3.1 Plasma Waves Below f_cH+: Alfvénic Turbulence and Ion Cyclotron Heating

We begin with waves in the lower frequency range below f_cH+. The emissions in this range are the most intense both in electric and magnetic field spectral densities, as shown in Figures 2b and 2c. Using MAG, Gershman et al. (2019) transformed magnetic field fluctuations into compressive and noncompressive (transverse) components. During passes of Jupiter's aurora, they found the power of the fluctuations predominantly in the transverse component between 0.2 and 5 Hz (frequency range was limited by noise). These were identified as Alfvénic turbulence, and their activity was pronounced during Io footprint tail crossings at longitudinal separations up to 90°.

On first inspection of the magnetic search coil data, it appears that the “stem” between 50 and ~800 Hz and at 09:20:35–09:20:54 in Figure 2c is an extension of the Alfvénic activity identified by MAG in Figure 2d. This can be tested by exploiting the orientation of the Waves instrument on the spacecraft with respect to the background magnetic field. The effective axis of the electric field antenna in the spin plane induces modulations in E_y at half the spacecraft spin period of 30 s. The spacecraft attitude was such that the spin axis was approximately perpendicular to a Jovian magnetic meridian plane. This fortuitous configuration meant that the E_y axis measured electric field fluctuations parallel and perpendicular to the background magnetic field, , and therefore the twice-per-spin peaks can be correlated with projections of E_y on . At the same time, the B_z axis of the search coil measured magnetic field fluctuations purely perpendicular to . Figure 3a shows the modulations of E_y spectral densities in the range below f_cH+ (f = 0.15 and 3.71 kHz), where Alfvén and ion cyclotron waves can propagate, and Figure 3b shows the angles of E_y (blue) and B_z (red) with respect to . It is clear that the E_y spectral density peaks near E_y⊥ and depresses near E_y∥ . This pattern holds for any frequency in this range and is consistent with transverse electric field fluctuations of Alfvén and ion cyclotron waves. Furthermore, we have continuous B_z⊥ , meaning that the wave emissions from the search coil (Figure 2c) can indeed be interpreted as an extension of the transverse MAG fluctuations (Figure 2d) in frequency space. Based on the spacecraft speed, transit time, and correcting for the oblique angle at which Juno crosses the flux tube, the estimated transverse length scale of the flux tube is ~1,000 ± 50 km.

Figure 3c combines power spectral densities of the measured transverse magnetic field fluctuations from both MAG and Waves. Interestingly, both frequency ranges can be connected by a power law of spectral index −2.35 ± 0.07 up to ~800 Hz. The semirelativistic Alfvén speed at high latitudes compared to the spacecraft speed of 51 km/s makes the effect of Doppler shift negligible; therefore, the measured fluctuations can be considered to be in the plasma frame. As indicated by Gershman et al. (2019), the dispersion relation in the semirelativistic Alfvén wave limit, that is, ω/k_∥ ~ c, means that the spectral index is equivalent to a turbulent cascade in k_∥, rather than in k_⊥ which is typically discussed in the context of Alfvénic turbulence (e.g., Chaston et al., 2008; Saur et al., 2018), where k is the wavenumber and ω = 2πf is the angular frequency. That said, Gershman et al. (2019) invoked partially developed critically balanced Kolmogorov cascade as a possible explanation for their resolved scaling of k_∥^{−2.29 ± 0.09} (0.2–5 Hz) associated with the main auroral emission at Jupiter's high latitudes. This type of cascade exhibits perpendicular and parallel spectral indices of −5/3 and −2, respectively. The resolved scaling of k_∥^{-2.35 ± 0.07} for the Io auroral flux tube is consistent with that of the main auroral emission suggesting a similar auroral mechanism.

Further, the calculated Poynting flux was ~3,000 mW/m² associated with the frequency range of 0.2–5 Hz (Gershman et al., 2019). We band-pass-filtered multiple waveform snapshots between 50 and 800 Hz, and the calculated root mean squares, δB, were in the range ~1–2 nT. This corresponds to Poynting fluxes, δB²c/μ₀, of ~0.2–1 mW/m² associated with magnetic field fluctuations that cascaded to scales in the range 50–800 Hz. Using this relation, for the frequency range between 0.2 and 800 Hz, the corresponding parallel wavelengths are cascaded from ~20 to 10⁻³ R_J. These Alfvénic magnetic signatures together with measurements of broadband precipitating electron fluxes in Figure 2e are also a characteristic feature of Alfvénic acceleration associated with footprint tail aurorae (Szalay, Allegrini et al., 2020; Szalay et al., 2018).

Since the magnetohydrodynamic (MHD) Alfvén wave propagates parallel to the magnetic field, it follows that the time of its detection is coincident with the time of the Io flux tube transit at 09:20:35–09:20:54. A dispersive feature becomes present above ~800 Hz and up to f_cH+, where higher frequencies are detected at times before and after the Io flux tube crossing, thereby displaying a “funnel” spectral feature. This is characteristic of plasma wave propagation along the resonance cone.

Figure 3d plots the indices of refraction, ck/ω, as a function of frequency for parallel-propagating right-hand and left-hand polarized modes as

(1)

where f_p and f_c are the plasma and cyclotron frequencies, respectively, and the subscript s denotes the species. The right-hand (R) and left-hand (L) polarized modes take the “+” and “−” signs, respectively, noting that f_c is negative for electrons (Gurnett & Bhattacharjee, 2017). For each mode, the dispersion relations are derived for an electron-proton plasma and another with added 10% S²⁺ and 10% O⁺ by composition. Note that these compositions are not derived from data as their same mass-to-charge ratios makes it difficult to separate their time-of-flight effects. They are merely to show that the inclusion of heavies changes the spectral character and yields an additional resonance at a lower cyclotron frequency for the left-handed mode, where (ck/ω)² goes to infinity. However, this frequency is the same for S²⁺ and O⁺ at ~270 Hz and does not explain the distinct spectral feature at ~800 Hz. It is worth noting that the lower frequencies in the Alfvén range do not necessarily continuously connect through to f_cH+. Since a characteristic frequency existing below f_cH+ (e.g., an ion hybrid frequency) requires additional species to an electron-proton plasma, we conclude that the distinct feature at ~800 Hz and the resonance cone above is strongly suggestive of the presence of heavies. Modeling efforts will be required (Santolík et al., 2016) once the heavy ions compositions are available to fully resolve the spectral significance at ~800 Hz.

For both plasmas, the left-handed modes undergo resonance at f_cH+, indicating that the observed intense plasma waves exhibiting a significant drop in power at f_cH+ are left handed. This signifies strong interactions with protons as they rotate in the same left-hand sense as the wave electric field. These emissions are consistent with the ion cyclotron mode and can, in theory, set up a resonance leading to efficient ion energization at a Doppler-shifted frequency that matches the cyclotron frequency of an ion (e.g., André et al., 1998; Chang et al., 1986; Lysak, 1986). This wave-particle interaction is likely responsible for the anti-planetward transport of thermal ions along diverging magnetic field lines, resulting in an ion conic distribution in velocity space observed during this Io event (Clark et al., 2020), representing the first observation of this kind in a moon-magnetosphere context. Such distributions are commonly observed at Earth (Carlson et al., 1998) and have been reported at Saturn (Mitchell et al., 2009).

Assuming all the wave power in this frequency range up to f_cH+ resides in the left-hand mode, the maximum ion cyclotron heating rate can be estimated, as derived by Chang et al. (1986):

(2)

where q and m_p are the charge and mass of a proton, respectively. A (maximum) electric field spectral density, S_E, at f_cH+ measured at ~10⁻⁵ V²m⁻² Hz⁻¹ will yield a heating rate of ~500 eV/s. Note that an exact calculation of the heating rate would require knowledge of the fraction of waves near f_cH+ that are both left-handed and resonating with ions; therefore, this may be considered as an upper limit. Together with the high-energy particle observations reported by Clark et al. (2020), there appears to be a causal link between these observed ion cyclotron waves and the ion conic distributions since (i) the observed ion energies on the order of 10–100 keV at low altitudes are consistent with the estimated heating rate along their travel path between the source and the spacecraft, suggesting that a large fraction of these waves are in resonance with the ions, and (ii) both the waves and the ions are found to be propagating upward from Jupiter (the wave propagation direction is shown in Figure S1 in the supporting information).

3.2 Plasma Waves Above f_cH+: Beam-Plasma Instability

Next, we explore the higher frequency range belonging to the electron scale. The most apparent emission is the larger V-shaped spectral feature between 09:13 and 09:22, between f_cH+ and a sharp upper frequency cutoff marked by the white trace and labeled f_pe, in Figures 2a–2c. This is characteristic of a whistler-mode auroral hiss emission. This class of plasma wave emissions is understood to be generated by a coherent beam-plasma instability (Maggs, 1989) at the Landau resonance. Here, the parallel phase speed of the wave almost matches the electron beam speed, ω/k_∥ ≈ v_beam. Since electron beams provide the free energy for their growth, they are typically observed in the presence of field-aligned currents such as in the auroral regions of Earth (James, 1976), Saturn (Gurnett et al., 2011), and Jupiter (Tetrick et al., 2017). Auroral hiss emissions are therefore diagnostics of electrodynamic coupling between conductive bodies and have been observed widely in Saturn's magnetosphere. The Cassini spacecraft observed their presence on magnetic flux tubes connected to Enceladus (Gurnett et al., 2011; Sulaiman, Kurth, Hospodarsky, Averkamp, Ye, et al., 2018) coincident with field-aligned currents and, surprisingly, connected to Saturn's main rings (Sulaiman, Kurth, Hospodarsky, Averkamp, Persoon, et al., 2018, 2019; Xin et al., 2006).

The propagation of whistler-mode auroral hiss along the resonance cone has a dispersion relation that goes as sin ψ_res ≃ f/f_pe (Gurnett et al., 1983). This is a special case in a highly magnetized regime descriptive of the near-Jupiter environment, that is, f_ce² ≫ f_pe², where f_ce and f_pe are the electron cyclotron and plasma frequencies, respectively. It follows that at lower frequencies, f, the ray path (or group velocity) angles, ψ_res, are more parallel to the magnetic field and become monotonically more perpendicular with higher frequencies. This explains the V-shaped “funnel” feature on the spectrograms in Figures 2a–2c as higher frequencies are detected farther away from the Io flux tube. The dispersion relation holds up to a maximum f = f_pe, which corresponds to the upper frequency cutoff in Figure 2a. Using this technique, the electron number density, n_e, can be derived as f_pe [Hz] = 8,980√n_e [cm⁻³]. This yields a density in the range of 8–40 cm⁻³.

We next examine the lower frequency cutoff for the whistler mode, which is the lower hybrid frequency, f_LH. This is achieved by numerically solving for the hybrid resonances at S = 0, where S is the appropriate element in the cold magnetized plasma dielectric tensor as defined by Stix (1992). This is given by

(3)

with the subscript s denoting the species. Assuming a quasi-neutral plasma of electrons and protons, in this highly magnetized regime where f_ce/f_pe ~ O(10²), the solution yields f_LH ≈ f_cH+. Contributions from O⁺ and S²⁺ are negligible as their comparatively large mass-to-charge ratios will act to only slightly reduce f_LH. Note this regime is exceptionally highly magnetized and in contrast to the magnetized regimes considered near Earth and Saturn, commonly approximated as f_LH ≈ f_pH+, where f_pH+ is the proton plasma frequency (e.g., Sulaiman et al., 2017). The significance of identifying f_LH is that it represents the surface at which the wave normal angles of the whistler mode rotate through 90° and are reflected. In other words, the frequencies are not continuous across f_cH+(≈f_LH), thereby decoupling the whistler mode from the intense wave emissions below f_cH+ in Figures 2b and 2c.

For the whistler-mode auroral hiss to grow, an electron beam is required to provide the free energy, and this explains the contemporaneous observations with field-aligned electrons as detected by JADE (Figures 2f and 2g). The waves are amplified via Landau resonance where the parallel phase speed ω/k_∥ almost matches the beam speed v_beam. The JADE-E instrument measured upward and downward field-aligned electron populations in the range 50 eV to 30 keV. To relate these energies to the observed whistler-mode auroral hiss, we consider the dispersion relation for waves in a cold collisionless plasma (Stix, 1992). The special case for electron scales is known as the Appleton-Hartree equation and is given by

(4)

where θ is the angle between the magnetic field and the wave vector . The reciprocal of the calculated index of refraction from Equation 4 can be related to electron energy via the Landau resonance condition, that is, ω/ck_∥ ≡ v_p∥/c ≈ v_beam/c, where v_p is the phase speed. Figure 3e shows the set of solutions in phase velocity space for which the whistler mode can exist, given the plasma properties during the Io flux tube crossing. The solutions can be classified into two parts: (i) points that lie on the quasi-electrostatic limit (low v_p∥/c) characterized by higher indices of refraction and (ii) points that depart from this limit are in the electromagnetic branch (high v_p∥/c). Taking the electron energy measured at 1 keV yields v_beam/c = 0.063, and the equivalent v_p∥/c on Figure 3e intersects a solution on the curve that just departed from the quasi-electrostatic limit. Higher electron energies, such as 10 keV and above, place the solution well within the electromagnetic branch. Measured δE/cδB ≳ 1 of the whistler-mode auroral hiss (Figures 2a–2c) imply an electromagnetic nature, and this is therefore consistent with their generation by electron beams most likely in the 1–30 keV range. Furthermore, quasiparallel propagation of whistler-mode waves excited by a cyclotron resonance could partly account for the observed electromagnetic nature, as observed in the flux tube of Saturn's moon Rhea (Santolík et al., 2011). However, the observed electron distribution and the funnel-shaped feature of the spectrogram make this unlikely.

In contrast, auroral hiss emissions observed by Cassini on the Enceladus flux tube were purely electrostatic (i.e., δE/cδB ≫ 1) and observed in the presence of electron beams up to 10 eV (=very low v_p∥/c), thus placing the solution well within the quasi-electrostatic limit (Gurnett et al., 2011; Sulaiman, Kurth, Hospodarsky, Averkamp, Ye, et al., 2018). By this association, auroral hiss observations may be used to constrain electron energies where particle observations are not available.

The Landau resonance condition, for the generation of whistler-mode auroral hiss, requires both waves and particles traveling in the same direction. Since the observed Poynting flux is upgoing (Figure S1), we can then infer that the whistler-mode auroral hiss emissions are associated with the upgoing electron population, that is, pitch angle ≈ 0° (Figure 2f). Enhanced whistler-mode radiation has been reported in Io's wake by Paranicas et al. (2019), where they suggested, consistent with modeling, that wave-particle interaction plays a key role in the simultaneously observed depletions of energetic ions and electrons. Such signatures were not observed during this pass, and this highlights the complexity of wave-particle processes on satellite flux tubes.