Global Modeling of the Electrostatic Lunar Surface Potential

Introduction: The surface of the Moon, like any object in a plasma, charges to an electrostatic potential that minimizes the total incident current [1]. The charging currents come from four main sources: photoemission of electrons (Jph), plasma electrons (Je), plasma ions (Ji), and secondary electrons (Jsec). (Jsec arises primarily from surface ionization by plasma electrons.) The lunar dayside typically charges positive, since Jph usually dominates (see Fig. 1). As a result a “photoelectron sheath” forms above the surface, which in the solar wind extends ~1m, and effectively shields the charged surface from the surrounding plasma [2]. On the nightside, the lunar surface usually charges negative since Je typically dominates. In this case a “Debye sheath” shields the surface potential [3] and can extend from meters to possibly ~1km above the surface [4]. However, there are significant uncertainties in lunar surface charging processes, and little is known about either spatial or temporal variations. Surface charging processes are thought to drive the transport of lunar dust grains with radii <10μm, particularly near the terminator [5,6]. The Surveyor landers observed ≈5μm grains levitating ~10cm above the surface [7,8]. During the Apollo missions 0.1μmscale dust in the lunar exosphere was observed up to ~100km altitude [9,10,11]. The most viable mechanisms proposed to explain these observations have been based on the principle that the like-charged surface and dust grains act to repel each other such that dust is lifted away from the surface. Under certain conditions, the heavier grains are predicted to electrostatically levitate near the surface [3,12], while the smaller grains are electrostatically “lofted” to ~10km in altitude [13,14]. These phenomena could present a significant hazard to future robotic and human exploration of the Moon [6,15]. Our objective here is to determine the global-scale variation of electrostatic potentials and electric fields on the surface of the Moon. We first focus on typical fast and slow solar wind cases, before using moments of the electron distribution function derived from Lunar Prospector Electron Reflectometer (LP/ER) data [16]. Also discussed is lunar surface charging in the magnetosphere, in particular during the Moon’s traversals through the plasma sheet. Surface Charging Model: We calculate the electrostatic surface potential, φS, using the equations given in [17]. We solve numerically to find φS such that the net incident current is approximately zero, i.e., Je + Ji + Jph ≈ 0, as described in [13,18]. (Jsec is not included here since for solar wind conditions it is not expected to be significant, as argued by [3].) Assuming 1-D Debye shielding above a plane, the lunar surface electric field is simply given by ES = φS / λD. Model Predictions: Fig. 2 shows predictions for lunar surface potentials and electric fields as a function of θ, given the typical fast and slow stream solar wind conditions [see 19]. As expected, charging on the dayside is photo-driven (φS > 0), while on the nightside it is electron-driven (φS < 0). A variation in surface potential is seen on the dayside due to the decrease in solar illumination (and surface photocurrent), as the terminator is approached. No variation is shown past the terminator on the nightside, since there is no solar illumination and the plasma environment there is initially assumed to be both uniform and stationary. Interestingly, Fig. 2 also shows that on the globalscale the transition from positive to negative surface potential is predicted to be well dayside of the terminator. This transition occurs at θ ≈ 70° for the fast stream and θ ≈ 35° for the slow stream conditions. We also note that the rate of change of surface potential (i.e.,