Introduction

Whistler-mode emission waves are commonly observed at planets in our Solar System1,2. Whistler-mode waves show coherent fine structures, such as rising and falling tones in the frequency domain with time variation3,4,5,6. These discrete, coherent elements are an important signature of the nonlinear growth of the whistler-mode waves7, and can effectively accelerate and scatter energetic electrons in planetary magnetospheres8,9,10. On Earth, the discrete whistler-mode chorus elements act to locally accelerate dangerous MeV electrons and contribute to the formation of dynamic radiation belts11,12,13. Although whistler-mode waves have been identified at Mercury14 and Ganymede15, which both have smaller magnetospheres than Earth, their fine structures remain unknown. Whistler-mode chorus waves have been observed within mini-magnetospheres on Mars2 and the Moon16, which are generated by localized magnetic anomalies. Identifying these fine structures in such small planetary magnetospheres is important to understanding electron acceleration physics and pitch angle scattering of energetic electrons, as well as for estimating whether resonant interactions occur within finite spatial regions in latitudes and longitudes. Particularly in confined magnetic latitudes in Mercury’s inner magnetosphere, whether resonant interactions occur has so far remained a prediction based on simulations and theoretical analyses17. The observational detection of coherent wave structures as direct evidence of resonant interactions thus provides confirmation of wave-induced plasma dynamics at Mercury, similar to those observed at Earth. Given the previously insufficient discussion of wave–particle interaction effects at Mercury, the detection of resonant interactions is essential for the quantitative understanding of the Mercury environmental system. Moreover, electron acceleration mechanisms in small bodies can be applied to laboratory plasma experiments18,19 and contribute to developing fusion plasmas20 for sustainable energy production, particularly within the limited spatial scale of industrial facilities.

The BepiColombo project, a collaboration between Japan and Europe, is the third mission aimed at comprehensively investigating Mercury’s environment21. The first mission, Mariner 10, identified the basic structure of Mercury’s magnetosphere22,23. The second mission, MESSENGER24, quantified the spatiotemporal structures of Mercury’s dynamic magnetosphere, including the fact that the magnetic moment is shifted 0.2 \({R}_{{{\rm{M}}}}\) northward from the planetary center25, where \({R}_{{{\rm{M}}}}\) is the planetary radius. The previous Mercury missions have revealed active magnetospheric dynamics, primarily associated with magnetic reconnection (flux rope and dipolarization events)26,27. However, neither of these missions was equipped with instruments necessary to observe plasma waves associated with electron cyclotron motions, leaving the role of wave–particle interactions in electron dynamics unresolved in the context of rapid electron acceleration and wave-induced pitch angle scattering effects in Mercury’s small magnetosphere. The Plasma Wave Investigation (PWI)28 onboard BepiColombo’s Mio spacecraft provides a valuable opportunity to observe plasma waves in Mercury’s magnetosphere and to investigate particle acceleration mechanisms in small planetary bodies29. The PWI is designed to comprehensively observe DC electric fields and electromagnetic waves over a wide frequency range (electric field from DC to 10 MHz, magnetic field from 0.3 Hz to 640 kHz)28, contributing to the direct observation of plasma waves for wave–particle interactions, which play a key role in kinetic electron dynamics. Before entering Mercury’s orbit in 2026, the Mio spacecraft had six opportunities for Mercury flybys (2021–2025).

Here, we present the spatiotemporal characteristics of Mercury’s whistler-mode waves, observed by the search coil magnetometers30 during these six flybys. These observations were made when the electric field sensors and MAST booms were not deployed, during the cruise phase. This digest of the flyby observations is crucial for efficiently detecting critical areas and wave spectral signatures, enabling the acquisition of scientific data across a region of interest with limited telemetry after the Mercury Orbit Insertion (MOI) in 2026. In particular, we show that the wave spectral details and localized spatial features on the dawn side lead to the nonlinear growth of whistler-mode waves. This provides important insights into electron dynamics in other small planetary bodies with small magnetospheres, such as that of Ganymede, where electron trapping is possible31.

Results

Spatial distribution of whistler-mode wave activity

The Mio spacecraft completed the six Mercury flybys, during which the PWI operated successfully. The PWI (see “Methods”, subsection “Mercury flyby observations”) detected clear whistler-mode wave activity during the first to fourth flybys as shown in Figs. 1 and 2. Figure 1a, b shows the orbit geometry of the Mercury flybys. The first to third flybys followed similar trajectories, passing from the night to the dawn sectors. The fourth flyby trajectory passed from the north to the south near the dawn side. The fifth flyby trajectory was outside of Mercury’s magnetosphere, beyond the range shown in Fig. 1, so the PWI did not detect clear whistler-mode wave activity. Finally, the sixth flyby trajectory passed from south to north in the midnight region, also without clear whistler-mode wave activity. The sixth Mercury flyby highlighted the difficulty of wave growth in the mid-nightside region of Mercury’s magnetosphere. These varied flyby trajectories were useful in characterizing the spatial distribution of whistler-mode waves before the MOI in 2026.

Fig. 1: Mercury flyby trajectories and wave activity.
Fig. 1: Mercury flyby trajectories and wave activity.
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Spacecraft trajectories (a, b) and spatial distribution of whistler-mode wave activity (c, d) during the Mercury flybys. The trajectories are drawn in Mercury Solar Orbital (MSO) coordinates. The black solid and dotted curves represent the typical locations of the bow shock and the magnetopause, respectively. The fine dotted line in the XZ-plane indicates Z = 0.2, marking the magnetic equator. Markers for the flyby trajectories (purple circle: 1st on 1 October 2021, green cross: 2nd on 23 June 2022, light blue triangle: 3rd on 19 June 2023, red square: 4th on 4 September 2024, and blue asterisk: 6th on 8 January 2025) are placed every 5 min in universal time (UT). In Fig. 1c, d, the green curves indicate the observed whistler-mode wave region, while the orange area represents the possible region for nonlinear wave growth17. Source data are provided as a Source Data file.

Fig. 2: Magnetic field wave spectra overview.
Fig. 2: Magnetic field wave spectra overview.
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Magnetic field wave spectra (a–d) observed during the Mercury flybys. The white curves represent the electron gyrofrequency, calculated using an empirical magnetic field model36. The harmonics in the kilohertz range and the constant interferences above 11 kHz (indicated by red arrows) are known noises originating from the spacecraft. Source data are provided as a Source Data file.

Figure 1c, d shows the spatial distribution of whistler-mode wave activity during five of the six Mercury flybys, excluding the fifth flyby, which passed outside the magnetosphere and did not exhibit clear wave activity. The magnetic latitudes ranged from +34° to −51°. The spatial distribution in the southern hemisphere was more widespread compared to that in the northern hemisphere. Furthermore, the wave activity was clearly localized in the dawn sector. Similarly to the wave activity, energetic electrons at Mercury exhibited an asymmetric dawn-to-dusk distribution32,33. This spatial localization on the dawn side may be related to energetic particle injections and dipolarization events at Mercury, which are most frequent in the dawn sector26,27. To theoretically account for this asymmetric wave distribution, we added a boundary criterion for nonlinear wave growth7 in Fig. 1d (see “Methods”, subsection “Spatial critical region for nonlinear wave growth”). The observed whistler-mode waves are thought to be generated through a two-stage growth process⁷. In the initial linear growth stage, incoherent whistler-mode waves are produced via the superposition of multi-frequency components. These weakly amplified waves resemble thermal noise and act as seed waves for subsequent coherent emission waves. The electron temperature anisotropy, caused by drift-shell splitting, Shabansky orbits34, and a larger (~30°) loss cone35, can generate the seed waves for whistler-mode activity according to linear theory. Once the amplitude of the incoherent (seed) waves exceeds a threshold amplitude required for nonlinear growth⁷, they undergo nonlinear evolution into coherent whistler-mode emission waves with sufficiently large amplitudes during the nonlinear growth stage. In this calculation of the spatial critical region for nonlinear wave growth, we used a weak temperature anisotropy of 1 across all sectors of magnetic local time (MLT) and an empirical KT17 magnetic field model36. The nonlinear criterion region shows a clear asymmetric distribution in MLT17, even under the assumption of uniform spatial distribution of temperature anisotropy. This is because nonlinear growth is influenced not only by temperature anisotropy but also by magnetic field inhomogeneity14,17. Mercury’s small magnetosphere, strongly distorted by the solar wind’s dynamic pressure, means that the criterion for nonlinear growth can be predominantly characterized by the magnetic field inhomogeneity at the source region. The observed regions of the whistler-mode waves align well with the nonlinear criterion region, and this spatial distribution strongly supports the idea that the observed waves undergo nonlinear growth characterized by magnetic field inhomogeneity at the source region, rather than being the result of wave propagation from other generation regions. In the inner magnetosphere, the magnetic field lines are more dipole-like, exhibiting weaker magnetic field inhomogeneity compared to the highly stretched field lines in the outer magnetosphere. The weak magnetic field inhomogeneity results in a lower threshold for nonlinear growth, facilitating the transition from linear to nonlinear growth of whistler-mode waves in these regions. Consequently, the spatial distribution of the nonlinear criterion region can appear to reflect the overall dipole-like shape of Mercury’s magnetosphere, as shown in Fig. 1d.

Figure 2 shows the wave spectra of the magnetic field from the first to fourth flyby observations (2021–2024). The typical spectrum intensity ranged from 2 to 3 pT/Hz1/2, except during the third flyby (2023) observation14. The typical wave amplitude was in the tens of pT, comparable to that of chorus emission waves in Earth’s outer magnetosphere. However, the spectrum intensity of the third flyby was approximately 10 pT/Hz1/2, which is about five times larger than the others, and the maximum wave amplitude reached approximately 150 pT. This strong spectrum intensity during the third flyby may be the result of the trajectory passing near the magnetic equator (less than the magnetic latitudes of 10°). Between 2021 and 2025, the Sun advanced toward solar maximum. Mercury, the closest planet to the Sun and possessing a weak intrinsic magnetic field, experiences significant fluctuations in the solar wind. While the solar wind speed near Mercury is comparable to that near Earth, both the solar wind density and magnetic field strength show a significant negative correlation with Mercury’s heliocentric distance37. Previous studies have indicated that such variations in solar wind parameters, driven by changes in heliocentric distance, affect the precipitation of solar wind protons into the cusp region38, as well as ultra-low frequency wave activity in the foreshock region39. The heliocentric distances during the first to fifth flybys were 0.38 AU, 0.38 AU, 0.33 AU, 0.32 AU, and 0.32 AU, respectively, while that of the sixth flyby was 0.45 AU. Although the sixth flyby operated during a year of heightened solar activity, the sixth flyby featured the largest heliocentric distance among all six flybys. The sixth flyby may reflect the influence of the negative correlation between heliocentric distance and plasma wave activity. A detailed investigation into the correlation between Mercury’s heliocentric distance and whistler-mode wave activity is expected following the MOI.

Coherent whistler-mode wave structures

Figure 3 shows the magnified spectral characteristics of the whistler-mode waves during the third flyby in 2023. Similar to Earth’s chorus emission waves, a wave damping effect was observed at half the gyrofrequency40, along with clear fine structures such as rising and falling tones3,4,5,6,41. The wave spectrum was distributed across both lower and upper bands relative to half the gyrofrequency. These fine structures are likely related to discrete chorus elements, as seen in other planetary magnetospheres1,2,10. The wave damping effect at half the gyrofrequency was not frequently observed during the six flybys, somewhat resembling the characteristics of the Moon’s chorus waves42. This may be due to the limited wave attenuation along Mercury’s short magnetic field lines, which reduces the efficiency of damping at half the gyrofrequency. The frequency sweep rates of the rising-tone elements ranged from 0.06 to 0.18 kHz/s around the magnetic equator in Mercury’s equatorial distance \({r}_{0{{\rm{M}}}}\) of 1.2–1.3 planetary radii. Due to uncertainties in the electron observation (such as the full pitch angle distribution), directly comparing the observed sweep rate with nonlinear theory is not sufficient. Instead, we analyze these properties based on a scaling law, which indicates that the observed sweep rate does not come from spacecraft noise. As illustrated in Fig. 4a, Mercury’s magnetosphere, in contrast to Earth’s, is largely occupied by the planetary region. However, in certain regions, the scaling law between the two magnetospheres is considered to be applicable. In Earth’s magnetosphere (\(5 < {r}_{0{{\rm{E}}}} < 9\), where the Earth’s equatorial radial distance \({r}_{0{{\rm{E}}}}\) is approximately \(\left(7.6\pm 0.4\right){r}_{0{{\rm{M}}}}\), see “Methods”, subsection “Scaling factor for planetary magnetospheres”), the frequency sweep rates can be empirically expressed by ref. 43

$$\frac{\partial f}{\partial t}=17719{r}_{0{{\rm{E}}}}^{-5.08}.$$
(1)

This relationship is not only supported by observational data, but can also be derived theoretically43. Since this formula is based on chorus waves near the Earth’s inner magnetosphere (specifically in the \({r}_{0{{\rm{E}}}}\) range of 5–9), additional chorus observations in the Earth’s outer magnetosphere44,45,46,47 are helpful for the validation. It is further compared with chorus wave data observed by the GEOTAIL spacecraft44 in the Earth’s outer magnetosphere (primarily in the \({r}_{0{{\rm{E}}}}\) range of 8–11). In Fig. 4b, the fine structures on Mercury were verified by comparing with chorus observations in the Earth’s outer magnetosphere (within the magnetic latitudes of 20° during 1992–2007) by the GEOTAIL mission. Based on the scaling law of Mercury’s magnetosphere and the comparison with chorus observations in the Earth’s outer magnetosphere44,45, the sweep rate falls within a comparable range of Earth’s chorus elements, as shown in Fig. 4b. The wave intensity reaching 150 pT is also considered a reasonable value. The validation of the frequency sweep rate based on the scaling law strongly suggests that the observed rising-tone elements are equivalent to Earth’s chorus elements and result in nonlinear growth. The observed fine structures also support early simulation results14, indicating the possibility of the nonlinear wave growth given specific electromagnetic parameters in Mercury’s magnetosphere.

Fig. 3: Magnified spectral characteristics of discrete whistler-mode wave elements with 1-s resolution.
Fig. 3: Magnified spectral characteristics of discrete whistler-mode wave elements with 1-s resolution.
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a Wave damping at half the gyrofrequency. b Rising-tone elements in the lower band. c Falling-tone element in the upper band. The white solid and dotted curves represent the electron gyrofrequency and half the gyrofrequency, respectively, calculated using an empirical magnetic field model36. Source data are provided as a Source Data file.

Fig. 4: Frequency sweeping rate of Mercury’s rising-tone elements based on the scaling law.
Fig. 4: Frequency sweeping rate of Mercury’s rising-tone elements based on the scaling law.
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a Image illustration of comparison of discrete chorus elements observed by Mio and GEOTAIL in the two magnetospheres. Figure 4a provides a schematic illustration of possible chorus wave propagation along Earth’s and Mercury’s magnetic field lines. The blue and pink curves suggest illustrative paths originating from the equatorial region of each planet, which are indicated in white. These trajectories are not based on precise modeling or observations, but are intended to qualitatively convey the general spatial relationship. The spacecraft are marked for reference. b Frequency sweeping rate of Mercury’s rising-tone elements (gray box) based on the scaling law of magnetospheric size in units of Earth’s radii \({R}_{{{\rm{E}}}}\). The blue and black dotted curves indicate the empirical model and its extended curve for the Earth’s outer magnetosphere, respectively. The colored dots indicate the chorus wave intensity and frequency sweep rates observed at the Earth’s outer magnetosphere by GEOTAIL44,45. Source data are provided as a Source Data file. Credits: a Earth image: NASA; Mercury image: NASA/Johns Hopkins University Applied Physics Laboratory/Carnegie Institution of Washington; BepiColombo image: ESA.

We theoretically estimated the spatial source size in the latitudinal direction (see “Methods”, subsection “Latitudinal critical distance for nonlinear wave frequency variation”) to estimate whether the nonlinear wave frequency variation can occur along the notably short magnetic field lines, compared to Earth. The critical distance7 in the latitudinal direction at \({r}_{0{{\rm{M}}}}=1.2\) was found to be \(0.035{R}_{{{\rm{M}}}}\) (approximately \(6c/{\Omega }_{{{\rm{e}}}0}\)) at a wave frequency of 0.3\({\Omega }_{{{\rm{e}}}0}\). The critical distance of \(0.035{R}_{{{\rm{M}}}}\) corresponds to a magnetic latitude of approximately 1.3°. Within the observed latitude range of 10°, sufficient frequency variation can be achieved via nonlinear wave growth. Despite the shorter magnetic field lines at Mercury compared to Earth, nonlinear frequency variation of waves can still occur. This is because the critical distance is determined by the magnetic field inhomogeneity. Mercury’s magnetic field lines are more distorted than those at Earth, and the magnetic field inhomogeneity can be up to four orders of magnitude greater than typical terrestrial values. Similar to the relationship between Earth and Mercury, the magnetic field inhomogeneity in Mars’ magnetic anomaly regions can reach values approximately 10,000 times greater than those at Mercury2. Therefore, Mars’ chorus elements are also expected to be generated along similarly confined magnetic field lines2, which is consistent with our findings for Mercury. Consequently, the critical distance becomes significantly shorter, allowing frequency variation due to nonlinear growth to occur even within Mercury’s small magnetosphere. Together with comparisons based on the scaling law established from GEOTAIL observations, our results support the universality of the nonlinear wave–particle interaction mechanism7 responsible for chorus generation within a limited latitudinal source region.

Simulations of nonlinear pitch angle scattering

The spatial agreement between whistler-mode waves observed by the Mio spacecraft (Fig. 1) and electron-induced X-ray fluorescence33 and high-energy electron precipitation events32 detected by the MESSENGER mission suggests that the coherent whistler-mode waves can effectively scatter high-energy electrons via nonlinear pitch-angle scattering. During BepiColombo’s first Mercury flyby, variations in energetic electrons48 were observed simultaneously with whistler-mode waves14. These electrons likely triggered X-ray fluorescence events through precipitation onto Mercury’s surface. The wave-induced pitch angle scattering may lead to direct precipitation onto Mercury’s surface. Based on the previous test particle simulation studies35, the trapping region for energetic electrons in Mercury’s magnetosphere is expected to extend up to approximately \({r}_{0{{\rm{M}}}}=1.6\). Furthermore, as shown in Fig. 1, whistler-mode wave activity is dominantly observed within this region. These findings suggest that the wave-induced pitch angle scattering is likely to occur within the closed magnetic field line domain (less than about \({r}_{0{{\rm{M}}}}=1.6\)). The wave and electron observations challenge the conventional view that electron precipitation is mainly driven by processes occurring far from the planet (\({r}_{0{{\rm{M}}}}\approx 3\)), such as magnetic reconnection and flux ropes49. To evaluate this near-planet source of electron precipitation, we conducted test particle simulations using coherent whistler-mode wave parameters derived from the six flyby observations (see “Methods”, subsection “Test particle simulation of nonlinear wave–particle interactions”). Both parallel and oblique (30° wave-normal angle) wave propagations were considered, as the latter allows not only cyclotron resonance but also Landau resonance to contribute to pitch angle scattering50. Assuming a dipole magnetic field at \({r}_{0{{\rm{M}}}}\) = 1.2, referred from Fig. 1, we account for Mercury’s much shorter field line lengths (approximately 1/30th of Earth’s, with \({r}_{0{{\rm{E}}}}\) around 10). As illustrated in Fig. 4a, this short field line length raises the question of whether significant pitch-angle scattering can still occur at Mercury.

Figure 5 shows the resulting loss rates of energetic electrons. The oblique propagation (Fig. 5b, d) produces a distinct loss peak near 1 keV due to Landau resonance, which is absent in the parallel propagation case (Fig. 5a, c). The results show that even an interaction with a single coherent whistler-mode wavepacket can cause substantial electron loss near the loss cone, up to approximately 8% via cyclotron resonance at energies of several keV, and about 3% via Landau resonance at 1 keV. Given multiple interactions50 with multiple wave packets, as shown in Fig. 3, nonlinear pitch-angle scattering could play a significant role in rapid electron precipitation within Mercury’s small magnetosphere, similar to processes observed at Earth. Our simulations used a constant-frequency coherent wave model without frequency sweep for simplicity. In reality, variations in wave frequency affect a broad energy range due to the differing resonant energies associated with each wave frequency51. We also did not include the northward dipole offset25 in our model, although this asymmetry likely affects the whistler-mode wave growth and can lead to north–south differences in electron precipitation51. Conventionally, X-ray fluorescence33 and high-energy electron bursts32 at Mercury have been attributed to direct solar wind precipitation, particularly near cusp regions and open–closed field line boundaries52. While previous models emphasized distant drivers such as reconnection or flux ropes, our results suggest that nonlinear pitch-angle scattering by coherent whistler-mode waves in Mercury’s inner magnetosphere provides a viable and efficient local mechanism for driving electron precipitation. The observations from the first Mercury flyby, including simultaneous wave and electron measurements, strongly support this idea.

Fig. 5: Test particle simulations of wave-induced precipitation.
Fig. 5: Test particle simulations of wave-induced precipitation.
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a, b Contour maps of electron loss rates as a function of pitch angle and energy, with color indicating the precipitation loss rate. c, d Loss rates as a function the initial energy. Figure 5a, c corresponds to the case of parallel wave propagation, while Fig. 5b, d corresponds to oblique wave propagation. Source data are provided as a Source Data file.

Discussion

Although detailed spectral and spatial characteristics of whistler-mode waves will become clearer after the MOI, the six current flyby observations (2021–2025) have already identified their features in Mercury’s inner magnetosphere. Through comparison with the Earth’s chorus observations by the GEOTAIL mission, we found discrete chorus emission waves in Mercury’s magnetosphere, equivalent to those observed in Earth’s magnetosphere, including rising and falling structures in the frequency domain. While the earlier first and second flybys could not confirm the presence of coherent wave elements, the present study provides direct observational evidence of such coherent structures at Mercury, indicating that nonlinear wave generation is a common feature across magnetized planets. However, unlike on Earth, no large-amplitude whistler-mode waves53 (approaching 1% of the background magnetic field) have been detected at Mercury. This discrepancy likely reflects differences in plasma and magnetic field conditions, particularly the scarcity of background cold and cool electrons due to Mercury’s thin exosphere54. Since warm electrons alone are more susceptible to cyclotron and Landau damping55, cold electron populations are crucial for sustaining wave growth, even though they possess low energy. Understanding these amplitude differences is key to interpreting the kinetic processes behind electron acceleration and precipitation in Mercury’s unique plasma environment.

The BepiColombo flyby observations of whistler-mode waves raise scientific questions regarding the kinetic dynamics associated with nonlinear whistler-mode wave activity in Mercury’s small magnetosphere. The first question is regarding the full spatial distribution of wave activity covering all MLT sectors. The six current Mercury flybys lack sufficient observations of the noon and dusk sectors. Theoretical predictions suggest that nonlinear growth at the noon side should be more active than in other MLT sectors because the noon side is highly compressed by dynamic pressure and has non-stretched field lines17. A spatial distribution covering all MLT sectors would help reveal the dynamic effects on wave-induced electron precipitation events. The wave-induced precipitating electrons may contribute to Mercury’s exospheric composition through electron-stimulated desorption (ESD)56, releasing volatile elements such as sodium, potassium, and calcium upon surface impact. The second question concerns asymmetric north-south effects51. Mercury’s magnetic field resembles that of a dipole, but with a northward shift25. This northward shift causes an asymmetric loss cone distribution between the northern and southern hemispheres across all MLT sectors. Computer simulations predict significant north-south differences in wave activity due to this asymmetric loss cone distribution51. If such effects are observed, it would provide evidence that magnetic field morphology controls plasma wave activity in planetary magnetospheres. Such understanding also provides important clues for exploring the diversity of asymmetric north-south electron dynamics associated with different Dungey cycles at Earth and Mercury’s small magnetosphere. The third question involves the effects of wave–particle interactions. It is believed that kinetic electron dynamics in Mercury’s magnetosphere are driven by wave–particle interactions17. Whistler-mode waves can play a dual role in electron acceleration and precipitation into the loss cone17,51. Our simulation results suggest a distinct driving source for energetic electron precipitation in Mercury’s inner magnetosphere: nonlinear pitch-angle scattering by whistler-mode waves. This mechanism is different from the previously proposed sources, such as plasma processes associated with reconnection and magnetic flux ropes located far (\({r}_{0{{\rm{M}}}}\approx 3\)) from the planet49. Although Mercury’s whistler-mode waves received limited attention in previous missions, they now offer deeper insights into plasma processes through nonlinear wave–particle interactions. Their broader implications from the magnetosphere to potential consequences for exospheric variability through the kinetic electron dynamics in Mercury’s environment have been made possible by the BepiColombo mission’s unique capability to measure plasma wave activity in detail.

Coordinated observations from wave28,30 and plasma57 instruments will be essential to identify dynamical energetic electron variations in Mercury’s small magnetosphere. This could provide fundamental insights into kinetic electron processes, not only at Mercury, but also in artificial plasma chamber experiments, which lack the spatial scale necessary for the plasma drift paths seen in small planetary magnetospheres or mini magnetospheres. The similarities and differences in planetary whistler-mode wave activity open frontier fields in Mercury’s magnetosphere, representing a critical early step toward understanding the fundamental differences between the space environments of Earth and Mercury, especially in preparation for full science operations following the MOI.

Finally, these six flyby observations, despite being obtained prior to the MOI, provide direct evidence of coherent whistler-mode waves in Mercury’s small magnetosphere and enable a confident evaluation of nonlinear pitch-angle scattering beyond the quasi-linear regime. They offer unique insights that extend the initial findings from the first and second flybys. Furthermore, to clarify the broader relevance of this study beyond Mercury-specific plasma environments, we note that the observational evidence of nonlinear wave–particle interactions in Mercury’s small magnetosphere, particularly the coherent wave structures, provides a valuable comparative framework for understanding similar processes in other planetary environments, including those with weak or crustal magnetic fields such as Ganymede or Mars.

Methods

Mercury flyby observations

The PWI was developed through international collaboration between Japan and Europe28, with the search coil magnetometers onboard the Mio spacecraft jointly developed by Japan and France30. The PWI successfully captured whistler-mode waves at Mercury during four of the six flybys conducted on 1 October 2021, 23 June 2022, 19 June 2023, 4 September 2024, 1 December 2024, and 8 January 2025. For all the datasets, the wave amplitude was calculated using the squared sum of the search coil output components along the beta and gamma axes30. The time resolution of the wave spectrum was 1 s during the first and third flybys, and 4 s during the second, fourth, fifth, and sixth flybys. The spatial coverage of BepiColombo’s six Mercury flybys included the dusk, night, and dawn sectors, as shown in Fig. 1. Due to limited data telemetry prior to the MOI, only spectral data without waveforms were collected. The polarization and wave normal vectors will be investigated after the MOI. The gyrofrequency was calculated using an empirical magnetic field model36. The frequency sweep rates were visually analyzed only for clearly distinguishable fine structures. Due to the uncertainty in the scaling law, the frequency sweep rate was shown as an area (gray box in Fig. 4) rather than as points. The sweep rate for Mercury was distributed at lower values compared to those observed by GEOTAIL. This may be due to the lower temporal resolution (1 s spectrum) of the PWI data, as opposed to the waveform data with 12 kHz sampling by GEOTAIL. The sweep rate \(\frac{\partial f}{\partial t}\) is proportional to the wave intensity \({B}_{{{\rm{w}}}}\) in the source region according to nonlinear theory7,45, but the PWI observed only two components (beta and gamma) from the search coil magnetometers with the same temporal and frequency resolutions. The quantitative relationship between wave intensity and sweep rate will be studied in future work after the MOI. In Figs. 2 and 3, the frequency resolution is not a constant in order to reduce data telemetry28.

Spatial critical region for nonlinear wave growth

Nonlinear growth7 can be characterized by the optimum amplitude \({\Omega }_{{{\rm{op}}}}\) and threshold amplitude \({\Omega }_{{{\rm{th}}}}\). To classify the wave growth into linear and nonlinear categories, the region criterion is defined by the wave amplitude ratio

$$\frac{{\Omega }_{{{\rm{op}}}}}{{\Omega }_{{{\rm{th}}}}} > 1,$$

where \({\Omega }_{{{\rm{op}}}}\) means the maximum ideal amplitude of a nonlinear whistler-mode wave, and \({\Omega }_{{{\rm{th}}}}\) is the threshold for the transition from linear to nonlinear growth7. The criterion is evaluated at the frequency corresponding to the maximum linear growth rate7,17. The magnetic fields used an empirical model36 and the background electron density used a diffusive equilibrium model, taking into account the magnetic field-aligned force for plasmas, the planet’s gravity, and centrifugal force17. We assumed a uniform spatial distribution of temperature anisotropy (with a value of 1) for energetic electrons across all MLT sectors, in order to impose the same free energy source for instabilities. The temperature anisotropy was simply set to 1, based on GEOTAIL observations45. Although temperature anisotropy is important for determining the absolute wave amplitude, but the dominant parameter controlling the spatial scale of nonlinear growth at Mercury is the magnetic field inhomogeneity, resulting from the strongly distorted field lines17.

Scaling factor for planetary magnetospheres

We calculated the scaling value based on the magnetic field inhomogeneity \(a\) of the planetary magnetosphere, as the magnetic field inhomogeneity can be a dominant parameter for characterizing nonlinear wave growth in distorted Mercury’s magnetosphere17. The threshold value for nonlinear wave growth7 can be characterized by the square of the normalized magnetic field inhomogeneity \({\widetilde{a}}^{2}\). The normalized magnetic field inhomogeneity is defined as

$$\widetilde{a}=a{c}^{2}/{\Omega }_{{{\rm{e}}}0}^{2},$$

where \(c\) is the speed of light, and \({\Omega }_{{{\rm{e}}}0}\) is the equatorial gyrofrequency. The magnetic field inhomogeneity \(a\) can be expressed as

$${\Omega }_{{{\rm{e}}}}\left(h\right)={\Omega }_{{{\rm{e}}}0}\left(1+a{h}^{2}\right),$$

where \({\Omega }_{{{\rm{e}}}}\) is the gyrofrequency and \(h\) is the small distance from the equator along a magnetic field line. We calculated the magnetic field inhomogeneity using the KT17 model36 for Mercury and the Tsyganenko 89 model58 for Earth. This approach has the advantage of determining the scaling factor by taking into account not only the magnetic field strength characterized by \({\Omega }_{{{\rm{e}}}}\) but also the influence of the magnetic field inhomogeneity. The scaling factor \(A\) is determined by minimizing the mean square error (MSE), given by

$${MSE}=\frac{1}{{NM}}{\sum }_{i=1}^{N}{\sum }_{j=1}^{M}{\left({\widetilde{a}}_{{{\rm{E}}}}^{2}\left({x}_{i},{y}_{j},0\right)-{\widetilde{a}}_{{{\rm{M}}}}^{2}\left(\frac{{x}_{i}}{A},\frac{{y}_{j}}{A},0\right)\right)}^{2},$$

where the subscript on \({\widetilde{a}}^{2}\) indicates each planet, and \(\left({x}_{i},{y}_{j},0\right)\) and \(\left(\frac{{x}_{i}}{A},\frac{{y}_{j}}{A},0\right)\) are the coordinates in solar magnetic (SM) coordinates for each planet. The domain in Earth’s SM coordinates was defined as \(5 < \left|{x}_{i}\right| < 12\) and \(5 < \left|{y}_{j}\right|\) \( < 10\). The scale factor \(A\) was distributed around \(7.6\pm 0.4\), even when assuming an extreme range for the disturbance index from 1 to 97 for Mercury and the Kp index from 0 to >6 for Earth. The value of the scale factor was similar to that reported in a previous study \(\left(8\pm 0.5\right)\), which was based on the magnetopause standoff distance23. However, the variation in the present scale factor is small, making it a more robust parameter for characterizing chorus wave properties compared to the scaling factor determined solely by the planetary magnetopause standoff distance.

Latitudinal critical distance for nonlinear wave frequency variation

In the nonlinear wave growth theory7, the critical distance can be expressed as

$${h}_{c}=\frac{{s}_{0}\omega {\Omega }_{{{\rm{w}}}0}}{5{ca}{s}_{2}{\Omega }_{{{\rm{e}}}0}},$$

where \(\omega\) is the wave frequency, \({\Omega }_{{{\rm{w}}}0}\) is the wave amplitude at the initial generation region, and \({s}_{0}\) and \({s}_{2}\) are dimensionless parameters representing the inhomogeneity factor in the nonlinear theory, respectively. Because Mercury’s magnetic field inhomogeneity is 10,000 times greater than that of Earth’s typical magnetosphere, the critical distance at Mercury becomes shorter even under similar plasma conditions. We assumed pitch angle \(\alpha=60\)° and \(\omega=0.3{\Omega }_{{{\rm{e}}}0}\) with \({\Omega }_{{{\rm{w}}}0}/{\Omega }_{{{\rm{e}}}0}=0.05\%\,\left({\Omega }_{{{\rm{w}}}0}\approx 56\,{{\rm{pT}}}\right)\) at the initial generation region (\({r}_{0{{\rm{M}}}}\) = 1.2) within the critical distance. The initial wave amplitude \({\Omega }_{{{\rm{w}}}0}\) can grow further during propagation beyond the critical distance if the resonance condition is satisfied. Based on a typical electron density of 10–100 \({{{\rm{cm}}}}^{-3}\) in Mercury’s inner magnetosphere59, a ratio of \({\omega }_{{{\rm{pe}}}}/{\Omega }_{{{\rm{e}}}}=10\) is assumed along the magnetic field line, where \({\omega }_{{{\rm{pe}}}}\) is the electron plasma frequency.

Test particle simulation of nonlinear wave–particle interactions

The resonance condition7 between a coherent whistler-mode wave and an electron is given by

$$\omega -{k}_{\parallel }{V}_{R}=\frac{n{\Omega }_{{{\rm{e}}}}}{\gamma },$$

where \({k}_{\parallel }\) is the parallel component of the wave number, \({V}_{R}\) is the resonance velocity, and \(\gamma\) is the Lorentz factor. The case \(n=0\) corresponds to Landau resonance, while \(n=1\) corresponds to the first-order cyclotron resonance. The change in the local pitch angles is given by

$$\frac{{{\rm{d}}}\alpha }{{{\rm{d}}}t}=\frac{1}{{u}^{2}}\left({u}_{\parallel }\frac{{{\rm{d}}}{u}_{\perp }}{{{\rm{d}}}t}-{u}_{\perp }\frac{{{\rm{d}}}{u}_{\parallel }}{{{\rm{d}}}t}\right),$$

where \(\alpha\) is the local pitch angle, \(u\) is the momentum magnitude, \({u}_{\parallel }\) and \({u}_{\perp }\) are the components of the momentum parallel and perpendicular to the background magnetic field line, respectively. In the simulation, the pitch angle changes are computed using the fourth-order Runge-Kutta method within a simple dipole magnetic field60, assuming a whistler-mode wave packet with constant frequency and constant wave amplitude along a magnetic field line. If the pitch angle is smaller than the loss cone angle, it is counted as a loss toward the planetary surface. Based on the wave observations, a constant wave amplitude of \(0.001{B}_{0}\) is assumed at a frequency of \(0.3{\Omega }_{{{\rm{e}}}0}\) with \({\omega }_{{{\rm{pe}}}}/{\Omega }_{{{\rm{e}}}}=10\), where \({B}_{0}\) is the equatorial magnetic field strength. The wave model is distributed from the magnetic equator up to a latitude of \(-20\)° in one hemisphere to estimate the loss rate from a single interaction. We injected 720 particles for each equatorial pitch angle, with a resolution of 0.5° in the relative angle between the wave and the electron.