Modeling Ion Conic Formation in Io's Auroral Footprint

Energetic ions outflowing from Jupiter's atmosphere was observed during Juno's 12th perijove crossing (PJ12) in the vicinity of Io's auroral footprint and reported by prior studies. It was hypothesized that Wave‐Particle Interactions (WPI) with ion cyclotron waves observed coincident with the ion outflow may be responsible for the heating and subsequent outflow. This study uses numerical simulation and data model comparison to test whether ion cyclotron resonant heating is indeed a plausible mechanism to explain the intense ion outflow observed. Our simulations assume that the wave heating is of limited duration due to Io's footprint motion. The simulations are moreover compared to the previously published Jupiter Energetic Particle Detector Instruments (JEDI) observations at high energies, and the lower energy Jovian Auroral Distributions Experiment (JADE) observations that were not previously reported. We find that the ion cyclotron resonant heating mechanism can indeed lead to ion conic formation and strong vertical transport under certain assumptions about the distribution of wave power with altitude. We also find that the ion outflow is energized quickly with very rapid formation of the ion conic distribution. The implications of the intense ion outflow are also examined and it is found that such strong wave heating can lead to a depletion of the topside ionosphere.


Introduction
The transport of ions from the ionosphere to the magnetosphere, known as ionospheric outflow, is observed to occur at many planetary systems.These outflows can be cold but supersonic, as in the case of the classical polar wind driven by an ambipolar electric field, or very heated as in the case of ion conics driven by Wave-Particle Interactions (WPI).The latter case is particularly interesting for understanding ion escape from a giant planet like Jupiter where a hydrogen atom would require in excess of ∼20 eV of energy to overcome the gravitational binding energy and escape the atmosphere.Recent observations by the Juno spacecraft at Jupiter observed very strongly accelerated ions streaming away from the planet with energies in excess of 40 keV (Clark et al., 2020).Understanding these observations using numerical modeling is the primary focus of this paper.
One of the main motivations for seeking to understand ionospheric outflows from planets is to uncover the origin of plasma in that planet's magnetosphere.A planet's magnetosphere derives its plasma from three primary sources: its satellites, the ionosphere, and the solar wind.At Earth only the latter two sources are significant with the solar wind providing H + while the ionosphere provides both H + and O + .As O + only comes from Earth's ionosphere, its observed presence in the magnetosphere was taken as the first proof that the ionosphere can indeed be an important supply of plasma to the magnetosphere (Shelley et al., 1972).The relative importance of ionospheric and solar wind plasma's has been a topic of intense scientific debate (e.g., Chappell et al., 1987).In general, both data and simulations demonstrate that the ionosphere can and does provide a significant amount of magnetospheric plasma particularly during geomagnetic storms (e.g., Glocer et al., 2020;Kistler et al., 2023).
In contrast to Earth, Jupiter's magnetosphere obtains a major portion of its plasma from its satellites.Among the satellites, Io stands out as a plasma source by ejecting volcanic gases comprised of S and O at a rate of about 1,000 kgs 1 which then become ionized, forming the Io plasma torus (Bagenal et al., 2004).The solar wind and ionosphere are both potential sources of protons, however, and the repeatedly observed presence of H + 3 (and to a lesser extent H + 2 ) is clearly suggestive of the existence of an ionospheric source of plasma to the magnetosphere.Note that H 2 is ionized in the planets upper atmosphere but then rapidly combines with H 2 to produce H + 3 (e.g., Atreya et al., 1974;Gross & Rasool, 1964).Just as O + serves as a clear marker of ionospheric outflow in Earth's magnetosphere, H + 3 serves this role in Jupiter's magnetosphere.H + 3 was first observed in the Jovian magnetosphere by the Voyager 2 spacecraft.Those findings were later confirmed by the Ulysses satellite (Seidel et al., 1997).This population has even been observed by the New Horizons spacecraft far down Jupiter's magnetotail (McComas et al., 2007).Protons observed in Jupiter's magnetosphere may also come from the ionosphere although their origin is more ambiguous to determine as they can be derived from either a local source (ionosphere or satellite) or from the solar wind.A study by Mall et al. (1993) tried to separate these sources by looking at the H + /He 2+ fraction and concluded that local sources of plasma are particularly important for the middle magnetosphere.While the presence of ionospheric outflow at Jupiter is clear, the magnitude of the ionospheric source, its variation, and its relative significance to other sources is not well established.
The presence of ionospheric outflow is clearly observed at Earth and Jupiter as well as at other planets, and it is important to understand the universal processes that can create these outflows of plasma.Of particular interest to this paper is the very heated outflow known as ion conics that can impart to the plasma a sufficient amount of energy to overcome the strong gravity of even a giant planet.Ion conics are generated by the heating of ions perpendicular to the local magnetic field by WPI.The waves responsible for the heating can be electrostatic ion cyclotron waves (e.g., Lysak et al., 1980), electromagnetic ion cyclotron waves (e.g., Chang et al., 1986), lower hybrid waves (e.g., Chang & Coppi, 1981), and dispersive Alfven waves (e.g., Chaston et al., 2004), among others.Particle interactions with any of these waves have been argued to heat the ion distribution function transverse to the magnetic field creating a 'pancake-like' distribution in velocity space.The magnetic mirror force then accelerates the ions parallel to the field.The mirror force is stronger for larger perpendicular velocities causing the edges of the distribution function to bend upward resulting the characteristic cone shaped distribution function in velocity space and giving rise to the name "ion conic."Ion conics are have been observed at a number of solar system bodies including Earth (e.g., Gorney et al., 1985), Saturn (e.g., Mitchell et al., 2009), and Jupiter (e.g., Clark et al., 2017).The characteristics can be quite different though.Ion conics at Earth typically exhibit transverse heating yielding perpendicular temperatures on the order of 100 eV (Bouhram et al., 2003).In contrast, ion conics at Saturn can have energies that are a factor of 100 higher than those conics observed at Earth, even though their general shapes are similar (Mitchell et al., 2009).The observed presence of ion conics at multiple different planets implies that similar heating processes may be at play.
Recently, energetic ion outflow associated with Io's auroral footprint was observed during Juno's 12th perijove crossing (PJ12).These observations are reported by Clark et al. (2020) who note that intense proton acceleration is observed with the Juno/Jupiter Energetic Particle Detector Instruments (JEDI) instrument at energies above the instrument detection threshold of ∼40 keV.The proton fluxes moreover exhibit a power law tail with energy.A detailed examination of the waves was provided by Sulaiman et al. (2020) who report the presence of intense ion cyclotron waves during this event.Using a back-of-the-envelope calculation of the heating rate, they show that these waves could generate the energetic ion conic observed.Clark et al. (2023) considered an expanded set of observations of ion heating events associated with the Io auroral footpoint, and provided additional evidence that the heating is likely associated with the observed waves.
In this paper, we present detailed modeling of the formation of the ion conic discussed by Clark et al. (2020) and Sulaiman et al. (2020).In particular, we use the Polar Wind Outflow Model (PWOM), a fluid-kinetic model of ion escape (Glocer et al., 2018), to look at the generation of energetic ion outflow in response to the observed waves.We will demonstrate that the intense ion cyclotron waves can indeed generate an ion conic that is consistent with the published Juno/JEDI observations as well as the lower energy Juno/Jovian Auroral Distributions Experiment (JADE) data given certain assumptions about the wave power distribution with altitude.We will moreover look at the implications for lower energy ranges and the topside ionosphere.Uncertainties in the observations and modeling will also be discussed.

The Polar Wind Outflow Model at Jupiter
This study uses the PWOM to understand the ion conic formation observed at Jupiter.In this section, we will first briefly describe the model and its adaptation to Jupiter.We will then describe the simulation and analysis approach.
A recent description of the physical and numerical approaches employed by PWOM is available in Glocer et al. (2018), but will be briefly summarized here.The PWOM models the transport of plasma along a given magnetic field line from the ionosphere of a planet to the magnetosphere.The magnetic field is simply assumed to be a dipole with Jupiter's dipole moment.At low altitudes, the model uses a fluid approach and solves the gyrotropic transport equations for all ion fluids (Gombosi, 1991).At high altitudes, the model solves a gyroaveraged kinetic solution for the ions using a hybrid Particle-In-Cell (PIC) approach.In this methodology, PWOM solves the gyroaveraged equation of motion for each macro particle each of which statistically represents some number of true particles.Collisions are also included utilizing a Monte Carlo methodology which allows the kinetic solution to be extended down into the transition region.The transition from fluid to kinetic occurs in the this transition region where both fluid and kinetic approaches are appropriate.
The electrons in PWOM are split into two populations: thermal and superthermal.The superthermal electrons can be treated with a fully kinetic approach (Glocer et al., 2017) or a two-stream representation with an adapted version of the GLOW code (Solomon, 2017;Solomon et al., 1988).In this study we use the two-stream approach due to its advantages in computational time.The superthermal electrons influence the outflow solution through ion production, the currentless condition, and thermal electron heating, and ultimately through the ambipolar electric field.The solar photon flux model used in the GLOW calculation is the EUVAC model (Richards et al., 1994) scaled to Jupiter's orbital location by assuming that the intensity drops with the square of the planets orbital distance.
The version of PWOM used in this study has been recently adapted to Jupiter.The details of this adaptation will be published in a separate study which will look at the role of particle precipitation and electron heat flux on thermal ion up-welling.Therefore, only a short summary of the key changes to the model to work at Jupiter are given here.The four main changes are, (a) the ions considered, (b) the chemical scheme, (c) the background neutral atmosphere, and (d) the two-stream transport solution.The ions considered at Jupiter are H + 3 , H + , H + 2 , all of which are transported dynamically.The chemical scheme is virtually identical to that used by PWOM at Saturn (Glocer et al., 2007).The background neutral atmosphere is provided by the Jupiter Global Ionosphere-Thermosphere Model (J-GITM) (Bell et al., 2013).That model self-consistently solves the time-dependent, 3-D Navier-Stokes equations of continuity, momentum, and energy, inheriting its numerical core from a validated Earth predecessor (Ridley et al., 2006) that has been successfully modified to several atmospheres including Titan (Bell et al., 2010a(Bell et al., , 2010b)), Mars (Bougher et al., 2008), and now Jupiter (Bell et al., 2013).For this study we use a single 3D output from the J-GITM model to fill in the background neutral density for our PWOM simulations.The background neutral atmosphere from J-GITM used in the calculation is shown in Figure 1.This profile is static in the simulations presented in this paper.Finally, the two-stream GLOW solution is adapted by including absorption, ionization, and secondary electron production crossections for H, H 2 , and CH 4 taken from the Atomic and Molecular Cross section for Ionization and Aurora (AtMoCiad) Database (Gronoff et al., 2021).
The altitudes considered in the Jupiter version of PWOM differ from those used at Earth.At Jupiter, the lower boundary of the model is located at 500 km and the upper boundary is at 60,000 km, while at Earth these boundaries are 200 and 8,000 km respectively.The relatively higher lower boundary at Jupiter is because most of the photoionization occurs above 500 km at this planet.The raised upper boundary at Jupiter is to ensure that we cover close to one planetary radii in altitude, and so that the Juno spacecraft location for the event studied is near the middle of the simulation domain.Likewise, the altitude of the fluid-kinetic transition moves to 10,000 km at Jupiter from 1,000 km at Earth.The motivation for this change is both physical and practical as the altitude is chosen to be inside the transition region, but not so low as to make the timestep in the kinetic model prohibitive as we must temporally resolve the particle motion between collisions.Therefore, we select the fluidkinetic transition altitude to be where the mean time between collisions is estimated to be between 0.1 and 1.0 s for each planet.
Of particular importance to the present study is the inclusion of WPI.WPI are included in the PWOM code in the high altitude kinetic region.In particular, the effect of ion cyclotron wave heating, which is hypothesized to be the source of the observed ion conics at Jupiter, is included as a stochastic process where the waves scatter the ions perpendicular to the field line.The perpendicular diffusion coefficient that describes the interaction of these waves with particles is given by Crew et al. (1990) as: here the value q is the charge of a particle, m i is the mass of ion 'i', Ω(s) is the gyro-frequency at a spatial position s along the field line and |E L | 2 is the left hand polarized portion of the electric field spectral density at a given position.
Using this formula together with a wave Power Spectral Density (PSD) at each position along the field line, the diffusion coefficient can be determined.
In the high-altitude kinetic region of PWOM, the WPI are applied by randomly perturbing the perpendicular velocity of each macro particle such that the distribution of velocity perturbations is consistent with the D ⊥ .This approach is commonly used to mimic the stochastic heating associated with WPI.In the present study, we define the waves by using power law fits to the observed wave power.The waves are assumed to be active only above 10,000 km.This altitude coincides with the fluid-kinetic transition location.

Summary of Observations During the PJ12 Io Auroral Footpoint Encounter
Juno passed above the Io auroral footpoint between about 09:20:35 and 09:20:55 UT on 1 April 2018 as described in detail by Clark et al. (2020).The altitude of the encounter was at 0.39 Jovian radii which corresponds to an altitude of approximately 27,882 km above the surface defined by the 1-bar pressure level.This event was part of the inbound leg of PJ12.Clark et al. (2020) also reported very energetic upward flow of ions instrument detection threshold of ∼40 keV.They also reported significant structure in the ion fluxes during the ∼20 s long encounter.Unfortunately it is impossible to disentangle spatial and temporal variability and it cannot be determined how much the variability in the ion fluxes is due to spatial structure of the energy input or time dependence of the acceleration mechanism.These observations were made using the JEDI (Mauk et al., 2017) which measures ions above about 10 keV for protons in six angular segments.Although not previously reported, the JADE instrument took ion data during this event and saw that the ion outflow extends to much lower energy than could be seen by JEDI.The JADE instrument provides measurements of ions between approximately 5 eV and 50 keV at an angular resolution of 22.5°at a ∼4 s time resolution.
Figure 2 presents the wave PSD as a function of frequency at six times during Juno's encounter with the Io auroral footprint during PJ12.These data are those discussed in Sulaiman et al. (2020).The ion cyclotron frequency ( f cH+ ) at the top and bottom of the model are indicated which shows the range of resonant frequencies in the simulation.f cH+ at the Juno altitude during the encounter is also shown.There is a wide spread in observed wave power that depends on the time of the observation, and possibly the alignment with the local magnetic field.We also note that there is a dip in wave power above the ion cyclotron frequency at Juno's altitude.A likely explanation for this dip is that wave power at these higher frequencies was partially absorbed by the particles via WPI at lower altitudes.In addition, three fits to the wave power are provided in Figure 2.These fits are labeled "low," "mid," and "high" and are intended to cover the lower, middle, and upper parts of the band of wave power.These fits will be used in our simulation plan to help define our case studies.

Simulation Plan
Unfortunately, we only measure the wave power at the spacecraft location, and must make assumptions about the altitudinal distribution of the waves below Juno's altitude.We therefore consider four simulations cases.• Case 1: The 'high' power law fit to the wave spectrum applies at all simulations altitudes above 10,000 km.
• Case 2: The 'low' power law fit to the wave spectrum applies at altitudes above 20,000 km, but the 'high' power law fit applies at altitudes below 20,000 km.• Case 3: The 'low' power law fit to the wave spectrum applies at altitudes above 20,000 km, but the 'high' power law fit enhanced by a factor of 10 applies at altitudes below 20,000 km.• Case 4: The 'high' power law fit to the wave spectrum only applies below 20,000 km altitude and no wave power is applied above.
The first three cases of wave power represent likely possible altitude distributions of the waves either constant with altitude or enhanced at low altitude to various degrees.Case 4, which only includes wave heating at low altitudes, is not an expected altitudinal distribution of the waves, but is included to help illustrate the relative effect of low altitude heating versus high altitude heating.As the ion velocity space distribution function entrains information about the ion heating with altitude, it is our expectation that comparing modeled ion distribution function with observations will help us understand both if heating with ion cyclotron waves is a likely explanation for the ion conics, as well as the relative intensity of waves at lower altitudes as compared to those observed at higher altitudes by Juno.Note that the 20,000 km altitude to separate low altitude and high altitude wave heating is somewhat arbitrary although testing moving that altitude lower to 18,000 km showed that results remained qualitatively similar.
It is also unknown what fraction of the waves is left hand polarized and therefore capable of interacting with the ions.This value is referred in to in this study as η.In this study we assume that η = 1/8, but it could be as large as 1.
The implications of varying η will be discussed in the conclusions.
Each case is intended to simulate the heating which the ionospheric plasma incurs as the Io auroral footprint passes over.Examination of images from Mura et al. (2018) show that the auroral spot associated with Io moves approximately two degrees of longitude in 5 min, and the spot itself is about half a degree wide in longitude.This implies that a given portion of the ionosphere is exposed to the auroral footprint for about 1 min before the spot moves on to a new unheated portion of the ionosphere.Therefore, our simulations cases are run for 2 min to fully capture the auroral footprint's interaction with the ionosphere, but our focus is on the first minute of the interaction which is most relevant.Given the short but intense duration of the heating, we expect the solution to be highly time dependent.To simplify the simulation set up, we take as the initial condition a stationary representative field line near the 64 o magnetic latitude of the Io footpoint.That field line does not move for the 2 min duration of the simulation.
Note that our estimate of the duration of the heating assumes that the ionosphere corotates with the planet and electrodynamic effects are neglected in the vicinity of the Io auroral footpoint.It is unfortunately difficult to accurately quantify the impact of electrodynamic effects on the duration of the heating.However, to get a handle on the maximum impact we can assume that the ion convection velocity are probably smaller than the anticorotational electrojet wind in the main oval, ∼3 km/s (Bougher et al., 2005).Such a velocity is on the order of 50% of the corotation speed at the Io auroral footprint.Therefore, we expect that including electrodynamic effects could change the estimated heating time by ± 50% at most.
In our simulations we will examine how well each case matches the observations and understand the implications for the formation of ion outflow above Jupiter's ionosphere.To do this we will integrate the ion distribution function to create simulated flux spectra which will be directly compared with JADE observations at lower energies and JEDI observations at higher energies.As an additional constraint, we can compare the angle of the ion conic in velocity space with the observed angle in the JEDI observations.For the wave power case that matches best with observations, we will further study the temporal evolution of the associated ion conic.Finally, we will also examine the simulated velocity space moments for this case to understand what the presence of the ion conic implies for the bulk outflow and the topside Jovian ionosphere density and bulk velocity profile.

Results
Our first step is to see how each of our wave heating cases compare with the Juno particle observations.To do this comparison, we must convert the simulated ion distribution functions at the Juno satellite location into flux spectra.This conversion is done by constructing bins in velocity space that correspond to spherical shells with inner and outer radius at fixed velocity and energy.The energy spacing of a given bin is defined by the width of the corresponding shell.Macro particles in a given altitude cell from the PWOM simulation are sorted into these bins after first adding the spacecraft velocity vector to the particle velocity vector to put the simulated solution into the spacecraft frame.Then the differential flux is calculated based on this binning.The resulting flux spectrum is now ready to be directly compared to the spacecraft observations.
Figure 3 presents the differential energy flux as a function of energy and time for each of the cases considered.These plots help to illustrate the effect of the waves at different altitudes.In general, the plots show that there are two populations contributing to the observations at the Juno spacecraft altitude: (a) The locally heated populations and (b) the population heated at lower altitudes and transported to the observation point.This is particularly clear in Case 4 which only includes wave heating at low altitudes.In that plot there is a clear low energy and unheated population that persists throughout the simulation, and separate hot population that appears about 10s into the simulation.That separate hot population is heated below the spacecraft location and transported to higher altitudes.It exhibits an energy dispersion with the more heated particles arriving sooner and the less energetic particles arriving later.
The different cases can be compared to draw insights into how the altitudinal distribution of wave heating affects the particles measured at the spacecraft.For instance, juxtaposing Case 3 and Case 4 demonstrates the effect of heating at the spacecraft location.The low energy population that remains unheated in Case 4 picks up substantial energy from the local waves in Case 3. The locally heated population starts to merge with the high energy population heated at lower altitudes at around 1 keV.The locally heated population in Case 2 is largely similar to Case 3 as the local wave power is the same.However, the high energy population between Cases 2 and 3 are quite different.Both cases have enhanced wave heating at low altitudes, but Case 3 has 10 times the wave heating at low altitudes as Case 2. The result is that the high energy population in Case 2 arrives later in the simulation and at a substantially lower energy.In contrast, Case 1 has strong heating at all altitudes and so the locally heated population quickly merges with the population transported from below into a single population and leaving a dearth of flux at low energy.Much of what was noted in Figure 3 is also visible in Figure 4, but the additional comparison with the data illustrates what cases are most realistic.In particular, Cases 1 and 4 both do a reasonable job representing the JEDI data at high energies, but they do a poor job matching the JADE data below 10 keV.This indicates that strong wave heating locally is not realistic, neither is no wave heating.In other words, there must be some wave heating, but if it is too strong or too weak the agreement in the JADE energy range will be poor.Cases 2 and 3, which include weaker wave power above 20,000 km that is still consistent with observations, as well as higher wave power at lower altitudes, do the best job matching the JADE data.However, Case 3 does a better job than Case 2 at reproducing a higher transient flux at high energy seen by JEDI due to the enhanced wave heating assumed at low altitudes.Additionally, it is interesting to note that the fluxes seen by the JADE and JEDI instruments do not precisely align, indicating that there could be some inter-calibration issues which could impact the details of the data model comparison.The lack of alignment in the two data sets could also be due to the rapid temporal variation during the heating event and the data shown from each instrument represents a different part of that variation.Nevertheless, both the data and the model are in qualitative agreement with each other for Cases 3. From the data model comparisons in Figure 3 and the extended time evolution in Figure 4 we make the following conclusions.Wave heating at the satellite location is important for explaining the JADE observations below 10 keV.Too much or too little heating will both result in underestimation of the observed fluxes.However, applying wave power on the lower end of the observed spectrum results in good agreement with the JADE data.Moreover, including stronger wave power at low altitudes is required to get significant fluxes above 40 keV as seen by JEDI.Additionally, the ion fluxes exhibit transient behavior and vary significantly during the onset of heating.The agreement with the data therefore depends on how far into the heating process the spacecraft encounters the plasma.Of course none of the cases perfectly reproduce the data, and there is consistently a discrepancy between the observed data and the simulated flux in the range of 0.1-10 keV.This is likely due to our limited knowledge of the spatial and temporal wave inputs and the initial plasma conditions.Additionally, the modeled fluxes in the high energy tail of the distribution (above 100 keV) are not well captured by the model.This is a limitation of the hybrid PIC method as the tail of the distribution is always going to poorly sampled relative to the core.These limitations on the model mean that the qualitative agreement with the data is the most that can be realistically achieved.
In addition to the ion flux energy spectrum, we can also examine the comparison of the "conic angle" between the simulation and the observations.Ion conics refer to the cone shaped velocity space distribution functions formed by the combination of heating of ions transverse to the magnetic field combined with the contribution of the mirror force.As the mirror force acts more strongly on particles with higher perpendicular velocities, the parallel velocity of a particle increases more rapidly for particles with higher perpendicular velocities causing the edges of the ion distribution to curl up in the characteristic cone shape which gives the conic its name.The angle of the cone, or "conic angle," is therefore an indicator of the amount of transverse heating which occurred below the spacecraft location.Note that this statement holds if the mirror force is the only parallel acceleration mechanism acting along the field line.
Figure 5 presents the effect of the assumed wave altitude profile on the ion distribution function and conic angle at three different times after the onset of wave heating.In each panel, the vertical axis represents the parallel velocity while the horizontal axis represents the absolute value of the perpendicular velocity.The color contour is the phase space density in arbitrary units.All four cases of wave profiles are included.Additionally, a dashed white line corresponding to the ∼50°conic angle reported by Clark et al. (2020) in the JEDI data is included for comparison.For Case 1, in which the wave power profile is assumed to be constant in altitude, we find that the conic angle is close to 90°and is in poor agreement with the 50°angle reported in the JEDI observations.Cases 2-4 all show the velocity/energy dispersed arrival of the population heated at low altitude with the arriving population filling in the distribution function roughly along the ∼50°conic angle dashed line.Case 2 shows the heated population from below arriving at the spacecraft later and at lower velocity/energy than in Cases 3 and 4. Cases 2 and 3 exhibit stronger heating of the local core plasma population as compared to Case 4 where the lack of local waves leaves the core plasma unheated.
From Figure 5 it is clear that the waves must be stronger at lower altitudes to explain the observed conic angle.
The degree to which the wave heating is enhanced at low altitude also is critical to the peak fluxes observed at higher velocity/energy.The presence of two populations, locally and non-locally heated, is also evident in most cases making for a very non-Maxwellian distribution function that is double humped and exhibits velocity dispersion in time.While details of the distribution may be different at other altitudes, it is notable how dynamic the conic formation is once the background plasma is exposed to the waves.Given the short, ∼1 min, time scales for plasma heating by the Io auroral foot print, Juno may encounter the plasma at any stage in the early temporal evolution of a conic.
Such strong wave heating of the ions over an extended altitude range is expected to have a significant impact on the topside ionosphere.When an ion conic forms, the intense perpendicular heating also leads to strong parallel motion via the mirror force.This effective conversion of random perpendicular motion into organized parallel motion results in a vertical lift that should evacuate the plasma from the topside ionosphere.This effect should be visible in the simulation when looking at altitude profiles of the plasma moments.from the solution to the fluid equations while above the boundary the moments are directly integrated from the particle distribution function.As expected the topside ionosphere is strongly depleted by the effect of the waves as the transverse heating leads to a strong vertical flow.A significant density cavity forms by about 45 s into the simulation below 20,000 km, and that plasma is lofted to higher altitudes.The lofting of plasma to high altitudes is consistent with the JADE measurements which show densities in the 10 s cm 3 .Note that the density depletion forms more rapidly at low altitudes (10,000-20,000 km) where the wave heating is assumed to be stronger, and more slowly at higher altitudes (above 20,000 km) where the waves are weaker.The result is a density cavity in a restricted altitude range below the spacecraft location.
The temporal evolution of the bulk velocity profile is also interesting to consider.A discontinuity in the velocity is seen at 20,000 km, and, like the density cavity at low altitudes, is due to the change in the assumed intensity of the wave heating.The bulk upward velocity at the spacecraft altitude near 28,000 km is transient and quite intense.Indeed, the vertical velocity reaches on the order of about 1,000 km/s.At higher altitudes the velocity can exceed even 1,500 km/s.Proton bulk flow velocities of 1,000 km/s correspond to an energy of 5.2 keV.The strong plasma waves in this region therefore have a significant impact on the local topside ionosphere.

Discussion and Conclusions
The main purpose of this study was to use numerical simulation to test the hypothesis that WPI through ion cyclotron resonant heating can be responsible for the intense ion conics observed at Jupiter in the Io auroral footprint.Moreover, we explored how different assumptions about the distribution of the waves with altitude affect the agreement with data.In particular, we considered four cases which are chosen to evaluate the importance of high and low altitude wave heating, and what assumptions about the waves are required to explain the observations.We used comparisons with the observed flux spectra and ion conic angle to find which assumptions about the wave power both at and below the Juno satellite location yields the best results.We also examined the temporal evolution of the heated ion distribution function and associated energy spectrum during this short duration heating event.A summary and discussion of the key points are given below.
A key result of the study was that it is plausible that ion cyclotron resonant heating through WPI is the mechanism responsible for heating the ions.We also found that the wave power must have been even more intense at low altitudes than at high altitudes.This conclusion is due to the fact that the simulation with wave power on the more modest end of the observations at high altitudes, combined with more intense waves at low altitudes did the best job in reproducing both the energy spectrum and the conic angle of the observations.
In examining the simulated flux spectra and comparing to observations, we found that there are two distinct populations.A locally heated population and a non-locally heated population that is energized at low altitudes by intense waves and transported to the spacecraft location.The locally heated population is mostly below 10 keV and is observed by JADE, while the non-locally heated population falls mostly above 10 keV is observed by JEDI and in the upper energies of the JADE instrument.Adjusting the relative intensity of the waves at high and low altitudes directly alters the two populations of particles, and we were able to find a reasonable attitudinal wave distribution that was able to reproduce the combined JADE and JEDI observations.One caveat is that all our simulations assume a fixed fraction of left hand polarized waves at all altitudes.Changing that fraction or letting it vary with altitude would change the precise intensity of the waves required to reproduce the observations, as a different amount of wave intensity would be required to produce the same heating.Another limitation of our calculation is that wave heating is only included above 10,000 km.Including wave heating at lower altitudes would most likely increase the non-locally heated population that appears at the spacecraft above 10 keV.Unfortunately, lowering the altitude where wave heating is included is outside the current capabilities of the model.
In the observed wave power spectrum, there is seen to be a drop in wave power at frequencies above the ion gyrofrequency.These higher frequencies correspond to gyro-frequencies at lower altitudes.A possible explanation for this dropout is that wave power in this portion of the spectrum has been reduced via WPI at lower altitudes.In other words, the energy in the waves is transferred to particles at the lower altitude gyro-frequencies.It is interesting to note that ion conics at Earth are frequently observed with wave power concentrated at and below the local ion cyclotron frequency (e.g., Crew et al., 1990).It is possible that the lack of power in these cases could similarly be due to absorption of the wave power by the particles at lower altitudes.If this is true, the implication is further that the wave power is actually produced at lower altitudes and propagates to higher altitudes with a portion of the wave power absorbed in transit.As the origin of the waves is unknown this is an intriguing possibility.Such a scenario would also be consistent with stronger wave power at lower altitudes, which is what the simulations require to explain the observations.
Beyond the shape of the spectrum, we also examined the temporal evolution of the ion distribution function and the implications for the topside ionosphere.It was found that the heating occurs extremely rapidly and the ion distribution function undergoes significant changes during the short period of heating associated with the Io auroral footprint.Note that depletion is even more drastic if allowed to reach steady state, so timescales of Io's foot point passing over a particular region are important to take into account.The ion conic also is associated with strong vertical flows.Our simulations show that the associated vertical transport rapidly evacuates a portion of the topside ionosphere creating a density cavity at altitudes above where the waves are most intense and lofting plasma to high altitudes.As a result of the heating due to waves, the bulk velocity in the model exceeds 1,000 km/ s at the spacecraft location.The energy associated with such a bulk flow velocity corresponds to about 5.2 keV which is considerably more than the ∼20 eV required for a proton to overcome the gravitational binding energy.This flow is also considerably more intense than a typical O + conic observed at Earth whose typical bulk flow of 14 km/s corresponds to an energy of 0.01 keV (Glocer et al., 2018).Nevertheless, the actual energization mechanism applied in this study for conic formation is identical to that applied in studies at Earth.This points to the universality of the ion outflow problem across different planetary systems.It is further interesting to note that intense wave heating and density depletions are reported above the auroral regions of Jupiter (Sulaiman et al., 2022) which appears consistent with the results of the present study.
The reason that the ion conic is more intense is likely a combination of more intense wave heating and a larger altitude range of heating at Jupiter compared to Earth.Crew et al. (1990) includes a table summarizing three different O + conic events observed at Earth.The wave power at the O + cyclotron frequency in these typical Earth conics ranges from approximately 10 6 -10 5 V 2 m 2 Hz 1 which is roughly comparable to the wave power seen in Figure 2 by Juno at the H + cyclotron frequency.The wave heating at Jupiter however operates over a range of almost 20,000 km before reaching the observation point and the simulations indicate that the heating was even more intense at lower altitudes.The difference in species is also important.The perpendicular diffusion coefficient in Equation 1 depends directly on the wave power, but depends inversely on the square of the mass.As H + is 16 times lighter than O + , the perpendicular diffusion of H + , and hence the associated heating, is 256 times greater than for O + for the same wave power.
Examining the same physical processes in different planetary systems operating at different scales and in different parts of parameters space is an interesting aspect of this study.The instruments on board the Juno spacecraft are very advanced as compared to those NASA missions looking at outflow at Earth on missions 20 or more years ago.Moreover, comparative magnetospheric studies such as this an excellent opportunity to explore the universal processes driving ionospheric outflow from planets.The combination of advances in instrumentation and exploration of a very different parameter space, make studying ion cyclotron resonance heating using Juno's observational data appealing for looking for new insights into the physics behind ion outflows in general and the ICRH mechanism in particular.
This paper focuses primarily on the role of waves in generating the observed outflowing ions, and does not consider the possibility of additional acceleration mechanisms such as large parallel electric fields or ponderomotive forces.Such parallel acceleration mechanisms could not produce the perpendicularly heated distribution functions observed.However, if they operate in concert with the wave heating they can indeed reduce the pitch angle and complicate the interpretation of the cone angle of the ion distribution functions.However, the presence of a strong parallel acceleration would also result in an increase in the observation of energetic particles at low pitch angles which are accelerated below the spacecraft.The JEDI data from Clark et al. (2020) show that the flux is very peaked in angle with very little flux found at high energies outside this angle.Therefore, it is unlikely that these other mechanisms contribute significantly to the higher energy outflows seen by JEDI.It is, however, possible that they could contribute at lower energies and may be an interesting avenue for future investigations.
Finally, it is important to note that the ion conics observed in PJ12 coincident with the Io auroral footprint are particularly intense.Future work should expand this study to other conics observed by Juno which may be less intense.Such an effort would help to establish if WPI via ion cyclotron resonant heating is a plausible source of all ion conics observed at Jupiter, or if it is just at play for the more intense conic studied here.

Figure 1 .
Figure 1.Altitude profile of neutral atmosphere background at the simulation location from the Jupiter Global Ionosphere-Thermosphere Model calculation.

Figure 2 .
Figure 2. Wave Power Spectral Density as a function of frequency for several time periods during the Juno encounter with the Io auroral footprint.Three power law fits are plotted to cover the low, middle, and high range of the observed waves.The proton ion cyclotron frequencies (Fci) at the observation location, as well as the top and bottom of the model are shown as vertical dashed lines.

Figure 4
Figure 4 presents the comparison of the PWOM simulations to the Juno particle observations at multiple times after the onset of the wave heating.Here we switch to using differential number flux instead of differential energy flux and also convert to the same units as previously used in Clark et al. (2020).As discussed earlier, the interaction time of the ionospheric plasma with the Io auroral footprint is on the order of 1 min and thus most of the heating is expected to occur during this time.The simulation results from Case 1 are shown with the blue dots, Case 2 is shown with the orange dots, Case 3 are shown with the green dots, and Case 4 are shown with red dots.The black dots represent the data with the values below 10 keV coming from the JADE instrument, and the black x's are the values at higher energies coming from the JEDI instrument.The JADE and JEDI observations are not varying in time.The JADE data represent an average during the encounter with the shaded region showing the variability.The JEDI data are at a fixed time around the peak flux.Further note that the JEDI observations represent the far tail of the ion distribution function.

Figure 3 .
Figure3.Differential energy flux spectra as a function of proton energy and time after start of wave-particle interactions for wave power selected in Cases 1-4.The altitude of the output is 27,826 km which represents the closest model output to the Juno spacecraft altitude during the encounter.The time resolution is 1 s and is selected to capture the evolution of the heating.The energy grid goes from 0.1 eV to 500 KeV in 40 log spaced steps and is selected to cover both the Jovian Auroral Distributions Experiment and Jupiter Energetic Particle Detector Instruments observational range.

Figure 4 .
Figure 4.A comparison of the proton energy flux spectra from Polar Wind Outflow Model simulations for wave power selected in Cases 1 (blue), 2 (orange), 3 (green), and 4 (red) with Juno Jovian Auroral Distributions Experiment (JADE) and Jupiter Energetic Particle Detector Instruments (JEDI) observations (black).The simulation results evolve with time while the observations are fixed.The variation of the JADE data during the encounter is shown by the shaded region while the average value is show by the black circles.The JEDI data is at a fixed time around the peak flux.The Juno spacecraft at this time is at an altitude of approximately 0.39 R J and the model output is at a nearly equivalent an altitude of 27,826 km.

Figure 6
Figure 6 presents the altitude profiles of the temporal evolution of the plasma moments from Case 3 over the first 60s of simulated time.The plot on the left of the Figure shows the altitude profile of number density while the plot on the right shows the altitude profile of bulk velocity.The fluid-kinetic transition line is also shown which additionally corresponds to the lower altitude boundary of the wave heating.Below the boundary the moments are

Figure 5 .
Figure 5.The modeled proton distribution functions near the Juno spacecraft altitude for wave power selected in Cases 1-4 at 15, 30, and 45 s after onset of the wave heating.The white dashed line corresponds roughly to the ion conic angle observed by the Jupiter Energetic Particle Detector Instruments instrument, which is a 50°a ngle in the tail of the distribution function.

Figure 6 .
Figure 6.Temporal evolution of the altitude profiles of density and bulk velocity for Case 3. Time zero is shown as a solid blue line, while later times are dotted colored lines.The fluid-kinetic transition of the model is shown as a dashed line at 10,000 km.This is also the line above which the wave heating is applied.We also show a dashed line at 20,000 km which represents the transition between low and high altitude heating.