Larry W. Esposito

Far‐ultraviolet (FUV, ∼135–165 nm) dayglow emissions from N ₂ ‐rich Solar System Objects (SSOs) are dominated by the Lyman–Birge–Hopfield (LBH) band system. Consequently, observations from the Cassini Ultraviolet Imaging Spectrograph (UVIS) at Titan and the Global‐scale Observations of the Limb and Disk (GOLD) mission at Earth use the LBH emission for upper atmospheric remote sensing at both SSOs. However, FUV dayglow‐based remote sensing analysis has been hampered by large uncertainties in existing LBH emission cross sections, particularly at low photoelectron energies. We present laboratory measurements of emission cross sections obtained at low electron energies (16, 20, and 30 eV). Our laboratory apparatus employs a high‐resolution, state‐of‐the‐art monoenergetic electron beam source and a large (1.5‐m diameter) chamber. With this apparatus, we produce single‐particle excitation of the optically forbidden upper state of N ₂ ( a ¹ Π _g ‐state), including cascade and collision induced excitation from nearby electronic states. The low energy electron impact cross sections from this study (at 16, 20, and 30 eV) are combined with our previous results to fit an analytic LBH cross section as a function of energy (16–200 eV). The “analytic” cross‐section is then used in a radiative transfer dayglow model to quantify LBH brightness without needing corrections for cascade contributions.

Saturn’s narrow, clumpy F ring is in a region disturbed by chaotic orbital dynamics. The ring appears dominated by dust in camera images, but the main mass of this ring resides in a core of elongated clumps called kittens, observed by Cassini UVIS and RSS ring occultations. Approximating this chaos as a random process, I model the F ring core as a finite Markov chain of transient aggregates [20m < dr < 3 km]. The model includes perturbations due to Prometheus encounters, resonance confinement, and mutual collisions. The best description for the current ring is the stationary state of this stochastic process. In this model, the persistence of the F ring is due to negative diffusion [described by Sickafoose and Lewis 2024, to explain the persistence of Chariklo’s rings], where the ring is confined by Prometheus aligning particles when they are driven to collide when their streamlines cross. The F ring is thus shepherded by a combination of a Prometheus corotation and a Lindblad resonance. Whenever the center of mass of the material in the F ring is located at the Lindblad resonance with Prometheus, perturbations will drive negative diffusion to maintain that location. Likewise, negative diffusion can maintain apse alignment and thus ring eccentricity. If the F ring originated from the destruction of a small moon on an elliptical orbit, negative diffusion preserves the original orbital elements of the moon against differential precession and collisional spreading.The stages in F ring history are as follows. A progenitor moon, say ‘Festus’, accretes from viscous spreading of Saturn’s rings material that crosses the Roche limit. Later, Prometheus accretes. Prometheus, being larger, moves out faster, with a tidal evolution time scale of 10-100 million years… and captures Festus in a mean motion resonance. After that, the two evolve together with the exact resonance evolving chaotically with Prometheus own history of jumps and glitches. If Festus is thus ever out of resonance it is soon re-captured. The mean motion resonance excites Festus eccentricity. Festus (in an eccentric orbit, caught in or near resonance) is shattered by an impact (the estimated lifetime is of the order of 100 million years); the debris mass would be dominated the largest objects (kittens); they would experience anisotropic collisions at streamline crossing that would maintain the moon’s original [a, e, φ] via the negative diffusion. Fragments trapped in nearby resonances have lower optical depth, negative diffusion is weaker and the fragments gradually diffuse away; or they leak into capture within the resonance site with the most original mass. The evaporation of ring material where regular diffusion dominates leaves behind the confined eccentric F ring. Caught in resonance with Prometheus, it will evolve further from Saturn and may eventually re-accrete into a small moon like Anthe.

This study investigates the water plumes of Saturn's moon, Enceladus, using Direct Simulation Monte Carlo (DSMC) modeling to analyze venting dynamics and plume structures. Building on prior research, we employ a parametrized DSMC approach to model water vapor and ice particle flows, leveraging Cassini spacecraft data from instruments such as the Ion and Neutral Mass Spectrometer and the Ultraviolet Imaging Spectrograph. The study explores whether vent conditions, such as mass flow rates, mixture temperatures, and particle sizes, can be inferred from observational data. We develop a computational framework to expand plume simulations beyond 10 km altitudes, incorporating gravitational and inertial forces in an Enceladus‐fixed reference frame. A sensitivity analysis correlates vent parameters with observed data, identifying critical contributors such as vent orientation and location, mass flow rate, exit temperature, and ice grain characteristics. This approach reduces the dimensionality of fitting procedures, enabling robust parameter constraints and a more detailed understanding of plume dynamics. Key findings include constrained values for mass flow rates, ice grain radii assuming single‐size particles, and exit temperatures (∼44–61 K), consistent with theoretical predictions. Additionally, variations in vent orientation and positional parameters were refined from the work of Porco et al. (2014, https://doi.org/10.1088/0004‐6256/148/3/45 ). These results highlight the importance of collision dynamics in shaping plume structures. This work establishes a computationally efficient methodology for analyzing cryovolcanic plumes applicable to future missions exploring icy moons such as Enceladus or Europa. By prioritizing sensitive parameters, the study offers insights for optimizing observational strategies to maximize scientific yield.

The far ultraviolet (FUV) dayglow emissions have been observed from Titan and Earth by the Cassini Ultraviolet Imaging Spectrograph (UVIS) and Global-scale Observations of the Limb and Disk (GOLD), respectively, operating in the same wavelength range between 135–165 nm. Both Solar System Objects (SSO) are fascinating environments where N2 is the most abundant thermosphere-ionosphere (T-I) species. They both exhibit similar UV spectra. The UV spectra consist of strong emissions from the Lyman-Birge-Hopfield (LBH) band system a 1Πg → X 1Σg+ of N2 excited from photoelectrons. The dayglow’s of both SSOs are most intense at its own ionosphere altitude [900 km at Titan vs 120-150 km at Earth] with similar thermodynamic conditions for atmospheric N2 density [1010-1011 cm-3]. Titan and Earth have vastly different T-I temperatures (150 K vs ~700K) and the presence of minor constituents [ CH4 on Titan vs O, O2 on Earth]. The FUV dayglow spectra of both SSOs are shown over plotted in Fig. 1. Titan’s nitrogen dominated atmosphere is the densest of any moon in the solar system and Earth’s nitrogen dominated atmosphere has the densest N2 content of any planet in the solar system. We propose to present a new model analysis of the full FUV (115–190 nm) disk airglow observations of Titan’s and Earth’s atmosphere based on UV laboratory optically thin electron impact fluorescence studies of the LBH band system. The experiments will be performed at SSO atmospheric T-I density and temperature that must occur to accurately determine the relevant emission cross sections. The experimental apparatus at the University of Colorado has installed a new high energy resolution electron gun to study the threshold energy (10-30 eV) behavior of the LBH band system, where photoelectron distribution functions peak in energy. This work is under contract to the University of Colorado by NSF Aeronomy and NASA Cassini Data Analysis Program Offices.Fig. 1 A comparison of GOLD (2019) and Cassini UVIS (2009)FUV dayglow spectra between 136-155 nm, both containing the LBH bands.The rotational temperatures of both SSO are very different and representthe upper atmosphere T-I kinetics temperature.

The selection of three new missions to Venus opens a new era to explore the planet and its evolution: ESA’s EnVision and NASA’s VERITAS and DAVINCI missions plan to observe Venus in the next decade. ESA and NASA established a joint Venus Science Coordination group (VeSCoor) as a forum for dialogue within the broader Venus scientific community, in support of the upcoming ESA and NASA missions to Venus [1].The NASA VERITAS mission will study the surface and interior with an interferometric synthetic aperture radar and infrared instrument that provide global topography, imaging, rock type, and targeted surface deformation, plus radio science for interior structure [2].The NASA DAVINCI mission a descent probe that will determine the composition and history of Venus’ atmosphere as well as make additional measurements of the planet’s surface and atmosphere. DAVINCI consists of a spacecraft hosting a carrier and a descent probe, with seven in-situ, imager and spectrometer instruments [3].EnVision, an ESA orbital mission in collaboration with NASA, will simultaneously investigate Venus’ history, activity and climate, from its inner core, to its surface, and further up to its upper atmosphere. EnVision’s science payload consists of five instruments (radar, spectrometers, sounding radar and radio science experiment) [4].These missions will offer unprecedented complementary views of Venus and determine fundamental characteristics of the planet and its long term evolution [5, 6].In this scenario, VeSCoor’s primary goals are to identify new, unanticipated scientific approaches and outcomes based on synergies among the missions to Venus and suggest studies to enhance overall scientific return. However, VeSCoor will not evaluate or propose changes to the current mission profiles, scientific objectives, or requirements.The group was initially made up of 12 members from the Venus science community (Figure 1), 6 selected by ESA and 6 by NASA, plus 3 representatives of the EnVision, VERITAS and DAVINCI missions [7]. Membership in VesCoor is initially set to a 2 year term, but may be renewed at the discretion of NASA and ESA. A scientific observer from South Korea has subsequently joined the group along with two members selected by JAXA.VeSCoor members’ expertises cover different scientific disciplines to provide a comprehensive view of Venus as a planet, and hence, as a complex system.Representatives from NASA and ESA agencies are involved as observers to provide support to the group’s activities.The Group meets in-person twice a year to discuss science objectives and receive updates on the missions’ development. The outcomes of the discussion will be part of public documents available soon. Three working groups (Interiors, Surfaces, and Atmospheres) have been created to address the identified topics, and to discuss specific actions that could facilitate progress in advance of the missions.The first in-person meeting was held in February 2024 in Virginia, USA (Figure 2). Mission representatives from VERITAS, EnVision, and DAVINCI presented descriptions of mission science payloads, timelines, expected science returns, and current activities. VeSCoor members worked on developing the "Rules of the Road" document that establishes rules of conduct and communication.The second in-person meeting of VeSCoor was held in the ESA ESTEC establishment on November 2024 (Figure 3). We included in the discussion the Earth-based observation of Venus and talked about the Korean earth-based satellite for Venus exploration (CLOVE) [8].To improve the scientific discussion, four speakers were invited to present specific topics identified by the Group as strategic:- Sara Seager presented the ‘The search for life in the Venus’ clouds’ goal of the Morning Star mission.- Sebastien Lebonnois presented a review on the Venus Global Climate Models.- Edgar Steenstra talked about his recent laboratory set up to support the EnVision observations.- Lorenzo Bruzzone, PI of the radar Sounder SRS onboard EnVision presented the objectives and foreseen capabilities of this instrument to explore the subsurface of Venus.The third in-person meeting of VeSCoor was again held at the Lansdowne Resort in Leesburg in March of 2025 (Figure 4). The group received updates on NASA developments from Delia Santiago-Matarese, and status reports from EnVision, VERITAS, and DaVinci mission leadership. Three speakers were invited this time:- David Grinspoon (NASA’s Senior Scientist for Astrobiology Strategy) discussed the Astrobiological Potential of Venus.- Michael Chaffin presented the Photochemical Hydrogen Loss from Venus and the Fate of an Earth-like Water Inventory.- Debra Buczkowski described the status of the Venus Geologic Mapping Efforts.The preliminary results of the discussion emphasize the importance of on-going studies and experimental work in preparation for the new missions.The importance of completing the Venus mapping programme and generating ongoing discussion on common mapping standards for the international Venus community was emphasized. Also, facilitation of analog field studies to test the instrument performance, operational routine and scientific data integration was supported.International collaboration is fundamental to unite the efforts for successful exploration of Venus.The Group also discussed the need to establish workshops for the international Venus community (COSPAR, etc.) and maintain contact with other Venus-focused groups (i.e., VEXAG).Acknowledgments:The Group would like to express their thanks to ESA and NASA representatives for supporting our activities and particularly to Ramon De Paula who has recently retired from NASA.References: [1] NASA-ESA Venus Science Coordination (VeSCoor) – Terms of Reference 2022, [2] Smrekar, S.E. et al. (2022) In: 2022 IEEE aerospace conference; [3] Garvin, J.B. et al. (2022) Planet Sci J 3:117;...

Saturn’s narrow, clumpy F ring is a region disturbed by chaotic orbital dynamics. We therefore model it as a stochastic process (specifically, a finite Markov chain). The ring appears dominated by dust in camera images, but the main mass of this ring resides in a core of elongated clumps called kittens, observed by ring occultations. Cassini UVIS sees such features about 1/3 of the time, the same frequency as the radio occultation detections of the F ring core; both have similar size distribution. We model the F ring core as kittens (transient aggregates with size100 m < 𝚫r < 3 km), including perturbations due to Prometheus encounters, resonance confinement, and mutual collisions. We solve for the stationary state. Without confinement, the probability of detecting the kittens is uniformly distributed. With corotation resonance confinement [1], the stationary state is sharply peaked, consistent with the longitudinal distribution of detections of the F ring by radio occultation. Considering shepherding alone, the Cassini radio observations are nonetheless better fit by the non-confinement stationary distribution, and even better by just 20% confined. We find acceptable fits for fractions up to 70% of the clumps shepherded in the 109:110 Prometheus CER. This alternative combines with the explanation of [1] to conclude that some fraction of the population, or some fraction of the time, the F ring is shepherded by Prometheus. We argue that the persistence of the F ring due to negative diffusion [2][3], where the ring is confined by Prometheus aligning particle when they are driven to collide when streamlines cross. We include the negative diffusion in the Markov chain using an Ehrenfest diffusion model [4]. A small asymmetry explains the distribution in resonant argument of the radio occultation detections. In all cases, Prometheus is the agent for confinement. The F ring is thus shepherded by a combination of a Prometheus corotation and a Lindblad resonance. When the center of mass of the material in the F ring is ever located at the Lindblad resonance with Prometheus, perturbations will drive negative diffusion to maintain that location. For our combined model: Shepherded fraction has the range fshep < 0.2; Diffusion asymmetry factor Pneg has the range 0.48 - 0.50. The negative diffusion thus can maintain the longitudinal distribution either alone, or in combination with shepherding, if the mean motion resonance coincides with the true core of the F ringComparing 3 models to the kittens detected in the Cassini radio occultations. Red line showing the purely negative diffusion model (no shepherding, only negative diffusion with Pneg = 0.40). The quality of the fit is similar to that of the Cuzzi et al. (2024) hypothesis (green line). Cuzzi, JN al. (2024). Saturn’s F ring is intermittently shepherded by Prometheus.Science, 10 May 2024. Lewis, MC al. (2012). Negative diffusion in planetary rings with a nearby moon. Icarus 213, 201. Sickafoose, AA and Lewis, MC (2024). Numerical simulations of Chariklo’s rings with a resonant perturber. Planetary Science Journal, February 2024. Feller, W (1968). An Introduction to Probability. Wiley.

Stellar occultation measurements of Saturn’s rings from the Cassini Ultraviolet Imaging Spectrograph (UVIS) High Speed Photometer (HSP) reveal dozens of regions in the heart of the B ring that are opaque at the sensitivity level of the measurements (Colwell et al. 2021, 2024). We have identified 24 regions with an average transparency less than 0.25%, including 9 with an average transparency less than 0.1% and radial extents greater than 10 km. There are broad expanses within these opaque regions where the transparency is indistinguishable from zero. Occultations of the star Beta Centauri with photon count rates of up to 600 per 1 ms integration period provide the strongest constraints on transparency. The elevation angle B (sin(B)=0.918) and brightness of Beta Centauri make it best suited among the UVIS stellar occultations to probe high optical depth regions. The radial resolution of these occultations is about 8 meters, while the azimuthal resolution in the frame co-moving with the ring particles is ~20-30 meters. Each measurement samples an area in the frame of the particles of ~400 m2. The average transparency of each designated opaque region is > 0 because of the presence of narrow, transient features we dub “phantoms” that increase the average transparency of the region. Phantoms are analogous to the ghosts observed by Baillie et al. (2013) and Green et al. (2024) in the C ring and Cassini Division. While ghosts were defined by being indistinguishable from 100% transparent in an otherwise moderate optical depth background, phantoms are defined as narrow, non-axisymmetric features with non-zero transparency in an otherwise opaque background (Figure 1).Figure 1: Stacked and offset (by 5%) transparency profiles of the O1 opaque region in Saturn’s B2 ring region as measured by the Cassini UVIS HSP. The different curves are for different observations of the same star system: Beta Centauri. Narrow spikes in transparency are identified as phantoms. The vertical dashed lines indicate the boundaries of the opaque region. We observed phantoms that are only a single HSP measurement, indicating a radial extent of < 10 m, but most span several measurements. Phantom transparencies range from a few percent up, but in some cases the transparency exceeds 10% and can approach 50%. There are 15 measurements of the B ring with Beta Centauri occultations, and the phantoms do not repeat from one occultation to the next, highlighting their non-axisymmetric and/or temporally variable nature. The Beta Centauri system has two stars that contribute to the HSP signal, and the projected separation of these two components in the ring plane enables us to place limits on the azimuthal extent of some phantoms, which in some cases is < 100 m. At some locations there are clusters of phantom-like features that appear in all occultations at the same location. We identify these axisymmetric features “grassy regions” based on their appearance in plots of transparency (Figure 2). The average transparency of grassy regions is still low, typically less than 2%. The opaque regions are bordered by regions of higher optical depth (Figure 2).Figure 2: Stacked and offset (by 5%) transparency profiles of an opaque region in Saturn’s B2 ring region as measured by the Cassini UVIS HSP. The different curves are for different observations of the same star system: Beta Centauri. This opaque region is home to phantoms (isolated spikes in transparency) as well as several grassy regions, identifiable by their presence at the same location in all occultation profiles and marked by blue dashed lines. The measured optical depth of the opaque stretches between phantoms can exceed 6 in some cases (see for example the bottom curve in Figure 2 between 100,250-100,300 km). N-body simulations have struggled to reproduce such high optical depths. Individual ring particles in the simulations clump together due to their mutual gravity, leaving gaps which elevate the overal transparency of the region. We will present results of simulations with modified boundary conditions and particle properties to try to explain the existence of such high-optical-depth regions and the sub-structure of phantoms and grassy regions within them. Baillié, K., J. E. Colwell, L. W. Esposito, and M. C. Lewis 2013. Meter-sized Moonlet Population in Saturn’s C Ring and Cassini Division. Astron J. 145, 171, doi:10.1088/0004-6256/145/6/171. Colwell, J. E., M. Brooks, R. Jerousek, C. Coleman, M. S. Tiscareno, K.-M. Aye, M. Lewis, L. W. Esposito 2021. Irregular Structure in the Core of Saturn’s B Ring. 2021 AGU Fall Meeting P34A-01. Colwell, J. E., A. Goforth, C. Coleman, R. Jerousek, L. W. Esposito 2024. Saturn’s B Ring Phantoms: Frequency, Properties, and Distribution. 2024 Meeting of the American Geophysical Union. P33F-2931. Green, M. R., J. E. Colwell, L. W. Esposito, R. G. Jerousek 2024. Particle sizes in Saturn’s rings from UVIS stellar occultations 2. Outlier populatinos in the C ring and Cassini Division. Icarus 416, 116081.

We present a comparative occultation analysis of narrow, eccentric ringlets in the Saturnian and Uranian ring systems, focusing on how mesoscale structure and particle size distributions vary with orbital phase (true anomaly). Our study combines the full suite of Cassini stellar and radio occultation profiles of Saturn’s narrow ringlets, obtained by Cassini’s UVIS (λ = 150 nm), VIMS (λ = 2.84 μm), and RSS (Ka-, X-, S-band experiments). We compare our results with a reanalysis of Voyager 2 PPS and RSS occultations of Uranus’s ε, α, β, η, and δ rings.We group Saturn ringlet profiles into four orbital quadrants—periapsis, apoapsis, and the streamline divergence/convergence sectors—to isolate phase-dependent structure (Figure 1). In each quadrant, we model viewing-geometry dependent normal optical depth using the irregularly spaced, three component, granola bar self-gravity wake model of Esposito et al. (2025) (Figure 2). The model fits the dimensional ratios and cant angles of aligned structures such as self-gravity wakes, particle-depleted lanes, or both. Following Green et al. (2024), we compute the normalized central moments of UVIS HSP occultation transparencies to constrain the size of the largest ring particles (amax) and to characterize the clumpiness of the ringlets with orbital phase. We compare these moments to predictions from Esposito et al. (2025) for wake-dominated rings. Simultaneously, we perform multi-wavelength particle size distribution fits by selecting UVIS, VIMS, and RSS profiles at similar orbital phase and with similar viewing geometries to constrain the power-law index (q) and minimum particle radius (amin) (Figure 3).For the Uranian rings, we use the σ-Sagittarii and β-Persei Voyager 2 PPS occultations to extract radial optical depth profiles of the dense narrow rings, supplemented by RSS S/X-band differential attenuation. While the geometry does not allow for true-anomaly-resolved comparisons, we compare Voyager 2 PPS occultation statistics and RSS S and X band optical depths to enable structural comparison.Our approach incorporates a self-consistent model of wavelength and viewing-geometry dependent optical depths with an analysis of photon counting statistics (Cassini UVIS HSP and Voyager 2 PPS). We find that Saturn’s ringlets exhibit significant variation in both self-gravity wake dimensions and inferred size distributions between quadrants (Figure 4).By applying a common framework across two planetary ring systems, we aim to identify techniques to constrain the phase-dependence of the particle size distribution, surface densities, and structure of dense narrow rings from in-situ occultations. This approach is intended not only to advance current understanding but also to inform the design of future occultation experiments at Uranus.Figure 1. Ringlet edge radii from UVIS, VIMS, and RSS occulations colored by sine of the ring opening angle for the Maxwell Ringlet. Occultations are separated into quadrants (Groups 1 – 4) in true anomaly for orbital phase-dependent analysis.Figure 2. The irregularly spaced granola bar self-gravity wake model of Esposito et al. (2025). 𝐸[𝜆T] is the expected value of the Toomre critical wavelength or the largest unstable wavelength toward gravitational collapse (Julian and Toomre 1966): λΤ = 4π2GΣ/κ2 where Σ is the local surface mass density and κ is the local epicyclic frequency. The black dashed arrow is the line of sight from Cassini to the occulted star (or to Earth in the case of radio occultations. The red square is the area over which light is collected during a single integration of the UVIS instrument. (see Jerousek et al. (2024) for details on the integration area).Figure 3. The Maxwell ringlet contains a prominent spiral density wave driven by an outer Lindblad resonance (OLR). We fit optical depths in the first trough of the wave. Structure nearly disappears at apoapsis when particle streamlines are most widely separated. At other orbital phases, the model best matches a structure with broad radial spacing and variable vertical extent.Figure 4. Example of particle size distribution fits for the Maxwell ringlet at two orbital phases.. Best-fitting parameters are consistent with Jerousek et al. (2020) for the background C ring near periapsis where q is much larger. Ring particle radii generally range from several millimeters up to 5 – 10 m.References:Green, M. R., Colwell, J. E., Esposito, L. W., & Jerousek, R. G. (2024). Particle sizes in Saturn’s rings from UVIS stellar occultations 2. Outlier Populations in the C ring and Cassini Division. Icarus, 416, 116081.Esposito, L. W., Colwell, J. Ε., Eckert, S., Green, M. R., Jerousek, R. G., & Madhusudhanan, S. (2025). Statistics of Saturn's ring occultations: Implications for structure, dynamics, and origins. Icarus, 429, 116386.Jerousek, R. G., Colwell, J. E., Esposito, L. W., Tiscareno, M. S., Lewis, M. C., Pohl, L., & Benavides, D. A. (2024). The smallest structures in Saturn’s rings from UVIS stellar occultations. Icarus, 415, 116069.

Saturn’s narrow, clumpy F ring is a region disturbed by chaotic orbital dynamics. We therefore model it as a stochastic process (specifically, a finite Markov chain). The ring appears dominated by dust in camera images, but the main mass of this ring resides in a core of elongated clumps called kittens, observed by ring occultations. Cassini UVIS sees such features about 1/3 of the time, the same frequency as the radio occultation detections of the F ring core; both have similar size distribution. We model the F ring core as kittens (transient aggregates with size 100 m < dr < 3 km), including perturbations due to Prometheus encounters, resonance confinement, and mutual collisions. We solve for the stationary state. Without confinement, the probability of detecting the kittens is uniformly distributed. With corotation resonance confinement [1], the stationary state is sharply peaked, consistent with the longitudinal distribution of detections of the F ring by radio occultation. Considering shepherding alone, the Cassini radio observations are nonetheless better fit by the non-confinement stationary distribution, and even better by just 20% confined. We find acceptable fits for fractions up to 70% of the clumps shepherded in the 109:110 Prometheus CER. This alternative combines with the explanation of [1] to conclude that some fraction of the population, or some fraction of the time, the F ring is shepherded by Prometheus. We explain the persistence of the F ring due to negative diffusion [2][3], where the ring is confined by Prometheus aligning particle phases. We include the negative diffusion in the Markov chain using an Ehrenfest diffusion model [4]. A small asymmetry explains the distribution in resonant argument of the radio occultation detections. In all cases, Prometheus is the agent for confinement. The F ring is shepherded by a combination of a Prometheus corotation and a Lindblad resonance that yields non-isotropic collisions: For combined model: Shepherded fraction

Much‐needed emphasis has been placed on supporting early career scientist. However, the mentoring and support of mid‐career scientists has not received an appropriate level of attention. We define mid‐career as having established a body of work that characterizes one's contribution to, and role in, the research community. At mid‐career, scientists have needs that are distinct from early career. They require mentoring relationships that are more collegial than those typically applicable at early career. In addition, stable funding is needed to support students, post‐docs, and longer‐term projects, to allow for the sustained development of a scientific vision over a decade or more. Programs to provide appropriate support targeted at the needs of mid‐career scientists could be enhanced, along with other types of non‐monetary recognition, and encouragement for collegial relationships that help build careers at this stage.