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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Modeling and analysis of the tritium fuel cycle for ARC- and STEP-class D-T fusion power plants

Abstract The limited tritium resources available for the first fusion power plants (FPPs) make fuel self-sufficiency and tritium inventory minimization leading issues in FPP design. This work builds on the model proposed by Abdou et al (2020 Nucl. Fusion 61 013001), which analyzed the fuel cycle (FC) of a DEMOnstration nuclear FPP-class FPP with a time-dependent system-level model. Here, we use a modified version of their model to analyze the FC of an Affordable, Robust, Compact (ARC)-class tokamak and two versions of a Spherical Tokamak for Energy Production (STEP)-class tokamak. The ARC-class tokamak breeds tritium in a 2LiF + BeF 2 liquid immersion blanket, while the STEP-class tokamak breeds tritium utilizing either a liquid-lithium blanket design or an encapsulated breeding blanket. A time-dependent system-level model is developed in Matlab Simulink ® to simulate the evolution of tritium flows and tritium inventories in the FC. The main goals of this work are to assess tritium self-sufficiency of the ARC- and STEP-class designs and to determine quantitative design requirements that can be used to analyze the adequacy of a proposed FC system. These design requirements are aimed at achieving a low tritium inventory doubling time ( t d ) and a low start-up inventory ( I s t a r t u p ) while keeping the required tritium breeding ratio (TBR r ) as low as possible. We also consider how improvements in FC technology and POs affect TBR r and I s t a r t u p . The model results show that TBR r for ARC- and STEP-class FPPs should be achievable if the tritium burn efficiency (TBE) reaches 0.5%–1% (TBR r < 1.2). This assumes significant, but attainable, improvements over current abilities. However, the model results indicate that an FPP must achieve ambitious performance targets, including FPP availability > 70%, tritium processing time < 4 h, and the implementation of direct internal recycling (DIR). If future research yields major improvements to achievable TBE, it may be possible to achieve tritium self-sufficiency while operating at lower availability and without implementing DIR.

Physics↗
DOE OSTI2023

Probabilistic Failure Criterion of SiC/SiC Composites Under Multiaxial Loading

Owing to its excellent mechanical properties and stability under high temperature and neutron irradiation conditions, SiC/SiC composites have emerged as a promising material for light water reactors (LWRs) in the development of accident-tolerant fuel (ATF) systems. Structural integrity and retention of hermeticity are two crucial requirements for SiC/SiC claddings during normal operations, and both of them are closely related to the proportional limit stress (PLS) of the material. Understanding the behavior of SiC/SiC composites under multiaxial stress states and developing a probabilistic approach for evaluating the structural vulnerability are of paramount importance for reliability-based analysis and design of SiC/SiC composite claddings. So far, there has been very limited effort towards experimental and analytical investigations of probabilistic failure of SiC/SiC claddings. This critical knowledge gap motivates this research. A probabilistic failure criterion for SiC/SiC composites under multi-axial loading is developed, and this criterion is incorporated into reliability analysis of the structural integrity of SiC/SiC fuel cladding. The research consists of two parts: 1) experimental investigation of multiaxial failure behavior of SiC/SiC composites, and 2) theoretical modeling of time-dependent probabilistic failure of SiC/SiC cladding. In the experimental investigation, the PLS is determined through the examination of stress-strain response, the acoustic emission measurement, as well as the X-ray computed tomography. The theoretical framework is derived by combin- ing the finite weakest-link statistical model and the subcritical damage growth model. This theoretical model captures the time-dependent failure mechanism of the material, which has a major consequence for predicting the lifetime distribution of the cladding. Meanwhile, the model also predicts that the failure statistics of the cladding depends strongly on the cladding length. The results of the multiaxial experiments reveal the level of statistical variation of the PLS of SiC/SiC materials under different stress states. The theoretical model provides a robust analytical tool for extrapolation of small-scale laboratory test results to the behavior of full-scale claddings. These findings establish a scientific foundation for the development of reliability-based design of SiC/SiC fuel claddings, which will play an essential role in improving the structural safety and integrity of LWRs.

42 ENGINEERING↗
NASA NTRS1973

Derivation of a three dimensional numerical water quality model for estuary and continental shelf application

A derivation is given for a three dimensional mass transport equation which is appropriate for numerical modeling of estuary and continental shelf water quality variations for both the time dependent and steady state cases. A finite difference approximation to the derived equation is presented and a solution scheme for the resulting equations outlined. Preliminary results are obtained using the model for the extremely simple problems which have analytical solutions. The numerical model, as presented, will provide a scheme to study water quality problems in coastal waters for both steady state and time dependent cases.

Spaulding, M.↗
NASA NTRS1987

Calculation of helicopter rotor blade/vortex interaction by Navier-Stokes procedures

Interactions of a modern rotor blade with concentrated tip vortices from the previous blades can have a significant influence on the airloads and the aeroacoustics of a helicopter. A better understanding of the blade/vortex interaction process and a method of analyzing its flow field would provide valuable help in the design of helicopters. The work discussed herein represents an initial effort in applying a 3-D, time-dependent Navier-Stokes simulation to the blade vortex interaction problem. The numerical approach is the Linearized Block Implicit (LBI) technique. In this initial effort, consideration is given to the interaction of a wing of idealized geometry and a vortex whose axis is aligned at an arbitrary angle to the wing. The calculations are made for laminar, subsonic flow, and show the time dependent pressure distribution and flow fields resulting from the interaction.

Kim, Y.-N.↗
NASA NTRS2000

Mesosphere Dynamics with Gravity Wave Forcing: Planetary Waves - 2

We present results from a non-linear, 3D, time dependent numerical spectral model (NSM) which extends from the ground up into the thermosphere and incorporates Hines' Doppler Spread Parameterization for small-scale gravity waves (GW). Our focal point is the mesosphere where wave interactions are playing a dominant role. We discuss planetary waves in the present paper and diurnal and semi-diurnal tides in the companion paper. Without external time dependent energy or momentum sources, planetary waves (PWs) are generated in the model for zonal wavenumbers 1 to 4, which have amplitudes in the mesosphere above 50 km as large as 30 m/s and periods between 2 and 50 days. The waves are generated primarily during solstice conditions, which indicates that the baroclinic instability (associated with the GW driven reversal in the latitudinal temperature gradient) is playing an important role. Results from a numerical experiment show that GWs are also involved directly in generating the PWs. For the zonal wavenumber m = 1, the predominant wave periods in summer are around 4 days and in winter between 6 and 10 days. For m = 2, the periods are in summer and close to 2.5 and 3.5 days respectively For m = 3, 4 the predominant wave periods are in both seasons close to two days. The latter waves have the characteristics of Rossby gravity waves with meridional winds at equatorial latitudes. A common feature of the PWs (m = 1 to 4) generated in summer and winter is that their vertical wavelengths throughout the mesosphere are large which indicates that the waves are not propagating freely but are generated throughout the region. Another common feature is that the PWs propagate preferentially westward in summer and eastward in winter, being launched from the westward and eastward zonal winds that prevail respectively in summer and winter altitudes below 80 km. During spring and fall, for m = 1 and 2 eastward propagating long period PWs are generated that are launched from the smaller eastward zonal winds that prevail in these seasons. PWs generated in the model produce large amplitude modulations of the diurnal tides at altitudes above 80 km and contribute to their seasonal variations.

Mayr, H. G.↗
DOE OSTI2025

Immersive Scientific Visualization of Molten-Salt Reactor Waste Characteristics Using Virtual Reality

Immersive visualization is changing how we explore, communicate, and understand complex scientific systems. In nuclear energy, an area in which data are often multidimensional, time-dependent, and difficult to interpret, virtual reality (VR) represents a powerful and intuitive informational medium. This work introduces a VR-based platform that visualizes the post-shutdown behavior and waste management lifecycle of molten-salt reactors (MSRs), a next-generation reactor type with unique operational and safety characteristics. The platform, built in Unity, is streamed on the Meta Quest 3 headset. It transforms high-fidelity simulation data into an interactive, immersive experience. Users can explore time-dependent reactor characteristics such as nuclide decay, which is a key factor for evaluating reactor waste strategies. The datasets were generated using the MOOSE (Multiphysics Object-Oriented Simulation Environment) framework and then processed through ParaView scripting for smooth integration into Unity. From a visualization standpoint, the platform emphasizes spatial storytelling, temporal exploration, and user-centered interaction. Users can navigate 3D reactor geometries, slice through volumetric data, and manipulate time to observe how physical phenomena evolve. Real-scale rendering and embodied interaction make the experience feel tangible. The interface is designed to be accessible, even to those without nuclear or simulation expertise. This lowers the barrier for stakeholders, policymakers, and the general public, while still supporting expert analysis and collaborative decision-making. This work shows how immersive visualization can function as both a scientific tool and a communication interface. By integrating simulation, processing, and visualization into a cohesive workflow, we offer a scalable framework for immersive scientific storytelling. The modular design supports future extensions to other reactor types and lifecycle stages, from shutdown to long-term storage, making the platform adaptable for both research and outreach.

99 - GENERAL AND MISCELLANEOUS↗
DOE OSTI2025

High-Fidelity Modeling of Fuel-To-Coolant Thermomechanical Transport Behaviors Under Transient Conditions

This report summarizes the work completed under NEUP project number 21-24006. The objectives of this project are to advance the high-fidelity modeling capabilities and important phenomena that is important for high-burnup UO 2 and accident tolerant fuels (ATF) during transient conditions. Accurate modeling of the time-dependent phenomena that impact material performance must be used to determine the figures of merit and safety margin. Phenomena such as fuel fragmentation, cladding oxidation, pellet-clad interaction, clad ballooning, and clad rupture are examples that pose challenges to modeling during these transients. This project focused on the development of high-fidelity tightly coupled multiphysics models that can capture the time-dependent material response and associated thermal hydraulic conditions during these events. These models can then be validated against existing separate effects tests and in-pile integral experiments and will be used to model Transient Reactor Test facility (TREAT) loss-of-coolant accidents (LOCA) experiments. To achieve the project objective, we used a combination of NEAMS and NRC codes to model various LOCA test sets for the separate effects and in-pile integral experiments. BlueCRAB tool set, which can accurately predict material response at a sub-fuel pin level, as well as modeling the entire reactor system response to these events. Fuel performance was modeled using BISON (various versions) and FAST (version 1.2.1). BISON and FAST can model on a sub-fuel pin level the fuel performance under transient conditions. Both have simplified thermal hydraulic models that are capable of providing basic coolant boundary conditions. To better capture the thermomechanical interaction between the fuel, clad, and coolant, more sophisticated thermal hydraulic models are necessary.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS1977

Dynamical response of the solar corona. III - Numerical simulation of the 1973 June 10 coronal transient

A spherically symmetric adiabatic single-fluid model is outlined for simulating the nonlinear time-dependent response of the corona to solar events that are simulated by perturbations in the appropriate physical variables from their steady-state values at the coronal base. Several observed features of the coronal transient that occurred on June 10, 1973, are simulated by using a particular steady-state solar wind, a specific combination of density and temperature perturbations, and a particular time dependence of the perturbations. A different steady-state solar wind, a perturbation of shorter duration, and other perturbation combinations are also employed to simulate the same transient so that the effect of each quantity can be determined. It is found that the model cannot adequately simulate all the observational results for the investigated transient, that the steady-state solar wind is relatively unimportant in such numerical simulations, and that studies which attempt only to reproduce observed shock trajectories may lead to erroneous conclusions regarding the physics of the solar event that produced the transient.

Steinolfson, R. S.↗
NASA NTRS1980

On Rosen's theory of gravity and cosmology

Formal similarities between general relativity and Rosen's bimetric theory of gravity were used to analyze various bimetric cosmologies. The following results were found: (1) physically plausible model universes which have a flat static background metric, have a Robertson-Walker fundamental metric, and which allow co-moving coordinates do not exist in bimetric cosmology. (2) it is difficult to use the Robertson-Walker metric for both the background metric (gamma mu nu) and the fundamental metric tensor of Riemannian geometry( g mu nu) and require that g mu nu and gamma mu nu have different time dependences. (3) A consistency relation for using co-moving coordinates in bimetric cosmology was derived. (4) Certain spatially flat bimetric cosmologies of Babala were tested for the presence of particle horizons. (5) An analytic solution for Rosen's k = +1 model was found. (6) Rosen's singularity free k = +1 model arises from what appears to be an arbitary choice for the time dependent part of gamma mu nu.

Barnes, R. C.↗
NASA NTRS1982

Ionospheric hot spot at high latitudes

Schunk and Raitt (1980) and Sojka et al. (1981) have developed a model of the convecting high-latitude ionosphere in order to determine the extent to which various chemical and transport processes affect the ion composition and electron density at F-region altitudes. The numerical model produces time-dependent, three-dimensional ion density distributions for the ions NO(+), O2(+), N2(+), O(+), N(+), and He(+). Recently, the high-latitude ionospheric model has been improved by including thermal conduction and diffusion-thermal heat flow terms. Schunk and Sojka (1982) have studied the ion temperature variations in the daytime high-latitude F-region. In the present study, a time-dependent three-dimensional ion temperature distribution is obtained for the high-latitude ionosphere for an asymmetric convection electric field pattern with enhanced flow in the dusk sector of the polar region. It is shown that such a convection pattern produces a hot spot in the ion temperature distribution which coincides with the location of the strong convection cell.

Schunk, R. W.↗
NASA NTRS1990

A fully Sinc-Galerkin method for Euler-Bernoulli beam models

A fully Sinc-Galerkin method in both space and time is presented for fourth-order time-dependent partial differential equations with fixed and cantilever boundary conditions. The Sinc discretizations for the second-order temporal problem and the fourth-order spatial problems are presented. Alternate formulations for variable parameter fourth-order problems are given which prove to be especially useful when applying the forward techniques to parameter recovery problems. The discrete system which corresponds to the time-dependent partial differential equations of interest are then formulated. Computational issues are discussed and a robust and efficient algorithm for solving the resulting matrix system is outlined. Numerical results which highlight the method are given for problems with both analytic and singular solutions as well as fixed and cantilever boundary conditions.

Smith, R. C.↗
NASA NTRS2002

Outflow-Induced Dynamical and Radiative Instability in Stellar Envelopes with an Application to Luminous Blue Variables and Wolf-Rayet Stars

Theoretical models of the remnants of massive stars in a very hot, post-red-supergiant phase display no obvious instability if standard assumptions are made. However, the brightest observed classical luminous blue variables (LBVs) may well belong to such a phase. A simple time-dependent theory of moving stellar envelopes is developed in order to treat deep hydrodynamical disturbances caused by surface mass loss and to test the moving envelopes for dynamical instability. In the case of steady-state outflow, the theory reduces to the equivalent of the Castor, Abbott, and Klein formulation for optically thick winds at distances well above the sonic point. The time-dependent version indicates that the brightest and hottest LBVs are both dynamically and radiatively unstable, as a result of the substantial lowering of the generalized Eddington luminosity limit by the mass-loss acceleration. It is suggested that dynamical instability, by triggering secular cycles of mass loss, is primarily what differentiates LBVs from the purely radiatively unstable Wolf-Rayet stars. Furthermore, when accurate main-sequence mass-loss rates are used to calculate the evolutionary tracks, the predicted surface hydrogen and nitrogen abundances of the blue remnants agree much better with observations of the brightest LBVs than before.

Stothers, Richard B.↗
NASA NTRS1994

Using FU Orionis outbursts to constrain self-regulated protostellar disk models

One-dimensional, convective, vertical structure models and one dimensional time-dependent, radial diffusion models are combined to create a self-consistent picture in which FU Orionis outbursts occur in young stellar objects (YSOs) as the result of a large-scale, self-regulated, thermal ionization instability in the surrounding protostellar accretion disk. Although active accretion disks have long been postulated to be ubiqitous among low-mass YSOs, few constraints have until now been imposed on physical conditions in these disks. By fitting the results of time-dependent disk models to observed timescales of FU Orionis events, we estimate the magnitude of the effective viscous stress in the inner disk (r approximately less than 1 AU) to be, in accordance with an ad hoc 'alpha' prescription, the product of the local sound speed, pressure scale height, and an efficiency factor alpha of 10(exp -4) where hydrogen is neutral and 10(exp 3) where hydrogen is ionized. We hypothesize that all YSOs receive infall onto their outer disks which is steady (or slowly declining with time) and that FU Orionis outbursts are self-regulated, disk outbursts which occur only in systems which transport matter inward at a rate sufficiently high to cause hydrogen to be ionized in the inner disk. We estimate a critical mass flux of dm(sub crit)/dt = 5 x 10(exp 7) solar mass/yr independent of the magnitude of alpha for systems with one solar mass, three solar radius central objects. Infall accretion rates in the range of dm(sub in)/dt = 1-10) x 10(exp -6) solar mass/yr produce observed FU Orionis timescales consistent with estimates of spherical molecular cloud core collapse rates. Modeled ionization fronts are typically initiated near the inner edge of the disk and propogate out to a distance of several tens of stellar radii. Beyond this region, the disk transports mass steadily inward at the supplied constant infall rate. Mass flowing through the innermost disk annulus is equal to dm(sub in)/dt only in a time-averaged sense and is regulated by the ionization of hydrogen in the inner disk such that long intervals (approximately 1000 yr) of low-mass flux: (1-30) x 10(exp -8) solar mass/yr are punctuated by short intervals (approximately 100 yr) of high-mass flux: (1-30) x 10(exp -5) solar mass/yr. Timescales and mass fluxes derived for quiescent and outburst stages are consistent with estimates from observations of T Tauri and FU Orionis systems, respectively.

Bell, K. R.↗
DOE OSTI2024

Project DarkStar: Vision for LLNL in 2030

DarkStar was a Strategic Initiative (FY2021-FY2024) to investigate applications of Artificial Intelligence (AI) and Machine Learning (ML) to scientific problems of complex hydrodynamics, shockwave physics and energetic materials. The research focused on physics and engineering design as a process that can be tremendously accelerated through merging AI with advanced physics simulation on exascale-class platforms, and to experimentally validate this revolutionary new approach through dynamic materials campaigns. A central thread of scientific inquiry was in the application of AI to enable human understanding of how to control hydrodynamic instability (which has impacts to areas such as inertial confinement fusion) via engineering features and time-dependent sources. Motivated by an unfinished line of research started by Dr. Johnny von Neumann, AI-enabled simulation approaches were developed that allowed DarkStar researchers to uncover several ground-breaking discoveries regarding hydrodynamic instability, including how to completely suppress Richtmyer-Meshkov instability (RMI). These S&T discoveries, along with other advances, have shown the way for an entirely new approach to time-dependent problems known as inverse design – the idea that complex systems can be developed directly from a final state that is to be achieved and resolve the initial design via satisfying several constraints simultaneously via AI/ML. Through experimental campaigns conducted across a wide range of facilities in the NNSA complex (the High Explosive Application Facility at LLNL, the Dynamic Compression Sector/Advanced Photon Source at Argonne National Lab, and Special Technologies Laboratory at MSTS) the radical new AI/ML approach to engineering complex material dynamics was verified, establishing a new field of study within the realm of shock physics. As advanced manufacturing capabilities continue to develop, the great importance of inverse design as a means to apply that technology effectively for NNSA missions will feature prominently over this decade. DarkStar has positioned NNSA as a world-leader in this newly emerging cross-disciplinary area of AI methods for advanced physics simulation and pioneered multiple novel approaches that have enabled the broader scientific community. By allowing us to see past the horizon, to 2030 and beyond, DarkStar has illuminated the vast potential of AI/ML to impact a wide range of new national security missions and, consequently, multiple areas of further research have already emerged across the NNSA and DOD complex.

42 ENGINEERING↗
DOE OSTI2021

Multiphysics and Multiscale Modeling of Coupled Transport of Chloride Ions in Concrete

Chloride ions (Cl−)-induced corrosion is one of the main degradation mechanisms in reinforced concrete (RC) structures. In most situations, the degradation initiates with the transport of Cl− from the surface of the concrete towards the reinforcing steel. The accumulation of Cl− at the steel-concrete interface could initiate reinforcement corrosion once a threshold Cl− concentration is achieved. An accurate numerical model of the Cl− transport in concrete is required to predict the corrosion initiation in RC structures. However, existing numerical models lack a representation of the heterogenous concrete microstructure resulting from the varying environmental conditions and the indirect effect of time dependent temperature and relative humidity (RH) on the water adsorption and Cl− binding isotherms. In this study, a numerical model is developed to study the coupled transport of Cl− with heat, RH and oxygen (O2) into the concrete. The modeling of the concrete microstructure is performed using the Virtual Cement and Concrete Testing Laboratory (VCCTL) code developed by the U.S. National Institute of Standards and Technology (NIST). The concept of equivalent maturation time is utilized to eliminate the limitation of simulating concrete microstructure using VCCTL in specific environmental conditions such as adiabatic. Thus, a time-dependent concrete microstructure, which depends on the hydration reactions coupled with the temperature and RH of the environment, is achieved to study the Cl− transport. Additionally, Cl− binding isotherms, which are a function of the pH of the concrete pore solution, Cl− concentration, and weight fraction of mono-sulfate aluminate (AFm) and calcium-silicate-hydrate (C-S-H), obtained from an experimental study by the same authors are utilized to account for the Cl− binding of cement hydration products. The temperature dependent RH diffusion was considered to account for the transport of Cl− with moisture transport. The temperature and RH diffusion in the concrete domain, composite theory, and Cl− binding and water adsorption isotherms are used in combination, to estimate the ensuing Cl− diffusion field within the concrete. The coupled transport process of heat, RH, Cl−, and O2 is implemented in the Multiphysics Object-Oriented Simulation Environment (MOOSE) developed by the U.S. Idaho National Laboratory (INL). The model was verified and validated using data from multiple experimental studies with different concrete mixture proportions, curing durations, and environmental conditions. Additionally, a sensitivity analysis was performed to identify that the water-to-cement (w/c) ratio, the exposure duration, the boundary conditions: temperature, RH, surface Cl− concentration, Cl− diffusion coefficient in the capillary water, and the critical RH are the important parameters that govern the Cl− transport in RC structures. In a case study, the capabilities of the developed numerical model are demonstrated by studying the complex 2D diffusion of Cl− in a RC beam located in two different climatic regions: warm and humid weather in Galveston, Texas, and cold and dry weather in North Minnesota, Minnesota, subjected to time varying temperature, RH, and surface Cl− concentrations.

composite theory↗
DOE OSTI2023

Strong ultrafast demagnetization due to the intraband transitions

Abstract Demagnetization in ferromagnetic transition metals driven by a femtosecond laser pulse is a fundamental problem in solid state physics, and its understanding is essential to the development of spintronic devices.Ab initiocalculation of time-dependent magnetic moment in the velocity gauge so far has not been successful in reproducing the large amount of demagnetization observed in experiments. In this work, we propose a method to incorporate intraband transitions within the velocity gauge through a convective derivative in the crystal momentum space. Our results for transition-element bulk crystals (bcc Fe, hcp Co and fcc Ni) based on the time-dependent quantum Liouville equation show a dramatic enhancement in the amount of demagnetization after the inclusion of an intraband term, in agreement with experiments. We also find that the effect of intraband transitions on each ferromagnetic material is distinctly different because of their band structure and spin property differences. Our finding has a far-reaching impact on understanding of ultrafast demagnetization.

Physics↗
NASA NTRS1975

Calculations of unsteady turbulent boundary layers with flow reversal

The results are presented of a series of computational experiments aimed at studying the characteristics of time-dependent turbulent boundary layers with embedded reversed-flow regions. A calculation method developed earlier was extended to boundary layers with reversed flows for this purpose. The calculations were performed for an idealized family of external velocity distributions, and covered a range of degrees of unsteadiness. The results confirmed those of previous studies in demonstrating that the point of flow reversal is nonsingular in a time-dependent boundary layer. A singularity was observed to develop downstream of reversal, under certain conditions, accompanied by the breakdown of the boundary-layer approximations. A tentative hypothesis was advanced in an attempt to predict the appearance of the singularity, and is shown to be consistent with the calculated results.

Nash, J. F.↗
NASA NTRS1976

Thermospheric winds and exospheric temperatures from incoherent scatter radar measurements in four seasons

The time-dependent equations of neutral air motion are solved subject to three constraints: two of them are the usual upper and lower boundary conditions and the third is the value of the wind-induced ion drift at any given height. Using incoherent radar data, this procedure leads to a fast, direct numerical integration of the two coupled differential equations describing the horizontal wind components and yields time dependent wind profiles and meridional exospheric neutral temperature gradients. The diurnal behavior of the neutral wind system and of the exospheric temperature is presented for two solstice and two equinox days. The data used were obtained by the St. Santin and the Millstone Hill incoherent scatter radars. The derived geographic distributions of the exospheric temperatures are compared with those predicted by the OGO-6 empirical thermospheric model.

Antoniadis, D. A.↗