On the Response of Protons to Dynamical Reconfigurations of Mercury's Magnetosphere

Abstract

We examine the dynamics of protons during tail-like to dipole-like reconfigurations of Mercury's magnetosphere. Such reconfigurations that frequently occur in the highly dynamical Hermean environment are accompanied by induced electric fields leading to short-lived convection enhancements. Using test particle calculations, we show that, under the effect of such induced electric fields, protons may be subjected to prominent energization while being injected into the inner magnetosphere. We demonstrate that this energization occurs in a nonadiabatic manner and can reach several tens of keV, possibly leading to particle trapping around the planet. Recent observations from BepiColombo during Mercury's third flyby provide evidences of energetic protons drifting in the vicinity of the planet. The present impulsive energization process is a possible mechanism for the build-up of such populations.

Key Points

• Observational evidences of energetic protons (tens of keVs) in the inner magnetosphere of Mercury

• Electric field induced by rapid reconfigurations of the magnetosphere may lead to proton energization up to this energy range

• This energization occurs in a nonadiabatic manner and contributes to ring current trapping in the inner magnetosphere

Plain Language Summary

The electric field induced by short-lived relaxation of the magnetospheric field lines at Mercury may lead to prominent energization (tens of keV) of protons. As a result, these ion populations may be injected into the ring current in the inner magnetosphere.

1 Introduction

Mercury's magnetosphere is a highly dynamical environment with a typical Dungey cycle of a few minutes (e.g., Slavin et al., 2010). Despite its small spatial scales, this magnetosphere is an efficient particle accelerator. Indeed, the pioneering in-situ measurements of Mariner 10 in 1974–1975 provided evidences of energetic particles up to several tens of keVs (e.g., Eraker & Simpson, 1986). Subsequently, both EPS (Ho et al., 2011) and FIPS (Raines et al., 2013) instruments onboard MESSENGER revealed energetic ions (from keVs up to a few tens of keV) in Mercury's plasma sheet. The presence of such ions was confirmed during the third flyby of BepiColombo in June 2023. Ion analyzers that are parts of the MPPE (Mercury Plasma Particle Experiments) consortium onboard Mio (Saito et al., 2021) indeed recorded protons with energies well above 10 keV down to low altitudes, suggesting a closed ring current in the vicinity of the planet. In the present paper, we investigate a possible mechanism for the production of such energetic ion populations, namely, the effect of the electric field induced by rapid (a few seconds) magnetospheric reconfigurations. Such reconfigurations are known to frequently occur at Mercury with time scales of the order of several seconds, that is, much smaller than that of the Dungey cycle (e.g., Sundberg et al., 2012). Dewey et al. (2020) also demonstrated that they are associated with the formation of a current wedge in a like manner to substorm dipolarization at Earth. Here, we examine the response of proton populations to such events.

2 Model Ion Trajectories

To investigate ion transport during relaxation of Mercury's magnetotail, we performed test particle calculations in simplified models of electric and magnetic fields. For the magnetic field, we adopted a modified version of Luhmann and Friesen (1979) (hereinafter referred to as LF-79) that consists of a planetary dipole and a Harris-type current sheet with half-thickness L and asymptotic tail lobe field B_T. Note that, for simplicity, the northward offset of the magnetic dipole (e.g., Anderson et al., 2011) was not considered here. As for the large-scale convection electric field, it was derived from a two-cell Volland-Stern potential distribution (Volland, 1978) and calculated at each trajectory step assuming that magnetic field lines are equipotential (Delcourt et al., 2003).

The relaxation of the magnetic field lines was modeled by letting LF-79 evolve from a given state to a less disturbed (more dipolar) one. In practice, the half-thickness L in LF-79 was kept constant (set to 1,000 km, consistently with the ∼0.39 R_M thickness reported by Poh et al. (2017)) while the asymptotic field B_T was varied from a given value to a smaller one. This B_T variation was modeled as:

$$${B}_{T}\,(t)={B}_{pre\mbox{-}}+f(t)\,\left({B}_{post\mbox{-}}-{B}_{pre\mbox{-}}\right)$$$ (1)

where t is the time, B_pre- and B_post- are the tail lobe field magnitudes before and after the relaxation (set to 80 and 40 nT, respectively), and f(t) is a polynomial of degree 5 that varies between 0 at t = 0 and 1 at t = τ_B (τ_B being the time scale of the magnetic transition). Such a polynomial description for f(t) ensures that the electric field induced by the time-varying magnetic field (namely, E = −∂A/∂t where A is the vector potential) vanishes both at the onset and at the end of the magnetic transition (see Delcourt (2002) for details on this calculation technique).

Figure 1 shows model trajectories of protons originating from the high-latitude dayside sector in the presence of such a rapid reconfiguration of the magnetotail. The protons considered here are produced via ionization of exospheric neutrals released from the planet surface by a variety of processes (solar wind sputtering, thermal desorption, meteoritic impact). Once ionized, these particles are transported from dayside to nightside over the polar cap. In Figure 1, test H⁺ are launched from the same location with identical energy (1 eV) but at different times. Because of these different ejection times, the ions are struck by the magnetic transition in distinct regions of space. Looking first at the trajectory coded in black, it can be seen in the left panels of Figure 1 that the reconfiguration occurs well after crossing of the equator. More precisely, this particle experiences an energy gain up to ∼300 eV upon crossing of the tail current sheet in the steady pre-dipolarization state and it subsequently travels back toward the planet. The magnetic moment (μ) profile in the lower right panel of Figure 1 reveals that the net μ change during crossing of the tail current sheet is moderate, a behavior first reported by Speiser (1965) and referred to as quasi-adiabatic (e.g., Büchner & Zelenyi, 1989). Because this particle is located at low altitudes when the relaxation strikes, it is not affected by the magnetic transition.

Figure 1

Model trajectories of protons launched from the high-latitude dayside sector with 1 eV energy and distinct (color coded) initial times (left) trajectory projections in the noon-midnight meridian plane and in the equatorial plane (right) electric field magnitude, kinetic energy and magnetic moment (normalized to the initial value) versus time. A 5-s magnetic transition is considered, starting at t = 0 (shaded area in the right panels). In the upper left panel, dotted and solid gray lines show the magnetic field lines in the initial and final configurations, respectively. Also closed circles along the particle paths delimit the trajectory sequences during which the magnetic transition occurs. During the first portion of the trajectories, black, blue and red paths are overlapping.

For the trajectory coded in blue in Figure 1, the particle has been launched 20 s after the first one. In this latter case, it is apparent from Figure 1 that the particle is struck by the magnetic transition immediately after equatorial crossing. After experiencing a quasi-adiabatic motion, this particle is subjected to a large μ increase (by about five five orders of magnitude) under the effect of the surging electric field. More precisely, it can be seen that the μ change occurs in two steps: first due to the reversal of the magnetic field at equator (spatial nonadiabaticity), second due to the time-varying magnetic field off-equator (temporal nonadiabaticity). While spatial nonadiabaticity can be characterized by weighing field line curvature radius versus Larmor radius, temporal nonadiabaticity can be characterized by weighing magnetic transition time scale versus cyclotron period. It should be stressed that, while the energy gain in steady state is constrained by the dawn-dusk potential drop (set here to 10 kV), there is no well-defined limit for particle energization under the effect of the induced electric that solely depends upon the amplitude (∆A) and the time scale (τ) of the magnetic transition (equivalently, E ≡ ∆A/τ). In fact, it can be seen in the middle right panel that the particle coded in blue experiences an energization up to ∼25 keV (i.e., well above the dawn-dusk potential drop) during the magnetic transition, which contrasts with the modest energy gain of the particle coded in black. Also, under the effect of the surging electric field, the particle coded in blue experiences a prominent duskward drift and ultimately precipitates onto the planet surface in the post-terminator region.

The trajectory coded in red in Figure 1 still shows another type of behavior. In this latter case, the particle has been launched from the same location in the dayside sector but 50 s after the particle coded in black. In the upper left panel of Figure 1, it can be seen that the field line relaxation strikes before crossing of the equator so that the H⁺ evolves through a different field reversal and does not display a Speiser orbit. This latter H⁺ is strongly affected by the surging electric field: it experiences a μ change by ∼6 orders of magnitude and energization up to ∼40 keV. Also, in the lower left panel of Figure 1, it can be seen that this particle is rapidly brought into the dayside sector and ultimately precipitates in the mid-afternoon sector.

The various trajectories in Figure 1 demonstrate the co-existence of two distinct types of nonadiabatic regimes during short-lived reconfigurations of the magnetosphere: one is due to spatial gradient of the magnetic field while the other is due to temporal variation of the magnetic field and may go together with prominent perpendicular energization. Figure 1 also puts forward a clear trajectory dependence upon bounce phase, with a variety of behaviors depending upon the particle position when the magnetic transition occurs.

3 Particle Injection Into Ring Current

The large perpendicular energization experienced by protons under the effect of the surging induced electric field is of importance for the long-term ion behavior. This is illustrated in Figure 2 that shows the trajectories of test H⁺ launched from the same position in the dayside sector, either in steady state (top panels) or in the case of a rapid magnetic transition (bottom panels). In the top panels, it can be seen that during its transport in the magnetospheric lobe over the polar cap, the H⁺ experiences a weak acceleration of a few eVs. This acceleration can be understood by examining the parallel equation of motion. In the absence of a parallel electric field, this equation writes (see, e.g., Delcourt et al. (2002)):

$$${\overset{.}{V}}_{//}={\mathbf{V}}_{\boldsymbol{E}}\cdot \left[\frac{\partial \mathbf{b}}{\partial t}+{V}_{//}\frac{\partial \mathbf{b}}{\partial s}+{\mathbf{V}}_{\boldsymbol{E}}\cdot \nabla \mathbf{b}\right]$$$ (2)

where V_// is the parallel speed, V_E, the E × B drift velocity, b, a unit vector in the B direction, and s, the curvilinear abscissa along the field line. While the second term on the right-hand side of (Equation 2) describes the acceleration due to the curvature of the magnetic field lines, the third term describes the centrifugal acceleration experienced by the particle as it E × B convects across the magnetic field lines. This latter term thus does not depend upon curvature of the magnetic field lines but upon curvature of the E × B drift paths. At Earth, this latter centrifugal acceleration is responsible for some parallel acceleration in the magnetospheric lobes (e.g., Yau et al. (2012)). It is more pronounced at Mercury because of the small spatial scales of the Hermean environment (Delcourt et al. (2002)). It can be fairly significant for heavy ions of planetary origin (e.g., Na⁺), yielding energy gains up to a few hundreds of eV during their transport in the magnetospheric lobes (Delcourt et al. (2003)).

Figure 2

Model trajectories of protons launched from the high-latitude dayside sector with 1 eV energy (top) in steady state and (bottom) in a 5-s magnetic field reconfiguration (starting at t = 0) (left) trajectory projections in the equatorial plane (center) kinetic energy versus time (right) magnetic moment (normalized to the initial value) versus time. In the bottom left panel, closed circles delimit the trajectory sequence during which the magnetic transition occurs.

Subsequently, it can be seen in the top panels of Figure 2 that as the test H⁺ intercepts the neutral sheet, it experiences an energization up to several hundreds of eV. This trajectory sequence goes together with some μ increase; hence, particle trapping at high altitudes. Ultimately, the test H⁺ precipitates onto the planet surface after several bounces in the pre-midnight sector.

The bottom panels of Figure 2 display a different long-term behavior if field line dipolarization occurs at some point during transport. Indeed, the test H⁺ is here struck by a surging electric field immediately after crossing of the equator and this goes together with an energization up to a few tens of keV. This energization essentially occurs in the perpendicular direction, as evidenced from the prominent μ enhancement experienced by the particle (lower right panel). As a result of this large μ increase, the test H⁺ remains trapped at high altitudes and rapidly drifts toward the dayside sector. Subsequently it pursues this longitudinal drift around the planet back into the nightside sector. Figure 2 thus clearly demonstrates the possible formation of trapped energetic populations encircling the planet due to transient reconfiguration of Mercury's magnetosphere.

4 Equatorward Focusing

Another consequence of the electric field induced by magnetic field line relaxation is the equatorward focusing of plasma sheet populations. This can be appreciated in Figure 3 that shows selected H⁺ trajectories during a 10-s magnetic transition.

Figure 3

Identical to Figure 1 but for protons initiated in the nightside sector (open circle) with 1 keV energy and two distinct (color coded) times. A 10-s magnetic transition is considered. Closed circles along the particle paths delimit the trajectory sequences during which the magnetic transition occurs.

Looking first at the trajectory coded in black, it can be seen that this test H⁺ executes a quasi-adiabatic motion upon crossing of the current sheet and experiences a net energy gain up to ∼2 keV. Once it leaves the equator, this H⁺ remains temporarily confined to low latitudes while the magnetic field lines evolve toward a more dipolar configuration. This focusing toward equator can be very pronounced as illustrated by the second trajectory (coded in red) in Figure 3. In this latter case, the particle is initiated a few seconds after the first one and it can be seen that it remains confined to the very vicinity of the equator. Although its net μ change is similar to that of the trajectory coded in black, this latter H⁺ experiences a gradual energy loss. This loss in the parallel direction ranges from a few keV down to about 100 eV.

The above equatorward focusing and associated deceleration can be better understood using Figure 4 that shows, for a given magnetic field line, the time evolution of the E × B drift speed (top panel) as well the magnitude of the E × B related centrifugal acceleration (bottom panel). It is apparent from the top panel of this figure that the E × B drift speed at equator peaks at $${\sim} 200$$ km/s at half-relaxation. Also, in the bottom panel, the equatorward centrifugal acceleration (last term in Equation 2) peaks at 100 km/s² immediately above and below the equator where the E × B drift path curvature is maximum. As a consequence of this centrifugal acceleration, particles leaving the equator with insufficient parallel speed (due to nonadiabatic pitch angle scattering upon current sheet crossing) may be turned back toward the equator in the course of the magnetic transition. This is the case of the test H⁺ coded in red in Figure 3, that remains confined to the equatorial vicinity until the end of the magnetic transition. Figure 3 thus suggests that equatorward focusing during field line relaxation may lead to the build-up of ion populations with low parallel energy near the equator.

Figure 4

Color-coded contours of (top) E × B drift speed and (bottom) centrifugal acceleration along the E × B drift paths (last term in Equation 2) during a 10-s magnetic transition. These contours are shown for a magnetic field line intercepting the equator at 2.5 R_M in the initial taillike configuration. In both panels, white lines show the E × B paths during the magnetic transition.

5 Planetary Proton Transport During Dipolarization

To get insights into the global response of protons to magnetospheric reconfigurations, we performed systematic trajectory calculations, launching test H⁺ from different latitudes (between 60° and 90°) and longitudes (between 1000 MLT and 1400 MLT) in the cusp region. These ions were first traced in steady state within a three-dimensional grid of 0.05 R_M edge. Each of the trajectory bins obtained was subsequently tracked within a 10-s magnetic transition. Figure 5 shows the average ion energy obtained in different X–Z planes (from top to bottom) and at different times (from left to right). Equatorial (X–Y) cuts in the dusk sector are also shown in the top panels of this figure.

Figure 5

Average energy of planetary H⁺ at various times (from left to right t = 0, t = 3 s, t = 6 s, t = 10 s, and t = 30 s) and in different X–Z planes (from top to bottom Y = 0, Y = −0.5 R_M, Y = −1.0 R_M, and Y = −1.5 R_M) during a 10-s magnetic transition. The lower parts of the top panels show the ion average energy in the dusk equatorial plane. Energy is coded according to the scale at bottom.

In the upper left panel of Figure 5 that shows the initial steady state configuration, it can be seen that the planetary H⁺ flow from high-latitude dayside sector into pre-midnight magnetotail over the polar cap. With a convection potential drop of 10 kV, these H⁺ are energized up to several keVs upon drifting across the magnetotail and populate the dusk flank of the magnetosphere. It is also apparent from the lower left panels of Figure 5 that, after drifting into the dayside sector, the keV H⁺ are recirculated at high latitudes in the plasma mantle. While traveling along this route, these protons of planetary origin may mix with populations originating from the magnetosheath and gain access to the distant plasma sheet. Such a recirculation scheme follows from the existence of a magnetic field minimum in the outer cusp so that ions that are trapped near the equator bifurcate toward high latitudes and gradually drift toward the tail as proposed for example, by Seki et al. (1998).

Moving from left to right in Figure 5, several features of interest can be identified in the course of the magnetic transition. First, it is apparent that, while the innermost nightside magnetosphere (typically, inward of 1 R_M altitude) remains essentially unaffected, prominent H⁺ energization (up to tens of keV) is achieved in the more distant tail. In this respect, the heavy dashed lines in the uppermost panels of Figure 5 indicate the location where the relaxation time scale-to-cyclotron period ratio, τ_B/τ_C, is of the order 1 for protons. It is clearly apparent here that most of the H⁺ energization occurs tailward of this boundary. As mentioned above, this is because, at such large distances, the H⁺ gyromotion occurs on the time scale of the magnetic transition. Under the effect of the surging induced electric field, the particle is subjected to an acceleration that does not average out after a full cyclotron turn. This prominent energization tailward of τ_B/τ_C ∼1 is reminiscent of the “injection boundary” postulated by McIlwain (1974) to explain the sudden injection of energetic ions in the mid-tail during substorms at Earth. In McIlwain interpretation framework, the origin of this so-called injection boundary was not elucidated. Figure 5 suggests that this boundary may be associated with some temporal nonadiabaticity threshold and result from the action of the induced electric field at some distance from the planet.

As the magnetospheric reconfiguration progresses, it is apparent from Figure 5 that the newly energized H⁺ gradually drift toward the afternoon sector and populate regions closer and closer to the planet. In the lower panels of Figure 5, the build-up of an energetic proton layer (with typical thickness of ∼0.2 R_M) in the mid-tail is clearly noticeable. It extends on both sides of the central plasma sheet. Finally, in the rightmost panels that show the H⁺ distribution 20 s after the magnetic transition, it is apparent that the energetic proton population (tens of keV) is gradually lost at the magnetopause and replaced by a population at lower energies (keV range) as in the initial steady state configuration. The central plasma sheet now exhibits a more dipolar configuration.

6 Conclusion

This study demonstrates the key role of the induced electric field in the dynamics of magnetospheric protons. The computations performed reveal that H⁺ may be accelerated up to tens of keV after convection from high-latitude dayside exosphere into nightside plasma sheet. This energization occurs in a nonadiabatic manner due to gyromotion time scale comparable to that to the magnetic transition (temporal nonadiabaticity). These results put forward energization by an inductive electric field as an efficient mechanism for the production of energetic proton populations in Mercury's inner magnetosphere.

Acknowledgments

The authors express their sincere thanks to all members of the Mio and BepiColombo mission for their careful contributions to the projects' operations and for their efforts in making the mission successful. The idea of this paper is based on observations obtained with BepiColombo, a joint European Space Agency (ESA)–Japan Aerospace Exploration Agency (JAXA) science mission with instruments and contributions directly funded by the ESA Member States and JAXA. The French participation in the BepiColombo mission is funded by the Centre National d’Etudes Spatiales (CNES).

Open Research

Data Availability Statement

Data used in the figures of this paper are available on Zenodo repository (Delcourt, 2024).