Surface Charging of Jupiter’s Moon Europa

Europa’s surface is exposed to a constant flow of plasma from its ionosphere and Jupiter’s magnetosphere. As these particles flow onto the surface, an electrostatic surface potential forms. We investigate the electrostatic charging of Europa’s surface using 3D particle-in-cell simulations. We find that surface potentials on Europa vary from −14 to −52 V. The predicted surface potentials vary as a function of location on Europa, illumination conditions, plasma environment, and surface properties. We reveal that the ionosphere has a significant “dampening effect,” limiting the formation of large negative surface potentials. Furthermore, we find that secondary emission is a key factor in determining the surface charge on Europa. We discuss how such potentials may be remotely detected by upcoming missions, such as Europa Clipper and JUICE. Our results may also be of use in the design of future missions to Europa’s surface, such as landers and other robotic explorers.


Introduction
Jupiter's moon Europa has been identified as a prime target in the search for life beyond Earth and will be visited by NASA's Europa Clipper (Howell & Pappalardo 2020) and ESA's JUpiter ICy moons Explorer (JUICE; Grasset et al. 2013) in the 2030s.Europa orbits deep within Jupiter's magnetosphere and is therefore immersed in a dense corotating plasma consisting of electrons, protons, and heavy ions (primarily O and S species; e.g., Bagenal et al. 2015;Kim et al. 2020).Europa possesses a tenuous atmosphere and associated ionosphere (Hall et al. 1995;Kliore et al. 1997), but this is not sufficiently dense to prevent magnetospheric plasma from flowing onto Europa's surface (Addison et al. 2021).Unlike planetary objects with thick atmospheres (e.g., Earth and Mars), Europa's ionosphere extends all the way down to the icy surface.Therefore, Europa's surface is exposed to both dense and cold ionospheric plasma as well as bombardment from the comparatively hot and tenuous magnetospheric plasma.
As Europa is immersed in plasma, its surface is exposed to electric currents driven by incident electrons and ions.In addition to this, sunlit parts of Europa's surface will experience additional charging currents due to photoemission from solar photons (Whipple 1981).In response to these currents, the surface will charge to an electric potential (f) such that the currents balance (Manka 1973;Whipple 1981): where I e is the current due to incident plasma electrons, I i is the current due to incident plasma ions, I s is the current due to emitted secondary electrons, and I ph is the photoelectron current in response to solar irradiation.The surface potential f is a value that satisfies Equation (1).
Surface charging is a well-known phenomenon at the Earth's Moon and has been extensively studied, both theoretically and observationally (e.g., Manka 1973;Freeman & Ibrahim 1975;Halekas et al. 2002Halekas et al. , 2009;;Poppe & Horányi 2010;Poppe et al. 2012;Stubbs et al. 2014).Surface charging has also been hypothesized to occur on a number of solar system bodies, including asteroids (Lee 1996;Hartzell & Scheeres 2013) and comets (Mendis et al. 1981;Flammer et al. 1986;Szego et al. 2014;Nordheim et al. 2015).Nordheim et al. (2014) reported strongly negative surface potentials at Saturn's moon Hyperion based on Cassini observations of upward-going electron beams when the spacecraft was magnetically connected to the moon's surface.Similar negative surface potentials have also been predicted to occur at the Saturnian moons Mimas, Tethys, Dione, and Rhea (Roussos et al. 2010;Nordheim et al. 2014).Surface charging has not been extensively studied for the Galilean moons, despite the fact that they are exposed to a comparatively high-density magnetospheric plasma environment.Ip et al. (1997) discussed the possibility of surface charging at Ganymede, but no quantitative predictions for the surface potential were presented.Lastly, the spacecraft charging environment near Europa has been explored (i.e., for Europa Clipper and JUICE; Garrett et al. 2017), but these studies did not consider the surface charging of Europa itself.
Here, we present the results of the first ever study of electric surface charging at Jupiter's moon Europa and discuss the possible implications for future observations by the Europa Clipper and JUICE missions, as well as possible future missions to Europa's surface (e.g., Pappalardo et al. 2013;Hand et al. 2022).

Simulations and Data
To simulate surface potentials at Europa we have used the Spacecraft Plasma Interaction Software (SPIS) package, which is a simulation package that models the interactions between objects (typically spacecraft) and plasma.SPIS is highly flexible, and users can simulate surface charging by defining incident plasma distributions, material properties (e.g., photoemission and secondary electron emission), and object geometries.SPIS simulates charging via the Poisson equation and a Particle-In-Cell (PIC) Monte Carlo solution to the Vlasov equation (Sarrailh et al. 2015), thus solving Equation (1).While typically used to study surface charging on spacecraft, SPIS can apply the same physics to study charging for any arbitrary object.We chose to use SPIS over alternative methods because it represents the state-of-the-art in PIC charging analysis, having been continuously developed for over 20 yr (Roussel et al. 2003).Here we chose a simple cylinder with a diameter of 1 m and a height of 3 m to represent Europa's surface.The cell size is 15 cm resulting in over 12,000 simulation cells in which the plasma dynamics must be calculated.This cell size was calculated based on the Debye length using the ionospheric electron temperature and density (see Table 1), in accordance with SPIS guidelines (Roussel et al. 2003;Sarrailh et al. 2015).When surface potentials are negative (−f), we treat the thermal electrons as a Boltzmann fluid, which speeds up the simulation run times.All ions and the suprathermal electrons are modeled using the full 3D PIC method.
Figure 1 illustrates Europa's position in Jupiter's magnetosphere.Jupiter's magnetosphere is populated by plasma originating from out-gassing and subsequent ionization at the moon Io (located interior to Europa, at a distance of 6 R J ).This plasma is transported outwards and corotates with the planet, and is centrifugally concentrated around Jupiter's equator.As the Jovian magnetic field is tilted by roughly 10°to its rotational axis (and the orbital plane of the moons), the Jovian magnetic field and the centrifugal plasma torus effectively wobbles up and down over the moon throughout one synodic rotation of Jupiter (11 hr).At Europa's orbital distance, the magnetospheric plasma corotates Jupiter at a greater velocity than the moon's orbital velocity (90 versus 14 km s −1 ).This results in a plasma flow that overtakes Europa at its (orbital) trailing hemisphere and flows over the moon toward the leading edge.This means that magnetospheric plasma does not impinge on Europa's surface in a uniform fashion, and therefore, conditions for surface charging vary depending on surface location.To capture this variability we simulate four scenarios representing different locations on Europa's surface; the sub-Jovian hemisphere (0°W), the leading hemisphere (90°W, downstream to the corotating magnetospheric plasma flow), the anti-Jovian hemisphere (180°), trailing hemisphere (270°W, upstream, facing into the corotating plasma flow).The leading hemisphere (90°W, downstream) case coincides with Europa's magnetospheric plasma wake, where the plasma densities are significantly depleted, which we capture in our model inputs (see Table 1).In addition to the variation in incident magnetospheric plasma, solar illumination conditions will vary across one Europa orbit (81 hr), so that surface locations will experience varying solar photoemission charging currents.To capture this solar variability, we conduct SPIS simulations at solar zenith angles 0°and 90°for each of the surface locations, except for the sub-Jovian hemisphere, which we have considered to be either experiencing local night or in eclipse by Jupiter.
Radio occultations by the Galileo mission revealed Europa to have a dense ionosphere that is both temporally and spatially  The leading hemisphere has a cooler Te iono owing to the formation of a magnetospheric plasma wake over this hemisphere.
Europa orbits Jupiter at 14 km s −1 , while the magnetospheric plasma corotates with Jupiter at 90 km s −1 , resulting in a wake forming at Europa's leading (downstream) hemisphere.Europa also possesses an ionosphere that is expected to be nonuniform and denser at the trailing (upstream) hemisphere.We capture this variability by simulating four discrete surface locations: sub-Jovian 0°, leading 90°, anti-Jovian 180°, and trailing 270°, in both sunlight and eclipse.
variable.To capture this variability, we select near-surface ionospheric electron densities taken from the Galileo E4 and E6 Europa occultations.During these flybys, the near-surface ionospheric electron density varied from Ne = 1 × 10 3 to 1 × 10 4 cm −3 .For the ionospheric plasma, we assume that the dominant ion is O 2 + .We define the electron and ion temperatures, and the magnetic field at the surface based on model results from magnetohydrodynamic (MHD) modeling of Europa by Harris et al. (2021Harris et al. ( , 2022;; see Table 1).
The upstream magnetospheric plasma parameters are taken from Table 5 in Bagenal et al. (2015), which itself is derived from Galileo and Voyager 1 data.This is widely regarded to be the best representation of the plasma environment at Europa.The Bagenal et al. (2015) data contain a hot/low and cold/high set of parameters, which represents the variability of the plasma environment across Jupiter's synodic rotation at Europa's orbit.The moon will move in and out of the magnetospheric plasma across these 11 hr, with the cold/high set of values representing plasma conditions at Europa when it is closest to the centrifugal equator.The plasma consists of a thermal (cold) and suprathermal (hot) population, as well as the ionospheric plasma described above.We also adopt the hot and cold variance for the ion temperature and plasma flow (Bagenal et al. 2015).
The secondary electron emission yield (δ E ) is a key material property and is an important parameter for determining the surface potential, particularly at high incident plasma electron temperatures (∼10-1000 s of eV; e.g., Halekas et al. 2009;Nordheim et al. 2014).We calculate δ E using the Katz et al. (1977) formula, where E is the average energy of the incoming electrons, max d is the maximum secondary emission yield = 0.78, E max is the maximum yield energy = 340 eV, and 4).We calculate max d by initially adopting the maximum secondary yield for water ice of 2.35 as calculated by Jurac et al. (1995).Halekas et al. (2009) investigated secondary electron emission at the Moon using observations by Lunar Prospector and found that the real secondary emission yields are a factor of ∼3× lower than those predicted from previous theoretical and laboratory studies.The authors argue that this may be due to surface roughness effects that are present on a natural surface compared to a pristine laboratory analog.We have used the same rationale for Europa's surface, and have set 2.35 3 0.78 max d = = .The complete set of SPIS simulation input parameters, including the magnetic field, can be found in Table 1, with references therein.

Surface Potentials
The following section presents the results from SPIS simulations.First, Figure 2 shows the surface potentials as a function of hemispheric location, illumination conditions, and magnetospheric plasma properties (hot or cold).In all hemispheres, photoemission reduces the surface potential by up to 2 V.This decrease is relatively small because the ionospheric, thermal, and suprathermal currents are 1 order of magnitude greater than the photoemission current.The trailing edge has the greatest potentials and this is because the plasma is flowing directly onto the surface, rather than away from (leading) or across it (suband anti-Jovian).This occurs despite a much denser ionosphere, which acts to suppress the overall potential.This is discussed further in Figure 3.In most cases, a hotter population results in a greater negative potential, especially in the leading edge.In this hemisphere, plasma is effectively flowing away from the surface and only electrons have access to the surface because of their increased thermal motion compared to the less mobile O + magnetospheric ions.A temperature increase from 200 eV (cold) to 1200 eV (hot) (per Bagenal et al. 2015), in the suprathermal population leads to significantly higher potentials (−14 versus −42 V) even when the plasma drift is effectively 0 m s −1 or negative.This effect is less pronounced on the other three hemispheres, because the O + ions have access to the surface, which acts as a positive current to quell the magnitude of the otherwise negative potential.In the trailing hemisphere, the colder and denser plasma population (i.e., when Europa is closest to the centrifugal equator), leads to a marginally stronger surface potential.This is attributable to the increased number of electrons that have access to the surface because of the plasma flow.The sub-Jovian hemisphere is slightly more negative than the anti-Jovian side and this is due to the 14% decrease in the ionospheric density (n sJ = 6000 cm −3 versus n aJ = 7000 cm −3 ; See Table 1).This is further evidence of ionospheric suppression.
Next, we examine the role of the ionosphere on surface charging.We select the trailing hemisphere during eclipse, compare it to the Table 5 parameters (hot and cold) from Bagenal et al. (2015), and reduce N iono from 10,000 to 100 cm −3 .The rationale for this examination is that our limited knowledge of Europa's ionosphere indicates that it likely generated in large part by impact ionization from magnetospheric electrons (Saur et al. 1998) and is both spatially and temporally variable (e.g., Kliore et al. 1997;Saur et al. 1998;Paterson et al. 1999).Figure 3 shows  that when all other parameters are fixed, a reduced ionosphere leads to a greater surface potential and this is especially the case with the hot parameters.This "ionospheric dampening" effect also acts to suppress surface potentials at the other hemispheres by a similar magnitude.
Finally, we turn our attention to the role of secondary electron emission.We compare our δ E = 0.78, with the original value of δ E = 2. 35 and E 340 eV max = for water ice provided by Jurac et al. (1995), and a nonconducting lunar regolith material, where 1.9 max d = and E 200 eV max = . Figure 4(a) shows the resulting secondary emission yield curves across the energy range 1 eV-1 MeV.It also highlights that the point at which the yield crosses unity, δ E = 1, varies from 30 eV (water ice and lunar regolith) up to 125 eV (this study).On the right, we see the consequences of this, where potentials for the cold trailing edge during eclipse shift from −50 to −5 V (Figure 4(b)), depending on what secondary emissions are assigned.While we emphasize that we have used the most accurate available secondary emission yield parameters for Europa's primarily water ice surface, we recognize the need for additional laboratory experiments on secondary emission yields, particularly for nonwater ice surface materials thought to exist on Europa (e.g., Grundy et al. 2007).

Discussion and Conclusions
Our simulations reveal that surface potentials on Europa vary as a function of location, solar illumination, magnetospheric plasma conditions, ionospheric density, and surface material.Predicted surface potentials are always negative, ranging from f = −14 V on the cold sunlit anti-Jovian hemisphere to f = −52 V on the cold trailing hemisphere in shadow.
Our results demonstrate that the ionosphere has a significant "dampening effect" on surface charging.This is due to the fact that the number density of ionospheric electrons is over 1 order of magnitude higher than that of the ambient magnetospheric electrons, and therefore, the ionospheric electrons represent the dominant charging current to the surface.At this point, the origin and temporal and spatial variability of Europa's ionosphere is not well understood.While modeling suggests that Europa's ionosphere should be primarily driven by electron impact ionization from magnetospheric plasma (e.g., Saur et al. 1998), the Galileo radio science observations indicate that solar photoionization may also play an important role (Kliore et al. 1997;McGrath et al. 2009).While photoionization will vary diurnally with the local solar zenith angle, the electron impact ionization rate will be highly nonuniform and depend on local aspects of Europa's magnetospheric interaction.Here we have chosen a near-surface ionospheric electron density of 100 cm −3 to represent a scenario where the ionosphere is locally depleted or collapsed.This has the consequence of shifting the potentials from −51 V (cold, dense) to −125 V (hot, depleted) (See Figure 3).Other complications are added by the 10°tilt of Jupiter's magnetic field and Europa's 81 hr orbit, the effects of which are seen in the background magnetospheric plasma (See Section 2) and the subsequent effect on surface charging (Figure 2).In short, our results indicate that the ionosphere plays a key role in surface charging at Europa, and that surface potentials are greatly enhanced when the ionosphere is locally depleted.
Solar illumination and subsequent photoemission can play a large role in the charging of solar system objects, especially when the incoming surface currents are small (Whipple 1981).We find that solar illumination and photoemission increase surface potentials f across all hemispheres (Figure 2), but it does not reduce the potentials by more than 2 V in any hemisphere.Sunlight may also play a secondary role in surface charging if the atmospheric photoelectron distribution possesses a high-energy tail, which would provide an additional local source of fairly hot (tens of eV) electrons.
Secondary electron emission plays a key role in the charging of planetary surfaces.Figure 4 shows that a change in max d can shift potentials from −52 to −5 V on the trailing hemisphere during eclipse under cold plasma conditions.While we have here assumed a pure water ice surface for our simulations, remote sensing observations indicate that significant quantities of nonwater ice material are locally present on Europa, particularly at low latitudes on the trailing hemisphere (e.g., Grundy et al. 2007;Ligier et al. 2016).If such nonwater ice material has significantly different secondary emission properties, then this may in turn affect the local surface potentials in this region.Clearly, additional laboratory work is needed to determine the secondary emission characteristics of nonwater ice candidate species expected to be present on Europa.However, we note that secondary electrons may also present a unique way to probe negative surface potentials at Europa.At the Earth's Moon (Halekas et al. 2005), and at Saturn's moon Hyperion (Nordheim et al. 2014), field-aligned electron beams were detected when spacecraft were magnetically connected to regions of highly negative surface potential.In these cases, the energy of the beam electrons is representative of the electrostatic potential difference between the spacecraft and the surface.Thus, plasma instruments on upcoming missions such as JUICE and Europa Clipper may be able to remotely probe the surface potential at Europa and the other Galilean moons.This also presents another intriguing opportunity: if these missions characterize the local charging environment at the moons well enough, then the observations of secondary electron beams can effectively be inverted to estimate the secondary emission yield, e.g., through the same type of surface charging simulations as we have conducted here.Such inversions were previously successfully carried out at the Earth's Moon by Halekas et al. (2009).If the secondary emission yields of relevant candidate surface materials are known (e.g., through laboratory experiments), then the secondary electron beam observation could feasibly be used as an additional remote probe of the local presence of nonwater ice species on the surface.
Finally, we note that several possible missions to Europa's surface have been previously studied (Pappalardo et al. 2013;Hand et al. 2022).Such missions would likely need to consider the local surface charging conditions at potential landing sites.While we do not suggest that the surface potentials predicted herein would be a hazard to a future mission, we urge that care should nonetheless be taken to avoid any unwanted effects, e.g., an electrostatic discharge between a lander and the surface.

Figure 2 .
Figure 2. Surface potentials as a function of location on Europa's hemispheres, solar illumination conditions, and magnetospheric plasma properties.

Figure 3 .
Figure 3.The effects of ionospheric density on surface potential on the trailing hemisphere during eclipse.

Figure 4 .
Figure 4. (a) Secondary emission yields δ E .(b) The impact on surface potentials at the anti-Jovian hemisphere during eclipse.