1 Introduction

The role of electron scattering and acceleration by whistler mode chorus has been a subject of stochastic models for some time. Acceleration by Doppler-shifted cyclotron resonant wave particle interactions has been shown to be significant in Earth’s and Jupiter’s radiation belts (Horne et al., 2008; Millan & Baker, 2012; Woodfield et al., 2014). Horne et al. (2008) presented an investigation of diffusive scattering using the Galileo observations of chorus emission. These results were followed by more extensive modeling as reported by Shprits et al. (2012) using the Versatile Electron Radiation Belt model and later by Woodfield et al. (2014) who combined wave particle interactions and radial diffusion at Jupiter using the Radiation Belt Model. All of these results indicate that chorus can accelerate the electrons present in the radiation zones at Jupiter, and significantly complement the effects of radial diffusion. Planetary radiation belt particles can experience significant acceleration to MeV energies.

The chorus source region lies outside the orbit of Io and near the magnetic equator (Hospodarsky et al., 2012; Menietti et al., 2008). Juno has been in orbit since July 2016 and has intercepted this region on numerous orbits, but as the orbit periapsis has precessed farther north the chorus source region has received better coverage.

Li et al. (2020) reported whistler-mode emission observed by the Juno spacecraft in orbits 1 through 25 (PJ1-PJ25), with observations extending from the magnetic equator to latitudes greater than 50°, and in a range of nightside magnetic local times (MLTs) and a range of M-shells, 6 < M < 15, with strongest near M ∼ 10, intensities up to ∼0.1 nT, over the frequency range f_ci < f < f_c (f_ci is the H+ cyclotron frequency; f_c is the electron cyclotron frequency). Li et al. (2020) reported Juno whistler-mode emission with increasing intensities for magnetic latitudes in the range 30° < λ < 50°, which had not been previously observed by the equatorial satellite, Galileo (cf. Menietti et al., 2016).

The range of latitude of whistler mode propagation is important, because pitch angle scattering by electrons is dependent on electron energy (eV to MeV), pitch angle, and the wave normal angle of the whistler mode emission (cf. Horne et al., 2008; Shprits et al., 2012; Woodfield et al., 2014). Pitch angle scattering of the chorus emission is a gyroresonant interaction and is dependent on the parallel energy resonant condition. However, Menietti et al. (2020) point out that Juno observations of whistler mode emission at magnetic latitudes 30° are likely to be auroral hiss emission from the Jovian polar regions with a larger range of wave normal angles than chorus emission, which has a source region near the magnetic equator, and a different free energy source. Reference to Figure 3 of Menietti et al. (2020) demonstrates that Jovian auroral hiss can also be bursty in morphology.

As in the previous survey (Menietti et al., 2020), we concentrate on the lower latitude emissions nearer to the chorus source region with intensities peaking at latitudes <31°. In this article, these waves are carefully sampled and binned in space and normalized frequency, f_ceq, relative to the magnetic equator mapped using the JMR09 magnetic field model (Connerney et al., 2018).

The role of Z-mode in the acceleration of radiation belt electrons has been discussed in the past by Glauert and Horne (2005) and Horne and Thorne (1998). While Z-mode, much like chorus, is potentially a significant source of pitch angle and momentum scattering of electrons, intense Z-mode is not often observed at Earth. Menietti et al. (2015, 2018) and Ye et al. (2010) reported significant intensities of Z-mode emission at Saturn in the low plasma density region near the inner edge of the Enceladus plasma torus ranging from just above the equator to higher latitudes. Menietti et al. (2020) first reported Juno observations of possible Z-mode emission at Jupiter confined between 20° and 50° magnetic latitude and ∼7 Jovian radii. Woodfield et al. (2018) presented results of stochastic modeling of electron scattering of chorus and Z-mode emissions in the Saturn magnetosphere. Their results indicate that Z-mode waves observed inside the orbit of Enceladus are very effective at accelerating electrons with a potential of increasing the electron flux by four orders of magnitude in a year. Saturn simulations by Yu et al. (2019) have further shown that the combined effects of equatorial chorus and higher latitude Z-mode emission are different from the individual action of each wave mode acting alone. Chorus waves can increase the acceleration and scattering of electrons already accelerated by Z-mode waves. Observations of more intense Z-mode at higher latitudes inside the orbit of Io at Jupiter that have been reported suggest similar results may be expected by the combined effects of Z-mode and equatorial chorus emission at Jupiter.

At the end of Juno’s primary mission, we present a follow-up analysis of plasma waves observed by Juno in the inner magnetosphere, reporting new observations of whistler mode chorus and Z-mode. Whistler mode chorus emission at Earth seldom extends down to f_lh, the lower hybrid frequency, and is relatively easy to distinguish from lower frequency whistler mode hiss emission, which has a more diffuse morphology and a broad range of wave normal angles (cf. Meredith et al., 2012). At Earth, Jupiter, and Saturn chorus emission is observed as bursty with frequency-drifting fine structure. However, at Jupiter, the distinction between chorus and lower frequency hiss emission is not so easily made. In this article, we discuss the bursty nature of Jovian whistler mode emission extending down to near f_ci, the ion cyclotron frequency. We also show further evidence identifying Z-mode emission that cuts off near the lower cutoff, f_z. We present parametric fits of both the whistler mode and Z-mode intensity as a function of frequency, magnetic latitude, and M-shell.

2 Juno Waves Instrument

The Juno Waves instrument (Kurth et al., 2017) measures electric signals in the frequency range ∼10–∼150 kHz on the low frequency receiver (LFR-hi), ∼50 Hz–20 kHz on LFR-lo, and magnetic signals in the range ∼50 Hz–20 kHz on the LFR-B receiver as described in the previous survey. In the survey mode used in this study, spectra are returned about once every second. The instrument also operates in a burst mode with greater spectral resolution. While in burst mode, the instrument can monitor frequencies close to f_c and survey at the rate of 1 spectrum/sec to frequencies up to 41 MHz. Because of the single dipole antenna of the Waves instrument, no polarization measurements are possible, but phase information between the electric and magnetic antennas allows the determination of the direction of the wave vector relative to the magnetic field as discussed in Gurnett (1966) and Kolmasova et al. (2018).

3 JEDI

The Jupiter energetic particle detector (JEDI) consists of three almost identical instruments that measure spectra and pitch angle distributions of electrons and ions (Mauk et al., 2017). In this study, we will focus on electron distributions that are measured over an energy range of about 25 eV–>800 keV. Sampling time for the electrons is 0.5 s.

4 Low-Latitude Whistler Mode Survey Methodology

Menietti et al. (2020) (“previous survey”) reported an initial low-latitude survey of whistler-mode emission observed by the Juno spacecraft during orbits 1–25, which orbited at a high inclination with a period of about 53 days. Juno’s line of apsides precesses about one degree per orbit, moving the perijove latitude north from its initial location near the equator at the beginning of the mission. Hence, later in the extended mission, the trajectory crosses the equator progressively closer to Jupiter on the inbound leg, allowing the traversal of the near-equatorial plasma sheet and the generation region for chorus. The methodology of the survey is the same as presented in Menietti et al. (2020) and will be discussed only briefly here.

In each 1 min period, 43 frequency channels are sampled from 50 Hz to 20 kHz (the instrumental range of the low-frequency receiver LFR-B) for the magnetic oscillations of the Waves plasma wave instrument on board Juno. The average and median intensity at each frequency is computed from the 60 measurements at each frequency. To avoid noise spikes in the data we limit the ratio (average intensity)/(median intensity) <10 for each frequency of each 1 min data sample. We have binned the Juno plasma wave data in M-shell, latitude, and local time, where M-shell is defined by the radial distance (in units of R_J) a magnetic field line crosses the magnetic equator, based on the JRM09 plus current sheet model (Connerney et al., 2018).

We define relative frequency, β_i = f_i/f_ceq, where f_i is the center frequency of the frequency bin, Δβ_i. For the lower band we define f_ci/f_ceq < Δβ₁ < 0.1, 0.1 < Δβ₂ < 0.2, 0.2 < Δβ₃ < 0.3, 0.3 < Δβ₄ < 0.4, 0.4 < Δβ₅ < 0.5, and f_ci is the hydrogen cyclotron frequency (f_ceq and f_ci are frequencies mapped along the magnetic field line from the local observation point to the magnetic equator as explained in Menietti et al., 2020). The wave magnetic intensity, P_B, is proportional to B²(nT²), and we determine B²(β_i) by integration of the measured magnetic spectral density over the frequency channels within Δβ_i for 1 min time steps, Δτ. Error bars are one standard deviation and shown only above the data point on semi-log plots presented in the survey which follows (Figures 5, 6, and 9). After binning the data and calculating averages, we sort the data relative to intensity and hand survey the strongest emissions to eliminate outliers due to spacecraft engine firings, instrumental interference, etc.

5 Models and Constraints

Except when noted, the plasma density is obtained using interpolated values of analytic density models as discussed in Imai et al. (2015) and Menietti et al. (2020). The magnetic field model is the JRM09 + CAN model (Connerney et al., 1981, 2018), which is used to map field lines from the satellite position to the magnetic equator. The subscript “eq” refers to a point at the equator along the same M-shell as the spacecraft at the time of observation. We assume a chorus source region near the magnetic equator (Hospodarsky et al., 2012), and trace the magnetic field line from the observation down to the magnetic equator to record the cyclotron frequency, f_ceq, lower hybrid frequency, f_lheq, and ion cyclotron frequency, f_cieq. We limit our presentation to emissions of whistler-mode emission for f < f_ceq/2 (lower band chorus).

A new Jovian plasma sheet model became available recently (Connerney et al., 2020). The new current sheet model was developed to account for smaller magnitude azimuthally varying current flows within the plasma sheet. By doing so the new current sheet model provides much-improved accuracy particularly important for identifying auroral and ionospheric footprints of the spacecraft and Jovian satellites with more distant magnetospheric observations of Juno. The size of the spatial bins of the wave intensity data used in the present survey (described below) are larger than the increase of resolution provided by the new current sheet model and would therefore have little impact on our results. Hence, we continue to use the CAN model herein.

6 Observations of Whistler-Mode Chorus

Figure 1 shows whistler mode emission observed by the Juno Waves instrument and electron flux from the Juno JEDI instrument near the magnetic equator during orbit PJ29. The top panel displays electric spectral density extending from 10 to 140 kHz, panels b and c show the electric and magnetic spectral density, respectively, in the frequency range 50 Hz to 20 kHz, and panel d is a spectrogram of the electron differential flux for the same time interval, showing a fine structure of intense flux extending to well above 300 keV at times. Panel e is E/cB where E and B are the electric and magnetic spectral densities. An interference band occurs in the approximate range 500–600 Hz across the spectrogram. The chorus emission seen in panels b and c is bursty and intense, and appears at times to extend down to very low frequencies. The hydrogen cyclotron frequency, f_ci, is below the lower cutoff of the receiver (∼50 Hz) throughout this period. Alfven wave modes may dominate at frequencies below f_ci, and this frequency was used as the lower cutoff of the previous whistler mode survey (Menietti et al., 2020). We have used model plasma density (assuming electrons and H+ ions) and cyclotron frequency to calculate f_lh, which we show plotted at all times in panels b, c, and e. The upper hybrid frequency, f_uh, indicated in the top panel is a function of the plasma frequency and can be used to determine the local density and the local lower hybrid frequency, f_lh for parts of this time period. The model values are generally quite close to those compared to observed values of f_uh and f_c. Whistler mode emission at oblique wave normal angles (between the wave vector and the magnetic field), such as auroral hiss or chorus that is reflected at higher latitude and subsequently propagates back toward the equator, would likely be reflected near f = f_lh. This is because the dependence of the whistler mode index of refraction on the wave normal angle allows only small angles to propagate for f < f_lh. Near f_lh whistler mode emission propagating toward the equator with larger wave normal angles (angle between the wave vector and the magnetic field) would likely be reflected. Chorus emission is believed to be generated at small wave normal angles by a gyroresonant mechanism (cf. Gurnett & Bhattacharjee, 2005). At Earth, for typical electron energies of 10s of keV, the typical frequency range of lower band chorus may be from ∼0.1f_ceq to f_ceq/2. At Jupiter, it appears in Figure 1 that the frequency range of bursty whistler mode emission, coincident with chorus, at times extends to frequencies lower than f_lh. Panel e indicates many time periods where E/cB is similar for the chorus emission at frequencies above ∼1 kHz and for frequencies below f_lh (i.e., ∼14:20–16:10; 16:44–16:52; ∼18:00–18:30). We can compare these ratios to those obtained by cold plasma theory for whistler mode. From Figure 1, we select the time 15:15:35 near minimum ratios of E/cB (bluish color) extending from 1 kHz down to ∼f_lh to investigate more carefully. At this time, we deduce from the observations, f_uh = 30.2 kHz, f_c = 4.4 kHz, f_p = 29.9 kHz (f_p is the plasma frequency), and f_lh = 104 Hz. Using plot software we find for f= 850 Hz the observed value is E/cB ∼1.18 × 10⁻¹. From cold plasma theory with the above plasma parameters and for a wave normal angle, ψ = 0. we obtain E/cB = 5.13 × 10⁻¹, and the ratio of observed to calculated value is ∼2.3. For both f = 200 Hz and for f = 70 Hz (f < f_lh) the observed value is E/cB ∼ 9.9 × 10⁻². From cold plasma theory E/cB = 2.72 × 10⁻² (f = 200 Hz) and E/cB = 1.65 × 10⁻² (f = 70 Hz), and the ratio of observed to calculated value is ∼3.6 and 6.0, respectively. The observed and calculated values for f = 850 Hz are reasonably close and agree with Hartley et al. (2015) who compared whistler mode ratios of E/cB at Earth to cold plasma theory. However, the values obtained for f = 200 Hz and f = 70 Hz, are considerably higher than expected from cold plasma theory. The Waves instrument has only one component of B and one of E, so the projection of the wave field to the antenna might artificially change the measurement of E/cB even for low wave normal angles. Warm plasma effects may be important as suggested by Hartley et al. (2015), as well as finite antenna-plasma impedance and nonlinear effects.

Kolmasova et al. (2018) have successfully compared the phase difference between burst mode waveforms observed on the electric antenna and search coil of the Waves instrument to obtain the wave direction relative to the ambient magnetic field direction. This allows one to determine if the observed waves have wave vector, k, parallel or anti-parallel to the ambient magnetic field. We have applied this process to analyze the data during a number of periods when the burst mode data were available in Figure 1. Figure 2a displays the analysis for a period from about 18:02 to 18:04. The range of the lower hybrid frequency during the time period of the plot panels is approximately 220 Hz < f_lh < 320 Hz, and is shown near the bottom of each panel as a thin, black line labeled “f_LH”. From top to bottom the panels are: E_y spectral density, B_z spectral density, mutual phase difference of φ_EyBz (degrees), mutual coherence C_EyBz, and the sign of the ambient magnetic field component relative to spacecraft + x axis. The mutual phase φ_EyBz determines if the waves are propagating parallel (toward) or anti-parallel (away from) the magnetic equator in the northern hemisphere, if the mutual coherence is high (near 1). Using the method and assumptions presented in Kolmasova et al. (2018), a comparison of the phase difference of the emissions in the third panel to the sign of ambient magnetic field in the spacecraft + x axis with the rotation of the spacecraft indicates the waves above f_lh are traveling away from the equator, consistent with chorus emission (Hospodarsky et al., 2012). Figure 2b shows a somewhat higher resolution of Figure 2a, 18:02:49–18:03:22, and indicates that some of the emission down to and below f_lh may also be directed away from the magnetic equator, consistent with the expected direction of chorus. However, this may not be true at all times as evidenced for other periods shown in Figure 2c. Here, the chorus for f > f_lh is intense with high mutual coherence propagating away from the equator, while much of the emission at the lowest frequencies, for f < f_lh often has lower coherence, without a well-defined propagation toward or away from the magnetic equator.

In the previous survey, it was shown that Jovian chorus emission is correlated with energetic electrons with energies exceeding 100 keV (cf. Figure 1, Menietti et al., 2020), and therefore whistler mode waves at low frequencies can be in gyroresonance with these electrons. Gurnett and Bhattacharjee (2005, Equation 9.3.50) show that when ω_c « ω_p (ω = 2π f) the whistler mode dispersion equation for quasi-parallel propagation can be written as:

(1)

Using Equation 5.38 of Treumann and Baumjohann (1997) for mildly relativistic electrons and the dispersion equation for whistler mode above, we solve for the parallel electron cyclotron resonance velocity as:

(2)

where

(3)

(4)

and

(5)

In Figure 3a, we plot the resonant frequency of observed whistler mode as function of semi-relativistic parallel electron kinetic energy. We have set  = 0, because for the plasma parameters used, the impact of on is negligible until the characteristic energy exceeds about 400 keV. The different curves represent times for which f_p and f_c were determined from the observations in Figure 1, near the magnetic equator. These curves indicate that the whistler mode resonant frequency can be lower than 200 Hz for parallel electron energies above ∼100 keV, and down to 100 Hz or lower for E 200 keV. Figures 3b and 3c display the integral energy flux and characteristic energy, respectively, as measured by JEDI that ranged from about 150 to 200 keV, and Figure 1c shows that significant energy flux extends to over 300 keV at times during orbit 29. The characteristic energy is the ratio of integral energy intensity and integral number intensity (Clark et al., 2018; Mauk et al., 2004). It is a similar to a weighted mean over the energy range of JEDI. For this new survey, we have used both f_ci, as in the previous survey, and also the lower hybrid frequency, f_lh, as a lower cutoff frequency of the whistler mode emission for direct comparison.

7 Survey of Whistler Mode

The data for this survey were sampled from Juno orbits PJ01 through PJ33. In Figure 4, we show survey plots of whistler-mode intensity in the M-MLT plane sorted in bins of magnetic shell (M-shell) and MLT and in the meridian plane. We only show the data through PJ32 in this figure (because of the time over which this study was conducted), using a lower frequency cutoff of f_ci. The binning of the data and the intensity calculations were conducted as explained in Menietti et al. (2020), and Figure 4 can be compared directly to Figures 4a and 5a of that article, which we refer to as the “previous survey”. The white bins indicate the spacecraft did not sample that spatial bin. Figure 4 presents the 1 min averaged intensity observed within each spatial bin, averaged over all latitudes <31.5° (Figure 4a), and averaged over all MLTs (Figure 4b). The intensities range from 10⁻⁵ nT² to about 10^−2.6 nT².

Compared to results reported by Li et al. (2020) and Menietti et al. (2020) for perijove orbits PJ01 through PJ25, this later survey of low-latitude whistler mode chorus shows more complete coverage of the near-equatorial inner magnetosphere including M-shells 5 < M < 20 with somewhat higher intensities observed for the more recent orbits. The most intense whistler-mode emission lies in the range 5 < M < 12, with the peak intensity near 3 × 10⁻³ nT² nearest dawn but with the range of M largest near dusk. Figure 4b shows the most intense whistler-mode is within 20° of the equator.

8 Parameter Fits to Whistler Mode Intensity

We present plots of the intensity of the whistler mode chorus emission as a function of M-shell, magnetic latitude (λ), and normalized frequency (β = f/f_ceq) in Figures 5 and 6. The binning and intensity calculations are described in the previous survey, and Figures 5 and 6 can be compared to Figures 6–8 of that article. The frequency bins were defined earlier. We plot whistler-mode intensity averaged over all MLTs and all latitudes for each ΔM = 1.0 in the range 5.0 < M < 20.0. The latitude bins range from −9° to +31°, with the width of the bins Δλ = 2° for |λ| < 16° and Δλ = 5° for |λ| > 16°. The southern hemisphere limit of −9° is due to the Juno orbit, which is not symmetric with respect to the magnetic equator. The more recent data extend to smaller M-shells than in the previous survey (M = 5 compared to M = 7), and the Juno orbit is near to the magnetic equator at smaller M-shells where the chorus source region extends. Over-plotted on Figures 5 and 6, are parametric fits to the chorus data. To accommodate modelers, we have restricted ourselves primarily to a Gaussian function, of the form I(nT²) = a₁ exp(−z²/2), z = ((x − a₂)/a₃), with x the independent variable: β (normalized frequency), λ (magnetic latitude) or M (M-shell). The fitting parameters for Figures 5 and 6 are given in Table 1 (lower cutoff = f_ci) and Table 2 (lower cutoff = f_lh) with conditions given for each independent variable. The M-shell was evaluated using the JRM09 model (Connerney et al., 2018) with CAN magnetic sheet model (Connerney et al., 1981). Each plot will include the results for two cases of lower cutoff frequency for the chorus emission, Case 1, f_ci (red) and Case 2, f_lh (blue). Because the analyses have taken time, the data for Case 1 were collected for orbits PJ1 through PJ32, while for Case 2 the data included orbits PJ01 through PJ33. Shown in Figure 5a for Case 1 (f_ci), the chorus intensities peak near M = 8.5 at 1.1 × 10⁻³ nT², about the same as the peak intensity of the previous survey, but the region of chorus observations is expanded. For Case 2 (f_lh), the intensities are lower generally by about a factor of 2–2.5 in the range 5.5 < M < =14, but are nearly the same for M > 14, where the difference between f_ci and f_lh is small. The secondary peak near M = 17.5 may be due to the presence of Ganymede, but this is uncertain at this time. Shprits et al. (2018) have reported significant enhancements of chorus intensity near Ganymede and Europa, commenting on the possible significance of these emissions via long term particle and wave interactions. The authors surveyed Galileo plasma wave data which included many close flybys of both Ganymede and Europa where the most intense whistler mode emission occurs. There are no close flybys of either Ganymede or Europa in the Juno data for orbits PJ01 to PJ33, but there are in the extended Juno mission. In Figure 5b, we plot intensity vs. β = f/f_ceq showing a constant negative slope as observed in the previous survey. The intensity in Figure 5b for Case 1 at the lowest frequency bin is 1.61 × 10⁻⁴ nT². We have performed a special limited analysis of Case 1 which includes orbit PJ33 data to determine the value of β in the lowest frequency bin, to compare directly to Case 2 in Figure 5b. Including PJ33 data in Case 1 in the lowest frequency bin makes only a minor change to the average intensity to 1.76 × 10⁻⁴ nT². Neither Case 1 nor 2 shows any significant distinct narrow band feature for the chorus emission, rather the intensity increases with decreasing frequency. As commented above in the discussion of Figure 3, we believe that some of the extensions of the whistler mode emission to low frequency may be generated by electron energy flux extending to energies >100 keV.

The chorus intensity propagating from probable source regions near the magnetic equator is observed to increase in intensity above the equator before decreasing with latitude. The latitude of the peak intensity is a function of M-shell, but is believed to be less than 30°. The whistler mode intensity, however, continues to increase to beyond 50° latitude (cf. Li et al., 2020) due to the improving visibility of auroral hiss emission with latitude (Menietti et al., 2020).

Chorus intensity vs. magnetic latitude is plotted in Figure 6 (fitting parameters in Tables 1 and 2). For Case 1 (f_ci) in red, Figure 6a shows a peak of ∼9 × 10⁻⁴ nT² near 15° for and flattening out at higher latitude in the range 5 < M < 7. The previous survey reported no data for λ < 20° for this range of M-shell. The small increase in intensity at λ = 28.5° is likely due to the influence of auroral hiss observed at higher latitudes (not shown) as explained in the previous survey. For Case 2 (f_lh) in blue, the peak of ∼2 × 10⁻⁴ nT² near λ = 11° is more pronounced, and all other points are lower in intensity than Case 1 by about an order of magnitude. In Figure 6b (7 < M < 10), the Case 1 peak occurs at ∼1.2 × 10⁻³ nT² for λ = 3° compared to Figure 7b of the previous survey with a peak of ∼10⁻³ nT for λ = 7° indicating little variability in latitude between the two surveys. Case 2 peak is ∼6 × 10⁻⁴ nT² for λ = 3°, and other values are all less than an order of magnitude different from Case 1 values. In Figure 6c (10 < M < 13) for Case 1, we observe a peak intensity of ∼4 × 10⁻⁴ nT² at λ = −3° with intensity slowly decreasing for |λ| > 3° until λ = 30° where it begins to increase, probably due to auroral hiss as explained in the previous survey. The previous study showed a similar trend, with slightly lower intensities. Case 2 values peak at ∼2.2 × 10⁻⁴ nT² at λ = 3°, and all of the other latitude intensities are within an order of magnitude of Case 1. Finally, in Figure 6d, Case 1 shows a slowly decreasing intensity from a peak ∼1.5 × 10⁻⁴ nT² for λ = −7°. Case 2 intensities are nearly the same and follow a similar profile, because both f_ci and f_lh are less than 50 Hz, the lower cutoff of the frequency channels for the Waves instrument.

9 Z-Mode Survey

The previous survey also reported probable observations of Z-mode emission, the low-frequency branch of the extraordinary (X) mode. We have extended this survey for PJ01 through PJ33. Z-mode propagates below the upper hybrid frequency:

(6)

and above:

(7)

At Jupiter, this emission is generally less intense and is usually observed at higher frequencies than whistler mode. Z-mode emission is commonly spin-modulated with a satellite spin period of ∼30 s, producing a signal modulation of ∼15 s. Following the methodology explained in Menietti et al. (2020), we have calculated a linear least squares fit of the data to a sinusoidal function.

As in the previous survey, Z-mode emission and frequency ranges are selected by eye and digitized in 1 min periods. Because polarization of the waves is not measured by the Waves instrument, the identification as Z-mode is not certain, and the emission could sometimes be mixed with O-mode or whistler mode, for instance. Only those frequencies that lie in the range f_L = 0 < f < f_UH are selected. There were almost no distinguishable Z-mode observations above background for f < 20 kHz, which limits the data to electric signals using only the LFR-hi electric receiver. The magnetic intensity at each frequency is calculated assuming the cold plasma index of refraction, C_z(f, f_p, f_c), as defined in Equation 4.4.17 of Gurnett and Bhattacharjee (2005). This assumption has been shown to be reasonable for the case of Z-mode observed at Saturn (cf. Menietti et al., 2015; Ye et al., 2010). We evaluate C_z at each frequency channel and average over each spatial bin. Based on Z-mode observations at Saturn (Menietti et al., 2018), we have assumed a constant wave normal angle of 20°. We spatially bin the data in r, λ, and MLT, with Δr = 0.5 R_J, Δλ = 10°, and ΔMLT = 1h, and values of B² are averaged in each spatial bin (Figure 9).

As an example, Figure 7 displays a spectrogram of emission we identify as Z-mode. Also identified are f_c and f_uh during the time of observation. Two other possible wave modes would be the whistler and ordinary mode that may also be observed in this frequency range. O-mode cannot propagate below the plasma frequency, which at this time is in the approximate range 25 kHz < f < 60 kHz. However, O-mode can propagate freely across the cyclotron frequency. Whistler mode will not propagate above the plasma frequency or cyclotron frequency, whichever is lower. The emission labeled f_uh is rather broad banded, perhaps due to warm plasma effects and emission from multiple source regions, so we have chosen regions of maximum intensity within the band at specific times to calculate f_p = √(f_uh² − f_c²). From the latter, we can calculate f_z from Equation 7 above and this is over plotted in Figure 7 showing a reasonable agreement with the lower cutoff of the emission, supporting the identification as Z-mode. Analysis methods identifying plasma wave modes in the Jovian environment characterized by the condition f_c/f_p » 1 have been systematically discussed by Sulaiman et al. (2021) and also discussed by Elliott et al. (2021).

Z-mode magnetic intensities displayed in the r-MLT and meridian planes in a format similar to Figure 4 are shown in Figures 8a and 8b. These plots can be compared to Figures 10 and 11 of the previous survey (Menietti et al., 2020). The overall distribution in intensity is similar to that reported in the previous study, but the region of observation is expanded due to the increased global coverage by the Juno spacecraft. Z-mode is observed with most intensity in a rough band extending approximately over radial distances 3.5 < r < 6.5 R_j and 20 h < MLT < 5 h (counterclockwise), and over magnetic latitude range of about 20° < λ < 50°. The intensities in the southern hemisphere are much weaker than the northern. This is likely due to the orbit of Juno that traverses higher magnetic latitudes in the southern hemisphere, because of the tilt of the magnetic axis relative to the spin axis and precession of the orbit that moves perijove about 1° to the north each orbit. This will continue in the extended mission.

The results of spatial binning of the intensity along with parametric fits are shown in Figure 9, and fitting functions and parameters are given for Z-mode emission in Table 3, with the conditions given for each independent variable. These plots can be compared to Figure 12 of the previous survey. We again limit ourselves to a Gaussian function, except in a few cases where a polynomial function is selected. Figure 9a depicts the Z-mode intensity vs. frequency. For f < 55 kHz, intensity increases reaching a peak of ∼8 × 10⁻⁶ nT², before dropping to ∼1 × 10⁻⁷ nT² after ∼50 kHz and remaining low at higher frequencies. Because of the non-symmetric orbit relative to the magnetic equator and the observation of Z-mode only at middle to high latitudes, we average the bins from the north and south magnetic hemispheres in analyzing the magnetic latitude distribution. Figure 9b shows the intensity vs. |λ|, averaged over all MLT and r for the times of the emission. Z-mode intensity rises to just over 4 × 10⁻⁵ nT² in the bin centered at 45°, but falls precipitously beyond 50°. This may be a clue to the source location possibly lying in the polar region, along an active magnetic field line, perhaps containing electron beams, with emission propagating at small wave normal angles in a relatively narrow emission cone as we discuss below. Z-mode intensity vs. M-shell, averaged over all MLT and |λ| for the times of the emission is shown in Figure 9c. We have used three distinct Gaussian fits for 3 ranges of M-shell. The peak intensity is ∼4 × 10⁻⁴ nT² for 5 < M < 9, followed by ∼4 × 10⁻⁶ nT² for 9 < M < 11, and lastly ∼5 × 10⁻⁷ nT² for the range 11 < M < 14.5.

10 Summary and Conclusions

At the end of the Juno primary mission, we have presented an extended analysis of Jovian low-latitude whistler-mode chorus emission for orbits PJ01 through PJ33. A survey of intensity as a function of f, M-shell, λ, and MLT is conducted assuming sources mapped to the magnetic equator based on the JRM09 + CAN magnetic field model. The results indicate that chorus and whistler-mode emission intensity levels can be significant at Jupiter. Parametric fits to the data have also been calculated for use of modelers. We note that other, better fits are certainly possible for the data, but we have restricted ourselves to primarily Gaussian functions for ease in existing numerical models. Chorus emission is observed near the magnetic equator with generally increasing intensity peaking at magnetic latitudes varying between ∼5° and ∼25° dependent upon M-shell. Beyond latitudes of ∼30°, the chorus intensity decreases at all M-shells, but the influence of auroral hiss becomes dominant and extends beyond 50° magnetic latitude (cf. Li et al., 2020). As a function of M-shell the chorus emission peaks in the range 8 < M < 9, at intensities ∼1.2 × 10⁻³ nT² for Case 1 (f_ci as the lower frequency cutoff) or ∼6 × 10⁻⁴ nT² for Case 2 (f_lh as the lower frequency cutoff). The whistler mode emission observed at Jupiter appears as bursty and more broad-banded than at Earth, often extending below f_lh (Figure 1). Figure 2 indicates that the whistler mode emission above f_lh has a wave direction, away from the magnetic equator, the same as expected for chorus. The low-frequency, bursty emission that extends to frequencies below f_lh sometimes may have a wave direction away from the magnetic equator as seen in Figure 2b near 18:02–18:03, but at other times the wave direction for this emission is not as well defined. Figure 1c indicates many time periods where E/cB is similar for the chorus emission at frequencies above ∼1 kHz and for frequencies below f_lh (i.e., ∼14:20–16:10; 16:44–16:52; ∼18:00–18:30). However, caution is necessary because only one component of E and B is available on the Waves instrument. The lowest frequency emission in Figure 1b appears sometimes to be connected to the higher frequency chorus, but at other times (e.g., ∼15:30–16:15) the higher frequency chorus is distinct from the lower frequency bursty whistler mode. These observations may be due to the free energy electron population for chorus emission with characteristic energies that extend to over 200 keV as shown in Figure 3, implying resonant wave frequencies extending down to f ∼ 100 Hz or lower, and with wave growth rates that are energy and time dependent. We suggest that these higher energy electrons may generate at least some of the low-frequency whistler mode emission. The electron differential flux is bursty throughout the period of chorus observations. From ∼14:30 to 15:30 characteristic energy, E_c, slowly increases to a peak prior to intense chorus and low-frequency whistler mode. In Figure 3, we note that from ∼16:20 to ∼18:10 E_c ramps up to a peak at least three times corresponding to periods of enhanced bursty whistler mode at lowest frequencies. The times of enhanced low-frequency bursts are seen in Figure 1b centered near 16:50, 17:30, and 18:00.

A survey of possible Z-mode emission in the inner Jovian magnetosphere is limited by the orbit of Juno, but the extended mission of Juno may lead to observations in the region near the equator inside the orbit of Io, a region only partially sampled by the Juno primary mission. Z-mode is observed in the Juno Waves data primarily in the region at middle latitudes in the region near and inward of M ∼ 10. These waves are typically two orders of magnitude less intense than chorus, but are about 50 times the typical intensity of Z-mode observed at Saturn (Menietti et al., 2018). Z-mode emission is difficult to positively identify at Jupiter because the Wave instrument does not measure wave polarization. At times, however, it is possible to determine the local value of f_z, the lower cutoff of Z-mode, to compare to the observations. While very often Z-mode does not propagate down to its lower cutoff, there are some interesting cases where this is the case such as shown in Figure 7, where emission cuts off near f_z and is unlikely to be whistler or O-mode, thus supporting identification as Z-mode.

The source region of Z-mode emission is another outstanding question. Figure 9b shows the intensity vs. |λ|, averaged over all MLT and r for the times of the emission, rising from |λ| ∼ 20° to nearly 4 × 10⁻⁵ nT² in the bin centered at 45°, but falling precipitously beyond that latitude bin. The sharp decline in Z-mode intensity beyond latitudes of 50° may be a clue to at least one source location in the auroral or polar region, propagating at relatively small wave normal angles from an active magnetic field line possibly also containing source regions of Jovian auroral hiss, kilometric, hectometric, and/or decametric emission. As Juno approaches the Jovian polar region it observes Z-mode at mid-latitudes until it nears the source region and rapidly drops under the rather narrow emission cone, streaking toward perijove near the Jovian equator. This can be visualized in Figure 1a of Imai et al. (2017). For the Juno trajectory depicted in the latter figure, Z-mode emission is observed by Juno on PJ01 for r < 6 R_j with intensity peaking near λ ∼ 55°, before decreasing rapidly as the spacecraft dips toward perijove near the Jovian equator. This is consistent with a source region of Z-mode along the field line containing a bKOM source identified by Imai et al. (2017). Z-mode is believed to propagate at relatively small wave normal angles (<25° as reported at Saturn, Menietti et al., 2018) and would not be seen outside the relatively narrow emission cone of the active magnetic field line. Further observations of both Z-mode and whistler mode both inside and outside the orbit of Io in the extended Juno mission will be necessary to seek answers to questions only partially addressed in this work.