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At least 1,117 records · Page 62
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

A reduced model for the ITER divertor based on SOLPS solutions for ITER Q = 10 baseline conditions: A. identifying options for the control parameters*

Edge codes such as SOLPS coupled to neutral codes such as EIRENE have become so comprehensive and sophisticated that they now constitute, in effect, 'code-experiments' that, as for actual experiments, can benefit from interpretation using simple models and conceptual frameworks, i.e. reduced models. The first task is the identification of options for the reduced model control parameters that are best suited for control of the action of the divertor, i.e. for control of target power loading and sputter-erosion, primarily. A strong correlation between the electron temperature at the divertor target, T e,t , and the neutral deuterium D 2 density at the target, n D2,t , flux-tube resolved, has recently been reported for a number of code studies including SOLPS-4.3 modeling of a set of ~50 ITER baseline cases: Q DT = 10, q 95 = 3, P SOL = 100 MW, metallic walls, and Ne seeding. This part A of the present study reports new results for largely the same ITER cases, confirming the strong correlations reported earlier between local values of T e,t , and (i) n D2,t , and (ii) normalized volumetric losses of power and pressure in the divertor. Strong correlations have now also been found, and are reported here for the first time, between T e,t and all of the divertor target quantities of practical interest. A physical explanation for this surprising result has not been fully identified; nevertheless it has encouraging implications for reduced modeling of the ITER divertor. For such ITER conditions, (i) the global Ne injection rate, Inj Ne [Ne/s], and (ii) the electron temperature at the location on the target where the peak power deposition occurs, T e,t @q ⊥,pk (eV), are found to be promising reduced model control parameters. In the companion report, part B, a reduced model for the ITER divertor is developed and described in detail, based on reversed-direction 2 point modelling, Rev2PM. The input to the reduced model is a value of the variable pair (T et @q ⟂,pk ,Inj Ne ) and the output are values of the various target as well as divertor-entrance quantities of practical interest, e.g. q ⊥,pk , n e,Xpt (the electron density at the poloidal location of the X-point), etc. In part B the reduced model is quantitatively characterized using one half of the code cases; it is then used to successfully predict (replicate) the code values of e.g. n e,Xpt for the other half of the cases.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS2019

Astrochemical Bistability: Autocatalysis in Oxygen Chemistry

The origin of bistable solutions in the kinetic equations describing the chemistry of dense interstellar clouds is explained as being due to the autocatalysis and feedback of oxygen nuclei from the oxygen dimer (O2). We identify four autocatalytic processes that can operate in dense molecular clouds, driven respectively by reactions of H+, He+, C+, and S+ with O2. We show that these processes can produce the bistable solutions found in previous studies, as well as the dependence on various model parameters such as the helium ionization rate, the sulfur depletion and the H+ electron recombination rate. We also show that ion–grain neutralizations are unlikely to affect the occurrence of bistability in dense clouds. It is pointed out that many chemical models of astronomical sources should have the potential to show bistable solutions.

Dufour, Gwenaelle C.↗
NASA NTRS2019

Astrochemical Bistability: Autocatalysis in Oxygen Chemistry

The origin of bistable solutions in the kinetic equations describing the chemistry of dense interstellar clouds is explained as being due to the autocatalysis and feedback of oxygen nuclei from the oxygen dimer (O2).We identify four autocatalytic processes that can operate in dense molecular clouds, driven respectively by reactions of H+, He+, C+, and S+ with O2. We show that these processes can produce the bistable solutions found in previous studies, as well as the dependence on various model parameters such as the helium ionization rate, the sulfur depletion and the H+3 electron recombination rate. We also show that iongrain neutralizations are unlikely to affect the occurrence of bistability in dense clouds. It is pointed out that many chemical models of astronomical sources should have the potential to show bistable solutions. It is pointed out that many chemical models of astronomical sources should have the potential to show bistable solutions.

Gwenaelle Dufour↗
NASA NTRS2019

Astrochemical Bistability: Autocatalysis in Oxygen Chemistry

The origin of bistable solutions in the kinetic equations describing the chemistry of dense interstellar clouds is explained as being due to the autocatalysis and feedback of oxygen nuclei from the oxygen dimer (O2).We identify four autocatalytic processes that can operate in dense molecular clouds, driven respectively by reactions of H(+), He(+), C(+), and S(+) with O2. We show that these processes can produce the bistable solutions found in previous studies, as well as the dependence on various model parameters such as the helium ionization rate, the sulfur depletion and the H3(+) electron recombination rate. We also show that ion–grain neutralizations are unlikely to affect the occurrence of bistability in dense clouds. It is pointed out that many chemical models of astronomical sources should have the potential to show bistable solutions.

Gwénaëlle Dufour↗
DOE OSTI2023

Elucidating the Molecular Origins of the Transference Number in Battery Electrolytes Using Computer Simulations

The rate at which rechargeable batteries can be charged and discharged is governed by the selective transport of the working ions through the electrolyte. Conductivity, the parameter commonly used to characterize ion transport in electrolytes, reflects the mobility of both cations and anions. The transference number, a parameter introduced over a century ago, sheds light on the relative rates of cation and anion transport. This parameter is, not surprisingly, affected by cation–cation, anion–anion, and cation–anion correlations. In addition, it is affected by correlations between the ions and neutral solvent molecules. Computer simulations have the potential to provide insights into the nature of these correlations. We review the dominant theoretical approaches used to predict the transference number from simulations by using a model univalent lithium electrolyte. In electrolytes of low concentration, one can obtain a quantitative model by assuming that the solution is made up of discrete ion-containing clusters–neutral ion pairs, negatively and positively charged triplets, neutral quadruplets, and so on. These clusters can be identified in simulations using simple algorithms, provided their lifetimes are sufficiently long. In concentrated electrolytes, more clusters are short-lived and more rigorous approaches that account for all correlations are necessary to quantify transference. Elucidating the molecular origin of the transference number in this limit remains an unmet challenge.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Theoretical model of dielectrophoretic water vapor condensation during multiphase flow of electrically charged water droplets in air

Water droplet growth in air, influenced by vapor diffusion and electrical charging, has significant implications for indoor air quality, cloud formation, and aerosol dynamics. Here, this study presents a comprehensive theoretical model that describes the growth dynamics of electrically charged water droplets under external electric fields, incorporating diffusion, electrostatic, and dielectrophoretic forces to enhance understanding and practical applications in air dehumidification and environmental control. A theoretical model was established to analyze the growth dynamics of the charged water droplets. The approach extended the thermodynamic framework of the Modified Kelvin-Thomson equation by integrating electrostatic and dielectrophoretic effects, enabling a comprehensive evaluation of vapor concentration near the surface of charged droplets. A sensitivity analysis was performed to assess the roles of droplet size, electric field intensity, surface charge, and vapor concentration on condensation rates. The study progressed beyond the classical diffusion-limited growth of neutral droplets, addressing the behavior of charged droplets in electrohydrodynamic environments. The model highlighted the significance of dielectrophoretic drift flux for dipolar vapor molecules, especially in micron-sized droplets ranging from 10 to 100 µm. Findings demonstrated that, for smaller droplets subjected to elevated electrical charge, average growth rates varied from 0.3 to 1.6 µm/s if the air relative humidity increased from 50 to 100 %. Analytical results are corroborated by numerical simulations, which exhibited strong concordance, thereby validating the proposed theoretical approach. This research introduced an innovative and scalable analytical methodology for electric field-enhanced droplet growth, offering valuable insights into the advancement of energy-efficient air dehumidification, water desalination, and atmospheric water harvesting technologies.

42 ENGINEERING↗
NASA NTRSDate not supplied

Sampling the ENSO response to tropical volcanic eruptions in the GISS-E2-1 model: physical & biogeochemical ocean effects

Despite observational evidence that an El-Niño is likely to follow tropical volcanic eruptions (Predybaylo et al, 2017), modelling studies have so far reached no consensus on either the sign or physical mechanism of El Niño response to volcanism (Khodri et al, 2017) . A previous modelling study found that following the Pinatubo eruption, the tropical Pacific developed El Niño-like conditions that triggered a decrease in the upwelling of DIC and increased carbon uptake (Eddebbar et al., 2019). However, the carbon cycle response to volcanisms as it depends on ENSO phase remains unclear. Here we perform thirty ensemble control simulations using the GISS-E2-1-G model to sample the pre-industrial control ENSO cycle and thirty more to superimpose a Pinatubo-like volcanic eruption. We find that the model tends to favor the development of a weak El-Niño following the volcanic eruption only in the case of a volcano that erupts at the start of a neutral ENSO phase. In response to the weak El-Niño, some anomalies have the same sign as those that develop from a strong El-Niño, such as weaker winds, shallower mixed layer depths, less direct but more diffuse radiation at the surface of the ocean, less nitrate, and lower primary productivity. However, other anomalies show the opposite sign as those from a strong El-Niño, such as more precipitation, less surface DIC, and less surface ocean pCO 2 . In contrast to the neutral phase, the volcanic response during positive ENSO and negative ENSO phases are swamped by the model’s internal variability.

ENSO↗
DOE OSTI2024

Confinement performance predictions for a high field axisymmetric tandem mirror

This paper presents Hammir tandem mirror confinement performance analysis based on Realta Fusion's first-of-a-kind model for axisymmetric magnetic mirror fusion performance. This model uses an integrated end plug simulation model including, heating, equilibrium, and transport combined with a new formulation of the plasma operation contours (POPCONs) technique for the tandem mirror central cell. Using this model in concert with machine learning optimization techniques, it is shown that an end plug utilizing high temperature superconducting magnets and modern neutral beams enables a classical tandem mirror pilot plant producing a fusion gain Q > 5. The approach here represents an important advance in tandem mirror design. The high fidelity end plug model enables calculations of heating and transport in the highly non-Maxwellian end plug to be made more accurately. The detailed end plug modelling performed in this work has highlighted the importance of classical radial transport and neutral beam absorption efficiency on end plug viability. The central cell POPCON technique allows consideration of a wide range of parameters in the relatively simple near-Maxwellian central cell, facilitating the selection of more optimal central cell plasmas. These advances make it possible to find more conservative classical tandem mirror fusion pilot plant operating points with lower temperatures, neutral beam energies, and end plug performance requirements than designs in the literature. Despite being more conservative, it is shown that these operating points have sufficient confinement performance to serve as the basis of a viable fusion pilot plant provided that they can be stabilized against MHD and trapped particle modes.

FOS: Physical sciences↗
DOE OSTI2020

Time-dependent modeling of coupled plasma-wall dynamics

Effects of dynamic wall outgassing on divertor plasma during an ELM-like heat pulse are modelled using newly coupled edge plasma code UEDGE and all reaction-diffusion code FACE. Different divertor regimes are simulated depending on the degree of the plasma detachment. It is shown that hydrogen outgassing from the divertor target plate induced by ELM pulse in the semi-detached regime can trigger deep plasma detachment. The induced detachment does not spontaneously reverse after the pulse due to ineffective implantation of low energy plasma hydrogen in the target material. Furthermore, we demonstrate that plasma neutrals play essential role in heat transport in a detached divertor. The modelled hydrogen dynamics in the wall material demonstrates that the heat pulse leads to enhanced hydrogen transport toward the wall bulk.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1997

The Wardle Instability in Interstellar Shocks: Gas Temperture and Line Emission - 2

We have modeled the gas temperature structure in unstable C-type shocks and obtained predictions for the resultant CO and H2 rotational line emissions, using numerical simulations of the Wardle instability. Our model for the thermal balance of the gas includes ion-neutral frictional heating; compressional heating; radiative cooling due to rotational and ro-vibrational transitions of the molecules CO, H2O, and H2; and gas-grain collisional cooling. We obtained results for the gas temperature distribution in-and H2 and CO line emission from-shocks of neutral Alfvenic Mach number 10 and velocity 20 or 40 km/ s in which the Wardle instability has saturated. Both two- and three-dimensional simulations were carried out for shocks in which the preshock magnetic field is perpendicular to the shock propagation direction, and a two-dimensional simulation was carried out for the case in which the magnetic field is obliquely oriented with respect to the shock propagation direction. Although the Wardle instability profoundly affects the density structure behind C-type shocks, most of the shock-excited molecular line emission is generated upstream of the region where the strongest effects of the instability are felt. Thus the Wardle instability has a relatively small effect on the overall gas temperature distribution in-and the emission-line spectrum from-C-type shocks, at least for the cases that we have considered. In none of the cases that we have considered thus far did any of the predicted emission-line luminosities change by more than a factor of 2.5, and in most cases the effects of instability were significantly smaller than that. Slightly larger changes in the line luminosities seem likely for three-dimensional simulations of oblique shocks, although such simulations have yet to be carried out and lie beyond the scope of this study. Given the typical uncertainties that are always present when model predictions are compared with real astronomical data, we conclude that Wardle instability does not imprint any clear observational signature on the shock-excited CO and H2 line strengths. This result justifies the use of one-dimensional steady shock models in the interpretation of observations of shock-excited line emission in regions of star formation. Our three-dimensional simulations of perpendicular shocks revealed the presence of warm filamentary structures that are aligned along the magnetic field, a result that is of possible relevance to models of water maser emission from C-type shocks.

Neufeld, David A.↗
NASA NTRS1999

Photodissociation Regions in the Interstellar Medium of Galaxies

The interstellar medium of galaxies is the reservoir out of which stars are born and into which stars inject newly created elements as they age. The physical properties of the interstellar medium are governed in part by the radiation emitted by these stars. Far-ultraviolet (6 eV less than h(nu) less than 13.6 eV) photons from massive stars dominate the heating and influence the chemistry of the neutral atomic gas and much of the molecular gas in galaxies. Predominantly neutral regions of the interstellar medium in which the heating and chemistry are regulated by far ultraviolet photons are termed Photo-Dissociation Regions (PDRs). These regions are the origin of most of the non-stellar infrared (IR) and the millimeter and submillimeter CO emission from galaxies. The importance of PDRs has become increasingly apparent with advances in IR and submillimeter astronomy. The IR emission from PDRs includes fine structure lines of C, C+, and O; rovibrational lines of H2, rotational lines of CO; broad middle features of polycyclic aromatic hydrocarbons; and a luminous underlying IR continuum from interstellar dust. The transition of H to H2 and C+ to CO occurs within PDRs. Comparison of observations with theoretical models of PDRs enables one to determine the density and temperature structure, the elemental abundances, the level of ionization, and the radiation field. PDR models have been applied to interstellar clouds near massive stars, planetary nebulae, red giant outflows, photoevaporating planetary disks around newly formed stars, diffuse clouds, the neutral intercloud medium, and molecular clouds in the interstellar radiation field-in summary, much of the interstellar medium in galaxies. Theoretical PDR models explain the observed correlations of the [CII] 158 microns with the COJ = 1-0 emission, the COJ = 1-0 luminosity with the interstellar molecular mass, and the [CII] 158 microns plus [OI] 63 microns luminosity with the IR continuum luminosity. On a more global scale, MR models predict the existence of two stable neutral phases of the interstellar medium, elucidate the formation and destruction of star-forming molecular clouds, and suggest radiation-induced feedback mechanisms that may regulate star formation rates and the column density of gas through giant molecular clouds.

Hollenbach, David J.↗
NASA NTRS2000

Photodissociation Regions

The interstellar medium of galaxies is the reservoir out of which stars are born and into which stars inject newly created elements as they age. The physical properties of the interstellar medium are governed in part by the radiation emitted by these stars. Far-ultraviolet (6 eV< hNu < 13.6 eV) photons from massive stars dominate the heating and influence the chemistry of the neutral atomic gas and much of the molecular gas in galaxies. Predominantly neutral regions of the interstellar medium in which the heating and chemistry are regulated by far ultraviolet photons are termed Photodissociation Regions (PDRs). These regions are the origin of most of the non-stellar infrared (IR) and the millimeter and submillimeter CO emission from galaxies. The importance of PDRs has become increasingly apparent with the advances in IR and submillimeter astronomy. The IR emission from PDRs includes fine structure lines of C, C(+) and O; rovibrational lines of H2; rotational lines of CO; broad mid-IR features of polycyclic aromatic hydrocarbons; and a luminous underlying IR continuum from interstellar dust. The transition of H to H2 and C(+) to CO occurs within PDRs. Comparison of observations with theoretical models of PDRs enables one to determine the density and temperature structure, the elemental abundances, the level of ionization, and the radiation field. PDR models have been applied to interstellar clouds near massive stars, planetary nebulae, red giant outflows, photoevaporating planetary disks around newly formed stars, diffuse clouds, the neutral intercloud medium, and molecular clouds in the interstellar radiation field-in summary, much of the interstellar medium in galaxies. Theoretical PDR models explain the observed correlations of the [CII] 158, micrometers with the CO J=1-0 emission, the CO J=1-0 luminosity with the interstellar molecular mass, and the [CII] 158 micrometers plus [OI] 63 micrometers luminosity with the IR continuum luminosity. On a more global scale, PDR models predict the existence of two stable neutral phases of the interstellar medium, elucidate the formation and destruction of star-forming molecular clouds, and suggest radiation-induced feedback mechanisms that may regulate star formation rates and the column density of gas through giant molecular clouds.

Hollenbach, David J.↗
DOE OSTI2024

False vacuum decay and nucleation dynamics in neutral atom systems

Metastable states of quantum many-body systems with confinement offer a means to simulate false vacuum phenomenology, including nonequilibrium dynamical processes like decay by nucleation, in truncated limits. Recent work has examined the decay process in one-dimensional (1D) ferromagnetic Ising spins and superfluids. Here, in this paper, we study nucleation dynamics in 1D antiferromagnetic neutral atom chains with Rydberg interactions, using both numerical simulations and analytic modeling. We apply a staggered local detuning field to generate the metastable and ground states. Our efforts focus on two dynamical regimes: decay and annealing. In the first, we corroborate the phenomenological decay rate scaling and determine the associated parameter range for the decay process; in the second, we uncover and elucidate a procedure to anneal the metastable state from the initial to the final system, with intermediate nucleation events. We further propose experimental protocols to prepare the required states and perform quenches on near-term neutral atom quantum simulators, examining the experimental feasibility of our proposed setup and parameter regime.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

The emergence of macroscopic currents in photoconductive sampling of optical fields

Photoconductive field sampling enables petahertz-domain optoelectronic applications that advance our understanding of light-matter interaction. Despite the growing importance of ultrafast photoconductive measurements, a rigorous model for connecting the microscopic electron dynamics to the macroscopic external signal is lacking. This has caused conflicting interpretations about the origin of macroscopic currents. Here, we present systematic experimental studies on the signal formation in gas-phase photoconductive sampling. Our theoretical model, based on the Ramo–Shockley-theorem, overcomes the previously introduced artificial separation into dipole and current contributions. Extensive numerical particle-in-cell-type simulations permit a quantitative comparison with experimental results and help to identify the roles of electron-neutral scattering and mean-field charge interactions. The results show that the heuristic models utilized so far are valid only in a limited range and are affected by macroscopic effects. Our approach can aid in the design of more sensitive and more efficient photoconductive devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2013

Jovian Plasmas Torus Interaction with Europa. Plasma Wake Structure and Effect of Inductive Magnetic Field: 3D Hybrid Kinetic Simulation

The hybrid kinetic model supports comprehensive simulation of the interaction between different spatial and energetic elements of the Europa moon-magnetosphere system with respect to a variable upstream magnetic field and flux or density distributions of plasma and energetic ions, electrons, and neutral atoms. This capability is critical for improving the interpretation of the existing Europa flyby measurements from the Galileo Orbiter mission, and for planning flyby and orbital measurements (including the surface and atmospheric compositions) for future missions. The simulations are based on recent models of the atmosphere of Europa (Cassidy et al., 2007; Shematovich et al., 2005). In contrast to previous approaches with MHD simulations, the hybrid model allows us to fully take into account the finite gyroradius effect and electron pressure, and to correctly estimate the ion velocity distribution and the fluxes along the magnetic field (assuming an initial Maxwellian velocity distribution for upstream background ions). Photoionization, electron-impact ionization, charge exchange and collisions between the ions and neutrals are also included in our model. We consider the models with Oþ þ and Sþ þ background plasma, and various betas for background ions and electrons, and pickup electrons. The majority of O2 atmosphere is thermal with an extended non-thermal population (Cassidy et al., 2007). In this paper, we discuss two tasks: (1) the plasma wake structure dependence on the parameters of the upstream plasma and Europa's atmosphere (model I, cases (a) and (b) with a homogeneous Jovian magnetosphere field, an inductive magnetic dipole and high oceanic shell conductivity); and (2) estimation of the possible effect of an induced magnetic field arising from oceanic shell conductivity. This effect was estimated based on the difference between the observed and modeled magnetic fields (model II, case (c) with an inhomogeneous Jovian magnetosphere field, an inductive magnetic dipole and low oceanic shell conductivity).

Jovian magnetosphere↗
DOE OSTI2025

Confinement performance predictions for a high field axisymmetric tandem mirror

This paper presents a Hammir tandem mirror confinement performance analysis based on Realta Fusion’s first-of-a-kind model for axisymmetric magnetic mirror fusion performance. This model uses an integrated end plug simulation model including, heating, equilibrium and transport combined with a new formulation of the plasma operation contours (POPCONs) technique for the tandem mirror central cell. Using this model in concert with machine learning optimization techniques, it is shown that an end plug utilizing high temperature superconducting magnets and modern neutral beams enables a classical tandem mirror pilot plant producing a fusion gain Q > 5. The approach here represents an important advance in tandem mirror design. The high-fidelity end plug model enables calculations of heating and transport in the highly non-Maxwellian end plug to be made more accurately. The detailed end plug modelling performed in this work has highlighted the importance of classical radial transport and neutral beam absorption efficiency on end plug viability. The central cell POPCON technique allows consideration of a wide range of parameters in the relatively simple near-Maxwellian central cell, facilitating the selection of more optimal central cell plasmas. These advances make it possible to find more conservative classical tandem mirror fusion pilot plant operating points with lower temperatures, neutral beam energies and end plug performance requirements than designs in the literature. Despite being more conservative, it is shown that these operating points have sufficient confinement performance to serve as the basis of a viable fusion pilot plant provided that they can be stabilized against magnetohydrodynamic and trapped particle modes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1989

Formation and eruption of solar prominences

A model for the magnetic field associated with solar prominences is considered. It is shown that flux cancellation at the neutral line of a sheared magnetic arcade leads to the formation of helical field lines which are capable, in principle, of supporting prominence plasma. A numerical method for the computation of force-free, canceling magnetic structures is presented. Starting from an initial potential field we prescribe the motions of magnetic footpoints at the photosphere, with reconnection occurring only at the neutral line. As more and more flux cancels, magnetic flux is transferred from the arcade field to the helical field. Results for a particular model of the photospheric motions are presented. The magnetic structure is found to be stable: the arcade field keeps the helical field tied down at the photosphere. The axis of the helical field moves to larger and larger height, suggestive of prominence eruption. These results suggest that prominence eruptions may be trigered by flux cancellation.

Van Ballegooijen, A. A.↗
NASA NTRS2010

Jovian Plasma Torus Interaction with Europa: 3D Hybrid Kinetic Simulation. First results

The hybrid kinetic model supports comprehensive simulation of the interaction between different spatial and energetic elements of the Europa-moon-magnetosphere system with respect to variable upstream magnetic field and flux or density distributions of plasma and energetic ions, electrons, and neutral atoms. This capability is critical for improving the interpretation of the existing Europa flyby measurements from the Galileo orbiter mission, and for planning flyby and orbital measurements, (including the surface and atmospheric compositions) for future missions. The simulations are based on recent models of the atmosphere of Europa (Cassidy etal.,2007;Shematovichetal.,2005). In contrast to previous approaches with MHD simulations, the hybrid model allows us to fully take into account the finite gyro radius effect and electron pressure, and to correctly estimate the ion velocity distribution and the fluxes along the magnetic field (assuming an initial Maxwellian velocity distribution for upstream background ions).Non-thermal distributions of upstream plasma will be addressed in future work. Photoionization,electron-impact ionization, charge exchange and collisions between the ions and neutrals are also included in our model. We consider two models for background plasma:(a) with O(++) ions; (b) with O(++) and S(++) ions. The majority of O2 atmosphere is thermal with an extended cold population (Cassidyetal.,2007). A few first simulations already include an induced magnetic dipole; however, several important effects of induced magnetic fields arising from oceanic shell conductivity will be addressed in later work.

Lipatov, A. S.↗