Modeling Spacecraft Charging and Charged Dust Particle Interactions on Lunar Surface

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1 Modeling Spacecraft Charging and Charged Dust Particle Interactions on Lunar Surface J. Wang 1, X. He 2, and Y. Cao 3 Virginia Polytechnic Institute and State University Blacksburg, VA Abstract This paper presents particle simulation models for spacecraft charging and charged dust particle interactions on lunar surface. Full particle PIC simulations are carried out using real ion to electron mass ratio to obtain plasma sheath and wake, and the floating potential of lunar lander in the lunar terminator region. Dust-in-plasma simulations are carried out to study electrostatic levitation of dusts and dust transport around lunar lander. 1 Introduction Dust clouds suspended above the lunar surface were first observed as horizon glow by the Surveyor spacecrafts [12] and later by the Apollo astronauts[3]. Figure 1 shows a sketch by Capt. Gene Cernan, commander of Apollo 17, of his observations of the sunrise on lunar surface from the lunar orbit, showing horizon glow and streamers of dusts[10]. It is well documented that lunar dust can cause a wide range of serious problems for spacecraft and/or astronauts on extra-vehicular activities (EVA). For instance, Capt. Gene Cernan made the following remarks at the Apollo 17 technical debriefing:...i think probably one of the most aggravating, restricting facets of lunar surface exploration is the dust and its adherence to everything no matter what kind of material, whether it be skin, suit material, metal, no matter what it be and it s restrictive friction-like action to everything it gets on...we tried to dust them and bang the dust off and clean them, and there was just no way...i think dust is probably one of our greatest inhibitors to a nominal operation on the Moon. I think we can overcome other physiological or physical or mechanical problems except dust... Problems caused by lunar dust include vision obscuration, false instrument reading, clogging of equipment, clogging of equipment, seal failures, contamination of surface leading to thermal control problems, abrasion of space suits, and breathing problems (and potential long term respiratory problems) for astronauts on the Moon. Dust particles have also caused both science and engineering concerns for Mars and comet missions. The Moon is directly exposed to the solar wind. A spacecraft on lunar surface will become electrostatically charged by the impingement of the solar wind plasma and the emission of photon electrons under sunlit. While spacecraft charging did present a problem during the Apollo mission, 1 Associate Professor, Department of Aerospace and Ocean Engineering 2 Graduate Research Assistant, Department of Mathematics 3 Currently Associate Professor, Department of Mechanical Engineering, Harbin Institute of Technology Shenzhen Graduate School 1

2 later studies of spacecraft observations suggest that charging could be a serious issue under certain conditions. For instance, Criswell and De observed intense localized charging in the lunar sunset terminator region and found that the lunar surface potential suddenly changed from about +10V to about -100V[2]. Berg observed that the lunar surface potential can become charged to more than 500V negative when the moon goes into the magnetotail region[1]. Spacecraft charging and dust interactions are two closely related problems. While micrometeoroid impacts and/or disturbances by human activities (e.g. lunar lander,lunar vehicle, astronauts. etc) can contribute to the lift off of dusts from the lunar surface, electrostatic levitation is generally accepted as the primary mechanism (see, for example [7, 4, 14, 11]and references therein). The transport of charged dusts is also controlled by the electrostatic field near lunar surface and surrounding a spacecraft. Hence, the objective of this paper is to investigate spacecraft charging and charged dust interactions due to electrostatic levitation on lunar surface. 2 Modeling Approach 2.1 Plasma Interaction Characteristics We shall consider the average solar wind plasma condition at 1AU in this paper. Typical solar wind parameters on lunar surface relevant to this study are: plasma density n sw 5cm 3, solar wind speed v sw 400km/s, electron temperature T e 10eV, solar wind magnetic field B sw 10 4 G. (For simplicity, here we only consider the core population for the solar wind electrons and ignore the halo population.) The solar wind Debye length is λ D 10.4m. Near sunlit surfaces, the photoelectron emission characteristics are: photoelectron density n ph0 64cm 3 and photoelectron temperature T ph 2.2eV. The photoelectron Debye length is λ D 1.4m. These parameters will be used throughout this paper. From these parameters, we find that the plasma interactions have the following two important characteristics: a) the plasma flow on lunar surface is mesothermal v ti << v sw << v te ; hence a spacecraft or a rock on lunar surface would generate a plasma wake and a fairly complex electrostatic field. b) the photoelectrons will dominate the plasma sheath for sunlit surfaces. The plasma interaction characteristics present a significant challenge to the development of a simulation model. First, in order to resolve the photoelectron sheath correctly, a full particle simulation model is required which uses the kinetic approach to simulate both the electrons and ions. Second, in order to maintain the correct mesothermal velocity ratio, full particle simulations must be carried out using the correct ion to electron mass ratio. Additionally, as the lunar surface is a dielectric surface, the simulation model must have the capability to calculate differential charging self-consistently within the model. The simulation model presented in this paper resolves all these challenging issues. 2.2 Charged Dust Interaction Characteristics We shall assume the following parameters for lunar dust: mass density ρ d 3.7g/cm 3 and dust radius r d 0.01µm. 2

3 While numerous laboratory experiments have been carried out to study the charging properties of lunar dust simulant [13, 14, 15] and electrostatic levitation of dust grains [8, 9, 14] under simple settings, few modeling studies currently exist that are directly applicable to charged dust interactions on lunar surface. There are at least two aspects of the interactions which are extremely challenging to model. The first is the dusty-plasma interaction aspect. Computationally it is not yet feasible to simulate coupled charged dust and plasma interactions due to the orders of magnitude differences in time scales between dusts and plasmas. The second is the dust-surface interaction aspect. No models currently exist that describe the charging process for coupled dust grains and charge transfer between contacting dust surfaces. The charged dust interaction model in this paper assumes that there is no coupling between charged dusts so the calculation of dust charging and dust dynamics can be carried out individually for each dust grain. This type of calculation is referred as dust-in-plasma calculation. Moreover, charge transfer between contacting dust surfaces are not considered. The initial charge for dusts sitting on lunar surface is taken to be an input based on experimentally measured dust charge. 2.3 Simulation Model We have developed a simulation model using a two-step approach. In the first step, a full particle PIC code is developed to simulation plasma interactions. Both the ions and electrons are treated as macro-particles and particle simulations are carried out using the real proton to electron mass ratio so the correct mesothermal speed ratio can be maintained. The PIC code is based on the immersed-finite-element (IFE) PIC algorithm[16, 17]. One of the features of the IFE is that the object inside the simulation domain may be as part of the simulation domain rather than as an external boundary. This feature allows one to perform calculate the electric field inside an object based on local charge deposition, (ɛ Φ) = ρ s (1) where ρ s is the surface charge density. This code resolves lunar surface charging and spacecraft charging are calculated self-consistently inside the PIC code from local charge deposition. The second step of the model performs dust charging and transport calculations. Dust dynamics is obtained from F = m d a = Q d E md g (2) where Q d is dust charge and the electric field obtained from the plasma simulation. The initial charge for dust-on-surface is based on experimental values. Once a dust is levitated from the surface, individual dust charging is calculated from dq d dt = I sw,i I sw,e I pe, Q d = CΦ d (3) where the current collection by dust is assumed to follow the orbital motion limited (OML) theory and is based on plasma density distributions obtained from the first step. A 4th order Runge-Kutta method is used to integrate the above equation numerically. 3

4 3 Simulation Results This section presents results from two different simulations. The first one concerns lunar surface charging and spacecraft charging on lunar surface. Figure 2a illustrates the simulation setup for spacecraft charging simulations. We consider a lunar lander sitting on a flat lunar surface. The lunar lander is assumed to be a perfectly conducting box with a dimension similar to that of the ESA lunar surface access module. The lunar surface is taken to be a dielectric surface. The second concerns electrostatic levitation of charged dusts on flat lunar surface and transport of charged dusts around the lunar lander. Figure 2b illustrates the setup for charged dust simulations. We consider the lunar terminator region for all these cases where the sun elevation angle is taken to be between 0 o and 10 o. 3.1 Lunar Surface Charging and Spacecraft Charging Figure 3 shows the potential profile above a flat lunar surface in the absence of a spacecraft for sun elevation angles of 0 o, 5 o, and 10 o. Under average solar wind conditions, we find that the floating potential of the lunar surface ranges from about -22V at 0 o to slightly positive at 10 o. Figures 4 and 5 show the results for a lunar lander on a flat surface for sun elevation angles of 0 o and 5 o, respectively. The figures shown include the potential contours, ion density contours, and photoelectron density contours around the lunar lander where the structure of the plasma wake generated by the lander is obvious. The results also show that the lander is uniformly charged while the lunar surface is differentially charged, consistent with the assumption that the lander is a perfect conductor where the lunar surface is a dielectric surface. For sun elevation angle of 0 o, the spacecraft potential is about -5V. The negative floating potential is due to electrons collected by the shadow surfaces which more than balanced the photoelectron emission on the sun facing surfaces. For sun elevation angle of 5 o, the spacecraft potential is about 0V. 3.2 Charged Dust Interactions We next consider electrostatic levitation of dust particles initially at rest on a flat lunar surface. The dust particles considered here have a radius of r d 0.01micron. Previous experiments have shown that such dusts can acquire an initial charge of 10 5 e. The simulations show that such dusts can become electrostatically levitated from the lunar surface under typical solar wind and solar UV conditions at the terminator region. Figure 6a shows the result for sun elevation angle of 0 o (dust upward velocity vs. height) Due to the larger lunar surface potential, the dusts escapes the maximum height of the simulation domain. Figure 6b shows the result for sun elevation angle of 5 o (dust height vs. time). For this case, the dust oscillates around an equilibrium height of about 5m above the lunar surface. We finally consider transport of charged dusts around the lunar lander. Figure 7 shows dust trajectories overlayed with the potential contours. We find that at dusts at the lunar terminator region can become easily levitated due to lunar surface charging and become deposited on the lander surface. 4

5 4 Summary In summary, a simulation model is developed to investigate spacecraft charging and charged dust particle interactions on lunar surface. The simulation model consists of two components. The first is a 3-D full particle PIC model which uses macro-particle to represent solar wind protons, electrons, and photoelectrons, and calculates charging and differential charging of dielectric surface self-consistently. Simulations are carried out using real ion to electron mass ratio to obtain plasma sheath and wake and spacecraft charging for the terminator region. The second is a dust-in-plasma model which solves the charging and transport of individual dusts. Initial results are presented on lunar surface charging, lunar lander charging, electrostatic levitation of dusts, and charged dust transport around a lunar lander for average solar wind conditions. Future work need to consider more detailed charging models for dust-on-surface and coupled dust grains as well as dusty plasma interactions. Acknowledgment We acknowledge many useful discussions with Dave Brinza and Henry Garrett of JPL, and Joe Minow and Dale Ferguson of NASA MSFC. The work of JW was supported in part by the Jet Propulsion Laboratory and NASA Marshall Space Flight Center. References [1] O. Berg, A Lunar Terminator Configuration, Earth and Planetary Science Letters, 39, , [2] D. Criswell and B. De, Intense Localized Photoelectric Charging in the Lunar Sunset Terminator Region 2. Supercharging at the Progression of Sunset, J. Geophysical Research, 82(7), , [3] J. Gaier, The Effects of Lunar Dust on EVA Systems During the Apollo Missions, NASA TM , [4] J. Halekas, D. Mitchell, R. Lin, L. Hood, M. Acuna, and A. Binder, Evidence of for Negative Charging of the Lunar Surface in Shadow, Geophysical Research Letters, 29(10), [5] O. Havnes, C. K. Goertz, G. E. Morfill, E. Grun and W. Ip. Dust Charges, Cloud Potential and Instabilties in a Dust Cloud Embedded in a Plasma. Journal of Geophysical Research, 92: , [6] M. Horanyi and D. Mendis, The Dynamics of Charged Dust in the Tail of Comet Giacobini-Zinner, Journal of Geophysical Research, 91(A1), , [7] M. Horanyi, B. Walch, S. Robertson, and D. Alexander, Electrostatic Charging Properties of Apollo 17 Lunar Dust, Journal of Geophysical Research, 103(E4), ,1998. [8] P. Leung, et al., Electrostatic Effects on Dust Particles in Space, NASA CP-3127, [9] P. Leung, J. Wang, and A. Wong, Space Environment and Dust Plasma Interactions, AGU Western Pacific Geophysics Meeting, [10] J. McCoy and D. Criswell, Proc. 5th Lunar Conf., ,

6 [11] T. Nitter, O. Havnes, and F. Melandso, Levitation and Dynamics of Charged Dust in the Photoelectron Sheath Above Surfaces in Space, J. Geophysical Research, 103(A4), , [12] J. Rennilson and D. Criswell, Surveyor Observations of Lunar Horizon-Glow, The Moon, 10, , [13] A. Sickafoose, J. Colwell, M. Horanyi, and S. Robertson, Experimental Investigations on Photoelectric and Triboelectric Charging of Dust, Journal of Geophysical Research, 106(A5), , [14] A. Sickafoose, J. Colwell, M. Horanyi, and S. Robertson, Experimental Levitation of Dust Grains in a Plasma Sheath, Journal of Geophysical Research, 107(A11), 1408, [15] Z. Sternovsky, S. Robertson, A. Sickafoose, J. Colwell, M. Horanyi, Contact Charging of Lunar and Martian Dust Simulants, Journal of Geophysical Research, 107(E11),5105, 2002 [16] J. Wang, Y. Cao, R. Kafafy, J. Pierru, V. Decyk, Simulations of Ion Thruster Plume Spacecraft Interactions on Parallel Supercomputer, IEEE Trans. Plasma Science, 34(5), , [17] R. Kafafy and J. Wang, A Hybrid Grid Immersed-Finite-Element Particle-in-Cell Algorithm for Modeling Spacecraft Plasma Interactions, IEEE Trans. Plasma Science, 34(5), ,

7 Figure 1. Sketch by Apollo 17 Commander Gene Cernan on lunar sunrise observed from the lunar orbit 4m a b Solar wind flow 11m 2m Lunar Lander Solar wind flow Photoelectron emission surface Lunar Lander Photoelectron emission surface Figure 2. Simulation setup

8 Figure 3. Potential profile vs. height above the lunar surface for sun elevation angles of 0 o, 5 o, and 10 o. (Potential is normalized by 2.2eV and z is normalized by 1.4m) Figure 4. Lunar lander on flat lunar surface (sun elevation angles of 0 o ): potential, ion density, and photoelectron density contours. Figure 5. Lunar lander on flat lunar surface (sun elevation angles of 5 o ): potential, ion density, and photoelectron density contours.

9 a) sun elevation angle 0 o b) sun elevation angle 5 o Figure 6. Electrostatic levitation of dust from lunar surface. a) sun elevation angle 0 o b) sun elevation angle 5 o Figure 7. Transport of charged dust around lunar lander.