechanical properties of the dust, withtightly packed dust exhibiting different behavior than looselypacked dust. Experimental results on near-surface electric fieldsare presented in this paper following a brief review of the obser-vational evidence for charged dust dynamics near the lunarsurface.

The problem of lunar dust levitation conditions has been stud-ied theoretically and numerically and is reviewed in Colwell et al.!2007". Particle levitation is made possible by the gradient in theplasma properties near the surface producing a near-surface elec-tric field. The variation of the electric field strength with distancefrom the surface depends on the distribution of electrons and ionsin this sheath region. Analytic solutions for idealized electronenergy distributions for a one-dimensional photoelectron sheath!Grard and Tunaley 1971" have been used to calculate electricfield strengths as well as charging currents to particles in thesheath !e.g., Colwell et al. 2005; 2007". Particle-in-cell calcula-tions of the vertical distribution of electron densities in a photo-electron sheath are presented and copared to the standard analyticsolution. Results of simulations of the dynamics of charged grainsabove the lunar surface for different conditions and locations onthe Moon are also presented.

Observations

Direct observations of dust above the lunar surface were made bythe Surveyor 5, 6, and 7 spacecraft !Rennilson and Criswell1974"; Fig. 1. Apollo 17 astronauts in the orbiting command mod-ule reported and sketched high altitude streamers that have beenattributed to dust leaving the lunar surface at high speeds !McCoyand Criswell 1974; Zook and McCoy 1991; Stubbs et al. 2006".The star-tracker camera on the Clementine spacecraft also imageda glow along the lunar horizon that may be due to levitated lunardust !Zook et al. 1995". The Lunar Ejecta And Meteorites Experi-ment !LEAM" deployed on the surface by the crew of Apollo 17showed evidence for lunar regolith dust particles moving over thesurface with enhanced activity near sunrise and sunset !Berg et al.1973; 1976; see also Colwell et al. 2007". Taken together theseobservations argue for levitation of dust from the lunar regolith

above the lunar surface with peak activity occurring near sunriseand sunset where strong terminator electric fields are predicted!Criswell 1974; Criswell and De 1977; De and Criswell 1977". Atthe terminator, particularly strong local electric fields !1 kV /m,over a spatial scale of 1 cm or less" can be generated at shadowboundaries due to photoelectron emission from the unevenly illu-minated surfaces.

Apollo astronauts placed lunar laser reflectors on the lunarsurface to measure the distance to the Moon with high !millime-ter" precision !Bender et al. 1973". The fact that all of these re-flector arrays !Apollo 11, 14, and 15, and Lunokhod 2" stillperform without any increased attenuation of the return signal is apossible counterargument for the effects of lunar dust levitationand transport. However, these reflectors are made of glass corner-cube arrays and may have continued to perform due to theirslanted smooth surfaces !the arrays are placed on a slanted plat-form", or due to their similar electrostatic charging properties asthe glassy lunar soil. The experiments described in the followingshow that dust redistributes itself to minimize gradients in surfacepotential, and the reflector surfaces, being glass like the regolith,may charge to a potential similar to the lunar surface. A thinveneer of submicron dust particles also may not render the reflec-tors unusable.

There is still much that is unknown about the conditions thatlead to charged dust activity on the Moon. Observational limits onthe prevalence and magnitude of charged dust transport can beplaced by noting the static nature of the lunar regolith during andbetween manned and unmanned visits. Thirty-one months afterthe Surveyor 3 spacecraft landed on the Moon the Apollo 12astronauts visited the spacecraft and returned pieces of the space-craft and photographs of the area near the Surveyor !Fig. 2".Although dust was clearly deposited on the mirror of Surveyor 3’stelevision camera system, this may have been deposited duringthe landing of Surveyor 3 !or by the Apollo 12 Lunar Module155 m away" when its engine blew dust off the lunar surface.!Indeed, this is another significant potential dust hazard for futuremissions." There are no measurements of the amount of dust onthe rest of the spacecraft and no way to determine if the distribu-tion of dust on the spacecraft was correlated with illumination ormaterial properties. The lunar surface, however, appeared undis-turbed since the landing of Surveyor 3. Patterns made by theSurveyor 3 landing gear in the regolith appeared unchanged whenthe Apollo 12 astronauts visited. More dust measurements nearthe lunar surface are needed to assess the extent of charged dustmovement.

The near-surface plasma environment, including the surfacecharge, determines the level of dust charge which in turn deter-mines the ability of charged dust to levitate and be transportedacross the surface. A general picture of the global lunar surfacepotential has been constructed based on measurements and mod-els of photoemission and of the solar wind !e.g., Manka 1973".Additional charging currents due to secondary electron emissionwhen the Moon passes through the Earth’s plasma sheet can en-hance the surface charge. This has been indirectly measured bythe Lunar Prospector, which detected electrons of moderate en-ergy !"500 eV# ascending from the lunar nightside, suggesting asurface potential of up to "500 V negative to accelerate the elec-trons to these energies !Halekas et al. 2005".

Experiments

The writers’ previous experimental studies of charging and levi-tation of dust in a plasma sheath have been reported in Sickafoose

Fig. 1. Surveyor 6 image 328141526.354 showing a glow on thewestern lunar horizon after sunset. The broad and high diffuse glow iszodiacal light from interplanetary dust. The low bright band just atthe horizon is lunar “Horizon Glow” apparently due to light scatteredfrom dust particles near the lunar surface. National Space ScienceData Center.

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Simulation: If enough grains collect in the plasma sheath, the sheath potential profile can be significantly altered [1]. A 1D hybrid code has been developed with fluid plasma and particle dust grains to constrain the properties of these clouds above airless bodies. Launching dust grains into the sheath, Poisson’s equation is solved at each time-step to determine the new potential, charging currents, and forces experienced by each grain. By equating the electric and gravitational forces on the dust grains, the maximum allowable grain radius [μm] which can be suspended in a sheath as a function of the local plasma conditions and g [m/s] can be found as where the grain size constant C is a function of the local plasma conditions and C = 0.4 for the solar wind conditions at 1 AU and an empty sheath.

Dust Levitation: Due to surface charging, like charged grains on the surface electrostatically repel each other. If this force overcomes gravity and cohesion forces, these grains can be lofted into the plasma sheath above the surface. In this model, grains are injected into the sheath with optimal velocities for levitation. To model the plasma sheath, a two fluid approach is used with Boltzmann electrons and cold, drifting ions [5]. As grains traverse the sheath, they charge according to charging currents dependent on the local plasma conditions and grain charge [5]. Given certain conditions such as initial velocity, grain size, and initial charge, grains have been shown to levitate in stable equilibria in the plasma sheath [5] as seen in Figure 3.

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Figure 1. Sheath and example trajectory using lunar parameters

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Future Work: Sheath properties are given for a variety of airless bodies. However, the sheath observed by Surveyor is still not reproduced. The model will be extended to 2D/3D to include topographical effects and photoelectron currents will be added to determine if these factors are sufficient to reproduce the Surveyor observations.

Airless Body Sheath: Using solar wind conditions at 1 AU for plasma input parameters, grains are launched from the surface in a Monte Carlo scheme with random sizes, velocities, and initial charges for bodies with g = 10-3 m/s to 1 m/s. For each value of g, sheaths are allowed reach their saturated equilibrium state, where the number of grains in the sheath reaches a constant value. At equilibrium, the largest grains are the most dense, reaching densities of approximately 100 m-3 regardless of g. The maximum grain size constant for saturated sheaths is C = 0.2, which means the maximum allowable levitated grain radius is reduced by a factor of 2 in the saturated sheaths. Figure 1 shows an example equilibrium sheath along with a single grain position and charge from this sheath using lunar parameters.

Figure 3. Dust trajectories and potential in a saturated dust sheath

Results: Using the largest grains as they are the most dense, an estimate of the optical depth for a variety of airless bodies can be made. Assuming a scale length of two Debye lengths, or L=20 m for the solar wind conditions at 1 AU, the optical depth of saturated clouds above airless bodies is given by,

Using this formula, the optical depth for saturated sheaths on selected airless bodies has been tabulated for a variety of airless bodies between Earth and Mars in Table 1. Note: the Surveyor estimate of a 5-6 μm characteristic grain size above the Moon is not reproduced by this model (~0.1 μm).

Table 1. Airless body saturated sheath parameters

X - 10 SZALAY AND HORANYI: DUSTY PLASMA SHEATHS

The heaviest grains are found to levitate 1-4�D or 10-40 m above the surface with dust

grain densities on the order of nd = 100 m�3. Given these densities, a maximum optical

depth, ⌧sat

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of ⌧sat

for select bodies.

4. Conclusion

Loaded dust sheaths above airless bodies from 1-1.5 AU have the largest grains and most

dense clouds in the region 10-40 m above the surface. The largest grain found in these

clouds is given by the simple relationship a

sat

= 0.2g�1/2µm. Smaller grains may also

be levitated in the sheath with much lower densities and higher altitudes. The maximum

optical depth for these saturated sheaths is in the range of 10�10 to 10�7.

As is, this model does not explain the large (10 µm) grains observed in the Surveyor

measurements, predicting grains on the order of 0.1 µm to be suspended above the moon

and only if they can gain 103 electrons before leaving the surface. Additional modeling

complexity may be necessary to explain this phenomenon.

The model described in this paper is one dimensional and uses a two component plasma.

A natural next step would be to model the three dimension dynamics of dusty plasmas

above the surfaces of airless bodies including photoelectron sources and sinks. Addition-

ally, topography is proposed to play a large role in electric field development and inclusion

of surface features into such a three dimensional model would quantify these e↵ects. A

fully three-dimensional study incorporating surface topography and complex plasma con-

D R A F T July 9, 2013, 11:14am D R A F T