X. Wang, 1,3 C. T. Howes, 1,3 M. Horányi, 1,2,3 and S. Robertson 2,3. 1. Introduction. 2. Experiments

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1 GEOPHYSICAL RESEARCH LETTERS, VOL. 4, , doi:1.12/grl.5367, 213 Electric potentials in magnetic dipole fields normal and oblique to a surface in plasma: Understanding the solar wind interaction with lunar magnetic anomalies X. Wang, 1,3 C. T. Howes, 1,3 M. Horányi, 1,2,3 and S. Robertson 2,3 Received 1 February 213; revised 13 March 213; accepted 13 March 213; published 14 May 213. [1] We experimentally investigated the solar wind interaction with moderate-strength lunar magnetic anomalies in which the electrons are magnetized but the ions remain unmagnetized. Previously, we studied the plasma sheaths above an insulating surface in a magnetic dipole field oriented parallel to the surface. In this paper, when the dipole field is oriented normal to the surface, the surface potential largely rises, and a potential bump forms in the sheath in the magnetic cusp region due to a significant magnetic mirror reflection of the electrons. It is also found that the electrons are shielded from the central dipole wings and diverted into the side of the wings. When the dipole field obliquely intersects the surface, an asymmetric potential distribution develops. Our experimental results indicate that lunar surface charging can be greatly modified in the magnetic anomaly regions, creating extreme local electrical environments. Citation: Wang, X., C. T. Howes, M. Horányi, and S. Robertson (213), Electric potentials in magnetic dipole fields normal and oblique to a surface in plasma: Understanding the solar wind interaction with lunar magnetic anomalies, Geophys. Res. Lett., 4, , doi:1.12/grl Introduction [2] The Moon does not have a global magnetic field, only patches of crustal magnetization (the so-called magnetic anomalies) that distribute over the lunar surface and are mainly clustered on the far side of the Moon. In situ observations and computer simulations have shown that the lunar magnetic anomalies have a strong influence on the solar wind flow and alter the interaction of the solar wind with the lunar surface. A number of electromagnetic processes have been observed, including limb shocks [Russell and Lichtenstein, 1975; Lin et al., 1998; Halekas et al., 28a], minimagnetospheres [Halekas et al., 26b, 28a; Wieser et al., 21; Lue et al., 211], magnetic and electrostatic reflection of particles [Saito et al., 212, 21], and electrostatic waves [Halekas et al., 26a, 28b; Hashimoto 1 Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, Colorado 839, USA. 2 Department of Physics, University of Colorado, Boulder, Colorado 839, USA. 3 NASA Lunar Science Institute: Colorado Center for Lunar Dust and Atmospheric Studies, Boulder, Colorado 839, USA. Corresponding author: X. Wang, Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, Colorado 839, USA. (xu.wang@colorado.edu) 213. American Geophysical Union. All Rights Reserved /13/1.12/grl et al., 21]. Theoretical work suggested the formation of the minimagnetospheres on the lunar surface [Hood and Schubert, 198; Harnett and Winglee, 2, 22, 23]. Poppe et al. [212] performed a 1.5-dimensional particle-incell simulation in a crustal magnetic cusp region and reproduced the recent KAGUYA spacecraft observations, including the presence of an ambipolar electrostatic field, and the heating of the solar wind ions. The magnetic anomalies have also been found to be strongly related to the high-albedo markings on the lunar surface, the lunar swirls [Hood and Schubert, 198; Garrick-Bethell et al., 211a; Kramer et al., 211b]. Recent laboratory work by Bamford et al. [212] demonstrated that small-scale collisionless shocks and minimagnetospheres can form on the electron inertial-scale length to deflect the solar wind ions, possibly being responsible for the formation of the lunar swirls. Because the strength of the lunar crustal magnetic field can be up to hundreds of nano- Tesla at the surface, a wide range of interaction modes between the solar wind and the magnetic anomalies can exist. In the case of strong, clustered crustal fields, the interaction behaves mainly in a magnetohydrodynamic (MHD) fashion. However, in the case of moderate or weak, isolated crustal fields, more kinetic features will emerge in the interaction. We have conducted a series of laboratory experiments to investigate the solar wind interaction with moderate strength magnetic anomalies where the solar wind electrons are magnetized but the ions remain unmagnetized. [3] In our previous experiment [Wang et al., 212], we measured potentials above an insulating surface in a magnetic dipole field oriented parallel to the surface in plasma. The results indicated that the lunar surface could be charged largely positively in some magnetic anomaly regions. The enhanced surface electric fields may change the dust dynamics in these crustal fields, possibly causing geological features, e.g., the lunar swirls. In this paper, we report the results of a study of the electrical environment in a dipole field that is oriented both normal and oblique to the surface in plasma. 2. Experiments [4] The experiments were conducted in a grounded stainless steel vacuum chamber, 28 cm high and 51 cm in diameter (Figure 1). Argon plasma with a neutral pressure Torr was created by impact ionization using energetic electrons of 4 ev emitted from a negatively biased and heated filament at the bottom of the chamber. A metal plate above the filament prevented the primary electrons from entering the bulk plasma, which was electrically floated to reduce the disturbance to the bulk plasma. A magnetic dipole field was created above an insulating surface by placing a cylindrical permanent magnet underneath. A large

2 Figure 1. Emissive Probe Langmuir Probe Filament Insulating Surface Vacuum Pump Schematic of experiment and diagnostic setup. (f = 2 cm) and a small (f = 1.25 cm) cylindrical permanent magnet were used to create dipole fields of different strengths. The maximum strength of the magnetic field was ~ 13 G at the surface in the center of both cylindrical magnets. Plasma was characterized by a cylindrical Langmuir probe inserted in the bulk region where the magnetic field was negligible. Potentials above the surface were measured using an emissive probe [Diebold et al., 1988]. [5] The plasma density was cm 3. Two electron populations were identified from the Langmuir probe current-voltage (I-V) characteristics: cold and hot electrons with temperatures 2.5 and 5.5 ev, respectively. The cold electrons were generated from ionization of the neutral gas and dominate the electron density (95% of the total density). The hot electrons could be secondary electrons emitted from the chamber wall due to energetic primary electrons bombardment [Sternovsky and Robertson, 24] or created during plasma diffusion from the plasma source to the bulk. The hot electron density was 5% of the total density. The Debye length was.4 cm, which is much smaller than the geometry of the dipole field >6 cm shown from Figure 2, similar to the lunar case. The gyroradius of 3 ev highenergy tail electrons was.2 cm at the surface, which is much smaller than the radii of the cylindrical magnets (.625 and 1 cm) used in these experiments. The electrons were thus magnetized. In our experiments, as shown later from the potential profiles, the ions were accelerated to have an energy >5 ev at the surface within the sheath. The gyroradius of the ions is thus larger than 2 cm at the surface, which is larger than the radii of both cylindrical magnets. The ions were thus unmagnetized. than in the dipole wings, and the surface itself is charged more positively in the center of the cusp than the surface near the edge of the cusp region. The most positively charged regions on the surface are in the middle of the wings and the most negatively charged regions are in the side of the wings. The potential contours are slightly asymmetric in the radial direction because the probe scan was slightly titled to the surface. The maxima and minima are marked as I, II, III, and IV and will be explained in detail in section Magnetic Mirror Reflection of the Electrons in the Cusp Region [7] Potentials above the surface were measured with two different cylindrical magnets and also without a magnetic field to examine how the magnetic mirror reflection modifies the potentials in the magnetic cusp region. As shown in Figure 3a, the magnetic field strengths are similar at the surface above the center of the two magnets but it decays more slowly with height above the larger magnet. Figure 3a shows that the potential on the surface in both of the magnetic cusps is more positive than without the magnetic field. In a magnetic cusp, a magnetized electron is reflected when its pitch angle (angle between the particle velocity and the magnetic field vectors) is greater than a critical angle θ, hpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffii θ ¼ sin 1 B min =B max (1) where B min is the minimum field strength and B max the maximum field strength. As described in section 2, the ions remain unmagnetized and do not feel a significant magnetic force. The 3 ev high-energy tail electrons are magnetized when B min is 2 Gauss at ~ 6 cm from the surface, and B max is 13 Gauss at the surface. According to equation (1), the critical pitch angle θ is 8. This indicates that only the electrons within this loss cone can reach the surface and a large portion of electrons will be reflected in the cusp before they reach the surface in addition to the electrostatic reflection within the sheath, causing the potential rise on the surface. The critical pitch angle θ should be similar for the large and small magnets because B max and B min are similar in the two 3. Results 3.1. Overview of the Potential Distribution in the Dipole Field Normal to the Surface [6] Potential distribution above the surface in the dipole field normal to the surface is shown in Figure 2. The potentials above the surface in the cusp region are more positive Figure 2. Potential contours above the surface with the magnetic field vectors (black arrows) and the field lines (white lines) of the large magnet. 1687

3 (a) (b) Figure 3. (a) Vertical potential profiles and magnetic field strength profiles above the surface in the center of the small (B 1 ) and large (B 2 ) magnetic cusps and the vertical potential profile without the magnetic field. The arrows indicate the location of the potential bumps and the corresponding magnetic field strengths, respectively. (b) Sheath modeling results of the vertical potential profiles in the magnetic cusps. The sheath edge is where the potential drops.75t e from the bulk. cases. A similar portion of the electrons should be reflected, resulting in a similar surface potential. However, the surface potential above the small magnet is 5 V more negative than that above the large magnet, indicating that more electrons reach the surface. Electron-electron collisions in the cusp region are found to response for this effect. The electrons moving along the magnetic field lines into the cusp can collide with the electrons reflected by the magnetic mirror effect. When the electrons collide, the pitch angle scatters so that more electrons can fall into the loss cone to reach the surface and charge it more negatively. Given the same maximum field strength, the small magnet has higher field intensity than the large magnet. The collision rate is thus higher above the small magnet than above the large magnet, causing the potential on the surface above the small magnet to be more negative than that above the large magnet. This explanation is in an agreement with the modeling results shown below. [8] The profiles in Figure 3a show a bump, indicating a nonmonotonic potential distribution in the sheath in the magnetic cusp. The location of the potential bump is closer to the surface in the magnetic field that decays faster with height from the surface. The magnetic field strengths at the location of the potential bumps are similar and are at a transition region where the field strength starts climbing rapidly so the magnetic mirror reflection of the electrons becomes significant. The sheath profiles in the cusp region are modeled with the Poisson s equation, 2 Φ 2 ¼ n iðφþ n c e ðφþ nh e ðφþ (2) where e is the vacuum permittivity, q is the elementary charge, Φ(x) is the sheath potential as a function of distance from the surface x, n i is the ion density, n e is the electron density with the superscripts c and h for the cold and hot electron components, respectively. The sheath edge is identified at the position where the potential drops.75t e from the bulk potential in this weakly collisional plasma. The surface potential is extrapolated from the sheath potential profile. The ions are unmagnetized, hence their flux in the sheath is conserved, giving rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n i ðφþ ¼ n sh c s = c 2 s 2q ð Φ Φ shþ (3) M where n sh is the ion density at the sheath edge, c s is the ion sound speed, Φ sh is the potential at the sheath edge, M is the ion mass. Assuming Boltzmann electrons in this plasma, n c e ðφþ ¼ anc e ðφ ΦÞ=T e c and n h e ðφþ ¼ anh e ðφ ΦÞ=T e h (4) where n is the electron density at the start position for the modeling, T e is the electron temperature and a is the fraction of the electrons that fall in the loss cone to the surface. For collisionless and isotropic electrons, a ¼ 2p 2p θ p 2 1 fðþv v 2 sinðθþdvdθd 1 ¼ 1 cosðθþ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 1 1 B Bx ðþ fðþv v 2 sinðθþdvdθd where B is the magnetic field strength at the start position and B(x) is the magnetic field strength at x. However, the electrons can be collisional as discussed before, a collision factor c is then inserted in equation (5) to represent the efficiencies of the pitch angle scattering to get the electrons into the loss cone, giving " sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi# a ¼ c 1 1 B : (6) Bx ðþ [9] The ion and electron fluxes J i and J e are balanced at the surface, so J i ¼ J c e ðφ s ÞþJ h e ðφ s Þ; where Φ s is the surface potential: (7) rffiffiffiffiffi T e J i ¼ n sh and n sh ¼ n bulk e eφpre=te ¼ :5n bulk ; (8) M (5) 1688

4 Figure 4. Potential contours above the surface in the dipole field oriented 45 to the surface. where n sh and n bulk are the plasma density at the sheath edge and the bulk, respectively. Φ pre is the plasma potential drop across the presheath and is.75t e in our plasma, giving a density drop factor.5. J c e ð Φ s rffiffiffiffiffiffiffiffiffi Þ ¼ n c eð Φ Te sþ c and Je h ð 2pm Φ s rffiffiffiffiffiffiffiffiffi Þ ¼ n h eð Φ Te sþ h ; (9) 2pm where m is the electron mass. From equations (4) (9) the collision factor c at the surface can be calculated. [1] For the case of the sheath profile above the small magnet, we model the sheath in two sections. The first section is between the sheath edge and the location of the potential bump (purple dashed line in Figure 3b). The factor a is assumed to be unity as only the electrostatic reflection of the electrons occurs. The second section is between the location of the potential bump and the surface (green dashed line in Figure 3b). In this section, the collision factor c is found to be 5.2 at the surface. It is also assumed that the factor c increases linearly with the increase in the magnetic field B. This assumption is based on the fact that collision frequency of the electrons is proportional to their gyrofrequency and thus the magnetic field B. Using the density profiles formulated in equations (3) and (4) in the Poisson s equation (equation (2)), the modeling shows a good agreement with the data (Figure 3b). For the case of the sheath profile above the large magnet, the collision factor c is found to be 4 at the surface. The modeling result is also in a good agreement with the data (pink dashed line in Figure 3b). The collision factor c for both dipole fields is larger than unity. It thus shows that the electrons are collisional and have a higher rate above the small magnet as discussed before. These self-consistent modeling results indicate that the enhanced electron reflection due to the magnetic mirror effect is responsible for the modification of the sheath profile and the surface charging Charging on the Surface in the Dipole Field [11] The maxima and minima of the potentials on the surface are marked with I, II, III, and IV in Figure 2. The charging processes that cause these potential extremes are described as follows: [12] I - Magnetic mirror reflection of the electrons. As described above, a large portion of the electrons is returned into the plasma due to the magnetic mirror effect while the ions reach the surface without feeling a significant magnetic force, leading to a large potential rise on the surface in the central cusp region. [13] II - Reduced magnetic mirror reflection at the edge of the cusp. This potential minimum is located at the edge of the cusp region where the magnetic field strength at the surface is one-third of that in the center. The critical pitch angle θ increases to 14, significantly enlarging the losscone, so that more electrons will escape the magnetic mirror and reach the surface, charging this surface area more negatively than the surface area in the center of the cusp region. [14] III - Electron shielding. The surface areas in the middle of the dipole wings are charged most positively by the unmagnetized ions while the electrons are magnetically shielded away from the center of the wings. Similar to the data shown in the previous work [Wang et al., 212], a nonmonotonic sheath profile is shown above the surface in the electron-shielding region due to the electrons that penetrate into the shielding region by electron-electron collisions in the cusp. [15] IV - Flux increase from the diverted electrons. This potential minimum is located near the boundary of the dipole field. The surface in this region is charged most negatively, even 1 V more negatively than the surface without the magnetic field as shown in Figure 3a. Electrons that are shielded from the center of the dipole wings will follow the field lines into the side of the wings and charge the surface in this region more negatively Potential Distribution in a Dipole Field Oblique to the Surface [16] Potentials were also measured above the surface in the magnetic field of a dipole with its dipole moment set at 45 from the surface normal, showing an asymmetric distribution (Figure 4). On the side of the plot where a full dipole wing is present, the surface features are similar to the case when the dipole moment was set normal to the surface (section 3.3), including a potential rise on the surface in the center of the cusp, a slightly more negative charging at the edge of the cusp, the electron shielding region in the dipole wing, and the most negatively charged region near the boundary of the dipole field. The other side of the plot, however, shows different charging processes due to the partial presence of the dipole wing. The potential distribution matches the orientation of the magnetic fields. 4. Conclusion and Discussion [17] We experimentally investigated the plasma-surface interaction in a magnetic dipole field oriented both normal and at an oblique angle to an insulating surface to understand the electric environment near the lunar surface in the magnetic anomaly regions. Our plasmas consisted of magnetized electrons and unmagnetized ions. When the dipole field was normal to the surface, the potential distribution above the surface has shown that the surface potential largely rises and a potential bump forms in the sheath in the magnetic cusp region due to a significant magnetic mirror reflection of the electrons. When the dipole field was set to intersect the 1689

5 surface at an oblique angle, an asymmetric potential distribution was found, matching the orientation of the magnetic field. The electrons were excluded from the center of the dipole wings, causing the surface areas in the middle of the wings to charge most positively. The excluded electrons followed the field lines into the regions near the dipole boundary and charged the surface there most negatively. It was also found that the electron-electron collision is important in shaping the potential distributions in the dipole field. [18] The magnetic anomalies on the lunar surface are more complicated in geometry than a simple dipole field. Our laboratory experiments were aimed to understand the fundamental charging processes and the electrical environment in these regions. Our results indicate that these processes can largely modify the solar wind interaction with the lunar surface in the magnetic anomaly regions, creating complex surface electric environments compared to regions without magnetic fields. Dust particles in these regions can be subsequently charged and transported by the strong localized electric fields, possibly resulting in geological features such as the lunar swirls. [19] So far we did not include UV radiation and a supersonic ion flow in these experiments. The photoelectrons, generated by solar UV reaching the lunar surface, have the density dominating in the plasma environment on the lunar dayside and are crucial in surface charging. Also, the surface charging is expected to be significantly different due to the supersonic solar wind ions with the energy ~ 1 ev as discussed in our previous work [Wang et al., 212]. These two important parameters will be addressed in future experiments to complement our understanding of the surface electrical environment in the lunar magnetic anomaly regions. [2] Acknowledgments. This work was supported by the NASA s LASER program (NNX8AY77G), and by the NASA Lunar Science Institute s Colorado Center for Lunar Dust and Atmospheric Studies (CCLDAS). References Bamford, R. A., B. Kellett, W. J. Bradford, C. Norberg, A. Thornton, K. J. Gibson, I. A. Crawford, L. Silva, L. Gargaté, and R. Bingham (212), Minimagnetospheres above the Lunar Surface and the Formation of Lunar Swirls, Phys. Rev. Lett., 19, 8111, doi:1.113/physrevlett Diebold, D., N. Hershkowitz, A. D. IIIBailey, M. H. Cho, and T. Intrator (1988), Emissive probe current bias method of measuring dc vacuum potential, Rev. Sci. Instrum., 59, Garrick-Bethell, I., J. W. IIIHead, and C. M. Pieters (211), Spectral properties, magnetic fields, and dust transport at lunar swirls, ICARUS, 212, , doi:1.116/j.icarus Halekas, J. S., D. A. Brain, D. L. Mitchell, and R. P. Lin (26a), Whistler waves observed near lunar crustal magnetic sources, Geophys. Res. Lett., 33, L2214, doi:1.129/26gl Halekas, J. S., D. A. Brain, D. L. Mitchell, R. P. Lin, L. Harrison (26b), On the occurrence of magnetic enhancements caused by solar wind interaction with lunar crustal fields, Geophys. Res. Lett., 33, L121, doi:1.129/ 26GL Halekas, J. S., D. A. Brain, R. P. Lin, and D. L. Mitchell (28a), Solar wind interaction with lunar crustal magnetic anomalies, Adv. Space Res., 41, Halekas, J. S., G. T. Delory, D. A. Brain, R. P. Lin, and D. L. Mitchell (28b), Density cavity observed over a strong lunar crustal magnetic anomaly in the solar wind: a mini-magnetosphere?, Planet. Space Sci., 56, , doi:1.116/j.pss Harnett, E. M., and R. M. Winglee (2), Two-dimensional MHD simulations of the solar wind interaction with magnetic field anomalies on the surface of the Moon, J. Geophys. Res., 15, 24,997 25,7. Harnett, E. M., and R. M. Winglee (22), 2.5D Particle and MHD simulations of minimagnetospheres at the Moon, J. Geophys. Res., 17, A12. Harnett, E. M., and R. Winglee (23), 2.5-D simulations of the solar wind interacting with multiple dipoles on the surface of the Moon, J. Geophys. Res., 19, 188, doi:1.129/22ja9617. Hashimoto, K., et al. (21), Electrostatic solitary waves associated with magnetic anomalies and wake boundary of the Moon observed by KAGUYA, Geophys. Res. Lett., 37, L1924, doi:1.129/21gl Hood, L. L., and G. Schubert (198), Lunar magnetic anomalies and surface optical properties, Science, 28, Kramer, G. Y., J.-P. Combe, E. M. Harnett, B. R. Hawke, S. K. Noble, D. T. Blewett, T. B. McCord, and T. A. Giguere (211a), Characterization of lunar swirls at Mare Ingenii: A model for space weathering at magnetic anomalies, J. Geophys. Res., 116, E48, doi:1.129/ 21JE3669. Kramer, G. Y., et al. (211b), M 3 spectral analysis of lunar swirls and the link between optical maturation and surface hydroxyl formation at magnetic anomalies, J. Geophys. Res., 116, EG18, doi:1.129/ 21JE3729. Lin, R. P., D. L. Mitchell, D. W. Curtis, K. A. Anderson, C. W. Carlson, J. McFadden, M. H. Acuna, L. L. Hood, and A. Binder (1998), Lunar surface magnetic fields and their interaction with the solar wind: results from Lunar Prospector, Science, 281, Lue, C., Y. Futaana, S. Barabash, M. Wieser, M. Holmstrom, A. Bhardwaj, M. Dhanya, and P. Wurz (211), Strong influence of lunar crustal fields on the solar wind flow, Geophys. Res. Lett., 38, L322, doi:1.129/ 21GL Poppe, A. R., J. S. Halekas, G. T. Delory, and W. M. Farrell (212), Particle-in-cell simulations of the solar wind interaction with lunar crustal magnetic anomalies: Magnetic cusp regions, J. Geophys. Res., 117, A915, doi:1.129/212ja Russell, C. T., and B. R. Lichtenstein (1975), On the source of lunar limb compression, J. Geophys. Res., 8, 47. Saito, Y., M. N. Nishino, M. Fujimoto, T. Yamamoto, S. Yokota, H. Tsunakawa, H. Shibuya, M. Matsushima, H. Shimizu, and F. Takahashi (212), Simultaneous observation of the electron acceleration and ion deceleration over lunar magnetic anomalies, Earth Planets Space, 64, Saito, Y., et al. (21), In-flight Performance and Initial Results of Plasma Energy Angle and Composition Experiment (PACE) on SELENE (Kaguya), Space Sci. Rev., 154, , doi:1.17/s x. Sternovsky,., and S. Robertson (24), Langmuir probe interpretation for plasmas with secondary electrons from the wall, Phys. Plasmas, 11, 361, doi:1.163/ Wang, X., M. Horányi, and S. Robertson (212), Characteristics of a plasma sheath in a magnetic dipole field: Implications to the solar wind interaction with the lunar magnetic anomalies, J. Geophys. Res., 117, A6226, doi:1.129/212ja Wieser, M., S. Barabash, Y. Futaana, M. Holmstrom, A. Bhardwaj, R. Sridharan, M. B. Dhanya, P. Wurz, A. Schaufelberger, and K. Asamura (21), First observation of a mini-magnetosphere above a lunar magnetic anomaly using energetic neutral atoms, Geophys. Res. Lett., 37, L1513, doi:1.129/29gl