# On the equatorial dayside ionosphere of Saturn – In-situ observations give evidence for a dynamic and layered structure in disequilibrium

J. -E. Wahlund, A. I. Eriksson, M. W. Morooka, S. Buchert, M. Persson, E. Vigren, J. Dreyer, W. S. Kurth, J. H. Waite, J. -P. Lebreton, et al.

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## To cite this version:

J. -E. Wahlund, A. I. Eriksson, M. W. Morooka, S. Buchert, M. Persson, et al.. On the equatorial dayside ionosphere of Saturn – In-situ observations give evidence for a dynamic and layered structure in disequilibrium. Icarus, 2025, 441, 10.1016/j.icarus.2025.116647. insu-05138422

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https://insu.hal.science/insu-05138422v1

Submitted on 1 Jul 2025

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Research Paper

# On the equatorial dayside ionosphere of Saturn – In-situ observations give evidence for a dynamic and layered structure in disequilibrium

J.-E. Wahlund<sup>a,∗</sup>, A.I. Eriksson<sup>a</sup>, M.W. Morooka<sup>a</sup>, S. Buchert<sup>a</sup>, M. Persson<sup>a</sup>, E. Vigren<sup>a</sup>,
J. Dreyer<sup>b</sup>, W.S. Kurth<sup>c</sup>, J.H. Jr Waite<sup>d</sup>, J.-P. Lebreton<sup>e</sup>, W.M. Farrell<sup>f</sup>, I. Müller-Wodarg<sup>g</sup>

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ARTICLE INFO

Keywords:

Cassini
Saturn
Ionosphere
Rings
Aerosol

A B S T R A C T

The Cassini observations of Saturn's ionosphere during the proximal orbits 288-293 in the altitude range 1450-4000 km (above 1-bar level) are revisited. A thorough re-analysis is made of all 159 available Langmuir probe sweeps of the Radio & Plasma Wave Science (RPWS) measurements. We relate them to the RPWS plasma wave inferred electron number densities and compare them with the available Ion Neutral Mass Spectrometer (INMS) measurements of the H⁺ and H₃⁻ number densities. Different analysis methods are used by RPWS to provide consistent electron number density values for the whole measured altitude interval. Consistent RPWS electron number density (n_e) and INMS positively charged ion number density (n_i,) profiles are derived for altitudes above ~2200 km. Below this altitude the inability of INMS to measure ions above 8 amu at the 34 km/s flyby speed lead us to infer the presence of heavy ions (> 8 amu) and a negatively charged ion component, presumably related to infalling material from the D-ring of Saturn with its associated local ion-molecule-aerosol chemistry. This lower altitude region shows a highly time variable layered structure. The Langmuir probe data in this region are strongly affected by secondaries emitted from the spacecraft and sensor surfaces when traversing a molecule-rich atmosphere at 34 km/s. There are clear signatures of secondary electron and ion emissions from the spacecraft and sensor surfaces in the data. In the Langmuir probe sweep analysis, we correct for the effect of such impact-generated products. This gives corrected total ion number densities that can be compared to the INMS ion number densities and the electron number densities. From this analysis the number of negative ions and/or nm-sized aerosol/dust particles can be constrained. A clear ionospheric peak is not identified, not even at the lowest observed altitude of approximately 1450 km. There are clear latitudinal variations and temporal evolving structures, which we infer are representative of the difference in infalling material from different regions of the D-ring. In addition, there are indications of a strong heating source for the ambient electrons that are well above expected thermal equilibrium levels (up to 4000 K). The cause of this heating is unknown but may be linked to collisional deacceleration of infalling ring material. The observational profiles presented here can be used for ionosphere theory/model comparisons in the future.

# 1. Introduction

The Cassini spacecraft repeatedly entered the region between the rings and Saturn's atmosphere during the proximal orbital phase (April–September 2017) and ended its observations in a final plunge into

Saturn on September 15, 2017. In-situ measurements monitored the ring material, as well as Saturn's ionosphere and thermosphere. The Radio and Plasma Wave Science (RPWS) initial observations of the topside ionosphere, closest to the D-ring, indicated the presence of negatively charged grains (<50 cm⁻³ charge carrier number density) and 15–20

<footnote><sup>a</sup> Swedish Institute of Space Physics (IRF), Uppsala, Sweden</footnote>

<footnote><sup>b</sup> Royal Observatory of Belgium, Brussels, Belgium</footnote>

<footnote><sup>c</sup> University of Iowa, Iowa City, IA, USA</footnote>

<footnote><sup>d</sup> Department of Physics and Astronomy, University of Alabama, Tuscaloosa, AL, USA</footnote>

<footnote><sup>e</sup> Laboratoire de Physique et Chimie de l'Environnement et de l'Espace (LPC2E), CNRS-Université d'Orléans-CNES, France</footnote>

<footnote><sup>f</sup> NASA/Goddard Space Flight Center, Greenbelt, MD, USA</footnote>

<footnote><sup>g</sup> Imperial College London, UK</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: jwe@irfu.se (J.-E. Wahlund).</footnote>
amu positively charged ions (Wahlund et al., 2017). Both the Ion and Neutral CAmera (INCA) and CHarge Energy Mass Spectrometer (CHEMS) of the Magnetosphere Imaging Instrument (MIMI), as well as the Cosmic Dust Analyzer (CDA), reported large amounts (~ 0.1–250 cm⁻³) of 1–50 nm-sized dust near the equatorial plane at 3000 km altitude (Mitchell et al., 2018; Hsu et al., 2018). The RPWS electric antenna also recorded µm-sized grain impacts on the spacecraft surface (Ye et al., 2018). This ring material, moving with speeds around 15–25 km/s relative to the atmosphere, was shown to collide with the atmospheric constituents (mostly H₂ and H) and thereafter undergo free fall under gravity and Saturn's magnetic field toward the planet (Ip et al., 2016; Mitchell et al., 2018; Hsu et al., 2018). When the dust impacts deeper atmospheric layers at large speeds, they partly ablate, sublimate, and deposit energy and mass at 1500–1900 km altitude above the 1-bar level (Hamil et al., 2018). The Ion and Neutral Mass Spectrometer (INMS) detected a very complex neutral chemistry including CH₄, NH₃, H₂O and organics up to 100 amu in addition to H₂ and He (Waite et al., 2018) and confirmed that an influx of ring material is continuously deposited at these altitudes. The mass influx of ring material was estimated to 4800–45,000 kg/s based on the INMS measurements alone, while the CDA measurements indicated a somewhat lower mass influx rate of 1800–6600 kg/s for particles of a few tens of nm size. The full influx estimates of ring material require knowledge of the complete dust size distribution, while each Cassini instrument only detects part of the distribution, and therefore different estimates have been given. Further processing of this infalling ring material will occur at ionospheric altitudes, triggering an organic-rich complex ion-molecule-aerosol chemistry there (e.g., Morooka et al., 2019; Moses et al., 2023). A comparison of RPWS electron densities with INMS total H⁺ and H₃⁻ densities indicated that the dayside equatorial ionosphere must be dominated by heavier ion species (> 4 amu), consistent also with ionosphere composition models with organic ion and/or H₃O⁺ dominance below 1700 km (e.g., Moore et al., 2018).

The RPWS Langmuir Probe (LP) data from Saturn's ionosphere have not yet been reported in detail, in particular the data from the chemistry-controlled region below about 2400 km where the heavy ions are inferred to be abundant. This is largely due to data interpretation problems associated with impact plasma and secondaries produced when a spacecraft traverses the denser regions of an atmosphere at about 34 km/s (corresponding to impact energies of the order 12–500 eV depending on species, and much more if aerosols/dust are impacting). The delay in the analysis is also due to timing comparison difficulties between on-board instruments (Dreyer et al., 2022). We therefore revisit the observational record and address the detailed observational challenges. Our analysis of INMS and RPWS data shows that a consistent interpretation of this region of Saturn's ionosphere can be reached when taking the aforementioned factors into account. The aim here is to give an observational in-situ record.

We have divided the paper into instrument descriptions, followed by several method sections with corresponding appendices for details, before putting together the RPWS and INMS observational results for Saturn's ionosphere, whereafter a discussion and conclusions completes this paper. The Cassini JPL/NASA ephemeris is used, and all RPWS and INMS data presented here are calibrated versus the INMS H₂ number density to reach a valid altitude comparison between different Cassini flybys (c.f., Appendix A).

## 2. Cassini instrument and data product descriptions

### 2.1. The RPWS plasma wave data & RPWS derived electron number densities

The RPWS instrument is described in Gurnett et al. (2004). In Section 2.2 we describe in more detail the Langmuir probe (LP) part of the RPWS instrument for clarity.

The electron number densities derived from observed broadband

whistler mode emissions and narrowband upper hybrid frequency emissions (nₑ,wave) using the RPWS electric antenna measurements in the Saturn ionosphere is described by Persoon et al. (2005, 2019). These plasma wave electron number densities range from the lowest measured altitude 1450 km (Rev-293) up to 15,000 km, and with only a handful of exceptions agree with Langmuir probe voltage sweep derived electron number densities (nₑ,LP) presented here (Appendix B, see further Sections 2.2 and 3.1 below). We consider these independently inferred electron number densities valid ionospheric values. The errors for the electron number density, inferred from plasma wave frequencies, varies between 9 % and 19 %. The effects of secondary electron emissions or other possible effects due to the interaction between the spacecraft and the streaming plasma/atmosphere on the electron number densities presented herein are therefore determined to within the same error-range.

### 2.2. The RPWS Langmuir probe (LP) data

The RPWS Langmuir probe configuration onboard Cassini is displayed in Fig. 1 (see also Gurnett et al., 2004). The spherical Langmuir probe sensor has a radius ($r_{LP}$) of 2.5 cm and is attached to a thin cylinder guard (stub) which is 10 cm long and which is kept at the same bias voltage as the spherical sensor. The spherical probe current (it does not include the current collected by the guard) is collected and recorded in the RPWS/LP receiver electronics. The spherical probe and thin cylinder guard is mounted on a deployed Ti-boom so that the LP sensor is about 1.5 m from the nearest spacecraft structure. The thin surface coating of TiN on the sensor and guard, with high mechanical durability and chemical inertness, was achieved with an extreme degree of adhesion by using a process of “baking”, i.e., conversion of the upper layers of a Ti sample to TiN by immersion in a nitrogen atmosphere at high temperature (Wahlström et al., 1992; Veszelei and Veszelei, 1993).

The boom voltage potential is related to the spacecraft surface potential, which both of vary as a response to the encountered plasma environment and solar EUV radiation. The LP sensor is mounted in such a way that it is always in the plasma ram direction if the INMS is pointed in the ram direction to ensure simultaneous sampling when both are operated.

The RPWS Langmuir probe is operated in current sampling mode for plasma diagnostics giving mainly electron and ion number densities (nₑ, nᵢ) as well as electron temperature (Tₑ) and the floating potential of the probe. The probe can be biased to a specific voltage (positive or negative) or stepped in bias voltage (a so-called Langmuir sweep), and the probe current is measured (Mott-Smith and Langmuir, 1926). When the Langmuir probe current is sampled for a fixed positive bias voltage, it gives the electron number density with high time resolution (1–100 samples/s, δnₑ), but which depends on $\sqrt{T_e}$ and the floating potential ($U_{float}$) – both assumed to vary slowly compared to the electron number density (nₑ); a systematic long term deviation can be detected in the fixed bias electron number density (δnₑ). During the proximal orbits in Saturn's ionosphere the RPWS operated the Langmuir probe as in Table 1.

When the probe is biased negatively, the current is usually dominated by ions attracted to the probe and/or photoelectrons emitted from a sunlit probe, while if the probe is positively biased it attracts electrons from the electron sheath expanding from the sensor for increasing bias voltages. This is often an oversimplified picture, and for the Cassini Langmuir probe measurements in the Saturn ionosphere there are many details regarding the resulting voltage-current characteristic of the probe response that need to be considered (c.f., Section 3). An example of a good model fit to a Langmuir probe sweep voltage-current characteristic taking these considerations into account is displayed in Fig. 2, together with a corresponding residual error in Fig. 3. The example is taken from the topside ionosphere during Rev. 289.

Instead of fitting physical parameters directly to the voltage-current
<figure><img src="image_5.png" /><figcaption>Fig. 1. The Cassini RPWS Langmuir probe configuration – deployed on the spacecraft (credit: NASA) and folded with ground support structure (credit: IRF).</figcaption></figure>

<table><caption>**Table 1**

RPWS Langmuir probe data during the proximal orbits.</caption><thead><tr><th>Revolution</th><th>Sweeps (n<sub>e</sub>, n<sub>l</sub>, T<sub>e</sub>), every 24–48 s</th><th>Continuous bias (δn<sub>e</sub>)</th></tr></thead><tbody><tr><td>Rev 288–291</td><td>±4 V sweeps, 512 bias points<sup>*</sup></td><td>+4 V, 1 samples/s</td></tr><tr><td>Rev 292</td><td>±4 V sweeps, 512 bias points<sup>*</sup></td><td>+4 V, 100 samples/s (but had data gaps)</td></tr><tr><td>Rev 293 (&lt; 2500 km)</td><td>±4 V sweeps, 1024 bias points (down &amp; up sweeps<sup>**S</sup>)</td><td>+4 V 20 samples/s</td></tr><tr><td>Rev 293 (&gt; 2500 km)</td><td>±32 V sweeps, 1024 bias points (down &amp; up sweeps)</td><td>+11 V, 20 samples/s</td></tr></tbody></table>

* Each sweep bias point consists of two samples (for checking if capacitive coupling to the plasma occurs). Note: No capacitive effects have been detected in sweeps within Saturn's ionosphere.

** From +4 V to -4 V, then from -4 V to +4 V. Checks for hysteresis due to a potentially contaminated probe surface. Note: no hysteresis has been detected in Rev 293 sweeps within Saturn's ionosphere.

characteristic (according to Langmuir probe theory) we make use of a stepwise iterative parametric fit procedure (c.f., Appendix C, and using the formalism in Appendix D). The concept of error handling of derived parameters from a Langmuir probe voltage-current characteristic is difficult to automate. The parametric fit is non-linear and the variations in current occur over 4–5 orders of magnitude (due to the different mobility of ions and electrons, from 0.1 nA to several µA). Different parts of the U-I-characteristic fit are also related to different fitted parameters. The residuals are the basis of the error estimates of the voltage-current characteristic. We have therefore made a variation of the fits for each fitted parameter and checked the fit and residual by eye for each of the analysed sweeps (see Appendix E). This gave error estimates (Table 2) which are valid for more than 90 % the parameter fits presented here. The random noise level is 100–200 pA for $U = U_{bias} + U_{float} < 0$ V, and an order of magnitude larger on the electron sampling side for $U > 0$ V. Systematic errors can be larger for $U > 0$ V compared to the LP sweeps model fits applied here but it tracks with the residual for each LP sweep fit.

The errors related to the secondary electron emission current (I<sub>SEE</sub>) below 2500 km are uncertain to ~30 % (c.f., Section 3.4) and are regarded as maximum values. The inferred total positively charged ion density, and the negatively charged ion density, are based on I<sub>SEE</sub> estimates and therefore associated with larger errors. The fitted secondary ion emission current (I<sub>ISIE</sub>) from the LP sweep data suggests a stable exponential decrease with altitude of both the SEE and SEI currents (c.f., Section 3.4). The possibility of hysteresis in the LP sweep data, due to contamination on the sensor surface, was investigated for Rev. 293 (where up and down sweeps were carried out). No significant hysteresis could be found in the U–I characteristic. The Langmuir probe response indicates a clean probe surface, which is also the case for all LP data

<figure><img src="image_6.png" /><figcaption>Fig. 2. An example of a RPWS LP voltage sweep from the topside ionosphere of Saturn on Rev. 289 (panels a, b, c are different representations (linear, log, log) of the same data). In panel c a linear fit (magenta, panel a and b) representing the ion ram current, has been removed from the data. A parametric model fit of the total current (red line) follows the LP data (blue dots) almost exactly. Details of the fit components and procedure is given in Section 3.1 and Appendix D. Current components are the main electron current corrected for geometry (green line), sheath-limited electron current (green dash-dot), hot electron tail (green dashed), ion ram current (magenta) and total sampled current (red line). The legends are floating potential ($U_{float}$), electron temperature ($T_e$), electron number density as determined from plasma wave frequencies ($N_{e,waves}$), electron density of main population determined by this model fit ($N_e$, this fit), the electron temperature of the hot electron tail population ($T_{e,sup}$), the electron number density of the hot electron tail population ($N_{e,sup}$), the Debye length ($\lambda_D$), the electron gyro-radius ($r_{g,e}$), the distance from the probe surface where the potential geometry and electron sheath expansion start become influenced by the guard ($s_{pot,eff}$), and the beta form factor due to the potential geometry affected by the guard ($\beta$). See text for explanations of the legends. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

taken near the moon Titan (not shown).

A known internal RPWS interference is an increased noise level between -3 V and -1 V, where the RPWS HF receiver sometimes causes enhanced noise in the LP current. This noise does not significantly affect the errors in this study. There are also occasional voltage end-effects in first or last bias voltage current data samples, which are ignored in the analysis since they are instrumental. No other instrumental effects have been detected. The lowest electron temperature that is possible to
<figure><img src="image_7.png" /><figcaption>Fig. 3. The residual data after the parametric fit has been removed corresponding to the voltage sweep displayed in Fig. 2. Linear residual (panel a) and logarithmic residual (panel b) where red denotes positive residual and blue negative residual. For negative bias voltage, often corresponding to the ion current, a residual less than 0.2 nA is usually achieved. For positive bias voltage, usually corresponding to an electron current, show a larger random noise of <2 nA and systematic deviations. The residuals are the basis of the error estimates of the voltage-current characteristic derived here (see further text). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<table><caption>**Table 2**

Error estimates of physical parameters presented here.</caption><thead><tr><th>Parameter</th><th>Error</th></tr></thead><tbody><tr><td>n<sub>e,LP</sub> (or c<sub>1</sub> in parametric fit)</td><td>&lt;5 %</td></tr><tr><td>T<sub>e</sub> (or d<sub>1</sub> in parametric fit)</td><td>&lt;10 %</td></tr><tr><td>U<sub>float</sub> (U<sub>bias</sub> position of U-I-char.)</td><td>&lt;0.01 V</td></tr><tr><td>n<sub>e,sup</sub> (or c<sub>2</sub> in parametric fit)</td><td>&lt;30 %</td></tr><tr><td>T<sub>e,sup</sub> or T<sub>SIE</sub> (or d<sub>2</sub> in parametric fit)</td><td>&lt;10 %</td></tr><tr><td>n<sub>i</sub> (or m, b in parametric fit)</td><td>&lt;10 % in topside ionosphere and dep. on V<sub>i</sub> ≈ V<sub>SC</sub><br>~30 % (see further Section 3.4)</td></tr><tr><td>d<sub>s</sub>, β (electron sheath form factor)</td><td>&lt;0.01 m, &lt;0.05</td></tr></tbody></table>

measure with the RPWS LP sweep characteristic is 0.015 eV (170 K), derived from the EMF smoothness of the spherical Langmuir probe, measured on ground before launch. A record of all RPWS/LP voltage sweeps used in this study can be found in a PDS3 repository (see Acknowledgements).

## 2.3. The INMS data

The INMS instrument is described in Waite et al. (2004). We have used the H₂, H⁺, H³⁺, He⁺ and total ion number densities in this study first reported in Waite et al. (2018) online supplement and later used in Dreyer et al. (2022, 2023). The ion optics were not designed for measurements of ions traveling into the instrument at 34 km/s thus limiting the mass range to <8 amu rather than the designed mass range of 1–100 amu.

# 3. Data analysis methods

## 3.1. Langmuir probe sweep analysis

For ionospheric plasma conditions in this study, the Debye length ($\lambda_D$) varies normally between 3 and 15 cm (but in a few topside ionosphere cases reached beyond 50 cm) and is therefore the same order of magnitude as the Langmuir probe radius ($r_{LP}$). Orbit motion limited

(OML) theory is therefore not applicable. We must consider the geometry of the expanding electron sheath around the Langmuir probe and make use of sheath limited theory for the electron current. In addition, for larger positive voltage bias values, where the electron sheath expands beyond the guard, the disturbing potential variations of the guard, spacecraft and boom surfaces must be considered in the evaluation of the voltage-current characteristic of the Langmuir probe voltage sweeps. For the S/C and boom voltage effects, a judgement must be made on a sweep-by-sweep basis. For the guard effect a simple geometric analysis procedure is implemented with good accuracy.

We make use of electron sheath limited (SL) current sampling by a spherical probe together with the empirical Parker sheath size (Bettinger and Walker, 1965; Whipple, 1965)

$$s_e = (0.83r_{LP}) \left(\frac{\lambda_D}{r_{LP}}\right)^{2/3} \sqrt{U/T_e[eV]} \quad (1)$$

in the expression for SL current $I = I_0f(U, n_e, T_e, s_e)$ and where U is the probe potential and $T_e$ the electron temperature. The theory expression for the SL current varies somewhat (e.g., Whipple, 1965; Laframboise, 1966; Conde, 2011; Darian et al., 2019; Chatain et al., 2021), and for all the cases presented herein give a significant reduction of the current with bias potential as compared to Orbit Motion Limited (OML) theory. We make use of the expressions by Whipple (1965) using a Parker electron sheath and Maxwellian electrons:

$$I_e = I_{e,0} \left[ 1 + \xi \left( 1 - \exp\left(\chi_e' \xi\right) \right) \right] \quad (2)$$

with $\xi = (s_e/\rho + 1)^2$ and $\rho = r_{LP}/\lambda_D$ and $\chi_e = U/T_e[eV]$.

A hot electron tail distribution is detected in some of the Cassini LP sweeps in the topside ionosphere. Darian et al. (2019) gives SL expressions for Kappa and Cairns distributions. In the cases where a hot electron tail is detected we have found it more practical to fit two different superposed Maxwellian distributions, one major electron population Maxwellian component and one added tenuous hot Maxwellian electron component. Note though, other contributors to the current may give a similar “hot tail” response, like impact generated secondary ion emissions from the probe surface, which we observe in the lower ionosphere (see Section 3.2). Since we do the model fit parametrically (see Appendix C), the physics is not lost in the fit results and can be sorted out afterwards.

Theoretically, the electron current to a spherical probe is symmetric from all directions. Experimentally this is not true, since the guard (and boom) modifies the potential pattern around the Langmuir probe sensor when the electron sheath expands from the spherical sensor (Pilling and Carnegie, 2007; Marholm and Marchand, 2020; Kjølerbakken et al., 2023, see Fig. 4). One therefore need apply an experimental form factor ($\beta$) to the electron current, $I = I_0f(\xi, \chi_e)^\beta$, which varies between $\beta=1$ (spherical) to $\beta=0.5$ (cylinder), and which takes effect when the expanding electron sheath has reached a certain distance ($d_s$) from the spherical probe surface. Applying these form factors does not give more information from the voltage current characteristic regarding the surrounding plasma, even if the form factors depend on the surrounding plasma conditions. It only models the reduction of current with increasing positive voltage bias beyond a certain sheath distance. Fig. 2 (in Section 2.2) gives a LP sweep example where this experimental effect has been implemented.

In this regard it is also necessary to consider effects that arise when the boom potential becomes different from the applied voltage of the probe and guard. The current for a large enough positive probe bias potential will become smaller or larger depending on the sign and amplitude of the boom (or S/C) potential. To understand this better consider the LP sweep presented in Figs. 5 and related predicted electron sheath in Fig. 6.

The Langmuir probe is sun-lit in the presented cases. The photo-
<figure><img src="image_8.png" /><figcaption>Fig. 4. Sketch describing the principles behind the experimental potential form factor of the expanding electron sheath around the sensor for different positive bias voltages (left, case for $U_{float} = 0$).</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 5. Same representation as in Fig. 2. An example of a RPWS LP voltage sweep from the ionosphere of Saturn on Rev. 290. A parametric model fit of the total current (red line) follows the LP data (blue dots) up to about +1 V. The potential region where the spherical probe, cylindrical guard, and boom (or S/C) affects the U-I characteristic is indicated. Compare with predicted electron sheath distance from probe surface in Fig. 6. The boom has in this case a slightly more positive potential compared to the probe/guard bias voltage as fewer electrons are sampled by the Langmuir probe. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

current (Einstein, 1905; Grard, 1973) from the probe is at Saturn of the order of 0.5–0.6 nA. This only affects parameter fits for electron number density estimates below about 10 cm⁻³ and therefore not of significant concern in this study. We have included this current contribution.

Most commonly the positive ion number density is derived from the sweep characteristic for negative voltage bias and for a drifting Maxwellian ion distribution as (e.g., Whipple, 1965; Fahleson et al., 1974; Jacobsen et al., 2009; Holmberg et al., 2012):

$$I_t \approx -q_i n_i A_{LP} V_i / 4 \left( 1 - \frac{U_{bias} + U_{float}}{W_i} \right) \quad (3)$$

where $q_i$ and $W_i$ are the charge and ram energy of the ions respectively, and $A_{LP}$ is the surface area of the probe. This gives a linear dependence for negative $U_{bias} + U_{float}$ values and is easily fitted. The derivation of $n_i$ in this study assumes $V_i \approx V_{SC}$, and this assumption could be modified if significant topside ionosphere plasma transport occurs as the LP samples

<figure><img src="image_10.png" /><figcaption>Fig. 6. The electron sheath distance from the Langmuir probe using sheath limited theory and Parker sheath for probe sampling. Around +1 V, the probe current start to be affected by a different boom potential compared to the probe/guard applied Voltage. This is confirmed in the Langmuir probe data (see Fig. 5).</figcaption></figure>

the ion flux to its surface.

However, Langmuir probe sweep analysis for a spacecraft traversing an aerosol/dust- and molecular-rich atmosphere/ionosphere at large speed (about 34 km/s) poses a specific problem not easily constrained by plasma chamber measurements on the ground during calibration and testing. For instance, the impact energies of Kronian atmospheric/ionospheric species like $H_2^+$ (≈10 eV), $H_2O^+$ (≈90 eV), 28 amu species like $C_2H_6^+$, $CO^+$ or $H_2CN^+$ (≈140 eV) or even Benzene $C_6H_6^+$ (≈390 eV) are approaching or even exceed the ionization threshold of respective species and may therefore produce secondary electrons (SEE) and ions (SIE) when impacting a surface (e.g., Schmidt and Arends, 1985; Johansson et al., 2022). Larger aerosol species may even partly ablate, sublimate, or break up into smaller products when hitting the spacecraft or Langmuir probe sensor, guard, or boom (e.g., Tomsic et al., 2000, 2003; Havnes et al., 2015; Morooka et al., 2019). In this case, an impact plasma (c.f., Sections 3.2 and 3.4) is created around the Langmuir probe by the emitted charged species from the sensor during the impact. This impact plasma in turn can be sampled by the sensor. And last, it is expected that negative ions can contribute significantly to the U-I-characteristic within Saturn’s ionosphere (e.g., Morooka et al., 2019), as has been detected in the ionosphere of Titan (e.g., Coates et al., 2007; Shebanits et al., 2013, 2016).
All these contributions have been implemented in the LP sweep model fits presented here. In summary, the following current contributions have been investigated for the observed voltage-current characteristic in this study:

* Main electron population (in an expanding sheath)

* Hot electron tail population

* Positive ion ram flow

* Negative ion ram flow

* Photoelectron emissions

* Secondary electron emissions (SEE)

* Secondary ion emissions (SIE)

* Impact plasma (creating a thermal electron-ion plasma around S/C and probe)

* Geometry of potential of combined probe + guard

* A judgement of when different boom potentials (compared to probe & guard) seem to have affected the U-I characteristic at high bias voltages.

These current contributions completely describe the observed Cassini RPWS Langmuir probe sweeps from Rev. 288–293 within the errors described in Section 2.2. The exact theoretical expressions used for these different contributions are presented in Appendix D.

## 3.2. Impact generated plasma and/or hot electron tail plasma

For Langmuir probe applications impact plasma has so far only partly been considered for impacting water (e.g., Schmidt and Arends, 1985) and impacting electrons with a few 100 eV energies (e.g., Garnier et al., 2013). The contribution of particle (molecules or aerosol/dust) impact generated plasma on the probe (or S/C) surface is illustrated in Fig. 7. The ion secondary emission current ($I_{SIE}$) to the Langmuir probe U-I-characteristic is estimated in this Section. The maximum impact generated secondary electron emission current ($I_{SEE}$) levels are derived from an indirect analysis presented in Section 3.4.

We display here four examples with model fits to the LP U-I-characteristic from Rev. 288, 290, 291, and 292 all from altitudes below 1900 km (Figs. 8, 9, 10 and 11). For the three examples during Rev. 290, 291 and 292, it is rather easy to identify a SIE component in the bottom panels of Figs. 8, 9, and 10 for $U_{bias}$ between -2 V to -0.5 V. The SIE current contribution is a very common feature in our data set, and most of these cases are at an order of magnitude lower amplitude compared to ambient electron and positive ion current contributions (as exemplified in Figs. 8, 9, and 10). Typical current levels for $I_{SIE} \approx 2 \cdot 10^{-9} - 5 \cdot 10^{-8}$ A would suggest a total yield of ejected ions due to atmospheric impacts of about $I_{SIE}/n_{atm} \sim 5 \cdot 10^{-9}$ nA/cm$^{-3}$ from the RPWS Langmuir probe. The corresponding SEE current contributions has a small impact on the estimation of ambient electrons parameters in the presented cases in

<figure><img src="image_11.png" /><figcaption>Fig. 8. Same representation as in Fig. 2. An example of a RPWS LP voltage sweep from the ionosphere of Saturn on Rev. 292. A parametric model fit of the total current (red line) follows the LP data (blue dots). The emitted ion component of the impact plasma (SIE) is best detected between -2 V and -0.5 V in the bottom panel. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

Figs. 8, 9, and 10 (see Section 3.4), and are here just set equal to $I_{SIE}$.

Note though, there is another possible process to be invoked for the interpretation of the data in Figs. 8, 9, and 10. A population of hot electrons constituting an added energetic tail to the ambient colder ionospheric electron population can also explain the observed voltage-current characteristic. Comparing the exponential expressions for SIE and a hot electron tail for $U = U_{bias} + U_{float} \le 0$ V (see further Appendix D),

$$I_{e,hot} = c_2 \exp(-U/T_{e,hot}[eV]) \quad (4)$$

and

$$I_{SIE} = C_{SIE} \exp(-U/T_{SIE}[eV]) \quad (5)$$

they are equivalent with a characteristic temperature $T_{exp} = T_{SIE} = T_{e,hot}$. The linear parts for $U > 0$ V differ, but at such low current levels in Figs. 8, 9, and 10 the linear parts don't modify significantly the ambient electron current of ~$10^{-6}$ A for $U > 0$ V. Thus, both processes may cause the exponential-like feature in the voltage-current characteristic for $U_{bias}$ between -2 V to -0.5 V. However, as shown in Fig. 24 (in Section 3.4), it is more compelling to interpret these results as due to SIE rather

<figure><img src="image_12.png" /><figcaption>Fig. 7. Cartoon of particle impact generated plasma and resulting current contributions to the LP U-I-characteristic sampling in such an environment. Particle impacts (blue) hit the probe surface, which give secondary electrons (green) and ions (red) and their corresponding current contributions in the LP U-I-characteristic (right). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>Fig. 9. Same as Fig. 8, but from Rev. 291. The emitted ion component of the impact plasma (SIE) is best detected between -2.5 V and -0.25 V in the bottom panel.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Fig. 10. Same as Fig. 8, but from Rev. 290. The deviation for U > +1 V we judge is due to a more positive spacecraft (boom) compared to Ufloat at the probe. The emitted ion component of the impact plasma (SIE) is best detected between -2 V and -0.5 V in the bottom panel.</figcaption></figure>

than a hot electron tail. The SIE response (magnitude and energy, C<sub>SIE</sub> and T<sub>SIE</sub>) depends on number and type of impact species, impact velocity and the LP surface coating.

There are eight LP sweeps sampled during Rev. 288 and three LP sweeps during Rev. 289 below an altitude of 2000 km that are certainly not in agreement with a hot electron tail interpretation. First, the sum of the derived electron number densities n<sub>e,LP,tot</sub> = n<sub>e,LP</sub> + n<sub>e,hot</sub> becomes significantly larger than n<sub>e,wave</sub> for model fits assuming a hot electron tail for these U-I-characteristic. Second, the Langmuir probe U-I-characteristic for U > 0 can no longer be fitted with a hot electron tail current contribution. One example is shown in Fig. 11. The difference for these occasions is the truly large current contributions from both SEE and SIE needed to explain the U-I-characteristic. Here I<sub>SEE</sub> ≈ I<sub>SIE</sub> ≈ 10<sup>-6</sup> A is required, and the constant value of I<sub>SIE</sub> for U > 0 V is needed to fit the U-I-characteristic and still keep n<sub>e,LP</sub> ≈ n<sub>e,waves</sub> for the main electron

<figure><img src="image_15.png" /><figcaption>Fig. 11. Same representation as in Fig. 2. An example of a RPWS LP voltage sweep from the ionosphere of Saturn on Rev. 288. A parametric model fit of the total current (red line) follows the LP data (blue dots) and is set here an equal number of emitted electrons and positively charged ions of about 1 µA from the probe due to impacts. The SEE temperature of emitted electrons is here assumed to be 2 eV. This value can be degenerated with the form factor, i.e., larger SEE temperature can be trade-off with a larger β (not shown). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

component. A corresponding hot electron population could not achieve a good fit for U > 0 V. The sweep in Fig. 11 is therefore only consistent with a significant impact plasma contribution. We therefore believe that most of the low altitude cases can be due to impact plasma secondary ions rather than hot electron tails (and this conservative interpretation is adopted in Section 3.3 below). Also, collisions between electrons and neutrals for the lower altitude range would limit the formation of hot electron tail distributions.

### 3.3. RPWS Electron temperatures below 4000 km

The electron temperatures (T<sub>e</sub>) and the hot electron tail temperatures (T<sub>e,hot</sub>) are derived from the RPWS LP sweep data from the exponential parts near U ≈ 0 V. Two examples, one from the topside ionosphere on Rev. 291 with an additional hot electron tail (Fig. 12), and another from the deeper ionosphere on Rev. 290 (Fig. 13), illustrate these estimates. In this Section (only) we have deliberately avoided LP sweep data with exponential SIE current contribution (see Section 3.2) detected below 2500 km altitude. The quality of the model fits shown in Figs. 12 and 13, which are good representations for most of the observed LP sweep data, give confidence in the presented electron temperatures. The altitude profiles of the LP sweep derived electron temperatures are presented in Figs. 14 and 15 for inbound and outbound data. Fig. 14 shows one flyby (Rev 291), while Fig. 15 superposes all flybys. See also Section 4.

One prominent feature is the increasing electron temperatures toward larger altitudes above about 2500 km, where also several cases of hot electron tail populations are detected. A possible reason is the electron heat conduction from the magnetosphere above. If we neglect viscous heating and chemical reactions, the resulting electron energy equation can be written (e.g., Schunk and Walker, 1970; Forme et al., 1993) as

$$ \frac{3}{2} k_B \frac{\partial T_e}{\partial t} + n_e k_B T_e \nabla \cdot \mathbf{V}_{d,e} + \frac{3}{2} n_e k_B \mathbf{V}_{d,e} \cdot \nabla T_e = - \nabla \cdot \mathbf{q}_e + \sum Q_e - \sum L_e \quad (6) $$

where temporal variation, adiabatic expansion and advection terms are
Cassini LP 2017.09.02 13:03:09.43 UT, 3272.5 km

<figure><img src="image_16.png" /><figcaption>Fig. 12. Same representation as in Fig. 2. An example of a RPWS LP voltage sweep from the topside ionosphere of Saturn on Rev. 291. A parametric model fit of the total current (red line) follows the LP data (blue dots). The main thermal electron sampling (green line in panels a and b) gives a good exponential fit and an inferred $T_e = 0.15$ eV, best seen in panels a and b near -0.25 V. A hot electron population (dashed green in panels a and b, dashed red in panel c) with a temperature of 0.8 eV is best detected in panel c between -2 V to -0.5 V. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

Cassini LP 2017.08.27 02:16:01.03 UT, 1655.5 km

<figure><img src="image_17.png" /><figcaption>Fig. 13. Same representation as in Fig. 2. An example of a RPWS LP voltage sweep from the topside ionosphere of Saturn on Rev. 290. A parametric model fit of the total current (red line) follows the LP data (blue dots). The main thermal electron sampling (green line in panels a and b) gives a good exponential fit with $T_e = 0.24$ eV most sensitive from -1.25 V to 0 V. No SIE current contribution was indicated in this U-I-characteristic. The measured "wave" feature between +0.75 V to +2.25 V will be described and reported elsewhere. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

on the left-hand side, while heat conduction and sums of heating and cooling rates are on the right-hand side. The Cassini MAG estimated intra D-ring field-aligned current densities to vary between 1 and 4 nA/m² (e.g., Dougherty et al., 2018; Agiwal et al., 2024). The heat flow vector $q_e = -\beta_e \hat{j} - K_e \nabla T_e$, for small field-aligned currents and small electron-neutral collisions in the topside ionosphere therefore reduces to

heat conduction parallel to the magnetic field lines as (Rees, 1989)

$$q_e \approx K_e \nabla T_e \approx -5/2 (k_B^2 T_e n_e / m_e L_{ei}) \nabla T_e \quad (7)$$

Thus, in the absence of any heating sources except hotter electrons in the magnetosphere,

$$\frac{\partial T_e}{\partial t} - \frac{2}{3} \frac{1}{C} \frac{\partial}{\partial z} \left( C K_e \frac{\partial T_e}{\partial z} \right) = Q_e \quad (8)$$

where z is along the field line, and the electron heat conduction from the magnetosphere above the topside ionosphere should dominate. Below about 2500 km, electron collisions with neutrals are important for the electron temperature decrease as $v_{en} = \frac{8}{3} n_{H_2} \sqrt{2k_B T_e / \pi m_e \sigma_{H_2}} > 1-1000 \text{ s}^{-1}$ (Schunk and Nagy, 2009). The electron heat conduction and resulting topside ionosphere altitude profiles in Saturn's ionosphere have been modelled by Sakai and Watanabe (2016). Their Fig. 5 is in qualitative agreement with our data above 2500 km altitude, although our presented data shows greater variability between the different flybys. Also, near the equatorial region the magnetic field is expected to be near horizontal and electron heat conduction to lower regions is limited.

The absence of significant electron collisions above 2500 km allows the formation of non-Maxwellian hot electron tails, which is occasionally inferred from RPWS LP sweep data (e.g., Fig. 12). Plasmasphere/ionosphere electron heating in the equatorial region is well known from Earth (e.g., Su et al., 1995; Abe et al., 1997; Khazanov et al., 2023), and similar processes are likely active at Saturn. The relation between electron density and electron temperature follows a polytropic relation, $T_e \propto n_e^{-1}$, with $\gamma \approx 0.5$, like in the ionosphere of Titan (Edberg et al., 2010). The anti-corelation suggest the electron plasma in the topside ionosphere is not expanding adiabatically and that available energy in the electron population is simply shared among the available electrons as the altitude increases.

The main ionospheric electron temperature data in Figs. 14 and 15 below 2500 km show a trend that increases with decreasing altitude, from 900 to 1200 K at 2500 km to 1700-4000 K at the lowest measured altitudes. The trend is visible for inbound and outbound cases. Morooka et al. (2019) reported this electron temperature increase, and we therefore included their results in Figs. 14 and 15, believing that our refined results including impact plasma current contributions to the RPWS LP sweep analysis would lower the inferred electron temperatures. However, the results of Morooka et al. (2019) are instead largely confirmed, within the errors, by our refined analysis. Also note the distribution of the main ionosphere electron population is based on a model fit of the U-I-characteristic that is constrained by $n_{e,LP} \approx n_{e,waves}$ for this main electron component. It is therefore the main ionospheric (near Maxwellian) electron distribution that is associated with the inferred high electron temperatures below 2500 km. We have looked for possible interpretation error between $T_e$ estimates as compared with an effect of an exponential component in the U-I-characteristic generated by secondary ions (SIE) but have not found an obvious relation.

A latitude distribution of the electron temperatures from all studied orbits is presented in Fig. 16. The low altitude (closest approach) electron temperatures show an increase for Rev. 288-292 near -6° LAT. The Rev. 293 low altitudes (closest approach) occur at +9° LAT. It is therefore notable that Rev. 293 show only temperatures near 1200 K except for the 1550 km sample which is near 2000 K (see Fig. 25).

The increase of the electron temperature below ~2500 km is difficult to understand, as more collisions with neutrals should occur in the denser atmosphere, and where not only elastic collision terms, but also in-elastic rotational and vibrational molecular energy loss terms become increasingly important at lower altitudes. For this part of the ionosphere the transport terms are negligible, and the electron energy equation in near equilibrium takes the form

$$\frac{3}{2} k_B \frac{\partial T_e}{\partial t} = \sum Q_e - \sum L_e \approx 0 \quad (9)$$
<figure><img src="image_18.png" /><figcaption>**Fig. 14.** The RPWS LP sweep derived electron temperatures from Rev. 291 (blue stars), from the study by Morooka et al., 2019 (red stars) and hot electron tail (green stars, this study). Inbound data (left panel) and outbound data (right panel). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>**Fig. 15.** The RPWS LP sweep derived electron temperatures from this study (blue stars), from the study by Morooka et al., 2019 (red stars) and hot electron tail (green stars, this study). Inbound data (left panel) and outbound data (right panel). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

where the cooling terms for electrons ($L_e$) in Saturn's thermosphere will be dominated by inelastic rotational and vibrational cooling with H$_2$ (Waite and Cravens, 1981) and to a lesser extent with rotational and vibrational cooling of H$_2$O (Cravens and Korosmezey, 1986) depending on the availability of water vapour and other organic molecular species.

For mid-latitudes in Earth's ionosphere there exist an electron temperature increase by about 1000 K toward lower altitudes just below the ionospheric F2-peak (e.g., Schunk and Nagy, 1978, their Fig. 10a; Hysell et al., 2015, their Fig. 8) measured by incoherent scatter radar facilities (Jicamarca and Arecibo). The electron heating rates amounts to $10^3-10^4$ eV/cm$^3$/s and is mainly due to photoelectrons but is also modified by electric fields and neutral winds (e.g., Varney et al., 2011). At Saturn the photo-electron production is a factor 100 lower than at Earth, and the peak photoelectron production is expected to be at 1500 km and amount to a few cm$^{-3}$ s$^{-1}$ (Moses and Bass, 2000; Chadney et al., 2022). This electron heating mechanism need be investigated to explain the electron temperatures presented here since there are much

fewer photo-electrons produced at Saturn as compared to Earth.

Morooka et al. (2019) attributed the large electron temperatures to the dusty plasma state of the ionosphere. Assuming the above electron energy cooling rates, 1–1000 eV/cm$^{-3}$/s heat input is needed for altitudes 1400–2500 km to explain the presented electron temperatures (Poizat, 2020). This number would require an equivalent large-scale convection electric field of 170 mV/m of Joule heating to explain the observed electron temperatures. Such electric field strengths have been observed in the Earth's auroral ionosphere region (e.g., Schlegel and St. Maurice, 1981; St-Maurice and Goodwin, 2021) and are known to excite intense wave heating by the Farley-Buneman instability at much lower electric field values (Buneman, 1963; Farley, 1963). The Farley-Buneman instability develops when there is an ionosphere drift through the atmosphere, as has been detected in the auroral E-region ionosphere at Earth (e.g., Schlegel and St. Maurice, 1981; Buchert et al., 2006, 2008; Liu et al., 2016), but also as part of the equatorial electrojet near the equator of Earth (e.g., Sudan, 1983; Pfaff et al., 1987). Of interest here is that Farley-Buneman instabilities can be created in the
<figure><img src="image_20.png" /></figure>

**Fig. 16.** Distribution in latitude of the RPWS LP sweep derived electron temperatures (blue stars), and hot electron tail (green stars). Closest approach occurs near -6° LAT except for Rev. 293 where it occurs near +9° LAT (compare with Fig. A1). A clear $T_e$ increase occurs near closest approach for Rev. 288–292, which is absent for the plunge (Rev 293, compare Fig. 25). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

presence of charged dust (e.g., Rosenberg and Chow, 1998), where the critical drift for the instability can decrease with increased charge density of the negatively charged dust. Polar dust layers in the D-region ionosphere at Earth (e.g., Rapp and Lübken, 2004) are often associated with highly turbulent plasma. A possible mechanism could therefore be electron heating by plasma inhomogeneities, caused by charged dust concentrations (Farrell et al., 2017) and convection electric fields driven by atmosphere dynamos (Khurana et al., 2018; Buchert, 2020).

We conclude that the enhanced electron temperatures below an altitude of 2500 km remains difficult to explain, and we do not see how the LP U-I-characteristic can be interpreted with a lower electron temperature for the main ionosphere dayside equatorial population at Saturn. The electron energetics of dust-plasma layers with an applied electric field need to be clarified in the future.

### 3.4. Large LP ion current & SEE current <2500 km altitude

A comparison between the altitude profiles of the derived RPWS electron number density and the derived positive ion number density reveals an apparent excess of positive ions below 2500 km. An example for the Rev. 288 inbound is given in Fig. 17 (notably the most extreme case), where an order of magnitude enhancement is detected in the positive ion number density compared to the electron number density.

This has been interpreted as a region where negative ions or negatively charged aerosol/dust grains exist and so account for the missing negative charge to meet quasi-neutrality (Morooka et al., 2019). Possible support of this view would be the substantial mass flux of D-ring dust grains and organics toward the equatorial ionosphere of several tons/s as observed by other instruments (e.g., Hsu et al., 2018; Waite et al., 2018; Perry et al., 2018), become negatively charged at comparably short ionospheric time scales (minutes up to an hour), and add to the ionosphere charge balance. However, this view has been questioned and Johansson et al. (2022) proposed that impacting atmospheric molecules (primarily water) produce secondary electron emissions (SEE) from the probe surface and account for the large apparent ion current contribution to the probe. The large spacecraft speed (34 km/s) through the atmosphere and the corresponding large ram energy of water (~100 eV) makes this scenario viable.

<figure><img src="image_21.png" /></figure>

**Fig. 17.** Derived RPWS electron and positive ion number density from Rev. 288 inbound Cassini flyby. Below 2500 km altitude the positive ion number densities becomes larger by an order of magnitude compared to the electron number densities. Assuming $V_{SC} = 34$ km/s and ion speed $V_i = V_{SC}$. Deviations from $n_e \approx n_i$ is detected in the two uppermost data points (near 3450 km and 3750 km), which can be due to $V_i \neq V_{SC}$ in this transport dominated part of the ionosphere.

We have therefore investigated both single sweeps for these effects (one example in Fig. 18), as well as the altitude/latitude profile characteristic for all data where a variation with the neutral atmosphere number density can be considered. We find that from different model fits to one LP sweep U-I-characteristic alone it is not usually possible to distinguish between a positive ion ram flow contribution and a SEE contribution. We use instead the observational variations (context) during a flyby (see below) and then check if the found maximum levels of $I_{SEE}$ are possible to fit the full observed LP sweep U-I-characteristic.

<figure><img src="image_22.png" /></figure>

**Fig. 18.** Same RPWS LP sweep as in Fig. 5. The model fit to the data includes here 50 % SEE with a temperature of 2 eV (black line) mitigating the positive ion ram current contribution (magenta line), but still giving a good total fit to the observed U-I-characteristic (red line). Thus, the derived ion ram current can partly be due to SEE, since these currents are usually much smaller than the electron current contributions for $U > 0$ V. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
For a specific LP sweep U-I-characteristic, the positive ion ram flow
contribution (magenta in Fig. 18) is derived from the slope (b) and dc
current level (m) of the leftmost part of the LP sweep U-I-characteristic
(see eq. 3, see also Appendix C regarding the fit procedure). For ±4 V
sweeps this corresponds to the sweep samples for U < -3 V. However,
both SEE and heavy negatively charged ions/dust could also affect the
observed current for U < -3 V. A negatively charged heavy ion/dust
component would have an exponentially varying contribution at these
bias voltages. However, the exponential contribution is too small to be
detectable due to the large speed (≈ 34 km/s) and large mass of these
negative particles, and these will give only a measurable dc-level
contribution to the U-I-characteristic. The sweep presented in Fig. 18
(bottom panel) shows a linear response for U < -3 V. Electrons emitted
from the probe by SEE give a constant (dc current level) contribution to
the U-I-characteristic for these bias voltages. When comparing different
flybys, there is no clear systematic difference in slope (b) values (as
expected, not shown). On the other hand, there are differences in dc-
levels (m) between different flybys below 2500 km. Thus, we will
investigate this closer below.

The SEE current contribution in the sweep U-I-characteristic can be postulated to be proportional to the atmospheric number density, i.e., $I_{SEE} = C \cdot n_{atm}$, where C is a constant and $n_{atm}$ is assumed to follow the $H_2$ number density, and there should be a clear increase of the m-values at lower altitudes. This is only true if a reasonably stable composition fraction (of the species contributing a SEE yield in the LP U-I-characteristic) exists in the atmosphere during the flyby. This turns out to be the case for Rev. 291, 292 and 293 (see Figs. 19 and 20). In Fig. 19, we display the m-values divided by the corresponding atmospheric $H_2$ number density (from INMS) versus geographic latitude, and in Fig. 20 we display the variation of the m-values with altitude for Rev. 291, 292 and 293. An increase of the m-values at lower altitudes is observed (Fig. 20), and a value of $C \approx 2 \cdot 10^{-8} \text{ nA/cm}^{-3}$ in total LP SEE yield is compliant with the data for Rev. 291, 292 and 293 (black, green, and magenta in Fig. 19). This “base value” cannot be increased further for these Revs without resulting in non-physical $n_i < n_e$ because of charge neutrality reasons. The value of $C \approx 2 \cdot 10^{-8} \text{ nA/cm}^{-3}$ is therefore a maximum SEE yield for Rev. 291, 292 and 293. Larger values of C and

<figure><img src="image_23.png" /></figure>

**Fig. 19.** The dc current value (m) of the U-I-characteristic divided by the atmospheric $H_2$ number density as a function of geographic latitude. All available data below 2500 km altitude from Rev. 288–293. A duplicate of Rev. 293 has been added shifted –7.5° (also magenta). Rev. 291, 292 and 293 display a common m/n($H_2$) base level, while Rev. 288, 289 and 290 display an enhancement above this base level in the latitude range – 11° to 8°. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

related $I_{SEE}$ also do not give valid full model fits to the observed LP
sweep U-I-characteristic (example in Fig. 21).

The corresponding data for Rev. 288, 289 and 290 do not follow this
simple relation and is instead enhanced by up to a factor 8 compared the
other Revs (Fig. 22). Here we instead use $I_{SEE} = k_{enh}C \cdot n_{atm}$, where $k_{enh}$ is
the latitude dependent enhancement factor for Rev. 288, 289 and 290.
For Rev. 291, 292 and 293, $k_{enh} = 1$. In this way we attain a maximum
current contribution from SEE for the whole dataset and still comply
with the $n_i < n_e$ requirement. For Rev. 288, 289 and 290 a minor atmospheric species (e.g., additional water) increases the $I_{SEE}$ above the
normal atmospheric induced SEE and this increase is latitude dependent.
An enhancement factor of up to 8 in this minor species number density is
required from our analysis, which would require a corresponding variability in atmospheric composition. Thus, a reduction in, e.g., the ring
material influx of SEE yield-contributing species over the period between the proximal orbits (~ week) could possibly explain these findings, as the base level steadily declines from 288 to 290 and then
remains stable for 291–293. However, INMS observations indicate the
largest influx of ring material occurs during Rev. 291 while Rev. 288 has
a lower influx (Miller et al., 2019; Serigano et al., 2022) and so contest
this conclusion. Alternatively, local chemistry (including dust) changes
of SEE yield-contributing species in the atmosphere over the same
period could also be an explanation for the observations. It is worth
noting that factors of several orders of magnitude variation are observed
flyby to flyby by INMS in volatiles inflowing from the rings that include
both water, methane, and carbon dioxide over this same period from
Rev. 288 to Rev. 293 indicating a complex and highly variable neutral
and ion environment (Waite and Cravens, 1981 online supplement).

Using this relationship for $I_{SEE}$, and using a modified $I_{i,eff} = I_i - I_{SEE}$,
for the modified positive ion current, result in altitude profiles that occasionally give cases complying with $n_e \approx n_i$, and in those cases no extra
negative ions/aerosols are required for quasi-neutrality. An example is
given in Fig. 23 from Rev. 291 outbound, where $n_e \approx n_i$ in the altitude
interval 2200–1800 km, which also confirms that our analysis approach
is reasonably valid. The cases below 2500 km, where $n_i > n_e$, should
then correspond to a real positive ion density increase and indirectly
infer a negatively charged ion or aerosol species being present to comply
with quasi-neutrality (as per Morooka et al., 2019). For Rev. 291
outbound (Fig. 23) a negatively charged species with a number density
of up to 3000–4000 cm$^{-3}$ would be inferred below an altitude of 1800
km. A maximum SEE contribution derived here cannot fully explain the
observed discrepancy between the electron number densities and the
apparently larger positive charged ion number densities inferred by the
LP sweeps for any of the flybys presented here (see Section 4.1). We
therefore conclude that a negatively charged heavy ion or dust/aerosol
component exists in Saturn’s ionosphere.

We sum up our derived currents for impact generated SIE and SEE for all six flybys (Rev 288, 289, 290, 291, 292 and 293) in Fig. 24. For most of the cases the $I_{SIE}$ is an order of magnitude less than $I_{SEE}$, i.e., $I_{SEE} \approx 10$ $I_{SIE}$. This agrees with Cassini spacecraft environment simulations including secondaries (Zhang et al., 2023). Only in a few exceptionally large current contribution cases $I_{SEE}$ can be estimated directly from the LP sweeps. For those few exceptional cases we find a roughly equal number of ejected electrons and ions from the probe surface, i.e., $I_{SIE} \approx I_{SEE}$, is required to maintain an overall quasi-neutral generated plasma. This must be true for cases when $I_{SIE}$ and $I_{SEE}$ dominate the contributions to the LP current as return currents are limited, and where otherwise a large Coulomb electric potential would build up in the Debye sheet near the sensor. In the few cases where $I_{SIE} \approx I_{SEE}$ the LP U-I-characteristic for $U_{bias} < -3$ V is not linear and show an exponential contribution. The resulting inferred ion current is therefore very uncertain in these cases and are indicated so in Section 4.
<figure><img src="image_24.png" /><figcaption>**Fig. 20.** The m-values (stars, black is inbound, red is outbound) as a function of altitude for Rev. 291, 292 and 293. The corresponding SEE current based on $I_{SEE} = 2 \cdot 10^{-8} \text{ n(H}_2\text{)}$ is superposed as a black and red line. The fitted $I_{SIE}$ values are circles. The change in slope of the data below about 2500 km toward a similar slope as the atmospheric number density is indicative that these are influenced by a SEE contribution. $I_{max,SEE}$ is about an order of magnitude larger than $I_{SIE}$. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

# 4. Saturn ionosphere results from RPWS & INMS (rev 288–293)

## 4.1. Number densities and electron temperatures below 4000 km

The final output of RPWS derived electron and ion number density altitude profiles are presented in Figs. 25 and 26 below and constitute an in-situ observational record of the dayside equatorial ionosphere of Saturn. The INMS instrument was operated in an ion sampling mode during Rev. 288 and Rev. 292, and we compare the INMS total ion, $H^+$ and $H_3^+$ number density altitude profiles with densities derived from the RPWS measurements. The inbound and outbound profiles are compared separately to gain information on the variations between the flybys but also separate the latitudinal dependency that exist between inbound and outbound profiles. The time between flybys is 6–7 days, and the duration of a flyby (inbound + outbound) below 4000 km is around 20 min and covers a latitude range of about 20° (see Appendix A, Fig. A1).

Several general observational features are worth pointing out based on Figs. 25 and 26. In the cases where there are INMS data are available (Rev 288 and 292) there is a very good match between the total positively charged ion number density by INMS (and RPWS) and the RPWS electron number density above an altitude of 2300 km (outbound) and 2500 km (inbound). The calibrations of both instruments (and their individual sensors) are therefore believed to be accurate and give simultaneously consistent results, considering the systematic dependence of $\sqrt{T_e}$ and $U_{SC}$ on the RPWS/LP fixed bias sampled electron

density ($\delta n_e$, c.f., Appendix B).

The time scales of ionosphere transport and chemistry can be estimated from the continuity equation $\partial n/\partial t + \nabla(nv) = \sum q - \sum l$, and can be compared with the behaviour of the observed number density profiles in Figs. 25 and 26. The boundary between transport-controlled and chemistry-controlled regions occurs roughly when the number densities reach around $1000 \text{ cm}^{-3}$. The transition between chemistry- and transport-controlled regions occurs where the respective timescales for chemical and transport ion loss processes are equal. Observationally this is the region with transitions from $H_3^+/\text{heavy ions}$ dominance to $H^+/\text{dominance (knowing that the chemical timescale for } H^+\text{ radiative recombination is much longer than for } H_3^+\text{)},$ but also where the electron temperatures increase toward larger altitudes and the electron number densities show sharp gradients. However, all these observations are only indicative for this boundary. Using the modelled diffusive transport timescale profiles from Moore et al. (2018) and recombination rates from, e.g., Moore et al. (2018) or Dreyer et al. (2022) to insert into the relation $\tau_{rec} \sim 1/\alpha n_e$ yields a transition for $H_3^+$ ions at densities of around $1000 \text{ cm}^{-3}$ where recombination is the dominant loss process, corresponding to ~2500 km altitude. Typical recombination time scales ($\tau_{rec} \sim 1/\alpha n_e$), using published recombination rates (e.g., Moore et al., 2018; Vigren et al., 2022) near this boundary are few hours (for $H_3^+$), but depend on ion species and electron temperatures involved. This means that the region below will reach chemical equilibrium on a time scale an order of magnitude larger than a flyby time span. If chemical
<figure><img src="image_25.png" /></figure>

Fig. 21. Example of a failed fit using a larger yield, $C = 3 \cdot 10^{-8}$ nA/cm$^{-3}$, causing the ion current (magenta) to become positive. $C = 2 \cdot 10^{-8}$ nA/cm$^{-3}$ therefore represent a max value. The failure is due to that the model fit result of the ion ram current becomes positive (unphysical). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

<figure><img src="image_26.png" /></figure>

Fig. 22. The enhancement factors of Rev. 288, 289 and 290 below 2500 km as compared to the m/n_atm base level for Rev. 291, 292 and 293. The plot demonstrates the decrease in SEE yield producing species composition in the atmosphere from Rev. 288 to Rev. 291, possibly caused by a change in the ring material influx rate over several weeks' time (or a local atmospheric composition variation).

equilibrium exists, smooth altitude profiles with stable scale heights should be the case (between flybys). This is not observed, and we conclude that the observed altitude profiles point toward an ionosphere that is not in photo-chemical equilibrium.

Large variations are detected between flybys in both the total plasma number densities and electron temperatures for the whole altitude range studied. For the higher altitude range above about 2300–2500 km, the variable plasma densities suggest a large variation in the transport/plasma drift there (also noted by Wahlund et al., 2017; Hadid et al., 2019). The infalling particles is expected to attain speeds of several km/s at 2500 km (Mitchell et al., 2018; their Fig. 4). Intensive (free falling

<figure><img src="image_27.png" /></figure>

Fig. 23. Derived electron and ion number density altitude profiles from Rev. 291 outbound. Electron number densities from plasma wave data ($n_{e,waves}$, black stars), LP sweeps ($n_{e,LP}$, blue stars), hot electron tail (green star), 1 sample per second with fixed bias voltage ($\delta n_e$, cyan line, $T_e$ and $U_{float}$ dependent). Positive ion number density ($n_i$) without SEE atmospheric correction (magenta) and with SEE correction (red). With a SEE atmospheric correction, the positive ion density agrees with the estimated electron density in the altitude region 2200–1800 km. The discrepancy at lower altitudes indirectly suggests the presence of a negatively charged species with a number density of 3000–4000 cm$^{-3}$. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

<figure><img src="image_28.png" /></figure>

Fig. 24. The measured $I_{SIE}$ (circles) and maximum estimated $I_{SEE}$ currents (stars) to/from the Langmuir probe for all data used in this study. During low sampled current conditions $I_{SEE} \approx 10$ $I_{SIE}$, while for very large secondary emission currents $I_{SEE} \approx I_{SIE}$.

energy and partly charged) influxes across near horizontal field lines induce strong time variable electric fields across these field-lines, affecting the ambient ionosphere plasma there, and therefore should drive the transport significantly. Field-aligned plasma transport along the flux tubes is also expected. The dynamical variations are faster than chemistry temporal scales at these and higher altitudes. The change in scales is more than a factor 2 difference in certain altitude ranges between flybys (e.g., Rev. 292 outbound between 2500 and 3000 km give an apparent scale height of slightly more than 200 km, while the same
<figure><img src="image_29.png" /><figcaption>**Fig. 25.** Saturn ionosphere inbound altitude profiles. Electron number density derived from RPWS plasma waves (black stars), RPWS LP sweeps (blue stars), RPWS LP sweep hot electron (green stars) and RPWS LP δnₑ (cyan line, may have a systematic dependence on 1/√Tₑ and Ufloat). INMS total ion (red line), INMS H⁺ (green dots), and INMS H₃⁺ (red dots) number density (Rev 288 and 292). RPWS total positive ion number density assuming no SEE (magenta stars) and max SEE (red stars). The red parentheses indicate that an exponential contribution exists in the LP U-I-characteristic for Ubias < -3 V and indicate maximum ion densities. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
<figure><img src="image_30.png" /><figcaption>Fig. 25. (continued).</figcaption></figure>

altitude interval on Rev. 288 outbound gives an apparent scale height of around 450 km, and $T_e \approx 900$ K in both cases). These observed changes may as well represent latitudinal and/or temporal changes. The magnetic field is dominated by the dipole field of Saturn, slightly shifted northward compared to the equator (Dougherty et al., 2018) and is

almost horizontal for the observed cases presented here. A convection electric field ($E_\perp$) can transport plasma perpendicular to the local magnetic field according to $V_\perp = (E_\perp \times B)/B^2$. The convection electric field can in this case be generated in the lower ionosphere north or south of the equatorial region, for instance by an atmospheric dynamo process
<figure><img src="image_31.png" /><figcaption>Fig. 26. Saturn ionosphere outbound altitude profiles. Same parameters as in Fig. 25.</figcaption></figure>

driven by neutral winds through the ionosphere (e.g., Khurana et al., 2018). Another possible source is the generated electric field by the charged D-ring material falling into and across magnetic field lines in the equatorial ionosphere and giving rise to an electric field ($E_d = -V_d \times$

B). With an infall speed of 1 km/s over 21 µT this gives ~20 mV/m generated in the topside ionosphere. Our observations presented here cannot distinguish between the processes. A dc electric field instrument would be needed for this.
<figure><img src="image_32.png" /><figcaption>Fig. 26. (continued).</figcaption></figure>

The lower altitude ionosphere, is expected to be controlled by chemistry, displays a complex and variable structure during the flybys. There exists a general increase of the electron number density (black and blue stars in Figs. 25 and 26) toward lower altitudes during all flybys, but there is no clear observation that the main ionospheric peak has been detected down to the lowest probed altitude (1450 km). The same statement is true when considering the RPWS positive ion number density altitude profiles (red stars in Figs. 25 and 26, corrected for SEE). The dominant ionization process is expected to be photoionization by solar EUV radiation and the observed altitude profiles presented here can be used to test this. The main ionosphere peak should then exist below or at the lowest observed regions, which is broadly in line with model results, e.g., Moses et al. (2023) and Moore et al. (2018).

The topside ionosphere, from the INMS data on Rev. 288 and Rev. 292, is dominated by $H^+$ ions above 2200 km (outbound) and 2800 km (inbound), while $n(H_3^+)$ is larger than $n(H^+)$ in an altitude band from 2200 to 2800 km (inbound). In the ionosphere below an altitude of 2200 km heavier ions with mass numbers more than 8 amu (INMS

measurement limit) must dominate when comparing with RPWS electron or ion number density profiles during Rev. 288 and 292. Large compositional variations are detected below 3000 km when comparing the Rev. 288 and Rev. 292 flybys, also detected between inbound and outbound parts of the flybys. The $H^+$ to $H_3^+$ crossover varies between 2000 and 3000 km, and the dominance of heavier ions (from comparing INMS and RPWS data sets) occurs below about 2200 km and the large variations in $H^+$ and $H_3^+$ in this lower part indicate large variations in the heavy ion chemistry (see more details in Section 4.2). The difference between inbound and outbound for a specific Rev. is related to a north-south latitude effect due to the high inclination polar orbit of Cassini and is in turn, at least partly, related to the latitude asymmetry of infalling D-ring material (e.g., Mitchell et al., 2018; Hsu et al., 2018), and associated effects on the ionospheric chemistry (Waite et al., 2018; Morooka et al., 2019).

The detailed structure of the electron number density is observed to locally decrease by a few 1000 cm$^{-3}$ below 2500 km during outbound Rev. 288, 289 and 291, and inbound Rev. 289 and 290. There is no
obvious reason why the electron number density should show sharp
drops, local maxima and layered features. Ring shadowing occurs for
mostly at larger altitudes or affect smaller scales (Hadid et al., 2018;
Dreyer et al., 2022). Instead, these local features in electron number
densities seem associated with a steady increase of the positive ion
number density, as if the electrons were removed by some process. An
exception is found partly during outbound flybys of Rev. 291 and 292. A
quasi-neutral plasma must exist and will be enforced by strong Coulomb
forces, and the apparent difference in positive ion number density and
electron number density therefore implies the presence of negatively
charged ions/aerosol (as suggested by Morooka et al., 2019), such that
$\sum q_i n_i = en_e + \sum q_i n_i^-$. The electron number density drops are there-
fore due to layers of either large amounts of negatively charged ion
species or singly or multiple negatively charged aerosol/dust grains,
very much like the case for the ionosphere of Titan (e.g., Coates et al.,
2007; Shebanits et al., 2013, 2016).

Figs. 25 and 26 reveal a layered structure of Saturn’s ionosphere below 2500 km that varies on time scales between flybys (~ week) but shows large variations also during a single flyby (minutes). The long-term variations between flybys (both inbound and outbound) show a general decreasing density trend of the inferred negative charged species from Rev. 288 through 293 suggesting a long-term variability of the infalling dust grains from the D-ring. This trend is detected in the chemistry-controlled lower altitude range in the equatorial region around 5°S LAT, while Rev. 293 (inbound) at a somewhat larger latitude (10°N LAT, compare with Fig. A1) does not follow this trend. The Rev. 293 case could therefore be a latitudinal variation rather than temporal. Since the measurements are from one spacecraft passing through similar latitudes and altitudes during all flybys (except Rev. 293) we cannot fully distinguish between a latitudinal and/or an altitude variation, nor a temporal variation. Cassini radio occultation data inferred an electron density decrease near the equator as a latitudinal effect (Kliore et al., 2014; their Fig. 2), and it is suggestive from the observations presented here to explain this as the effect of negatively charged grains produced by infalling D-ring material and subsequent ion-molecule-aerosol chemistry. Kliore et al. (2014) explained this as a result of ion-neutral photochemistry driven by the ring influxes peaking at the equator. Further studies are needed to distinguish the cause of this electron density decrease near the equator. Rings could therefore have a substantial effect on planetary atmosphere chemistry.

Even more fine structured electron number density features can be
detected in the δnₑ data (cyan line in Figs. 25 and 26), with scale changes
even less than 50 km (c.f., Section 4.2), suggesting further that the
ionosphere is in a state of disequilibrium and continuous evolution. We

suggest the small-scale structures for a specific altitude profile repre-
sents layers in altitude (evolving in time), while general differences
between inbound and outbound profiles mainly represent latitudinal
differences (also evolving in time).

## 4.2. Comparison with INMS and RPWS altitude profiles (rev 288 & 292) below 2500 km

A more detailed comparison between the RPWS and INMS number
density altitude profiles can be made for Rev. 288 and 292 for the lower
chemistry-controlled region (Figs. 27 and 28). When comparing the
INMS H⁺, H₃⁺ and RPWS electron number densities below 2100 km there
are large variations occurring on altitude scales (layers) from less than
50 km to several 100 km thickness. We would like to stress here that the
Cassini spacecraft move mostly in a horizontal direction, so the varia-
tions can in principle also be due to latitudinal or even temporal
changes. The H⁺ and electron number densities increase together while
at the same place/time the H₃⁺ number density decreases, and vice versa.
Saturn’s layered ionosphere structure can be attributed to differences in
ion chemistry, e.g., driven by two competing chemical processes (as
suggested by Vigren et al., 2022), and/or a variability in infalling ring
material flux and composition, and/or a layering of aerosol/dust layers,
and/or due to gravity waves in the background thermosphere. The large
variations in ion-molecule chemistry are difficult to identify on the scale
of a few tens of km in altitude to explain the changes in the H⁺/H₃⁺-ratio.
The small layered structures with different H⁺/H₃⁺-ratio on Rev. 288 and
Rev. 292 are clearly very different and have changed completely be-
tween the flybys for both inbound and outbound, and the H⁺/H₃⁺-ratio
has even changed dramatically on a larger scale in the topside iono-
sphere. An externally driven time-variable process is implied. For
example, the sudden drop in H₃⁺ around 1870 km in Fig. 27 could be due
to an abrupt increase in R-type heavies (see Vigren et al., 2022; which in
turn could be due to a latitudinal variation in ring influx composition).
But why would H⁺ (and He⁺, not shown) show an increase in this re-
gion? Less M-type species in this region could partially explain this, but
R-type species also react with He⁺ (Dreyer et al., 2023). So He⁺ should
decrease there, not increase. We conclude that a chemistry scheme
involving charged aerosol and negative ion chemistry should be
investigated.

Considering an electron temperature of 0.1 eV (see Section 3.3),
assuming Tᵢ < < Tₑ, and average ion masses of ≈ 20 amu, gives a
theoretical value of the ionosphere scale height (H = kₑTₑ/mᵢg) of
around 100 km if ambipolar diffusion restricts the layer sizes, thus in
rough agreement with many of the observed layered structures.

<figure><img src="image_33.png" /><figcaption>**Fig. 27.** A zoom in altitude of the Rev 288 and 292 inbound number densities. Same parameters as in Fig. 25.</figcaption></figure>
<figure><img src="image_34.png" /><figcaption>Fig. 28. A zoom in altitude of the Rev 288 and 292 outbound number densities. Same parameters as in Fig. 25.</figcaption></figure>

However, examples of even smaller structures can clearly be detected in all four altitude composition profiles in Figs. 27 and 28 below 2100 km. This is challenging to explain, unless sporadic-E type or noctilucent cloud processes involving charged dust, known from Earth, are invoked.

We suggest instead that localized layers of negatively nm-sized charged aerosol/dust, formed by continuous processing of infalling material from the D-ring, are responsible for these structured layers with highly variable resulting composition. The infalling ring dust partly ablates, sublimates, and deposits energy and mass at 1500–1900 km altitude above the 1-bar level (Hamil et al., 2018). The fragments from this material react further with the local ionosphere material. These reactions form a basis for continued local aerosol formation very much like the case of Titan’s ionospheric organic rich aerosol (e.g., Coates et al., 2009; Shebanits et al., 2013). Note also the potential similarity of observed charged water cluster ions in Earth’s mesosphere by numerous rocket measurements (e.g., Schulte and Arnold, 1992; Goldberg et al., 2001; Gumbel and Witt, 2002; Havnes et al., 2015), often associated with VLF broadband electric fields below a few kHz.

Small nm-sized dust grains become negatively charged rather fast in ionospheric plasma conditions at the distance of Saturn, since photo-detachment rates are slow compared to the electron attachment rates on grains in a dense ionospheric plasma. These negatively charged grains will therefore undergo ambipolar diffusion sedimentation under the influence of a strong mainly horizontal magnetic field near the equator of Saturn. A stratification of partly magnetised charged dust layers could therefore be a viable explanation for the observations presented here, which future theoretical models could investigate.

## 5. Discussion and conclusions

We report a detailed re-analysis of the Cassini RPWS Langmuir probe sweep data in Saturn’s ionosphere below 4000 km altitude and compare with RPWS electron number densities inferred from plasma wave emissions as well as INMS H⁺ and H₃⁺ number densities. We make sure the data sets are sampled simultaneously and calibrate different flybys (Rev 288–293) in altitude by using the INMS H₂ number density data.

We include several processes affecting the voltage-current characteristic of the RPWS Langmuir probe. These include thermal electrons

and ram flow positive ions, impact generated plasma, secondary ion (SIE) and electron (SEE) generation, photoelectron emission, hot electron tails, an expanding electron sheath, form variations of the potential pattern of the guard, and how a boom/spacecraft potential affects electron collection. Using this we infer refined values of the RPWS Langmuir probe sweep parameter output data (mainly nₑ, nᵢ, Tₑ, and Uₛₚ). The model fits to the RPWS Langmuir probe sweep voltage-current data are of high accuracy and consistent in detail with other RPWS sensor and INMS values. The ionospheric data reported herein can therefore be used for theoretical models of Saturn’s equatorial ionosphere.

The observations of the topside ionosphere (> 2500 km) show:

* Large variations in plasma density structure, both between flybys (weeks), as well as between inbound and outbound profiles showing latitudinal differences which evolve with time. Occasional localized enhanced plasma densities are identified.

* nᵢ ≈ nₑ.

* Rev. 288 and Rev. 292 are dominated by H⁺ ions above 2200 km (outbound) and 2800 km (inbound), while n(H₃⁺) is larger than n(H⁺) in an altitude band from 2200 to 2800 km (inbound).

* An increasing trend of electron temperature with altitude (except Rev. 289 and Rev. 290 inbound profiles) from 0.06 eV (outbound) or 0.08 eV (inbound) up to 0.2 eV. Large electron temperature variations between flybys (weeks) as well as between inbound and outbound profiles (latitude effect).

* Hot electron tails are occasionally identified with energies 0.12–2 eV.

The equatorial topside ionosphere is therefore dynamic and appears to be affected by convection electric fields (E⊥) mapped along the near horizontal magnetic field of Saturn. We suggest that these electric fields can either be produced by an atmospheric dynamo driven by neutral winds in the lower ionosphere north or south of the equatorial region or be produced by the infalling charged D-ring material across the magnetic field. We further suggest that heat conduction along magnetic flux tubes control the electron temperature. Since electron collisions with neutrals are few, hotter electron tail distributions can develop.
The observations in the lower part of the ionosphere (1450–2500 km) show:

* Large amounts of impact plasma (SIE and SEE) generated from the spacecraft (and sensor) surface due to atmospheric species impact with high yields (e.g., water). The Langmuir probe current from this process implies $I_{SEE} \approx 10$ $I_{SIE}$, but in large (dominant) current contribution cases $I_{SIE} \approx I_{SEE}$ to comply with overall quasi-neutrality. Based on the analysis presented here, secondary emissions need to be included in the interpretation, but are unable to fully account for the observed discrepancy between $n_e$ and $n_i$.

* Rev. 288 and Rev. 292 (below 2200 km) are dominated by heavy positively charged ions with mass numbers more than 8 amu. $H_3^-$ densities constitute a significant fraction above 2200 km.

* Positively charged ions densities reach at least $20,000 \text{ cm}^{-3}$ toward the lowest observed altitudes.

* A negatively charged species (ions/dust/aerosol) is implied to exist in regions where $n_i > n_e$. A long-term decreasing density trend of the inferred negatively charged species exists from Rev. 288 through 293 (both inbound and outbound).

* Localized electron depletions in density are found during several Revs with apparent vertical scales in the range 200–500 km, and most often associated with inferred negative charged species (ions/dust/aerosol) such that $\sum q_i n_i = en_e + \sum q_i n_i$.

* Small scale layered structures (variations) in densities and sharp changes in ion composition by an order of magnitude exist with scales from less than 50 km to several 100 km.

* An increasing trend in the electron temperature toward the lowest measured altitudes from 800 K up to 4000 K.

* We do not identify a clear ionospheric peak, not even at the lowest observed altitude around 1450 km. The main ionosphere peak must exist below during the time of the observations. Radio occultation measurements have identified low-latitude ionospheric peaks above 1450 km (Tamburo et al., 2023).

The equatorial ionosphere for altitudes 1450–2500 km exhibits abrupt and large variations over small scales in electron and ion densities measured by both INMS and RPWS. Other reported observations from this region show a heavy influx of infalling material (both neutral and charged grains) from the D-ring of Saturn (e.g., Waite et al., 2018 online supplement). Our observations suggest there exists a long-term variability of the interaction between infalling dust from the D-ring and the local chemistry and dust as there is a decrease in inferred negatively charged density from Rev. 288 toward Rev. 292, noting that Rev. 293 shows a larger amount and is $10^\circ\text{N}$ LAT from the other Rev. There are also clear inbound-outbound (latitudinal) variations, which mimic the difference in infalling material from the D-ring (e.g., Mitchell et al., 2018; Hsu et al., 2018). Any dust/aerosol existing in the ionosphere will be charged negative due to the low photo detachment rates

at this distance from the Sun, and the less massive species can be constrained in their ambipolar motion by the comparably strong horizontal magnetic field. This may result in localized aerosol/dust layers that evolve with time and with small vertical scale sizes below typical ionospheric scale heights. Gravity waves may affect these layers. The vertical wavelengths of gravity waves (e.g., Matcheva and Barrow, 2012; Müller-Wodarg et al., 2019) are of similar size to those presented here for the electron and ion number densities. Further complex ion-molecule-aerosol chemistry should occur in this chemistry-controlled part of the ionosphere. The strong electron heating above expected thermal equilibrium levels (up to 4000–5000 K) is problematic to explain. A possible mechanism may be Farley-Buneman electrostatic waves excited by a plasma drift through a dust-rich medium. In conclusion, we believe that a gas giant ionosphere/thermosphere with closeby rings is in strong disequilibrium and undergoes dynamic and chemical evolution at least in the equatorial regions.

### CRediT authorship contribution statement

**J.-E. Wahlund:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Project administration, Methodology, Investigation, Formal analysis, Data curation, Conceptualization.
**A.I. Eriksson:** Writing – review & editing, Formal analysis. **M.W. Morooka:** Writing – review & editing, Formal analysis, Conceptualization. **S. Buchert:** Writing – review & editing, Investigation, Conceptualization. **M. Persson:** Writing – review & editing, Investigation. **E. Vigren:** Writing – review & editing, Validation, Investigation, Formal analysis, Conceptualization. **J. Dreyer:** Writing – review & editing, Investigation. **W.S. Kurth:** Writing – review & editing, Investigation, Data curation. **J.H. Jr Waite:** Writing – review & editing, Validation, Investigation, Data curation. **J.-P. Lebreton:** Writing – review & editing, Validation, Investigation, Data curation. **W.M. Farrell:** Writing – review & editing, Investigation, Conceptualization. **I. Müller-Wodarg:** Writing – review & editing, Investigation, Conceptualization.

### Declaration of competing interest

Except for the funding dependencies stated in the Acknowledgement, the authors do not have relevant financial or non-financial interests to disclose. The authors do not have competing interests to declare that are relevant to the content of this article.

### Acknowledgements

The Swedish National Space Agency (SNSA) have supported the Langmuir probe implementation and its operations. The RPWS/LP sweep data can be found in PDS3 (10.17189/1519612). The Saturn ionosphere number density and electron temperature results from this study can be found at https://zenodo.org/records/15267542.

## Appendix A. Neutral atmosphere altitude & inter-orbit calibration

The neutral atmosphere number density, here represented by the measured $H_2$ number density by INMS, is the basis for comparison of different ionospheric depth profiles between different Cassini passes through Saturn's upper atmosphere. The geographic latitude coverage of the measured INMS $H_2$ number density is displayed in Fig. A1. The spacecraft moves from north toward south in a polar elliptical orbit where the closest approach of Saturn occurs on the dayside hemisphere.
In this study the INMS data have been corrected for the timestamp shift offset (Dreyer et al., 2022, their Appendix C), which amounts to −4.87 s, −4.91 s, −4.95 s, −4.99 s, −5.03 s and −5.07 s respectively for the proximal passes 288 through 293. In Fig. A2 the corresponding altitude profiles of the INMS measured H₂ number densities for each pass are displayed. Double-exponential minimum least square fits are used to calibrate the altitude of the Cassini ephemeris to a common H₂ number density. It is then possible to compare the RPWS and INMS ionospheric data from different orbits for the same H₂ number density values to an accuracy of about 5–10 km. The 1-bar pressure level is the 0-km reference for the altitude ephemeris and is calculated from Saturn’s ellipsoidal surface with an equatorial radius of 60,268 km and a polar radius of 54,364 km (Table 4 in Archinal et al., 2011).

<figure><img src="image_35.png" /><figcaption>Fig. A1. The Cassini proximal orbits passing through the upper atmosphere of Saturn consist of the near equatorial passes 288–292 (±16° LAT) and the final controlled crash pass 293 (plunge) occurring at northern geographic latitudes between +16° LAT to +9° LAT. The accuracy of the measurements becomes worse below an H₂ number density of 10⁸ cm⁻³. The Cassini spacecraft reaches atmospheric depths a few times above 10¹⁰ cm⁻³, which corresponds to nbar-levels (e.g., Yelle et al., 2018; Brown et al., 2020). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
<figure><img src="image_36.png" /><figcaption>Fig. A2. Inbound (N, blue) and outbound (S, cyan) atmospheric H₂ number density altitude profiles for the 6 proximal passes. Per definition, 0 km corresponds to the 1-bar level using the Cassini ephemeris. Exponential minimum least square fits (red & magenta) are used to calibrate the common RPWS and INMS ionosphere measurements to each other for a common H₂ number density. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

## Appendix B. Electron number densities

The ionospheric local electron number density is estimated from three different measurement methods.

* From observed broadband whistler mode emissions and narrowband upper hybrid frequency emissions using the RPWS electric antenna (n<sub>e,waves</sub>).

* From the electron sampling part of Voltage-Current (U—I) characteristic of the RPWS Langmuir probe voltage sweeps (n<sub>e,Lp</sub>).

* From the RPWS Langmuir probe current at 1–100 samples per second while the probe is set at a fixed positive bias voltage (δn<sub>e</sub>). The bias voltage is +4 V (when doing ±4 V sweeps in between) or +11 V (when doing ±32 V sweeps in between). The δn<sub>e</sub> = k·δI<sub>Lp</sub> for a fixed U<sub>bias</sub> is calibrated with a simple factor, k, for the whole data set to match the lower ionosphere part reasonably well.

The two first ones give very accurate and consistent absolute values, the third give a good temporal resolution estimate but is dependent on electron temperature (T<sub>e</sub>) and the floating potential (U<sub>float</sub>) according to I<sub>e</sub> ∝ √T<sub>e</sub>n<sub>e</sub> (1 + (U<sub>bias</sub> + U<sub>float</sub>)/T<sub>e</sub>) where U<sub>float</sub> ≈ U<sub>SC</sub> for the cases studied herein. Slow systematic variations can be detected in δn<sub>e</sub> if T<sub>e</sub> or U<sub>SC</sub> is assumed to vary slowly compared to the electron number density. This systematic variation is detected in the observed altitude profiles (Fig. B1) of the observed electron number densities.
<figure><img src="image_37.png" /><figcaption>Fig. B1. Electron density altitude profiles derived from three different RPWS measurements. See Appendix text for explanations.</figcaption></figure>
<figure><img src="image_38.png" /><figcaption>Fig. B1. (continued).</figcaption></figure>

## Appendix C. Iterative parametric fit analysis method to Langmuir probe sweep data

We have used the following semi-automatic iterative analysis procedure to model fit the observed RPWS Langmuir probe voltage sweeps (and resulting U-I-characteristic). The fit quality is determined by the residual between the data points and the model fit at the end of step 2 (point f).

1. Fit a linear function $I = m + bU$ for $U < -3$ V (eye check if valid data in range) determining m and b. Determines $n_i$, $v_i$ and photoemission afterwards.

a. Is there an exp-component for $U < -3$ V?

b. If so, do a NL-LS fit of $I = m + bU + c_2\exp(d_2U)$ to relevant data (using modified voltage range such that the main thermal electron exponential current is not included)

c. Use these resulting m and b instead

2. Fit main electron part (iterative loop)

a. Initiate with $n_e = n_{e,waves}$. Allow for adjustments of $n_{e,LP}$.

b. Use SL theory expression with a Parker sheath. Parametric fit of $c_1$ and $d_1$.

i. Gives $U_{float}$, $T_e = 1/d_1$, $n_{e,LP}$ afterwards. $U_{float}$ is set fixed for analysis below.

c. Fit potential form factors $\beta$ and $d_s$ (iterative loop)

d. Is there an exponential current component $c_2\exp(d_2)$ for $U < 0$ V in addition to the main electron exp-component $c_1\exp(d_1)$?

i. Make new NL-LS $m + bU + c_2\exp(d_2U)$ fit to relevant data using $U_{float}$ fixed.

ii. Use these m and b instead?

iii. Determine equivalent $n_{e,hot}$ and $T_{e,hot}$ (iterative)

iv. Test for negative ion current (iterative)

v. Test for impact plasma and SIE (iterative)

e. Is there SEE?

i. Test for different $m_{SEE}$ and $T_{SEE}$ (iterative)

f. Do we have a good fit? Check versus residual.

3. Make endSave of output parameters (sweep fit ready)
Side note: One fit attempt takes 5–15 min for a skilled user. Analysing all 159 sweeps thus takes about 40 h or ~ week.

## Appendix D. Langmuir probe Voltage-Current theory expressions

The expressions for the current contributions used here in model fits of the observed Langmuir probe voltage-current characteristic are given below.

**Main electron population (in an expanding electron sampling sheath).**

The expressions by Whipple (1965) using a Parker electron sheath and Maxwellian electrons, and including the geometry factor (β) of the potential pattern due to the guard, which start take effect when the electron sheath, s_e, have expanded to a distance d_s from the probe, looks like:

$$I_e = c_1 \exp(-d_1 U) \quad \text{for } U = U_{\text{bias}} + U_{\text{float}} \le 0 \text{ V},$$

$$I_e = c_1 \left[ \left( a_1/r_{LP} \right)^2 - \frac{1}{k_1} \exp(-k_1 d_1 U) \right] \quad \text{for } U = U_{\text{bias}} + U_{\text{float}} > 0 \text{ V and } s_e \le d_s,$$

$$I_e = c'_1 \left[ \left( a_1/r_{LP} \right)^2 - \frac{1}{k_1} \exp(-k_1 d_1 U) \right]^\beta \quad \text{for } U = U_{\text{bias}} + U_{\text{float}} > 0 \text{ V and } s_e > d_s,$$

with a_1 = r_{LP} + s_e and k_1 = r_{LP}/(a_1^2 - r_{LP}^2) and c_1 = en_e A_{LP} \sqrt{k_B T_e / 4\pi m_e} and d_1 = 1/T_e [eV].

At a certain distance the electron sheath reaches the neighbourhood of the boom (s_e > 10 cm), which have different potential, U_bomb, and is unknown, and therefore cannot be currently fitted. This effect must be judged for each sweep characteristic and is usually detected as a deviation from the fitted U-I-characteristic starting at a voltage corresponding to s_e ≈ 10 cm.

### 5.1.1. Hot electron tail population

A warm electron tail (with T_e,hot > T_e and n_e,hot < n_e) is treated as an additional electron population sampled in the expanding electron sheath:

$$I_{e,hot} = c_2 \exp(-d_2 U) \quad \text{for } U = U_{\text{bias}} + U_{\text{float}} \le 0 \text{ V},$$

$$I_{e,hot} = c_2 \left[ \left( a_1/r_{LP} \right)^2 - \frac{1}{k_1} \exp(-k_1 d_2 U) \right] \quad \text{for } U = U_{\text{bias}} + U_{\text{float}} > 0 \text{ V}.$$

where c_2 = en_e,hot A_{LP} \sqrt{k_B T_e,hot / 4\pi m_e} and d_2 = 1/T_e,hot.

### 5.1.2. Photoelectron and Secondary electron emissions (SEE)

Secondary electrons due to impacts (of molecules, dust, electrons at high energies) are treated in a similar way as photoemissions due to incident solar EUV/X radiation. The photoelectron current contribution is scaled to typical values at Earth and set to:

$$I_{ph} = - \Phi_{EUV} \cdot 5.6 \cdot 10^{-5} \cdot \pi r_{LP}^2 / R_{sun}^2 [\text{AMU}] \approx 0.5 - 0.6 \text{ nA} \quad \text{for } U \le 0 \text{ V},$$

$$I_{ph} = - \Phi_{EUV} \cdot \pi r_{LP}^2 / R_{sun}^2 [\text{AMU}] \cdot \left\{ 5.0 \cdot 10^{-5} \cdot \exp(-U/2.74) + 1.2 \cdot 10^{-5} \cdot \exp(-(U+10)/14.42) \right\}$$

for U > 0 V,

where Φ_{EUV} is the time variable EUV/X flux fraction compared to an average value for Earth. We set it to 0.5 nA based on previous magnetospheric observations with the Langmuir probe where the photo-electron current dominates, but it is a negligible contribution in our Saturn ionosphere cases.

The SEE contribution can be significant though, and we use:

$$I_{SEE} = -k_{enh,Rev} C n_{atm} \quad \text{for } U \le 0 \text{ V},$$

$$I_{SEE} = -k_{enh,Rev} C n_{atm} \exp(-U/T_{SEE}[eV]) \quad \text{for } U > 0 \text{ V},$$

where C ≈ 2·10⁻⁸ nA/cm⁻³ is a base SEE constant and k_{enh,Rev} is an enhancement of SEE depending on molecular conditions on each orbit (c.f., Section 3.4). In this study, applicable to Saturn's ionosphere, the temperature of the secondary electrons must be set T_{SEE} > 1 eV to comply with a good fit to the LP U-I-characteristic. We usually set it to 2 eV.

### 5.1.3. Secondary ion emissions (SIE) & Impact plasma

Secondary ion emissions are treated in a similar way as the SEE contribution as:

$$I_{SIE} = C_{SIE} \exp(-U/T_{SIE}[eV]) \quad \text{for } U \le 0 \text{ V},$$

$$I_{SIE} = C_{SIE} \quad \text{for } U > 0 \text{ V},$$

where C_{SIE} is a constant giving the level of SIE, and T_{SIE} is the temperature of the secondary ions (set equal to the parametric fit parameter, T_{exp}).
The problem to differ between an impact plasma SIE contribution and a hot electron tail contribution is discussed in Section 3.2.

### 5.1.4. Ion (positively & negatively charged) ram fluxes

The Cassini spacecraft traverses Saturn's ionosphere with a speed of ≈34 km/s, and sampled thermal currents are then negligible compared to the ram fluxes to the Langmuir probe:

$$I_{i+} \approx q_{i+} n_{i+} A_{LP} V_{i+} / 4(1 - U/W_{i+}) \quad \text{for } U \le 0 \text{ V},$$

$$I_{i+} \approx q_{i+} n_{i+} A_{LP} V_{i+} / 4 \exp(-U/W_{i+}) \quad \text{for } U > 0 \text{ V},$$

where $W_{i+} = m_{i+}V_{i+}^2/2e$ [eV] is the ram energy of the ions.

Similarly.

$$I_{i-} \approx q_{i-} n_{i-} A_{LP} V_{i-} / 4 \exp(-U/W_{i-}) \quad \text{for } U \le 0 \text{ V},$$

$$I_{i-} \approx q_{i-} n_{i-} A_{LP} V_{i-} / 4(1 - U/W_{i-}) \quad \text{for } U > 0 \text{ V},$$

for the negatively charged ions. For a ± 4 V Langmuir probe sweeps and considering the expected large heavy ion ram energies in the lower observed altitude range < 2500 km, $U/W_i$ becomes very small and therefore the exponential and/or slope is hard to separate in the presented Langmuir probe U-I-characteristic (c.f., Section 3.4).

## Appendix E. Example of a Langmuir probe sweep model fit sensitivity analysis

The Langmuir probe sweep on Rev. 292 at 00:00:29.2 UT on the day 2017.09.09 (see Fig. 8) from the lower part of the ionosphere of Saturn is used to illustrate the sensitivity of a parametric model fit (here with respect to the electron temperature, $T_e = 1/d_1$). Figs. E1 to E3 has $T_e$ chosen to be 0.085 eV, 0.105 eV and 0.125 eV respectively, i.e., a variation of only 0.02 eV between each model fit. All other parameters are fixed. The left panels show the fit to the data and the right panels the corresponding residuals between the measured Langmuir probe sweep data and the model fit in question. The sweep model fit in Fig. 8 is shown in Fig. E2.

From Figs. E1 through E3 there exist a slightly better model fit to the sweep data in Fig. E2 corresponding to 0.105 eV, which illustrates that an error sensitivity is clearly less than ±0.02 eV. Zoomed in versions reduce the possible spread in $T_e$ further. The measured sweep data points themselves are accurate according to the residual spread, and the residual between the measured sweep current and the model fit current is a measure of the fit quality in the “relevant” $U_{bias}$ ranges for the fitted parameter in question.

<figure><img src="image_39.png" /><figcaption>Fig. E1. (Left panels) Same representation as in Fig. 2, and same data as in Fig. 8. The parametric model fit of the total current (red line) use $T_e = 0.085$ eV instead of 0.105 eV (as in Fig. 8). (Right panels) Same representation as in Fig. 3. For $T_e$ the important $U_{bias}$ part is here −1 V to 0 V. A slight deviation of the fit from the data is seen best in the left bottom panel, with a residual reaching above 0.03 nA in this voltage range. Also, the total model fit show a large residual for $U_{bias} > 0.5$ V. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
<figure><img src="image_40.png" /><figcaption>Fig. E2. (Left panels) Same representation as in Fig. 2, and same data as in Fig. 8. The parametric model fit of the total current (red line) use $T_e = 0.105$ eV. (Right panels) Same representation as in Fig. 3. For $U_{bias}$ between -1 V to 0 V the model fit show an almost perfect fit to the data, with a residual just below 0.02 nA in this voltage range. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_41.png" /><figcaption>Fig. E3. (Left panels) Same representation as in Fig. 2, and same data as in Fig. 8. The parametric model fit of the total current (red line) use $T_e = 0.125$ eV instead of 0.105 eV (as in Fig. 8). (Right panels) Same representation as in Fig. 3. For $T_e$ the important $U_{bias}$ part is here -1 V to 0 V. A slight deviation of the fit from the data is seen best in the left bottom panel, with a residual reaching -0.02 nA in this voltage range. Also, the total model fit show a large residual for $U_{bias} > 0.5$ V. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

## Data availability

Data will be made available on request.

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