Reflected Protons in the Lunar Wake and Their Effects on Wake Potentials

Abstract

The refilling of the lunar wake is facilitated by the wake ambipolar electric potential arising from the electron pressure gradient. Incident solar wind protons can be reflected by the lunar crustal magnetic fields and the lunar surface on the dayside and repicked up, entering the lunar wake due to their large gyroradii. This burst of positive charges can cause the lunar wake potential to be reduced by hundreds of volts. We utilize over 7 years of ARTEMIS (Acceleration, Reconnection, Turbulence, and Electrodynamics of the Moon's Interaction with the Sun) measurements to systematically investigate how the reflected protons affect the lunar wake potential structure when the Moon is immersed in the solar wind. RPs have a peak occurrence rate of ~20% for downstream distances from the Moon at N × 2πR _g and a preference of high occurrence rates and high densities in the direction of the motional electric field of the solar wind. We show that reflected protons in the lunar wake can significantly change the electrostatic ambipolar potentials in the wake, leading in turn to the formation of field-aligned, accelerated electron beams. Our case study also suggests a nonmonotonic field-aligned potential structure in the presence of reflected protons in the wake. Lastly, our results show that when the reflected proton density is larger than ~30% of the local proton density from refilling solar wind protons, the wake potential scales as the logarithmic density of reflected protons, which can be explained by the Boltzmann relation.

Figure 1.

An orbit example of the ARTEMIS Probe P1 on 9 September 2015. From top to bottom, the time series of (a) the spacecraft position in the SSE coordinates and r_cyl is the distance from the X axis; (b) the spacecraft potential; (c) the magnetic field strength and vector components in the SSE coordinates; the averaged ion energy spectra for solar wind protons (d) and reflected protons (e); (f) the calculated ion density for solar wind protons (blue) and reflected protons (red); (g) the deduced wake potential from electrons traveling toward the wake, blue for parallel electrons and red for antiparallel electrons; (h) and (i) the electron phase space density [cm⁻³ (km/s)⁻³] for pitch angles (PAs) 0–15° and 165–180°, respectively; and (j–l) normalized pitch angle distributions for energy bins centered at 55, 286, and 857 eV, respectively. The vertical dotted lines mark where electron spectra in Figure 2 are taken.

Figure 2.

The electron phase space density [cm⁻³ (km/s)⁻³] against energy for pitch angles 0–30° (blue), 75–105° (green), and 150–180° (red) for 18:02 UT (a) and 18:11 UT (b), as indicated by the two dotted dashed line in Figure 1. In each panel, the dashed lines are for upstream solar wind electrons and the solid lines for electrons in the wake.

Figure 3.

The occurrence rate (a), the median density (b), and the median density ratio to the upstream solar wind density (c) for reflected protons as a function of X_E/(2πR_g), where R_g is the proton gyroradius, for r_cyl < 1R_L and |Z_E| < 0.5R_L. The thin lines in (b) and (c) are quartiles.

Figure 4.

The occurrence rate of reflected protons as a function of X_E/(2πR_g) for r_cyl < 1R_L and |Z_E| < 0.5R_L, separated for different conditions. (a) The blue line is the RP occurrence rate for R_g>1R_L and red for R_g < 1R_L. (b) The blue line is the RP occurrence rate for more perpendicular IMFs (60° < cone angle < 120°) and red for more parallel IMFs (cone angle < 60° or >120°).

Figure 5.

The occurrence rate (a and d), the median density (cm⁻³) (b and e), and the median density ratio to the local solar wind density (c and f) for reflected protons in different projections. The left column is in the Y_E-Z_E plane for X_E = [−2.0,−1.1]R_L and the right in the X_E-Z_E plane for Y_E = [−0.5,−0.5]R_L.

Figure 6.

The averaged wake potentials in the Y_E-Z_E plane for X_E = [−2.0,−1.1]R_L (a and b) and the right in the X_E-Z_E plane for Y_E = [−0.5,−0.5]R_L (d and e). The upper row is for when there is no reflected proton and the lower row for when there are reflected protons. The potential differences of these two scenarios, that is, averaged potentials in Figures 6b–6e subtracted by averaged potentials in Figures 6a–6d, are shown in Figures 6c and 6f, respectively.

Figure 7.

(a) The mean wake potentials as a function of the local solar wind density and the reflected proton density for X_SSE = [−2.0,−1.1]R_L. The dashed white line marks the 1-to-1 ratio. (b) The mean wake potentials as a function of the reflected proton density, different colors for different local solar wind densities, with error bars indicate errors to the mean values. The vertical dotted lines in both (a) and (b) mark the logarithmic mean values of each local SWP density range.