Resonant Plasma Acceleration at Jupiter Driven by Satellite‐Magnetosphere Interactions

The Juno spacecraft had previously observed intense high frequency wave emission, broadband electron and energetic proton energy distributions within magnetic flux tubes connected to Io, Europa, Ganymede, and their wakes. In this work, we report consistent enhancements in <46 keV energy proton fluxes during these satellite flux tube transit intervals. We find enhanced fluxes at discrete energies linearly separated in velocity for proton distributions within Io wake flux tubes, and both proton and electron distributions within Europa and Ganymede wake flux tubes. We propose these discrete enhancements to be a result of resonances between particles' bounce motion with standing Alfvén waves generated by the satellite‐magnetosphere interaction. We corroborate this hypothesis by comparing the bounce and field‐line resonance periods expected at the satellites' orbits. Hence, we find bounce‐resonant acceleration is a fundamental process that can accelerate particles in Jupiter's inner magnetosphere and other astrophysical plasmas.


Introduction
Due to the Juno spacecraft's elliptical polar orbits around Jupiter, it has routinely transited through magnetic flux tubes in the polar region connected magnetically to the orbits of the Galilean satellites-Io, Europa, Ganymede, and Callisto, thereby mapping either to the moons or their near or distant wakes.While crossing the Io flux tube, Juno consistently observed enhanced broadband (in energy) electron fluxes below ∼10 keV (Szalay et al., 2018), enhanced energetic proton fluxes between 50 keV and 1 MeV with conic pitch angle distributions (Clark et al., 2020), and intense electromagnetic emissions (Sulaiman et al., 2020) between 0.1 Hz and 3 kHz.The enhancement in particle flux or wave intensity was strongest at the main Alfvén wing and decreased with increasing longitudinal separation along Io's footprint wake (Clark et al., 2023;Sulaiman et al., 2023;Szalay, Allegrini, et al., 2020).Additionally, an accelerated population of protons with energies ∼keV were observed during Juno's 18th perijove (PJ18) (Szalay, Allegrini, et al., 2020;Szalay, Bagenal, et al., 2020).Similar to the Io and Io-wake flux tubes, enhancements in the electron fluxes were also observed during the Europa-wake flux tube crossings, where in contrast to Io, they were occasionally found to have peaks in the energy distribution (Allegrini et al., 2020;Rabia et al., 2023).These observations are almost certainly a result of the satellite's interaction with the magnetospheric plasma (Saur, 2021 and references therein).
Electron acceleration and corresponding broadband energy distributions in the satellite flux tubes as described above, and in the main auroral emission (Mauk, Haggerty, Paranicas, et al., 2017), could result from non-resonant interaction with Alfvén waves (Coffin et al., 2022;Damiano et al., 2019;Gershman et al., 2019;Hess et al., 2010;Janser et al., 2022).However, the mechanism that produces broadband energetic proton distributions in the Io flux tube remains a mystery.Electromagnetic plasma waves with a cut-off at the local proton cyclotron frequency (Sulaiman et al., 2020) were observed within the Io flux tubes and the intensity of the wave emission at this frequency was positively correlated with the energetic proton energy flux (Clark et al., 2023).This provided strong evidence for plasma interaction with electromagnetic ion-cyclotron waves (EMIC) waves.Moreover, the magnetospheric plasma at Io's orbit is composed mostly of heavy ions, for example, O n+ or S n+ , due to SO 2 from Io's volcanic activity and atmosphere, so the consistent existence and enhancement of energetic protons seen in the Io and Io-wake flux tubes is somewhat surprising.The protons could originate from the Jovian ionosphere via some outflow process (Szalay et al., 2021), but it is not clear why this outflow would intensify within the Io footprint and wake.
The satellite-magnetosphere interaction creates Alfvén wings that travel from the moon to the ionosphere (Neubauer, 1980).These Alfvén wings are a standing wave in the moons' rest frame (like a bow wave of a boat).Field line resonances (FLRs) are another kind of standing Alfvén wave in the magnetospheric frame (Southwood & Kivelson, 1981).FLRs require that a wave is restricted between two boundaries, which in the magnetospheric context could be the ionosphere, edges of the plasma torus, or the boundary of the ionospheric Alfvén resonator (Lysak et al., 2021(Lysak et al., , 2023;;Schlegel & Saur, 2022;Su et al., 2006).Odd mode FLRs have an electric-field wave structure symmetric about the equator whereas even mode FLRs are anti-symmetric.FLRs have been observed in Jupiter's magnetosphere via direct sampling of magnetic fluctuations (Glassmeier et al., 1989;Manners & Masters, 2019;Manners et al., 2018) or via periodicities in the auroral emission (Nichols et al., 2017;Pan et al., 2021).In particular, Glassmeier et al. (1989) proposed that the magnetic signatures of FLRs observed by Voyager 1 near Io could have resulted from the Io plasma interaction, but this was not proven definitively.
In this work, we expand on previous observations of enhanced electron and energetic protons (>50 keV) measured by the JEDI instrument (Mauk, Haggerty, Jaskulek, et al., 2017), and wave activity observed by the Waves instrument and report consistent simultaneous enhancements of lower energy (<46 keV) proton fluxes during the Io flux tube crossing intervals, as observed by the Jovian Auroral Distributions Experiment (JADE) on board Juno (McComas et al., 2017).We examine the energy distribution of lower energy (<46 keV) protons and electrons for different satellite flux tube crossings and report the existence of flux enhancements at discrete energy levels that are seen as "bands" in the energy spectra.Observations of the energy banded protons and electrons are discussed in Section 2. In Section 3, we interpret the energy bands as arising from bounce-resonant interaction with satellite-driven field-line resonances and summarize these findings and their implications in Section 4.

Observations
We analyzed 0.01-46 keV/q proton fluxes and 0.03-30 keV electron fluxes as measured by the JADE plasma instrument onboard Juno during intervals when Juno passed through magnetic flux tubes connected to the orbits of Io, Europa, and Ganymede, identified based on enhanced electron fluxes and magnetic field line tracing using the Jupiter magnetic field community codes (Wilson et al., 2023).These flux tube crossings occurred in the polar regions of Jupiter's magnetosphere, typically at altitudes less than 2 R J (1 R J ≡ 71,492 km).

Broadband Proton Fluxes Within the Io Flux Tube Crossings
Figures 1a-1c shows the energy spectra of protons and electrons observed by Juno's JADE, JEDI, and waves spectra from the Waves instrument (Kurth et al., 2017) during the PJ32 pass through a flux tube connected to Io's wake via the southern hemisphere.This representative transit exhibits several characteristic features often observed during Juno's Io flux tube crossings such as -enhancements in electron flux (e.g., Szalay et al., 2018) and energetic proton flux (e.g., Clark et al., 2020), and electrostatic waves (e.g., Sulaiman et al., 2020).Both panels (a) and (b) in Figure 1 combine the lower energy plasma observed by JADE with the higher energy particles observed by JEDI, where the transition between the instruments at 40-50 keV shows a change in apparent flux due to slightly different observing geometries and noise floors.Broadband proton (0.02-100 keV) and electron ( 0.04-5 keV) distributions were observed with higher fluxes within the crossing interval.Spatial substructure exists within the tail crossing with one prominent interval of lower flux and wave power embedded between those with higher fluxes and wave power.This is likely related to the Io's "split-tail" auroral feature seen in the infrared observations (Mura et al., 2018) and in the electron spectra (Szalay et al., 2018) (marked in Figure 1a).The proton distributions in Figure 1b exhibit "bands" with higher fluxes at discrete energies.This was found for many other crossings as well and will be discussed in the next section.We also determined all Io and Iowake flux tube crossings and calculated the proton and electron omnidirectional energy flux (OEF) (details in Supporting Information S1).

Energy-Banded Protons and Electrons Within Satellite-Wake Flux Tubes
During transits of the satellite flux tubes, proton and electron distributions observed by Juno often exhibited discrete energy bands.Figure 2 shows example proton and electron spectra for Io (PJ 23S), Europa (PJ41S), and Ganymede (PJ37S).In this Io wake crossing (Figures 2a and 2b), proton bands occur at 1.2 keV, 5.9 keV, 12.8 keV, and 21.8 keV.No bands were observed for the electrons, where the alternating "checkerboard" pattern in consecutive energy bins above 1 keV in Figure 2b is an instrumental artifact that occurs when sampling electron distributions that vary more rapidly than JADE-E's 1s sampling time.In the Europa wake crossing (Figures 2c and  2d), no bands were observed for the protons, while the electrons exhibited several bands around 0.25, 2.2, 4.0, and 6.3 keV.Likewise, multiple discrete energy bands were observed during the Ganymede wake flux tube crossing (Figure 2f), for electrons centered around 0.32, 0.72, 1.28, and 2 keV.The banded distributions shown in Figures 2a, 2d, and 2f are unlikely to be instrumental artifacts since each band covers a range of energies and the bands are only observed within flux tubes connected magnetically to the satellite wakes.
Figure 3 shows the average differential intensity from Figures 2a, 2d, and 2f for the species with banded distributions.The first row (panels a, d, and g) shows the differential intensity within the interval (solid black circles) and the average spectra in the 2-min period before and after the crossing interval (green triangles) for the three satellite crossings shown in Figure 2, as a function of particle energy.A kappa distribution that was fit to the data within the satellite flux tube (in log-space) is shown here as the dashed black curve (details in Supporting Information S1).The second row (panels b, e, and h) shows the log of the ratio of the original data with the kappa distribution, which better highlights flux increases and decreases associated with the bands.The uncertainty in the measurement calculated assuming a Poisson distribution of counts over the interval is shown in gray, although because of high counts this uncertainty is quite small.The third row (panels c, f, and i) shows the same log-ratio between the data and the kappa distribution as a function of particle speed instead of energy.A spline curve was fit to the banded part of the distribution and the peaks/maxima were identified (shown via blue arrows).The average speed separation between each consecutive maxima (∆v*) is 497 km s 1 for protons during the PJ 23-S Io crossing, 9,343 km s 1 for electrons during the PJ 41-S Europa crossing, and 5,454 km s 1 for electrons during the PJ 37-S Ganymede crossing.Banded energy distributions for all three events are observed at nearly all pitch angles (not shown).The last row (Figures 3d, 3g, and 3j) is explained later in the next section.
In addition to the examples shown in this text, we searched for similar signatures in all identified Io (N = 40), Europa (N = 14), and two Ganymede flux tube crossings.So far, we have observed proton bands at all three moons, but electron bands were only seen during Europa or Ganymede flux tube crossings.In addition, none of the intervals analyzed exhibit banding in both electrons and protons in the same interval, that is, for a specific interval, we observed either proton bands or electron bands, but not both.Not all intervals with bands are as coherent as those shown in Figures 2 and 3, and there are also instances where the energy distribution peaks at only one or two energies.Out of 40 total Io flux tube crossings that we analyzed; we determine using visual inspection that more than 12 have banding features in the proton energy distributions (30%).Similarly, out of 14 Europa flux tube crossings, we see 4 intervals with clear electron bands (29%) and 2 intervals with proton bands (14%).We examined two Ganymede crossings, one with banding in the distributions of protons and the other with electrons.Lastly, we note that weakly banded distributions were also seen during 3 intervals mapping to M-shells larger than 20, which were categorized as "unknown" as they may not be related to Jovian satellites.Details of all events analyzed are provided in the attached Supporting Information S1.

Interpretation
We suggest that the intensifications and depletions (i.e., "bands") observed for both protons and electrons, which are almost linearly spaced in speed, result from a resonant acceleration process operating at energies that correspond to harmonics of some fundamental resonance frequency of a plasma wave perturbation.Magenta lines are marked at linearly separated speeds.Saur et al. (2018) characterized the resonant interaction between a wave with frequency ω and parallel wavenumber k ∥ and particles with parallel velocity v ∥ and cyclotron frequency Ω that occurs when ω k ∥ v ∥ = nΩ (Stix, 1992), into Landau damping where the integer n = 0 and cyclotron damping when it is ±1.However, the frequency of cyclotron motion (i.e., the motion associated with the first adiabatic invariant) is independent of particle energy or speed and hence cyclotron resonance does not explain the existence of discrete energy bands and depletions observed by Juno.Likewise, Landau resonance also does not explain the observations as it requires that the phase velocity of the wave equals the velocity of the particles, which in Jupiter's polar regions could only occur at relativistic energies.However, resonant interaction can also occur between a lower frequency wave and the periodic motion associated with the second and third adiabatic invariants, that is, the bounce and drift motion (Southwood & Kivelson, 1981, 1982) when ω mω d = Nω b where ω d and ω b are azimuthal drift and bounce frequencies, respectively.We assume that the azimuthal drift frequency in Jupiter's magnetosphere is small (drift period for a 1 keV proton with α eq = 70°in at Io's M-shell is on the order of 900 min) and focus the rest of this discussion on bounce resonance with the wave, that is, when ω ≈ Nω b , where N is an integer.
For particles trapped in a dipole magnetic field, their bounce periods vary with energy, equatorial pitch angle and L-shell (synonymous with M-shell for a dipolar field) (Orlova & Shprits, 2011), Figure 3. Row 1 (a, d, g): Energy spectra during and outside the crossing interval, Row 2 (b, e, h): Log of the ratio between the measured fluxes and a fitted kappa distribution with the Poisson counting uncertainty in gray, as a function of particle energy; and in Row 3 (c, f, i): Log of the ratio between the measured fluxes and fitted kappa distribution, as a function of particle speed (black), uncertainty in gray, and fitted spline in red.Δv* is the average velocity separation of the spline peaks.(d, g, j) Peak velocities compared to velocities where resonance is expected with a symmetric/odd wave mode (v = Δv*, 2Δv*, 3Δv*…) and anti-symmetric/even wave mode (v = 0.5Δv*, 1.5Δv*, 2.5Δv*…), in red and blue respectively.
where y = sinα eq (α eq = sin 1 ( sin α ̅̅̅̅̅̅̅̅̅̅̅̅ ̅ B/ B eq √ ) is the equatorial pitch angle), λ is the magnetic latitude along the field line, and λ m is the magnetic latitude at the mirror point.The integrand depends only on the equatorial pitch angle and latitude and is independent of the particle energy.Hence, for a given equatorial pitch angle, the bounce frequency ω b ∝ 1/τ b is directly proportional to the particle speed, that is, ω b ∝ v.The observed bands which are linearly separated in speed also correspond to some characteristic bounce frequency ω * b , that could be in resonance with a wave with frequency ω when ω ≈ Nω * b .
Odd-mode or symmetric standing Alfvén waves are expected to resonate with particles when N = 0, ±2, ±4,…, whereas even-mode or anti-symmetric standing Alfvén waves resonate with particles when N = ±1, ±3, ±5… (Southwood & Kivelson, 1982;Takahashi et al., 2018).This means that for odd mode waves, resonance would occur when (considering positive values for clarity) ω ≈ 2ω * b ,4ω * b ,6ω * b … or at some particle speeds v = 2v*, 4v*, 6v*….Likewise, for even mode waves, resonance would occur when ω ≈ ω * b ,3ω * b ,5ω * b … or at some particle speed v = v*, 3v*, 5v*….In both cases, the speeds of resonating particles are linearly separated by Δv* = 2v*.Hence, if Δv* can be identified from the observations, then it is possible to identify whether the resonating wave is odd mode (symmetric) or even mode (anti-symmetric) based on whether the peak fluxes are observed at velocities of v = Δv*, 2Δv*, 3Δv*… or at v = 0.5Δv*, 1.5Δv*, 2.5Δv*….These cases are shown in Figures 3d, 3g, and 3j as blue and red arrows, where Δv* is the average speed separation between two peaks.Since the observed flux peaks are seen (by eye) close to Δv*, 2Δv*, 3Δv*… for all three intervals, the particles are likely resonating with an oddmode field-line resonance/symmetric standing Alfvén wave.The above analysis assumes that (a) the observed bands are produced by a single wave with frequency ω, and (b) flux enhancements are observed at resonating energies.In Figure 4a we show the dipolar bounce periods for protons and electrons with equatorial pitch angles between 1°a nd 10°at the orbits of Io, Europa, and Ganymede using Equation 1 (Orlova & Shprits, 2011).The bounce periods are shortest at Io's orbit and longest at Ganymede, owing to the different magnetic field geometry.For electrons between 100 eV and 10 keV, where the bands were frequently observed, bounce periods at different moons are expected to range between 0.3 and 15 min.Likewise, 0.1-10 keV protons have bounce periods between 20 and 600 min.
The satellite-magnetosphere interaction produce Alfvénic perturbations that reflect off density (and hence Alfvén speed) gradients in the magnetosphere and ionosphere (Neubauer, 1980;Schlegel & Saur, 2022), and could trigger standing Alfvén waves in the form of field line resonances.The natural frequencies for the standing wave and its harmonics are determined by the field line geometry, density, and variation of Alfvén speed along the field line (Lysak & Song, 2020).Field-line resonances with periods on the order of minutes have been observed in the Jovian inner and middle magnetosphere (Glassmeier et al., 1989;Manners & Masters, 2019).The observed field-line resonance periods are consistent with the two-way travel times for an Alfvén wave (Hinton et al., 2019;Hue et al., 2023).Glassmeier et al. (1989) calculated the fundamental eigenperiod for a toroidal standing wave at Io's orbit to be around 21.6 min and that of the first harmonic to be 13.1 min.Recent work by Manners et al. (2018) has suggested higher values, with the fundamental eigenperiod longer than 200 min and first harmonic on the order of 70-80 min Lysak and Song (2020) calculated the toroidal eigenperiods as a function of M-shell and while they find the fundamental to be larger than 80 min, the harmonics range from 2 to 35 min between the orbits of Europa and Ganymede.Note that these estimates are sensitive to the assumed density profile (Manners et al., 2018).A general range of field line resonance eigenperiods is highlighted in yellow in Figure 4a.
As shown in Figure 4, the bounce periods of the ions and electrons and the eigenperiods of field-line resonance at the orbital locations of the moons are of similar order, presenting a suitable opportunity for resonance.Also shown in Figure 4a are the bounce periods for the banded energies observed during the Io, Europa, and Ganymede flux tube crossing intervals, which often overlap with higher harmonics of the field-line resonance.Particles with bounce periods that are close to the resonant wave frequency, or its harmonics, can experience a net acceleration or deceleration over the course of successive bounces (shown in Figures 4c and 4d) by interacting with the low frequency electric field in the wave and gain or lose energy so as to be in resonance with the wave (Southwood & Kivelson, 1982).Figure 4c shows particles starting at different energies being accelerated over successive bounces, but a similar picture with decelerating particles is also feasible, in both cases driving particles to the resonant bounce periods, speeds and energies.That banded distributions are observed strongly within, but not outside, the satellite wake flux tubes, is consistent with this hypothesis as the satellites have strong localized Alfvénic perturbations.However, on occasion we have found other intervals with banded distributions that do not appear to be linked to the satellite interactions as they are observed at larger M-shells than Ganymede's (see Supporting Information S1).These may also be caused by bounce-resonance with standing Alfvén waves that are created due to other processes such as radial flux-tube interchange.For for example, banded energy distributions were observed by Thomsen et al. (2017) in Saturn's magnetosphere across a broad range of M-shells.Additionally, both proton and electron distributions could present bands at energies above 1 MeV due to resonance between the drift motion of the particles with the orbital motion of the moons, as modeled by Simpson et al. (1974) under the assumed absence of radial diffusion.This is a different process than the resonances discussed in the present work, which occur at keV energies or below.
Bounce-resonant interaction could be a fundamental process that operates at frequencies intermediate between quasi-static potentials and wave-particle resonance at cyclotron frequencies and non-resonant or stochastic acceleration in Alfvén waves, producing banded energy distributions that are different from the monoenergetic "inverted-V" and broadband distributions (Mauk et al., 2018) created respectively by those processes.Additionally, simulations of standing mode waves in the terrestrial magnetosphere (Damiano et al., 2019;Damiano & Johnson, 2012) illustrate banded structures superimposed on a monoenergetic electron energization signature (owing to the low frequency nature of the waves).It was suggested that this structure was due to a bounceresonant interaction between the electrons and the standing wave, but the relation between the bands and the monoenergetic energization has yet to be established.

Conclusions
We examined proton and electron distributions during several Io, Europa, and two Ganymede crossings made by Juno during its pass over Jupiter's northern and southern poles.We found that: 1. Broadband proton intensifications were consistently observed within the Io and Io-wake flux tube, simultaneous to broadband electron distributions, and wave power intensifications.2. Proton and electron distributions in the Io, Europa, and Ganymede (and respective wake) flux tubes often exhibit banded features or intensified fluxes at discrete energy levels that appeared linearly separated in speed with some spacing Δv*. 3. Particle fluxes peak at speeds Δv*, 2Δv*, 3Δv*… or bounce frequencies related as 2ω*, 4ω*, 6ω*, …, suggesting interaction with an odd mode field-line resonance or symmetric standing Alfvén wave.4. In the JADE energy range, bounce periods for protons and electrons between Io and Ganymede are on the order of minutes to tens of minutes, similar to eigenperiods of standing Alfvén waves published previously in literature. 5. Resonance between the particle bounce motion and the standing Alfvén wave generated due to the satellitemagnetosphere interaction can produce the banded distributions.
The observations are consistent with bounce-motion resonance and beckon additional questions: How much energy is transferred from wave to the particles?How and at what timescales is it dissipated?Where along the field line does the wave-particle interaction occur?We show here that bounce-resonant interaction is a fundamental process that can modify proton and electron energy distributions under appropriate conditions and may play a bigger role in auroral and moon-magnetosphere phenomena than previously understood.

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Proton and electron flux enhancements in satellite and wake flux tubes often occur at discrete energies linearly separated in speed • Broadband proton flux enhancements at <46 keV energies were also observed within satellite flux tube crossings • Particles can be accelerated via resonance between bounce motion and standing Alfvén waves generated by moon-magnetosphere interactions Supporting Information: Supporting Information may be found in the online version of this article.

Figure 1 .
Figure 1.(a, b) Spectra of electron and proton differential flux measured by the JADE and JEDI instruments (c) Electric field power spectral density as measured by the Waves instrument with the H + cyclotron frequency overlaid.

Figure 2 .
Figure 2. Proton and electron differential energy flux measured by JADE during (a, b) PJ 23-S Io (c, d) PJ 41-S Europa, and (e, f) PJ 37-S Ganymede flux tube crossings.Magenta lines are marked at linearly separated speeds.

Figure 4 .
Figure 4. (a) Electron and proton dipolar bounce periods at Io, Europa, Ganymede.Circled points are bounce periods of particles at the banded energies shown in Figures 2 and 3.The yellow region centered on 10 min is a general range of field-line resonance eigenperiods reported by various studies (b) Schematic of various poloidal field-line resonance modes along with Juno's trajectory through this structure (c, d) Illustration of how particles at different energies with different bounce periods can gain energy over the course of repeated mirroring and interaction with the low frequency wave, leading to the observed flux enhancements.