A slot region in the magnetosphere of Jupiter

Abstract

Understanding the balance between charged particle acceleration and loss is central to radiation belt research. Jupiter’s Galilean moons orbit within its intense radiation environment and can act both as sources and sinks of energetic particles. Using observations from the Juno spacecraft, we identify large-scale depletions of energetic electrons along Europa’s orbit. These depletions are too deep to result from direct absorption by the moon alone. Here we show that rapid electron losses, occurring within a timescale shorter than Jupiter’s rotation, are driven by pitch angle scattering via whistler-mode waves co-located with Europa’s orbit. This suggests that Europa maintains a plasma environment capable of sustaining a slot-like region, similar to the one seen in Earth’s Van Allen belts. However, this Jovian slot only partially extends along Europa’s path, implying that additional, unidentified acceleration mechanisms may act to refill the region and maintain high radiation levels close to Jupiter.

Introduction

The Van Allen radiation belts are regions of trapped high-energy charged particles within the terrestrial magnetosphere, which significantly affect satellites and other space-based technologies¹. Understanding the formation, structure, and dynamics of these belts has been a key scientific focus for decades². One notable feature within these belts is the slot region, a relatively low-radiation zone for electrons with energies above several hundred keV, located between the inner and outer electron radiation belts³. The slot region is formed as a result of a delicate balance between the inward transport of electrons and pitch angle diffusion driven by plasma waves⁴.

Although it is well understood that the formation and maintenance of the slot region in Earth’s radiation belts is primarily driven by the fundamental process of wave-particle interactions in geospace^2,3,4, the corresponding processes in Jupiter’s magnetosphere remain much less explored. Jupiter’s magnetosphere provides a unique plasma environment. It hosts extremely energetic particles^5,6 and complex plasma wave activities^7,8. In particular, Jupiter’s various natural moons act as both sources of plasmas and sinks for energetic particles^9,10, profoundly shaping the structure of the Jovian radiation belt and the broad magnetospheric environment^11,12,13. The electrodynamic coupling between the moons and the rapidly rotating magnetosphere significantly alters the distributions of charged particles and plasma waves^14,15,16. Observations have suggested that enhanced electron anisotropies near the orbits of moons such as Europa and Ganymede should be responsible for intensifying whistler-mode waves^8,15. These waves are believed to be key drivers of nonadiabatic electron acceleration and loss, playing an important role in regulating the energetic electron populations in planetary radiation belts^16,17.

However, previous studies have offered contradicting predictions about the exact role of wave-particle interactions in the particle variations of Jupiter’s magnetosphere. For instance, some researchers⁸ questioned whether enhanced whistler-mode waves at Ganymede and Europa would accelerate or deplete electrons. In contrast, some other studies¹⁷ seem to favor electron losses over acceleration at energies below 1 MeV. Theoretical researches suggested that whistler-mode waves could effectively scatter electrons at energies from several keV to several hundreds of keV¹⁷. At Saturn’s moons, such as Rhea, strong whistler-mode waves are excited by the electron loss-cone distributions, which may further contribute to spatially extended losses of energetic electrons observed in the vicinity of the moons^18,19. A Juno-era report²⁰ documented the absence of 100’s keV electrons near the magnetic equator within the Jovian M-shell range of 9–16 (the value of M-shell refers to the distance from the magnetic equator to Jupiter’s center, normalized by Jupiter’s radius R_J, where R_J = 71,492 km). In this study, the M-shell parameter is calculated based on the JRM33 internal magnetic field model (order 13)²¹ and the CON2020 current sheet model²² to characterize the magnetic geometry in our analysis. While this absence of electrons possibly hints at the existence of a slot-like region of Jupiter’s radiation belt, direct observational evidence of the slot formation in Jupiter’s magnetosphere remains scarce.

In this work, we present observational and modeling evidence for a slot region in Jupiter’s magnetosphere. By analyzing energetic electron fluxes and whistler-mode wave observations from Juno, we identify large-scale electron depletions near Europa’s orbit that are not attributable to direct moon absorption. We show that these depletions are driven by pitch angle scattering from locally enhanced plasma waves, forming a slot-like structure in the magnetosphere of Jupiter. Our findings offer new insights into the dynamic processes that regulate Jovian radiation environments and support the existence of slot formation mechanisms similar to those observed at Earth.

Results

Observations of electron loss and whistler-mode waves near Europa’s orbit

Previous studies using Galileo wave data have demonstrated the significant role of plasma waves in shaping Jupiter’s magnetosphere, especially through wave–particle interactions that can lead to both particle acceleration and loss^23,24. Juno spacecraft provides a unique opportunity to investigate the existence and formation mechanisms of slot-like regions in Jupiter’s radiation belt. In this study, a gap of energetic electrons from tens of keV to hundreds of keV is observed to be accompanied by strong whistler-mode waves near Europa’s orbit. The electrons at tens to hundreds of keV are the “seed” population for local acceleration to multiple MeV energies in the magnetospheres of Earth^25,26 and Jupiter²⁷. Figure 1 illustrates a representative whistler-mode wave event and the corresponding distributions of energetic electron flux observed by Juno during one inbound trajectory on July 10, 2017. The whistler-mode waves were detected at the magnetic latitudes of 20–50° around Europa orbit (M-shell about 9.5) during the time interval marked by two vertical dotted lines. Following the previous work²⁸, we categorize the whistler-mode waves at 0.05f_ceq < f <f_ceq frequencies (f is wave frequency, and f_ceq is the equatorial electron gyrofrequency) as chorus or high frequency whistler-mode waves (HFW) and the waves at f < 0.05f_ceq as hiss waves or low frequency whistler-mode waves (LFW) (Fig. 1a). LFWs with frequencies below 0.05f_ceq exhibited strong wave power, while HFWs above 0.05f_ceq displayed relatively weaker intensities. We calculate the whistler-mode wave amplitudes over the frequency range from 50 Hz to the equatorial electron gyrofrequency (see “Methods”). The whistler-mode wave amplitudes were mainly 30−70 pT with several instantaneous peaks reaching approximately 100 pT (Fig. 1f). During this period of the wave intensification, the fluxes of energetic electrons, ranging from tens of keV to several hundreds of keV, exhibited a noticeable decay (Fig. 1b−e). Notably, at 21:37 UT the Juno spacecraft passed the same magnetic field line (M-shell about 9.6) as that Europa crossed earlier at 20:00 UT (Supplementary Fig. 1). The decline in electron fluxes across the three selected energy channels spanned a wide range of local pitch angles. The increase of electron fluxes at 55 keV around UT 20:40 and UT 21:20 were likely caused by the electron injections²⁷ (Fig. 1b, c). This typical event indicates an observationally evident connection between the activity of whistler-mode waves and the energetic electron loss near Europa’s orbit in Jupiter’s magnetosphere.

Fig. 1: Simultaneous observations of the energetic electron flux decay and whistler-mode wave enhancement near Europa’s orbit on July 10, 2017.

a The frequency-time spectrogram illustrating the magnetic field power spectral density as observed by the WAVES instrument⁴³. The solid line marks the equatorial electron gyrofrequency (f_ceq), while the dashed line indicates 0.05f_ceq. b energy-time spectrograms of averaged electron differential fluxes (j_{diff, avg}) recorded by the Jupiter Energetic Particle Detector Instruments (JEDI)²⁹. c–e the pitch angle distributions of differential electron flux (j_diff) for three selected electron energies (55, 97, and 170 keV). f the 30 s averaged amplitude of whistler-mode waves (B_w) (upper panel) and the omni-directional electron fluxes (j_omni) in the lower panel across the three different energy channels: 55 keV, 97 keV, and 170 keV. Vertical dashed lines mark the interval of interest. The equatorial magnetic field intensity, M-shell (the distance from the magnetic equator to Jupiter’s center, normalized by Jupiter’s radius R_J, where R_J = 71,492 km), magnetic latitude (MLAT), and magnetic local time (MLT) are calculated using the JRM33 internal magnetic field model (order 13)²¹ and the CON2020 current sheet model²². UT refers to universal time, and R denotes the distance normalized to R_J from Juno to the center of mass of Jupiter. Source data are provided as a Source Data file.

High correlation between energetic electron slot and whistler-mode wave peak near Europa

With the availability of Juno measurements spanning from perijove-03 (PJ-03) to perijove-46 (PJ-46), a statistical analysis is conducted to investigate the global distributions of energetic electron fluxes and whistler-mode waves in Jupiter’s magnetosphere. Note that the Europa flyby data during PJ-45 are excluded from our analysis to avoid any potential effect of moon proximity. The averaged whistler-mode wave amplitudes exhibit strong peaks around Europa’s orbit along the magnetic field at both dawn and dusk local times, accompanied by a corresponding statistical decay in energetic electron fluxes (Supplementary Figs. 2 and 3). This indicates a clear spatial correlation between the intensification of whistler-mode waves and the loss of energetic electrons in Jupiter’s radiation belt. Notably, the average wave amplitudes near Europa are stronger on the dawnside than on the duskside, corresponding to a clear depletion region for electron fluxes in the dawn sector. This local time asymmetry suggests that electron loss due to whistler-mode waves near Europa in the dusk sector may be replenished relatively quickly through radial or energy diffusion. Consequently, our analysis focuses on exploring the spatial correlation between energetic electron fluxes and whistler-mode wave amplitudes, specifically in the dawn sector (00–06 MLT) of Jupiter (Fig. 2).

Fig. 2: Spatial correlation of energetic electron fluxes and whistler-mode wave amplitudes (B_w) in the neighboring environment of Europa.

MLAT denotes magnetic latitude, MLT means magnetic local time, and the M-shell is defined as the distance from the magnetic equator to Jupiter’s center, normalized by Jupiter’s radius. a–c the normalized electron fluxes in the magnetic meridian plane (Δ|MLAT| = 10°) for the three specified energy channels (55, 97, 170 keV) within the equivalent M-shell range of 5–15 (ΔM-shell = 0.5) in the dawn sector (MLT = 00–06). The normalized flux (f_N) is the ratio between the omni-directional electron fluxes (j_omni) and the maximum j_omni within each magnetic latitude bin within 5 < M-shell <15. d the averaged whistler-mode wave amplitudes in the magnetic meridian plane on the dawnside. Flux slot indicates the region of reduced electron fluxes, while wave peak highlights the region with enhanced wave amplitudes. e Spatial correlation between latitudinally averaged normalized electron fluxes for the three energy channels and averaged wave amplitudes, calculated within the shaded region of M-shell = 6.75−12.25 (shaded region). Due to limited data coverage within M-shell <9 within |MLAT| < 10°, the latitudinally averaged normalized electron fluxes and wave amplitudes are calculated within |MLAT| = 10−60°. Source data are provided as a Source Data file.

In order to investigate the extent of flux decay in detail, the omni-directional electron fluxes (j_omni) are further normalized by the maximum j_omni within each magnetic latitude bin for illustrative purpose. The normalized electron fluxes (f_N) for the three energy channels display a clear slot near Europa’s orbit, spanning M-shell = 9–10 (Fig. 2a−c). Correspondingly, the average amplitudes of whistler-mode waves present an enhanced ribbon structure in the same region (Fig. 2d). Such a strong negative correlation is confirmed quantitatively by analyzing the latitudinally averaged profiles of whistler-mode waves and normalized electron fluxes as a function of M-shell (Fig. 2e). Specifically, the corresponding correlation coefficients between the two profiles over M-shell of 6.75–12.25 are −0.94, −0.87, and −0.65, and the corresponding p values are 6.5 × 10⁻⁶, 2.5 × 10⁻⁴, and 2.2 × 10⁻² for each energy channel. The p values are all less than 0.05, indicating that there is a statistically real and highly correlated relationship between whistler-mode wave amplitudes and electron flux variations at Europa’s orbit. Hence, accumulated observations from Juno not only reveal an energetic electron slot in Europa’s neighboring region but also imply a close linkage of the occurrence of this slot region to the presence of intense whistler-mode waves.

Electron loss and slot formation driven by whistler-mode waves near Europa

To quantify the specific contribution of whistler-mode waves to the formation of observed slot of energetic electrons from tens of keV to hundreds of keV, the wave distribution model is developed based on the statistically averaged wave power spectral densities obtained from Juno measurements (Fig. 3a−c). Overall, the average power of LFWs is about one order of magnitude stronger than that of HFWs over a broad M-shell range. LFWs show small variations with the magnetic latitude, maintaining pronounced wave power up to |MLAT| = 60°. Interestingly, there exists a distinct wave power peak of LFWs around Europa. In contrast, HFWs within |MLAT| < 20° exhibit a larger average wave power by an order of magnitude, compared to those at |MLAT| > 20°.

Fig. 3: Spectral distributions of Whistler-mode waves and their quantitative scattering impact on Jovian radiation belt energetic electrons.

a, b the time-averaged wave intensities as functions of wave frequency and M-shell (the distance from the magnetic equator to Jupiter’s center, normalized by Jupiter’s radius) for |MLAT| < 20° (MLAT is the magnetic latitude) and |MLAT| = 20–60°. From top to the bottom, the solid line and two dashed lines represent f_ceq (equatorial electron gyrofrequency), 0.5f_ceq, and 0.05f_ceq based on the dipole magnetic field model. c the average wave intensity at M-shell = 9.5 for |MLAT| < 20° and |MLAT| = 20–60°. The shaded region indicates the frequency range of LFWs (low frequency whistler-mode waves), while the unshaded part corresponds to HFWs (high frequency whistler-mode waves). d, e the bounce-averaged pitch angle diffusion coefficient <D_αα> induced by LFWs and HFWs as functions of energy and equatorial pitch angles. f the combined <D_αα> from LFWs and HFWs. g–i Comparison of simulated electron pitch angle distributions (solid lines) with observations (dotted lines) for three energy channels (55, 97, 170 keV) at three simulation intervals (0, 5, and 10 h). The observed PSDs (phase space densities) are from the time interval between UT = 8:00 and UT = 8:30 (UT means universal time) in Fig. 1, excluding the interval of electron injections. Source data are provided as a Source Data file.

In this study, the averaged wave power densities observed within |MLAT| < 20° at M-shell = 9.5 (Fig. 3c) are used as inputs of LFWs and HFWs for quantifying the wave-driven electron scattering effects. It is further considered that LFWs (<0.05f_ceq) are present over the magnetic latitudes of 0–60° and that HFWs (>0.05f_ceq) are confined within the latitudes below 20°. LFWs and HFWs have different scattering effects on Jovian energetic electrons, according to the calculated bounce-averaged diffusion coefficients (Fig. 3d, e and Supplementary Fig. 5; see Methods for details of diffusion rate computation). LFWs primarily scatter electrons with energies >100 keV via cyclotron resonance at equatorial pitch angles (α_eq) <75° but can also resonate with electrons from about 10 to 1 MeV at higher pitch angles (α_eq > 80°) through Landau resonance (Fig. 3d). In contrast, HFWs predominantly scatter electrons at energies of 10 –100’s keV through cyclotron resonance (Fig. 3e). In combination, LFWs and HFWs can drive efficient diffusion of Jovian radiation belt electrons with energies of 10–1 MeV over a wide range of pitch angle (Fig. 3f). The net bounce-averaged pitch angle diffusion rates are 1–2 orders of magnitude greater than the mixed and momentum diffusion coefficients, and can approach the level of several 10⁻⁵ s⁻¹ (Supplementary Figs. 5 and Fig. 3f). This brings estimates of electron loss timescale of several hours, indicating that the dominant contribution of whistler-mode waves should be pitch angle scattering accounting for electron loss in Jupiter’s radiation belt.

With the net bounce-averaged diffusion coefficients at M-shell = 9.5 (Fig. 3f and Supplementary Fig. 5h, i) as inputs, the temporal evolution of phase space densities (PSDs) of Jovian energetic electrons is simulated by numerically solving the two-dimensional Fokker-Planck diffusion equation (see “Methods” for details of the model). The statistical electron PSD distribution at this location (Fig. 3g) is adopted as the initial condition for the simulations. The simulated results (Fig. 3h, i) clearly indicate that under the impact of whistler-mode wave-induced scattering, the energetic electron PSDs decay gradually and their pitch angle distributions evolve as a whole to reproduce very well the measured PSD distributions within 10 h. The simulation results show reasonable consistency with the observations, with the ratios of the averaged electron PSD between the simulations and observations for the three indicated energy channels being approximately 0.95, 0.95, and 0.98, indicating that the model captures the overall trend of the measured electron fluxes. This good agreement between the modeled and observed results justifies the significant role of whistler-mode waves in driving electron loss in Jupiter’s radiation belt and in producing the slot region near Europa. It is noted that the simulated electron PSDs tend to underestimate the observed levels at lower pitch angles (i.e., <30° or >150°), possibly due to undetermined field-aligned electron sources or limited electron measurements near the equatorial loss cone²⁹. Despite this, whistler-mode waves at Jupiter are efficient to remove the population of energetic electrons on timescales of hours, therefore critically shaping the Jovian radiation belt slot near Europa’s orbit.

Furthermore, the simulated energy spectrum of Jovian energetic electrons aligns closely with the observed shape after 10 h of wave-particle resonant interactions (Fig. 4a−c). Although the first thought might be that this energetic electron slot could be caused by absorption of Europa^10,11, our investigation demonstrates that it is mainly attributed to wave-induced scattering in the vicinity of the moon, in a manner similar to the depletion of MeV protons driven by ion cyclotron waves near Io¹². A single moon passage, for example Europa, primarily creates time- and longitude-dependent particle depletion in the wake of the moon (i.e., microsignatures)³⁰, which will be then refilled by fast inward radial diffusion. In addition, these microsignatures have the scale of a moon’s diameter, which corresponds to 0.022 R_J for Europa, much smaller than the depletion scales of the electron slot observed with Juno (Figs. 1c−e and 2a−c). The broader, longitude- and time-averaged effects of moon absorption on the radial particle distribution occur after multiple orbits, when losses from different microsignatures add up (i.e., macrosignatures)³⁰. However, these macrosignatures remain relatively weak near Europa’s orbit due to a relatively efficient radial diffusion process expected at Europa’s distance¹².

Fig. 4: Formation of an energetic electron slot in the vicinity of Europa under considerations of the contributions from different physical processes.

a–c Comparisons between simulations (solid lines) and observations (dashed lines) of the electron energy spectra from 30 to 200 keV at a pitch angle of 90° for three different simulation intervals (0, 5, and 10 h). M-shell denotes the distance from the magnetic equator to Jupiter’s center, normalized by Jupiter’s radius, and E_k is electron energy. d the dashed line represents the omnidirectional electron fluxes (j_omni) of electrons when considering the steady-state solution of the radial diffusion (RD) equation for 97 keV electrons, incorporating the absorption effect of Europa (EA). The solid line shows the result after including Europa absorption and wave loss (WL). The dotted line is the steady-state solution when the radial diffusion rates increase by 5 times, and the value of radial diffusion rate (D_LL) refers to the electron radiation model¹². The Europa absorption region spans M-shells 9.29–10.02, which is from the geometrical calculation based on the magnetic field model for Jupiter^21,22. The spatial coverage of wave-induced loss falls within M-shells of 8–10, following the statistical results in Fig. 2. Source data are provided as a Source Data file.

To better distinguish the specific contributions of wave-induced scattering and Europa’s absorption to electron loss, the radial profiles of 97 keV electron fluxes within M-shell = 7–12 are simulated using the radial diffusion equation with loss terms (Fig. 4d; see “Methods” for details of the model). Under the influence of radial diffusion and Europa’s absorption, the omni-directional fluxes of Jovian energetic electrons decrease monotonically with increasing M-shell, showing no signature of a slot but a weak decay near M-shell = 9.5 (dashed curve). In contrast, inclusion of whistler wave-driven scattering generates very pronounced electron loss in the vicinity of Europa to form a slot region (solid curve). Moreover, by further increasing the radial diffusion rates by 5 times, the energetic electron slot can be smoothed quickly by faster inward transportation (dotted curve). As a consequence, it is evident that the formation of the Jovian radiation belt slot and its evolution is a delicate interplay of different physical processes at Jupiter, including wave-particle interactions^8,17, moon absorption^10,11, radial diffusion⁷, and even possible electron injections²⁷. Our simulations highlight the dominant role of wave-particle interactions in forming the Jovian radiation belt slot, which can be readily incorporated into existing particle dynamic models that so far focus solely on moon absorption in Jupiter’s magnetosphere.

Discussion

The observations and simulations in the present study provide the evidence demonstrating that a slot-like region exists in Jupiter’s electron radiation belt and that strong whistler-mode waves near Europa’s orbit play a dominant role in forming this slot. A scenario is schematically illustrated in Fig. 5 to explain such a closely connected and coupled system between Jupiter’s magnetosphere and Europa. Firstly, the temperature anisotropy of hot electrons injected via interchange instability provides the free energy necessary for the excitation of whistler-mode waves over a broad region in Jupiter’s magnetosphere. HFWs and LFWs can resonate with approximately 1–50 keV electrons and >about 50 keV electrons, respectively, over the nearly entire pitch angle range. The source electron population at equatorial pitch angles of about 60–90° with anisotropic distributions is significant to the wave generation and amplification. It has been shown that injected electrons with typical energies of a few keV to approximately 50 keV and occasionally reaching above 300 keV, exhibiting temperature anisotropies, are capable of exciting whistler-mode chorus waves under typical Jovian magnetospheric conditions²⁷. The hot electron angular distribution can be further affected by depletions at low equatorial pitch angles due to Europa’s absorption^10,11 and by losses within neutral materials (e.g., the gas torus) due to scattering or energy dissipation through friction^31,32,33. Strong temperature anisotropies induced by these materials have been observed in protons near Europa³² and may similarly occur in electrons. The enhanced hot electron temperature anisotropies induced by these processes supply extra free energy for the growth of whistler-mode waves, amplifying their intensities around Europa’s orbit⁸. Consequently, intense whistler-mode wave emissions can strongly scatter Jovian energetic electrons for atmospheric loss through the pitch angle diffusion process, leading to the formation of an electron slot—an analog to the two-zone Van Allen radiation belts around Earth¹. The resultant precipitated electrons can also produce diffuse auroral emissions in Jupiter’s upper atmosphere³⁴, in a manner similar to that at Earth^35,36. These results reveal a first comprehensive demonstration of the significant contribution of whistler-mode waves near Europa to the formation of a Jovian radiation belt slot in a global context. Our findings can lay a useful baseline for future studies of radiation belts around other magnetized planets with satellites.

Fig. 5: A schematic diagram illustrating the formation of the slot region near Europa within the closely connected system of Jupiter and its moons.

Injected hot electrons due to interchange instability exhibit anisotropic pitch angle distributions, which provide the free energy necessary to excite whistler-mode waves within Jupiter’s magnetosphere. Material-driven losses at Europa’s orbit (such as moon absorption process, or loss by neural torus) will deplete electrons with low equatorial pitch angles to enhance electron anisotropies, leading to the generation of more intense whistler-mode waves. These increased waves efficiently scatter energetic electrons into Jupiter’s atmosphere, playing a dominant role in forming the electron slot region near Europa’s orbit and producing diffuse aurora. Source data are provided as a Source Data file.

Noteworthily, while the present analyses focus mainly on the slot and wave characteristics in the dawn sector of Jovian radiation belt, a statistical dawn-dusk asymmetry has been captured observationally in the average amplitudes of whistler-mode waves, with the corresponding electron slot near Europa being more pronounced in the dawn sector (Supplementary Figs. 2 and 3). Multiple dawn-dusk asymmetries have been reported within Jupiter’s magnetosphere, especially the corresponding charged particle distributions^{37,38,39,40,41}. In addition, the formation of the electron slot is characterized by a limited extent in magnetic local time, with the most prominent depletion observed in the dawn sector. This feature indicates that the slot is predominantly strongly influenced by the MLT-dependent wave activity. While our current simulation can explain the general formation of the energetic electron slot under the impact of whistler-mode waves near Europa, further analysis and modeling attempts are needed to fully understand the observations of this slot region at Jupiter. In the absence of strong whistler-mode wave fields, the remaining electron loss processes due to Europa absorption and energy losses in the moon’s neutral torus are insignificant on a global scale. Furthermore, the slot region can be refilled within the few hours that electrons need to drift between dawn and dusk. This fact points to either very fast electron radial diffusion or the presence of a yet unidentified acceleration processes that may quickly refill the depleted electrons and sustain high radiation levels near or inward of Europa’s orbit, which eventually power the Jupiter’s radiation belts.

Methods

Distributions of electron fluxes and whistler-mode waves in Jupiter’s radiation belt

The Juno data from perijove-03 (PJ-03) to perijove-46 (PJ-46) are used for analyzing the global distributions of energetic electrons and whistler-mode waves in Jupiter’s magnetosphere. The energy and pitch angle distributions of electrons over energy ranges from about 30 keV to approximately 1 MeV are provided by Jupiter Energetic Particle Detector Instruments (JEDI)²⁹. Observed electron distributions at different energies are obtained in every 30 s within every 5° pitch angle bin. The electron energy spectra were corrected according to the method proposed by Mauk et al.⁴² by removing artifacts caused by minimum ionizing peaks (about 100–200 keV) that result from the contamination by penetrating particles. In addition, we merge the flux data with low and high energy resolution and then pick up three electron energy channels (55, 97, and 170 keV) for our analysis. The averaged differential fluxes (j_{diff, avg}) are calculated as in Eq. (1).

$${j}_{{\rm{diff}},{\rm{avg}}}=\frac{\sum _{i=1}^{n}{j}_{{\rm{diff}}}^{i}}{n},$$

(1)

where j_diff is the electron differential flux, and n is the number of observation points. The omni-directional fluxes (j_omni) are as shown in Eq. (2).

$${j}_{{\rm{omni}}}=2\pi {\int }_{0}^{\pi }{j}_{{\rm{diff}}}\sin \alpha d\alpha,$$

(2)

where α is the local pitch angle.

To investigate the statistics of whistler-mode waves in Jupiter’s magnetosphere, we utilize electric and magnetic field power spectral density data within the 50–20 kHz frequency range under the survey mode, as recorded by the Juno/Waves instrument⁴³. The local magnetic field measurements provided by the Juno magnetometer⁴⁴ are mapped to the magnetic equator to estimate the equatorial field strength (B_eq) along the same field line using the JRM33 + CON2020 model^21,22. The following robust criteria are applied to select events of whistler-mode waves:

• (1). Since we are interested in the spatial correlation between whistler-mode waves and Jupiter’s moons, we consider whistler-mode waves in the range of M-shell = 5–15 and |MLAT| < 60°.

• (2). The wave spectra observed with the frequencies between 50 Hz and the equatorial electron gyrofrequency (f_ceq) are analyzed to cover a broad frequency range for whistler-mode wave identification.

• (3). To capture realistic wave emissions, the magnetic field power spectral densities for each frequency channel should exceed the maximum between the threshold value of 10⁻⁸ nT²/Hz and the daily median value of observed power spectral densities.

• (4). To exclude isolated emissions that are difficult to distinguish the properties, the selected events of whistler-mode waves should last more than 10 min per day, with each wave sample covering useful power spectral density data for at least three frequency channels.

• (5). The wave amplitudes are calculated using the trapezoidal integration method. The data points with the computed wave amplitudes <5 pT are excluded since it is difficult to distinguish these weak wave emissions from the background noise level.

• (6). All the wave amplitude data, originally with a 1 s resolution, are binned into a 30-s resolution to reduce the size of the entire dataset, which however, has little effect on the analysis results.

Wave-induced diffusion rate calculations in Jupiter’s JRM33 + CON2020 magnetic field configuration

In order to calculate the quasi-linear bounce-averaged electron diffusion coefficients driven by whistler-mode waves in Jupiter’s radiation belt, we adopt the background plasma density model following the work of Shprits et al.⁴⁵. Specifically, the plasma density N (L, λ) (λ is the magnetic latitude) is given by

$$N(L,\lambda )={N}_{\mathrm{eq}}(L)\,{e}^{\frac{-{L}^{2}(1-{\cos }^{6}\lambda )}{3{H}^{2}}},$$

(3)

Where the equatorial plasma density (N_eq, unit of cm⁻³) is calculated by

$${N}_{{\rm{eq}}}=3.2\times {10}^{8}{L}^{-6.9},$$

(4)

and H is the scale height. The value of H is calculated by

$$H={10}^{{a}_{1}+{a}_{2}r+{a}_{3}{r}^{2}+{a}_{4}{r}^{3}+{a}_{5}{r}^{4}},$$

(5)

where,

$$r={\log }_{10}(L),$$

(6)

The parameters are set as:

$${a}_{1}=-0.116,{a}_{2}=2.14,{a}_{3}=-2.05,{a}_{4}=0.491,{a}_{5}=0.126 .$$

(7)

The L value is approximately equal to the value of Jovian M-shell.

Ray tracing results show that high-frequency whistler-mode waves generated near the magnetic equator of Jupiter’s magnetosphere are typically confined within |MLAT| < about 20°, while low-frequency waves can reach higher latitudes⁴⁶. As these waves propagate, their wave normal angles become increasingly oblique due to the effects of field line geometry, plasma density gradient and wave refraction^28,46. Based on the statistics of whistler-mode wave distribution in Jupiter’s radiation belt, we assume that HFWs are confined within ∣MLAT∣ < 20° and LFWs are present up to ∣MLAT∣ = 60°. Different models of wave normal angle distribution are adopted to evaluate the electron diffusion rates induced by LFWs and HFWs separately. We follow a number of previous studies^47,48,49 to set the wave normal angle (ψ) distribution of whistler-mode waves as follows,

$$g(X)=\exp \left[\frac{-{(X-{X}_{{\rm{m}}})}^{2}}{{(\delta X)}^{2}}\right],\,{X}_{\mathrm{lc}}\le X\le {X}_{\mathrm{uc}},$$

(8)

where,

$$X=\,\tan (\psi ),\,\delta X=\,\tan (\delta \psi ),\,{X}_{{\rm{m}}}=\,\tan ({\psi }_{{\rm{m}}})X=\,\tan (\psi ),$$

(9)

$${X}_{{\rm{lc}}}=\,\tan ({\psi }_{{\rm{lc}}}),\,{X}_{{\rm{uc}}}=\,\tan ({\psi }_{{\rm{uc}}}) .$$

(10)

Here, δX is the angular width of the distribution, X_m is the peak value of the wave normal angle distribution. X_lc and X_uc represent the lower and upper bounds of the wave normal angle distribution, respectively. The bounds (X_lc ≤ X ≤ X_uc) indicate that the distribution is limited to the interval between X_lc and X_uc, outside of which the wave power is zero. The parameters adopted for the wave normal angle model are shown in Supplementary Table 1.

Following the diffusion rate computation equations in a non-dipolar magnetic field topology^17,50, we combine the JRM33 + CON2020 magnetic field configuration^21,22 and the statistically averaged whistler-mode wave power spectral intensity to quantify wave-induced bounce-averaged electron diffusion coefficients as a function of kinetic energy and equatorial pitch angle. The wave-particle interaction effects of both cyclotron resonances with the resonance order from −10 to 10 and Landau resonance are considered in the electron diffusion rate calculations.

Fokker-Planck diffusion simulations in Jupiter’s JRM33 + CON2020 magnetic field configuration

In order to simulate the evolution of electron phase space density under the impact of whistler-mode waves at the Jovian M-shell = 9.5 in the JRM33 + CON2020 magnetic field configuration^21,22, we solve numerically the two-dimensional (2-D) bounce-averaged Fokker–Planck diffusion equation as below,

$$\frac{\partial f}{\partial t}= \frac{1}{Gp}\frac{\partial }{\partial {\alpha }_{eq}}\left[G\left(\langle {D}_{\alpha \alpha }\rangle \frac{1}{p}\frac{\partial f}{\partial {\alpha }_{eq}}+\langle {D}_{\alpha p}\rangle \frac{\partial f}{\partial p}\right)\right]\\ +\frac{1}{G}\frac{\partial }{\partial p}\left[G\left(\langle {D}_{p\alpha }\rangle \frac{1}{p}\frac{\partial f}{\partial {\alpha }_{eq}}+\langle {D}_{pp}\rangle \frac{\partial f}{\partial p}\right)\right],$$

(11)

where f is the electron phase space density, p is the electron momentum, α_eq is the equatorial pitch angle. The value of G is given by

$$G={p}^{2}T({\alpha }_{{\rm{eq}}})sin{\alpha }_{{\rm{eq}}}\,\cos {\alpha }_{{\rm{eq}}},$$

(12)

with T(α_eq) as the normalized bounce period in a non-dipole magnetic field^17,50. <D_αα>,<D_αp>, and <D_pp> denote the bounce-averaged pitch angle diffusion rate, momentum diffusion rate and cross diffusion rate, respectively. The two cross diffusion terms, i.e., <D_αp> and <D_pα>, are equal to each other. These cross terms are included in our numerical diffusion simulations.

The initial condition of the electron PSD distribution function is obtained based on Juno measurements. Firstly, we convert observations of electron differential fluxes to electron PSD in terms of the following formula⁵¹,

$$f=3.33\times {10}^{-8}\frac{{j}_{{\rm{diff}}}}{{E}_{{\rm{MeV}}}({E}_{{\rm{MeV}}}+2{m}_{0}{c}^{2})},$$

(13)

where E_MeV is the electron kinetic energy in unit of MeV, m₀c² (approximately 0.511 MeV) is the electron rest energy with m₀ as the electron mass and c the speed of light. The electron differential flux (j_diff) has a unit of cm⁻² s⁻¹ sr⁻¹ keV^–1, and the electron phase space density has a unit of c³ MeV⁻³ cm⁻³. We acquire the initial electron PSD distributions near the magnetic equator based on the electron flux measurements from Jovian Auroral Distributions Experiment (JADE)⁵² (about 100 eV to approximately 100 keV) and JEDI-E²⁹ (about 30 keV to approximately 1 MeV). We analyze the statistical distributions of electron fluxes near the magnetic equator (|MLAT| ≤ 5°) at M-shell = 9.5, similar to the method described in the work of Ma et al.⁵¹, which are used as the initial conditions for the simulations. Specifically, the data from July 2016 to December 2023 are used, and the data are binned in 0.5 M-shell intervals. Regarding the set-up of boundary conditions, we assume that the electron PSD remains constant at both the lower and upper energy boundaries (i.e., E_k = 10 keV and 1 MeV). Furthermore, the boundary conditions for α_eq are defined as:

$$f({\alpha }_{{\rm{eq}}}\le {\alpha }_{{\rm{LC}}})=0 \,,$$

(14)

$$\frac{\partial f}{\partial {\alpha }_{{\rm{eq}}}}({\alpha }_{{\rm{eq}}}={90}^{\circ })=0 \,,$$

(15)

A hybrid finite difference method⁵³ is implemented to solve the 2-D bounce-averaged Fokker–Planck equation. We use fully implicit numerical method to solve the pitch angle diffusion and momentum terms, and an alternating implicit numerical method to solve the mixed terms. Such a combination of solving methods is called “hybrid”. We simulate the temporal evolution of Jovian electron PSD under the impact of HFW and LFW within 10 h. To facilitate quantitative comparisons of the numerical results with Juno observations, the simulated electron PSDs as a function of α_eq (equatorial pitch angle) are transformed into a function of α (local pitch angle), following the conversion equation

$${\alpha }_{{\rm{eq}}}=\arcsin (\sqrt{\frac{{B}_{{\rm{eq}}}}{{B}_{{\rm{o}}}}{\sin }^{2}\alpha }),$$

(16)

where B_o is the local magnetic field strength observed by Juno and B_eq is the equatorial magnetic field strength. B_eq is computed by mapping B_o along the field line to the magnetic equatorial plane under the JRM33 internal magnetic field model (order 13)²¹ and the CON2020 current sheet model²².

Radial diffusion simulations of steady-state electron distribution with incorporation of loss processes

To elucidate the physical mechanisms responsible for the formation of an electron flux slot near Europa’s orbit, we analyze the steady-state solution of the radial diffusion equation⁵⁴, with incorporation of electron loss effects due to moon absorption and wave-particle interactions. The radial diffusion equation including the loss terms is described below,

$$\frac{\partial f}{\partial t}={L}^{2}\frac{\partial }{\partial L}\left({L}^{-2}{D}_{{\rm{LL}}}\frac{\partial f}{\partial L}\right)-\frac{f}{{\tau }_{{\rm{w}}}}-\frac{f}{{\tau }_{{\rm{m}}}} .$$

(17)

Here, L is the Jovian magnetic shell, which is approximately equivalent to the M-shell in a dipole magnetic field. D_LL is the radial diffusion coefficient, which has been widely used for studying both Earth’s and Jupiter’s electron radiation belts. It is computed by the following formula¹²

$${D}_{{\rm{LL}}}=1.3\times {10}^{-10}{L}^{4.2} .$$

(18)

The term τ_m denotes the average electron lifetime due to Jupiter’s moon absorption. Following the work of Long et al.¹⁰, it is determined by

$${\tau }_{{\rm{m}}}=\frac{{\tau }_{{\rm{enc}}}}{-\,\mathrm{ln}(1-{P}_{{\rm{a}}})},$$

(19)

where τ_enc is the average encounter time between a moon and energetic electrons near the moon’s orbit, and P_a is the averaged absorption probability per encounter, influenced by factors such as electron energy, pitch angle, the moon’s size and orbit, and the background magnetic field^10,11. The term τ_w is the electron loss time scale due to pitch angle scattering by Jovian whistler-mode waves, which can be calculated by ref. ⁵⁵

$${\tau }_{{\rm{w}}}={\int }_{{\alpha }_{{\rm{LC}}}}^{\pi /2}\frac{1}{2\langle {D}_{{\rm{\alpha }}{\rm{\alpha }}}\rangle \tan {\alpha }_{{\rm{eq}}}}d{\alpha }_{{\rm{eq}}} \, .$$

(20)

Based on the simulation results in the JRM33 + CON2020 magnetic field configuration^21,22, the L-shell region of Jupiter’s moon absorption is between 9.29 and 10.02. In contrast, the Jupiter’s electron slot region induced by whistler-mode waves is mainly located within M-shell = 8–10. For simplicity, we assume that τ_w is constant for this spatial M-shell coverage and is derived using the electron pitch angle diffusion rates at M-shell = 9.5. By considering that the radial diffusion timescale of tens of days (Eq. (18)) is significantly longer than that of electron pitch angle scattering loss due to whistler-mode waves (about several hours) but comparable to the collisional loss timescale induced by Europa (about tens of days), we further set that the electron PSD remains constant at both the lower (M-shell = 7) and upper M-shell boundaries (M-shell = 12) so that the effect of wave-driven loss can be reasonably assessed. By adopting the initial electron fluxes given by the D&G electron flux model⁵⁶, we finally calculate the steady-state solutions of electron PSDs as a function of radial M-shell by setting the time derivative of the distribution function to zero and including/excluding different physical processes in Eq. (17), the results of which are shown in Fig. 4d for 97 keV electrons for illustrative purposes. All processed data used in this study are available at Figshare⁵⁷, ensuring full reproducibility of the results presented.