Jeremy A. Riousset

The application of advanced classical mechanics (specifically, the Lagrangian and/or Hamiltonian approaches) to real-world problems is not always straightforward, despite the mathematical rigor and elegance of this field. The objective of this work is to connect the relatively abstract concept of Lagrangian mechanics into the more familiar realm of orbital mechanics. We present a brief, yet complete and self-contained, derivation of the Jacobi integrals using the Lagrangian formulation. The result provides a useful example of how advanced classical mechanics may prove simpler and more efficient than standard methods using Newton's second law. We complement these results with two case studies in our Solar system: the Circular Restricted 3-Body Problems around Pluto and Charon and around Earth and the Moon. These examples provide useful illustrations of both unstable and stable Lagrange points. We further propose a representation of zero-velocity curves, which separate the permissible and forbidden regions of motion for the object, given a constant of the motion. This representation allows an interpretation of Jacobi constants using energy density. The use of S.I. units over normalization in our case studies departs from the traditional examples to offer a more pedagogical and intuitive approach to this problem.

In this work, we focus on plasma discharges produced between two electrodes with a high potential difference, resulting in the ionization of the neutral particles supporting a current in a gaseous medium. At low currents and low temperatures, this process can create luminescent emissions: glow and corona discharges. The parallel plate geometry used in Townsend's theory lets us develop a theoretical formalism, with explicit solutions for the critical voltage effectively reproducing experimental Paschen curves. However, most discharge processes occur in non‐parallel plate geometries, such as discharges between particles in multiphase systems and between cylindrical conductors. Here, we propose a generalization of the classic parallel plate configurations to concentric spherical and coaxial cylindrical geometries in Earth, Mars, Titan, and Venus atmospheres. In a spherical case, a small radius effectively represents a sharp tip rod, while larger, centimeter‐scale radii represent blunted tips. In cylindrical geometries, small radii resemble thin wires. We solve continuity equations in the gap and estimate a critical radius and minimum breakdown voltage that allows the formation of a glow discharge. We show that glow coronæ form more easily in Mars's low‐pressure, CO₂‐rich atmosphere than in Earth's high‐pressure, N₂‐rich atmosphere. Additionally, we present breakdown criteria for Titan and Venus, two planets where discharge processes have been postulated. We further demonstrate that critical voltage minima occur at 0.5 cm⋅Torr for all three investigated geometries, suggesting easier initiation around millimeter‐size particles in dust and water clouds. This approach could be readily extended to examine other multiphase flows with inertial particles.

Whitepaper #072 in the Decadal Survey for Solar and Space Physics (Heliophysics) 2024-2033. Main topics: space weather applications; basic research. Additional topics: space weather research/operations/research loop; other basic research; other space weather; system science.

In this work, we focus on plasma discharges produced between two electrodes with a high potential difference, resulting in the ionization of the neutral particles supporting a current in the gaseous medium. At low currents and low temperatures, this process can create luminescent emissions: the glow and corona discharges. The parallel plate geometry used in Townsend’s (1900) theory lets us develop a theoretical formalism, with explicit solutions for the critical voltage effectively reproducing experimental Paschen curves. However, most discharge processes occur in non-parallel plate geometries, such as discharges between grains or ice particles in multiphase flows. Here, we propose a generalization of the classic parallel plate configurations to concentric spherical and coaxial cylindrical geometries in Earth, Mars, Titan, and Venus atmospheres. In a spherical case, a small radius effectively represents a sharp tip rod, while larger, centimeter-scale radii represent blunted tips. Similarly, in a cylindrical case, a small radius corresponds to a thin wire. We solve continuity equations in the gap and estimate a critical radius and minimum breakdown voltage that allows ionization of neutral gas and formation of a glow discharge. We show that glow coronæ form more easily in Mars’s low-pressure, CO2-rich atmosphere than in Earth’s high-pressure atmosphere. Addition- ally, we present breakdown criteria for Titan and Venus. We further demonstrate that critical voltage minima occur at 0.5 cm·Torr for all three investigated geometries, suggesting easier initiation around millimeter-size particles in dust and water clouds and could be readily extended to examine other multiphase flows with inertial particles.

We utilize the Planet Model Code [1] to model the probability of survival of Earth-like life on habitable worlds (to 3 billion years post-abiogenesis). The Planet Model Code [1] was originally created by Tyrrell [2] to investigate the chances of intelligent life. This necessitates stability in a rather narrow temperature range. Here we expand the focus to the survival of any life, including extremophiles, with greater tolerance for variations in temperature. Specifically, we investigate the relationship between the long-term survival probability of life and larger temperature variations. Keywords: Exoplanet; Habitable; Prokaryote; Matlab; Planet Model Code References: 1. T. Tyrrell, Planets model code, (Oct. 2020) https://doi.org/10.5281/zenodo.4081451. 2. T. Tyrrell, “Chance played a role in determining whether earth stayed habitable”, Commu- nications Earth & Environment 1, 1–10 (2020).

Gigantic jets are atmospheric electrical discharges that propagate from the top of thunderclouds to the lower ionosphere. They begin as lightning leaders inside the thundercloud, and the thundercloud charge structure primarily determines if the leader is able to escape upward and form a gigantic jet. No observationally verified studies have been reported on the thundercloud charge structures of the parent storms of gigantic jets. Here we present meteorological observations and lightning simulation results to identify a probable thundercloud charge structure of those storms. The charge structure features a narrow upper charge region that forms near the end of an intense convective pulse. The convective pulse produces strong storm top divergence and turbulence, as indicated by large values of storm top radial velocity differentials and spectrum width. The simulations show the charge structure produces leader trees closely matching observations. This charge structure may occur at brief intervals during a thunderstorm’s evolution due to the brief nature of convective pulses, which may explain the rarity of gigantic jets compared to other forms of atmospheric electrical discharges.