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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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DOE OSTI2024

FLEXO: A Portably Performant Code for Pulsed Power Target Physics

FLEXO (Flux-Limited Extended-MHD Ohm's Law) is a production-line multiphysics code developed at Sandia to enable more predictive modeling of target physics on pulsed-power devices. FLEXO uses an extended magnetohydrodynamics (XMHD) model which includes a generalized Ohm's law (GOL), an electron inertia term, and Hall physics. This report describes the code's numerical methods, its computational performance, and test problems of interest.

42 ENGINEERING↗
DOE OSTI2024

Data-Driven Supervised Dimension Reduction for Scientific Discovery (LDRD QTI Report)

This report summarizes the findings of a four months FY24 Advanced Science & Technology (AS&T) LDRD Quick Targeted Investigation (QTI) project focused on the exploration of supervised dimension reduction approaches based on autoencoders. Autoencoders have been extensively employed in literature for unsupervised learning tasks, however, their use for supervised regression tasks, which are common within scientific applications, has been limited. Motivated by linear dimension reduction strategies like Active Subspaces and Adaptive Basis, we explored the possibility of employing autoencoders to discover a non-linear manifold able to represent the original function in fewer dimensions. In this report, we discuss a neural network architecture and we perform a numerical campaign on several problems ranging from simple two-dimensional functions to a model problem for magnetohydrodynamics in five dimensions. In our preliminary results, we show that the proposed approach is found to be superior to linear dimension reduction strategies in representing the target function even with a single latent variable.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A hybrid-kinetic simulation tool for non-thermal warm x-ray z-pinch sources, with gas-puff and wire array exemplars

Increasing the fluence of z-pinch x-ray radiation sources above ∼ 10 keV has been a long-standing goal for scientists at Sandia National Laboratories’ Z Machine. Optimizing sources for non-thermal “cold Kα” emission in higher atomic-number materials appears to be a promising path to increase warm x-ray yield. However, this emission is generated by supra-thermal electrons, which are not treated in the magnetohydrodynamic (MHD) codes that are typically used in z-pinch source development. MHD codes do not allow for charge separation or space-charge-generated electric fields, and constrain particle kinematics to Maxwellian distributions. The kinetic codes which do accommodate discrete, non-thermal energy distributions are computationally prohibitive when modeling plasmas near solid density and when modeling/tracking higher ionization states. Thus, modeling non-thermal z-pinch sources requires a new simulation tool. In this report, we present a new hybrid modeling capability that uses the fast features of MHD-type particles to the greatest extent possible, then transitions to the slower but more complete kinetic particle treatment to correctly capture the particle energy spectra that generate non-thermal emission. This capability is founded on the fully-relativistic particle-in-cell code Chicago, which already includes fluid particle treatments. The governing equations and hybrid methodology presented here are applied in simulations of an argon gas-puff and a molybdenum wire-array to provide preliminary code validation. The argon simulation is compared to measured implosion times and yields from Jones et al., Phys. Plasmas 22, 020706 (2015). The simulated x-ray yield is within 25% of measurements and the implosion times agree within a few percent. The molybdenum wire array simulation captures the implosion timing reported in Hansen et al., Phys. Plasmas 21, 031202 (2014), but work is needed to verify the available EOS table. These exemplar simulations represents the type of non-thermal sources that will be developed using the hybrid code capability going forward.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Coupled Experimental/Computational Investigation of the Dynamics of Interacting Magnetized Plasmas

The interaction, or interpenetration, of magnetized plasmas of different density and/or pressure occurs in a wide variety of natural and man-made systems. Such systems include extragalactic jets propagating into the intergalactic medium, solar coronal mass ejections into background solar wind, compact toroid (CT) fueling of magnetic fusion plasmas, and jets of capsule shell impurities into DT fusion fuel, which can lead to enhanced impurity mix in inertial fusion implosions. These plasmas may take the form of jets, with open, helical magnetic structure, or plasma “bubbles” with closed magnetic fields (B-fields), such as spheromaks or CT’s. Such structures, both open and closed B-field cases, can transport heat, particles and magnetic flux or magnetic helicity into background plasma regions. For example, the origin of extragalactic magnetic fields may be due, at least in part, to transport by astrophysical jets. The goal of this proposed work was to elucidate the detailed plasma and magnetic field dynamics of high-density plasma jets (open B-field) and bubbles (closed B-field) propagating into lower density background magnetized plasma through controlled laboratory experiments and closely coupled nonlinear MHD modeling. These experiments were conducted in the HelCat (Helicon-Cathode) linear plasma device at the University of New Mexico (UNM). Plasma jets and bubbles were launched via an existing compact coaxial plasma gun, mounted on the HelCat device. This gun produced plasmas tens of cm in scale and lasting tens of microseconds, thereby allowing detailed multipoint, space- and time-resolved measurements to be made routinely. The experiments were directly modeled using the extended magnetohydrodynamic (XMHD) PERSEUS code, developed at Cornell University [23,24]. Both experimental and numerical modeling work are ongoing. The main results to date are reported here. Additional supplemental funding for one year (8/1/2019 – 7/31/2020) supported numerical investigation of photoionization processes important in many low temperature plasmas, including the HelCat device. Initial results of this modeling work is also reported.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Euler equations and the Sod shock tube problem

The Euler equations are a subset of the magnetohydrodynamic (MHD) equations in the infinitely collisional, unmagnetized limit. MHD modeling is central to many areas of plasma physics, ranging from low-temperature glow discharges to inertial confinement fusion. An important aspect of the Euler equations is their ability to describe states with discontinuities, such as shock waves. A standard benchmark test for numerical implementation of the Euler equations is the Sod shock tube. In this test, the system is initialized at rest with a pressure and density discontinuity, which results in a shock wave traveling into the low-pressure region and a rarefaction wave traveling into the high-pressure region. Starting with the presentation of the Euler equations, a numerical algorithm is presented here to solve these equations in one dimension. This is followed by an overview of the Sod shock tube problem that includes the precise initial setup and the analytic solution. Finally, the analytic solution is compared with results from numerical simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Capability in Theory, Modeling, and Validation for a Range of Innovative Fusion Concepts using High-Fidelity Moment-Kinetic Models

A computational modeling capability is created and available to the fusion community to understand and design lower-cost and innovative fusion concepts. The approach uses high- fidelity kinetic, moment-kinetic, and moment models and includes sophisticated plasma- boundary interactions. A majority of fusion-relevant simulations are performed with magnetohydrodynamic models and hybrid particle-in-cell codes, with limited-fidelity electron and kinetic physics. However, in fusion configurations like Z-pinches, field-reversed- configurations, plasma jet magneto-inertial fusion, spinning mirrors, and others, kinetic effects (both electron and ions) are critical to understand the physics and design scaling into the highly kinetic regime of a burning fusion plasma. Furthermore, as present fusion machines move towards a burning plasma regime, liquid-metal blankets are needed to handle first-wall heat- flux, reduce erosion, and eventually for energy conversion and fuel breeding. The work performed under this ARPA-E BETHE Capability Team advances the state-of-the-art in modeling and understanding plasma dynamics in fusion devices and its coupling with liquid-metal dynamics. These are critical areas of research for fusion energy to become realizable. To address these complex problems, we have leveraged and extended computational capabilities through the code, Gkeyll (developed jointly with Princeton Plasma Physics Laboratory and academic partners), for kinetic and moment modeling of fusion plasmas. The Concept Teams supported by this Capability Team include the Wisconsin High-field Axisymmetric Mirror (WHAM), Centrifugal Mirror Experiment (CFME), Plasma-Jet Magneto- Inertial Fusion (PJMIF), and solid and liquid wall plasma-material interaction studies relevant to a number of fusion concepts including Zap Energy’s Z-pinch. This software is open-source and available to the fusion community as a high-fidelity tool for the design of lower-cost fusion experiments. 3D gyrokinetic simulations of WHAM are now possible for long enough time scales to understand the evolution of interchange instabilities. 3D multi-fluid simulations of CMFE at higher Mach numbers are now possible for detailed design iterations with the goal of stability. The state-of-the-art in understanding shock formation and shock mitigation regimes in merging liners for PJMIF have been furthered by our kinetic simulations. Our novel models and frameworks studying plasma-material interaction by incorporating wall emission for various solid wall materials of relevance to pulsed and steady fusion concepts have advanced the state-of-the-art in our understanding of particle fluxes, heat fluxes, and other quantities at cathodes and anodes. The results from this work may explain discrepancies between experimental and theoretical predictions of achieved current densities in pulsed concepts such as Z-pinches. Another significant contribution of this Capability Team is the development and deployment of a novel experimental platform, LEX (Liquid Electrode eXperiment), at Virginia Tech to understand liquid metal free-surface response to electromagnetic pulses. The novel experiments along with model validation quantified the effect of different materials and sizes of liquid metal droplets on the radiative power balance of fusion plasmas for pulsed concepts. Furthermore, these experiments provided mitigation strategies for violent liquid metal response for high current pulses as would be expected in fusion regimes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Simulation Center for Runaway Electron Avoidance and Mitigation (SCREAM SciDAC) (Technical Final Report)

Runaway electrons can severely damage the plasma facing components on ITER during a major disruption and pose a major risk for tokamak fusion. It has been recognized that an adequate disruption mitigation system (DMS) is essential for the safe operation of ITER. The United States is responsible for the design and implementation of the disruption mitigation system on ITER, and in July 2016 the Simulation Center for Runaway Electron Avoidance and Mitigation (SCREAM) was launched by DOE, in a joint Fusion Energy Sciences (FES) and Advanced Scientific Computing Research (ASCR) collaboration. SCREAM was a comprehensive theory and simulation SciDAC center that provided physics guidance in the avoidance and mitigation of runaway electrons, and in tandem with domestic and international experiments, helped establish the qualitative and quantitative bases for safe operational scenarios and viable mitigation techniques. The SCREAM center assembled a national team of experts in runaway electron physics, tokamak disruptions, magnetohydrodynamic (MHD) simulation, and advanced algorithms and computing. The team combined advanced simulation and analysis capability facilitated by direct participation of ASCR SciDAC institutes with theoretical models and code development by FES scientists to focus on the runaway risk for ITER and tokamaks in general. The research scope was focussed on integrated simulations of kinetic runaway electrons, including MHD and fluid models of impurity transport, within a research plan guided by theory. The specific research tasks were (1) establish the fundamental physics of runaway generation, saturation, and dynamical evolution in a tokamak; (2) examine the critical path toward runaway avoidance; and (3) investigate the viability and effectiveness of the leading candidate schemes for runaway mitigation. In all three areas, members of the team carried out scoping studies that established the readiness for rapid and critical advances, especially in the deployment and further development of large-to extreme-scale simulation tools. Our multi-pronged computational approach included (1) relativistic Fokker-Planck solvers with discretization in phase space, (2) self-consistent particle-in-cell techniques, (3) particle-based Monte-Carlo, and (4) MHD-particle hybrid simulations. Cross-check between these different methods provided an additional means for verification and further bolstered the fidelity of our physics prediction. Validation against experimental results brings confidence to the predictive capability for ITER and frequently leads to new ideas for understanding and mitigating the thermal quench driven runaway electron phenomenon.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

UNR Grant Proposal Contribution

The work of Carrier et. al. (citation needed for Matt’s effect of surface roughness on phase transitions/ETI paper) demonstrates that 1D and 2D resistive magnetohydrodynamic (MHD) simulations can reliably model exploding aluminum rods driven by megaampere currents. Close agreement between simulation results and photonic Doppler velocimetry data from the Mykonos electrothermal instability (METI-II) campaign builds confidence in predictive modelling capabilities for pulsed-power HED experiments. Furthermore, 2D MHD simulations show how machined features and micro-scale surface roughness can seed the electrothermal instability (ETI). Surface roughness was observed to reduce the time of melt by 19%, with ETI growth driving the enhanced heating of the rod surface.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Multi-fidelity equations of state and transport coefficient datasets for pulsed-power applications

Reliably simulating experiments relevant to the National Nuclear Security Administration (NNSA) requires a detailed description of material properties across a wide range of conditions. Such properties include the equations of state, charged-particle transport coefficients, and optical properties like the opacity. Together, these properties make up the material models used in radiation-magnetohydrodynamic simulations of nuclear fusion experiments. Many of these models do not incorporate uncertainties in the data used to produce them. It is unknown whether these uncertainties significantly impact the interpretation of simulation results and diagnostics. The purpose of this work is to quantify how such uncertainties impact simulations of pulsed-power experiments. We accomplished this task by first assessing discrepancies between approaches used to generate the data. This included bringing together members of the high-energy-density community spanning the three NNSA laboratories and multiple universities. Then, using these data, we developed a general framework that systematically incorporates physical uncertainties within the material models suitable for uncertainty quantification analyses. The framework utilizes machine learning, Bayesian inference, and incorporates multi-fidelity datasets. We demonstrated the framework by quantifying the impact that material model uncertainties have on simulations of pulsed-power experiments underway on Z at Sandia National Laboratories. As a result of this work, we discovered that modest uncertainties in material models (roughly 20%) correspond to significant uncertainties in the outputs from simulations. Our framework has enabled rapid construction of material models through an automated procedure and allows for the generation of material models of interest to the NNSA.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Nuclear Astrophysics through simulations of neutron star mergers using Monte‐Carlo neutrino radiation transport (DE-SC0020435 Final Technical Report)

Neutron star mergers are an important source of information for nuclear physics. Except for black holes, neutron stars are the densest macroscopic objects known to exist in the Universe. They provide us with a remarkable laboratory to study the poorly understood high-density states of matter, complementing the study of heavy nuclei performed by nuclear physics experiments on Earth. Collisions of neutron stars are of particular interest. They are among the most energetic events observable in the Universe, powering a broad range of signals across the electromagnetic spectrum as well as gravitational wave signals. These signals contain important information about the properties of extremely dense matter. Colliding neutron stars additionally eject large amounts of neutron-rich material into the surrounding interstellar medium -- material that then undergoes rapid neutron-capture (r-process) nucleosynthesis, the mechanism thought to be responsible for the production of about half of the heavy nuclei. In order to understand current and future observations of neutron star mergers, we need reliable models for the signals that they power. An important component in the construction of such models are numerical simulations of colliding neutron stars. These simulations are costly, running for multiple months on supercomputers, and require the inclusion of complex physics (general relativity, magnetohydrodynamics, neutrino physics, nuclear reactions). In this document, we describe the development of new methods for the treatment of neutrinos in merger simulations, as well as the first simulations capable of evolving the equations of neutrino radiation transport directly and their impact on our understanding of neutron star mergers and more broadly in nuclear astrophysics. We also discuss additional work performed in the study of nucleosynthesis and neutrino physics in neutron star mergers as part of Early Career Award DE-SC0020435.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Thermal Hydraulic Experimental Test Article: Second Year of Testing with Secondary Sodium System (Fiscal Year 2025 Final Report)

The Thermal Hydraulic Experimental Test Article (THETA) is currently installed in the Mechanisms Engineering Test Loop (METL) 28” test vessel #4. Both the primary and secondary sodium systems remain online to facilitate continued testing. This fiscal year, work was performed using a COMSOL Multiphysics magnetohydrodynamic model to characterize flow more accurately in the secondary electromagnetic flowmeters. Experimental campaigns were then performed to study the thermal hydraulic differences between sodium and water as a surrogate fluid in the THETA geometry as well as a study to better characterize and understand temperature oscillations that exist at the outlet of the core to the hot pool. A peer-reviewed article was published in the ASME Journal of Nuclear Engineering and Radiation Science detailing the THETA facility and providing an overview of a test that was performed with the primary and secondary system online [1]. Work continues to develop a database to house experimental THETA data to better facilitate collaboration with industry and laboratory partners for their use of the data for code benchmarking/validation. THETA remains fully operational and is positioned for continued testing in fiscal year 2026.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2026

Closure models for the feedback of energetic particles on plasma turbulence

Energetic particles interact with the plasma surrounding them, resonating with certain types of plasma waves to stabilize them while destabilizing others, and changing the character of the background turbulence in ways that have not been fully quantified or understood. Interaction with the turbulent background plasma is key to the acceleration of many types of energetic particles including high-energy cosmic rays, solar energetic particles, and pick-up ions. The acceleration of particles is a process that would ideally be described by a kinetic model, a type of model that follows a probability distribution function (PDF) for all particles in 7-dimensional (x, y, z, v x , v y , v z , t) space. Because of the high dimensionality of a kinetic model, simulations that solve kinetic equations use the largest computational resources currently available, and are yet unable to simulate a realistic number of particles, reach the large scales necessary for astrophysical problems, and use high-precision numerical methods. Two available alternatives to kinetic plasma models have been explored for this problem, with limited success. One is a multi-fluid model produced by a cumulant discarding closure, which evolves coupled equations for the velocity, magnetic field, and internal energy for both the background plasma and the fluid of energetic particles. However, simulations that solve multi-fluid magnetohydrodynamic (MHD) equations are able to include the interaction with energetic particles only in crude ways, typically as an add-on pressure term. The second alternative is to use a hybrid method to couple a fluid description of the background plasma to a kinetic model or a Fokker–Planck model for the energetic particles. These methods are hampered by the physical modeling of the coupling. In this work, we develop a new model, which follows the PDF for all particles; this can be viewed as a step toward physical realism above a multi-fluid MHD model, while also being more computationally efficient than a kinetic model. The equations we develop model both the background plasma and the energetic particles self-consistently. Over the last decade, similar PDF methods have been developed to a high level of sophistication to model reactive flows and turbulent combustion for engineering applications. For treatment of the feedback of the energetic particles on a background plasma, a PDF closure approach should evaluate the mean characteristics, including the density, with better statistical quality than will particle-sampling procedures.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Modeling Material Interfaces with the Six-Equation Model in FLEXO

FLEXO is a multiphysics code developed at Sandia National Laboratories for predictive simulation of pulsed power target physics with extended magnetohydrodynamics modeling. Given this application space, FLEXO must be able to perform high-fidelity simulations of pulsed-power systems that include multiple materials. This work presents the augmentation of FLEXO with a six-equation model for multimaterial flow. We design and analyze discretizations of the six-equation model, emphasizing desirable properties for robust multimaterial simulation. We also present solution limiting, bounds preservation, and pressure equilibration/relaxation techniques that enhance the robustness of the overall multimaterial scheme. We present a suite of test problems to document these new capabilities of the FLEXO code.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Predictive ALEGRA Simulations of the Mach Wave Concept on the Z Machine

This high level presentation introduces the Sandia Z machine, dynamic materials properties experiments including the Mach Wave concept, and Alegra magnetohydrodynamic modeling for a technical audience. Alegra models are shown to be highly capable, with predictive capabilities limited only by the quality and accuracy of material models.

Boerner, Jeremiah James [Sandia National Laborator↗
DOE OSTI2024

Importance of the Rotational Transform for L–H Transitions in the TJ-II Stellarator

We study the effect of the rotational transform profile on the L–H confinement transitions in the neutral beam-heated plasmas in the TJ-II stellarator. The rotational transform profile in the vacuum is determined by the external coil currents but is modified by the plasma current, Ip. We find that L–H confinement transitions systematically occur when the configuration and plasma current are such that a low-order rational is placed in the plasma edge region, with a distribution centered around ρ=0.8±0.05. It is suggested that magnetohydrodynamic turbulence plays an important role in triggering the L–H transitions at TJ-II.

van Milligen, Boudewijn Philip (ORCID:000000015344↗
DOE OSTI2024

Electron Heating in the Transrelativistic Perpendicular Shocks of Tilted Accretion Flows

Abstract General relativistic magnetohydrodynamic (GRMHD) simulations of black hole tilted disks—where the angular momentum of the accretion flow at large distances is misaligned with respect to the black hole spin—commonly display standing shocks within a few to tens of gravitational radii from the black hole. In GRMHD simulations of geometrically thick, optically thin accretion flows, applicable to low-luminosity sources like Sgr A* and M87*, the shocks have transrelativistic speed, moderate plasma beta (the ratio of ion thermal pressure to magnetic pressure is β pi1 ∼ 1–8), and low sonic Mach number (the ratio of shock speed to sound speed is M s ∼ 1–6). We study such shocks with 2D particle-in-cell simulations, and we quantify the efficiency and mechanisms of electron heating for the special case of preshock magnetic fields perpendicular to the shock direction of propagation. We find that the postshock electron temperature T e2 exceeds the adiabatic expectation T e2,ad by an amount T e 2 / T e 2 , ad − 1 ≃ 0.0016 M s 3.6 , nearly independent of the plasma beta and of the preshock electron-to-ion temperature ratio T e1 / T i1 , which we vary from 0.1 to unity. We investigate the heating physics for M s ∼ 5–6 and find that electron superadiabatic heating is governed by magnetic pumping at T e1 / T i1 = 1, whereas heating by B -parallel electric fields (i.e., parallel to the local magnetic field) dominates at T e1 / T i1 = 0.1. Our results provide physically motivated subgrid prescriptions for electron heating at the collisionless shocks seen in GRMHD simulations of black hole accretion flows.

Astronomy & Astrophysics↗
DOE OSTI2024

Evolving Outer Heliosphere: Tracking Solar Wind Transients from 1 au to the VLISM with IBEX and Voyager 1

Abstract Interstellar Boundary Explorer (IBEX) observations of energetic neutral atom (ENA) fluxes from the heliosphere have greatly enriched our understanding of the interaction of the solar wind (SW) with the local interstellar medium (LISM). However, there has been recent controversy surrounding the inability of most ENA models to produce as high an intensity of ∼0.5–6 keV ENAs as IBEX observes at 1 au, especially as a function of time. In our previous study (E. J. Zirnstein et al.), we introduced a new model that utilizes a data-driven magnetohydrodynamic simulation of the SW–LISM interaction to propagate pickup ions through the heliosheath (HS) after they are nonadiabatically heated at the heliospheric termination shock. E. J. Zirnstein et al. only simulated and analyzed IBEX observations from the direction of Voyager 2. In this study, we expand our model to include fluxes from the direction of Voyager 1, as well as in the low-latitude part (middle) of the ribbon (10° below the ecliptic plane). We show that the model results at Voyager 1 are consistent with E. J. Zirnstein et al.’s results at Voyager 2 in terms of a secondary ENA source contribution of ≲20% from both directions. Our results in the middle of the ribbon also reproduce the data, when including a time-dependent secondary ENA source. Finally, we demonstrate with our simulation that three large pressure waves likely merged in the VLISM and were observed by Voyager 1 as “pf2,” while at least one of the wave’s effects in the HS was observed by IBEX as a brief enhancement in ENA flux in early 2016.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Energy-dependent and Energy-integrated Two-moment General-relativistic Neutrino Transport Simulations of a Hypermassive Neutron Star

Abstract We compare two-moment-based energy-dependent and three variants of energy-integrated neutrino transport general-relativistic magnetohydrodynamics simulations of a hypermassive neutron star. To study the impacts due to the choice of the neutrino transport schemes, we perform simulations with the same setups and input neutrino microphysics. We show that the main differences between energy-dependent and energy-integrated neutrino transport are found in the disk and ejecta properties, as well as in the neutrino signals. The properties of the disk surrounding the neutron star and the ejecta in energy-dependent transport are very different from the ones obtained using energy-integrated schemes. Specifically, in the energy-dependent case, the disk is more neutron-rich at early times and becomes geometrically thicker at later times. In addition, the ejecta is more massive and, on average, more neutron-rich in the energy-dependent simulations. Moreover, the average neutrino energies and luminosities are about 30% higher. Energy-dependent neutrino transport is necessary if one wants to better model the neutrino signals and matter outflows from neutron star merger remnants via numerical simulations.

79 ASTRONOMY AND ASTROPHYSICS↗