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DOE OSTI2024

In situ oxidation of reduced graphene oxide membranes by peracetic acid for dye desalination

Graphene oxide (GO) membranes with tunable interlayer spacings are of interest for dye removal from salty textile wastewater, and the membranes are often reduced to improve their stability, which inevitably lowers water permeance. Herein, we demonstrate that reduced GO (rGO) membranes can be facilely modified using peracetic acid (PAA) in situ to dramatically enhance water permeance while retaining dye rejection. Specifically, PAA-modified membranes (PrGO) are synthesized by vacuum-filtering hydrazine-reduced rGO nanosheets onto Nylon substrate and then exposing them to PAA solutions. The effects of the rGO layer thickness, PAA content, and PAA exposure time on the membrane chemistry, nanostructures, and salt/dye separation properties are thoroughly examined. For example, the PAA oxidation of a 100 nm-thick rGO membrane for 10 min increases water permeance by 180 %, from 35 to 93 Liter m −2 h −1 bar −1 , and decreases Na 2 SO 4 rejection from 10 % to 3.3 % while retaining the rejection of Congo red at ≈99.7 %. The PrGO membranes exhibit stable water permeance and >99 % dye rejection in multi-cycle tests in a crossflow system, surpassing state-of-the-art GO membranes and showcasing their potential for practical applications.

Dye desalination↗

DOE OSTI2023

Cation-Driven Assembly of Bilayered Vanadium Oxide and Graphene Oxide Nanoflakes to Form Two-Dimensional Heterostructure Electrodes for Li-Ion Batteries

Lithium preintercalated bilayered vanadium oxide (LVO or δ-Li x V 2 O 5 ·nH 2 O) and graphene oxide (GO) nanoflakes were assembled using a concentrated lithium chloride solution and annealed under vacuum at 200 °C to form two-dimensional (2D) δ-Li x V 2 O 5 ·nH 2 O and reduced GO (rGO) heterostructures. Here we found that the Li + ions from LiCl enhanced the oxide/carbon heterointerface formation and served as stabilizing ions to improve structural and electrochemical stability. The graphitic content of the heterostructure could be easily controlled by changing the initial GO concentration prior to assembly. We found that increasing the GO content in our heterostructure composition helped inhibit the electrochemical degradation of LVO during cycling and improved the rate capability of the heterostructure. A combination of scanning electron microscopy and X-ray diffraction was used to help confirm that a 2D heterointerface formed between LVO and GO, and the final phase composition was determined using energy-dispersive X-ray spectroscopy and thermogravimetric analysis. Scanning transmission electron microscopy and electron energy-loss spectroscopy were additionally used to examine the heterostructures at high resolution, mapping the orientations of rGO and LVO layers and locally imaging their interlayer spacings. Further, electrochemical cycling of the cation-assembled LVO/rGO heterostructures in Li-ion cells with a non-aqueous electrolyte revealed that increasing the rGO content led to improved cycling stability and rate performance, despite slightly decreased charge storage capacity. The heterostructures with 0, 10, 20, and 35 wt % rGO exhibited capacities of 237, 216, 174, and 150 mAh g –1 , respectively. Moreover, the LVO/rGO-35 wt % and LVO/rGO-20 wt % heterostructures retained 75% (110 mAh g–1) and 67% (120 mAh g –1 ) of their initial capacities after increasing the specific current from 20 to 200 mA g –1 , while the LVO/rGO-10 wt % sample retained only 48% (107 mAh g –1 ) of its initial capacity under the same cycling conditions. In addition, the cation-assembled LVO/rGO electrodes exhibited enhanced electrochemical stability compared to electrodes prepared through physical mixing of LVO and GO nanoflakes in the same ratios as the heterostructure electrodes, further revealing the stabilizing effect of a 2D heterointerface. The cation-driven assembly approach, explored in this work using Li + cations, was found to induce and stabilize the formation of stacked 2D layers of rGO and exfoliated LVO. The reported assembly methodology can be applied for a variety of systems utilizing 2D materials with complementary properties for applications as electrodes in energy storage devices.

25 ENERGY STORAGE↗

DOE OSTI2025

Development of a Superconducting Adaptive Gap Undulator Prototype for NSLS-II

The photon flux and brightness of synchrotron radiation, crucial parameters for any light source, vary significantly depending on the type of source employed. Among the 23 Insertion Device (ID) sources at the National Synchrotron Light Source II (NSLS-II) at Brookhaven National Lab (BNL), the 12-year-old 3m-long In-Vacuum Undulator (IVU20) stands out for its superior performance, although it no longer represents the cutting edge of technology. Recently, there has been a shift in focus towards developing next-generation sources, particularly Superconducting Undulators (SCUs), characterized by smaller gaps, shorter periods, and maximum lengths. However, despite ongoing research and development efforts, SCUs have yet to surpass their predecessors, the Cryogenic Permanent Magnet Undulators (CPMUs), in terms of performance. This is largely attributed to the limitations posed by traditional superconducting wire, as well as challenges in the design of the magnetic structure and vacuum chamber. In this paper, we aim to overcome such limitations through the development of a unique prototype Superconducting Adaptive Gap Undulator (SC-AGU) magnet core and vacuum chamber design. This paper will outline a novel technical approach aimed at constructing a compact prototype magnet array utilizing state-of-the-art superconducting wire technology. This approach provides a more efficient magnetic structure, allowing for enhanced magnetic field strength and stability.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Organic Evaporation and Oxidation Testing in Support of Hanford Sample-and-Send

The Hanford site has approximately 56 million gallons of radioactive mixed waste stored in 177 underground storage tanks. The Hanford Waste Treatment and Immobilization Plant (WTP) is being built to treat and immobilize the tank waste. The baseline method for immobilization of Low Activity Waste (LAW) through the WTP is vitrification, but additional immobilization capacity is needed to supplement the initial LAW melters. An alternative cementitious waste form is being investigated for that future immobilization method to supplement vitrification. However, one impediment to a cementitious waste form is the presence of Land Disposal Restricted (LDR) organic chemicals in tank waste. This work evaluates potential avenues to eliminate that impediment to permit possible use of a cementitious waste form and work towards a decision whether additional LDR organic pretreatment would be required. Savannah River National Laboratory (SRNL) performed testing using simulants to examine evaporation as a method to remove some prevalent organics from LAW. Spiking the caustic LAW simulant with selected regulated organic chemicals found one that clearly decomposes because of caustic instability. Oxidation testing of other organic chemicals found some LDR organics degrade as desired and others are stable in the presence of peroxide and permanganate. In addition to studies with simulants, a literature review was performed to evaluate radiological stability of LDR organics. Descriptions of the experimental details, equipment, and results are included in this report. Evaporation testing consisted of preparing the LAW simulant, spiking that simulant with organic chemicals, and evaporating the mixture via differential distillation. The apparatus was a laboratory-scale vacuum evaporator operated at 60 ±5 torr absolute (vacuum evaporation) and also at atmospheric pressure. The LAW simulant represented the liquid expected to be retrieved from the Hanford tank farms at approximately 4.0 M [Na + ] total sodium ion concentration. The concentration of the organic chemicals added was significantly higher than typically found in the tank waste samples since the higher levels were necessary to assist in analytical measurement and tracking of the spiked species. Organic chemicals were chosen for the work with a consideration of how their volatility compares with that of methanol. This was done by comparing the ratio of the pure water Henry’s law coefficient (K h ) of methanol to that of the compound in question (hereafter termed the K h ratio), where ratios above unity indicated less volatility than methanol. Methanol was chosen because it is a common regulated chemical with relatively low volatility but which has been removed by evaporation in previous laboratory work. While organic separation results depend on evaporator design, laboratory experiments verified that organic partitioning to the overhead condensate stream by evaporation is a practical process. The work reported here found difficulties in quantitative analysis of the organic chemicals in aqueous samples. Most of the time there was insufficient analysis to close a mass balance for evaporator runs, but qualitative evidence of carryover was obtained. The methods were also able to show whether organic chemicals were susceptible or resistant to solution oxidation in permanganate or hydrogen peroxide tests.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2022

Polystyrene sulfonate (PSS) stabilized polyethylenimine (PEI) membranes fabricated by spray coating for highly effective CO 2 /N 2 separation

Greenhouse effect, largely caused by CO 2 emission, has become a major concern for global climate change. Post-combustion CO 2 capture is one of the critical strategies to mitigate this issue. Membrane technology for carbon capture has drawn significant attention because of the cost and energy efficiency and scalability. Many membranes for CO 2 capture are limited by the trade-off between CO 2 permeability and CO 2 /N 2 selectivity and the long-term stability under practical operating conditions. Facilitated transport membranes with efficient CO 2 carriers have demonstrated potential to surpass the permeability-selectivity trade-off, but these carriers are often lost under operational conditions. In this work, we designed and fabricated a polystyrene sulfonate (PSS) stabilized polyethylenimine (PEI) membrane by a facile and scalable spray-coating method. The deposited defect-free selective layer, in which the amine carriers in PEI can be stabilized electrostatically by PSS, exhibited superior CO 2 separation performance with good long-term stability under practical operating conditions. The separation performance was optimized by spray-coating cycles, CNT network loading, and PSS loading. Our membrane showed CO 2 permeance ranging from 820 to 1,770 GPU and CO 2 /N 2 selectivity varying from 395 to 460 under vacuum operation mode in the temperature range between 80 and 90 °C. Furthermore, the membrane was successfully scaled up to 200 cm 2 with good uniformity. These results might suggest a novel membrane structure and a scalable approach for fabrication of highly efficient CO 2 separation membranes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Overview of the physics basis for the ARC fusion power plant

Commonwealth Fusion Systems plans to build ARC as the first fusion power plant at a site in Chesterfield County, Virginia, USA by the early 2030s. We present an overview of analysis comprising the physics basis of the ARC V3A design, a high-magnetic-field tokamak with 𝐵 0 =11.4 T, 𝐼 𝑝 =12.0 MA, 𝑅 0 =4.62 m, 𝑎 =1.18 m. ARC V3A is designed to produce 𝑃 𝑓⁡𝑢⁢𝑠 ≈1.13 GW DT fusion power and deliver ⩾400 MW net electric power to the grid. This overview includes quantitative analysis of fundamental issues for design of and operational plasma scenarios for a tokamak power plant, and lays out the design targets and strategic choices for ARC, including empirical fusion performance projections, assessment of H-mode access, ion cyclotron resonance heating simulations, alpha particle physics and time-dependent full-pulse simulations. This is complemented by topical papers on fusion performance and transport, disruption physics, boundary physics and magnetohydrodynamic stability. Critically, these studies identify key model uncertainties and physics risks to be retired through SPARC operation. Due to the modular nature of ARC, early results from SPARC can be incorporated into the design of the first ARC as well as subsequent replacements of the ARC vacuum vessel.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Metallurgical and mechanical characterization of ATP-5 aluminum alloys for minimizing machining distortion

ATP-5 aluminum alloy was considered as an alternative to 6061-T651 aluminum alloy to minimize machining distortion. ATP-5 is a proprietary cast alloy that is compositionally similar to 5083 aluminum and is purported to have excellent machinability, stability, and corrosion response. Dimensional stability tests, mechanical testing, chemical analysis, microstructural analysis, and fractography were completed to understand the metallurgy of the ATP-5 alloy and assess its potential as a 6061-T651 alloy alternative. Ultimately, the ATP-5 was found to retain dimensional stability issues, albeit to a lesser extent, relative to the 6061-T651 alloy. Combined with the residual cast structure observed microstructurally and lot-to-lot mechanical property variation, the alloy was deemed not suitable for a structural application. Alternative uses of ATP-5 include tooling, molds, vacuum chucks, fixtures, and jigs, where the material can shine in non-load bearing applications with a need for dimensional control and machinability.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Influence of Copper Composition on Cu 2 BaSn(S,Se) 4 Solution-Deposited Films and Photovoltaic Devices with Over 5% Efficiency

Cu 2 BaSn(S,Se) 4 is currently in the spotlight for prospective environmentally friendly, stable, thin-film solar cell application, with demonstrated device power conversion efficiency (PCE) exceeding 5% for vacuum-deposited absorbers. As suggested by first-principles calculations, experimental studies involving related Cu 2 ZnSn(S,Se) 4 and Cu(In,Ga)(S,Se) 2 absorbers prove that the detailed chemical composition typically plays a sensitive role in altering defects and electronic properties of these complicated compound semiconductors. Herein, the copper composition of Cu 2 BaSn(S,Se) 4 has been systematically modified, employing a solution-based deposition approach, to provide a more complete picture of the phase stability and optoelectronic property sensitivity for this material. X-ray diffraction and scanning electron microscopy show that phase purity is preserved over a film Cu content range of nominally 0.94 ≤ [Cu]/[Ba + Sn] ≤ 1.01. Terahertz spectroscopy and Hall effect measurements reveal that the majority carrier hole density of ~10 13 cm –3 and mobility (~5 cm 2 /V s), as well as the minority carrier lifetime (a bulk lifetime of 180 ps and a surface recombination velocity >106 cm/s), are nominally independent of Cu content. The champion PCEs exceed 4.7% for all copper compositions in the phase-pure region, with a record value of 5.1%, similar to the reported values for record vacuum-deposited devices. Furthermore, these results suggest that Cu 2 BaSn(S,Se) 4 films and solar cells (at the current performance level) may be less sensitive to Cu stoichiometry compared to kesterite materials and therefore may provide a more stable material platform to prepare thin-film solar cells.

(CBTSSe)↗

DOE OSTI2023

Recent Beam Stability Analysis for the EIC

This document summarizes work done in WBS 6.02.02 during FY23. Additional details can be found in the EIC overview paper presented at IPAC’23 [1], and the references therein. Progress has been made in the ESR and HSR lattice design, dynamic aperture optimization, and the RCS lattice design. The impedance and Collective effects are progressing and include the impedance optimization process of the vacuum systems for RCS, HSR, and ESR; collective effects studies; collective effects and beam-beam interaction; coupled bunch instabilities and the crab cavities; low-level RF feedback system design and beam-ion instability. The reversed phasing RF system has been numerically studied for the ESR to mitigate Robinson instability and demonstrate reliable stable beam operation. Various codes, including C++, SPACE [2], ELEGANT [3], and Mbtrack2 [4] have been employed to benchmark the results. The simulation of HSR bunch splitting with beam loading has been performed at 275 GeV energy. The evaluation of Beam Position Monitors aimed to validate their expected performance, with the primary objective being to verify their accuracy. Calculations of Electron Polarization in the ESR, RCS, and HSR are showing good progress. In the RCS, preliminary studies indicate excellent polarization transmission over intrinsic spin resonances, achieving over 90% transmission with improved performance compared to the previous lattice. Preliminary simulations in the ESR indicate encouraging results in minimizing depolarization and improving equilibrium polarization.

43 PARTICLE ACCELERATORS↗

DOE OSTI2026

The interaction of acetonitrile with H-terminated and depassivated (100) diamond surfaces

Molecular adsorption on reactive semiconductor surfaces may enable novel surface functionalisation and atomically-precise dopant formation. In this work synchrotron-based x-ray photoelectron spectroscopy and near edge x-ray absorption spectroscopy are used to examine the interaction between acetonitrile and diamond (100) surfaces under ultrahigh vacuum (UHV) conditions. We observe two surface-bound nitrogen species on hydrogen terminated surfaces after thermal depassivation or following synchrotron radiation and subsequent exposure to acetonitrile, but find no evidence of nitrogen adsorption on the hydrogen-terminated diamond surface, at room temperature. Subsequent measurements explore the stability of the surface-bound nitrogen under various temperature conditions and with atmospheric exposure. While the nitrogen coverage achieved in this study is low, this study serves as a proof-of-concept demonstration of a UHV molecular dosing approach to selective nitrogen functionalisation of diamond surfaces as an alternative to plasma-based approaches. This development may be critical for proposed surface-based fabrication workflows using atomic placement of nitrogen-vacancy centres to create quantum devices.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2023

Scalable aqueous-phase fabrication of reduced graphene oxide nanofiltration membranes by an integrated roll-to-roll (R2R) process

Economic fractionation of multicomponent biomass-derived streams is a key challenge in biobased fuels and chemicals production. Kraft black liquor (BL) is generated at ~1 billion tons/yr globally from biomass pulping and contains ~15wt% total solids including lignin, hemicellulose fragments, and inorganics. Membrane-based BL concentration is attractive but challenged by low solute rejections and poor stability in BL, which combines alkaline pH (~13), high dissolved solids content (15+ wt%) and high temperature (70–85°C). Here we discuss the scaled fabrication and characterization of reduced graphene oxide (rGO) nanofiltration membranes by slot die coating on a roll-to-roll (R2R) with integrated vacuum filtration. Here, we obtain high-quality 90×30 cm rGO membranes (referred to as “R2R-rGO membranes” in this work) with ~100 nm average thickness supported on porous poly(ethersulfone) (PES) sheets, and an effective area of 2700cm 2 . We present characterizations of their microstructure and uniformity as mapped over large areas by scanning electron microscopy (SEM), ellipsometry, adhesion test and X-ray photoelectron spectroscopy (XPS). The constructed ellipsometry model for the rGO membrane/PES substrate composite was successfully applied to 48 different locations of the R2R-rGO membranes. The R2R-rGO membranes showed >98% lignin rejection with a steady state flux of ~12 LMH at 50bar in a 15.7wt% total solids (TS) kraft BL stream at 72°C and 2–3 gal/min crossflow rates. Slot die coating on a R2R platform with integrated vacuum filtration can enable rapid fabrication of high-quality GO membranes at scale without organic solvents or volatile organic compounds.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Visualizing Oxidation Mechanisms in Few-Layered Black Phosphorus via In Situ Transmission Electron Microscopy

Layered two-dimensional (2D) black phosphorus (BP) exhibits novel semiconducting properties including a tunable bandgap and high electron mobility. However, the poor stability of BP in ambient environment severely limits potential for application in future electronic and optoelectronic devices. While passivation or encapsulation of BP using inert materials/polymers has emerged as a plausible solution, a detailed fundamental understanding of BP's reaction with oxygen is imperative to rationally advance its use in applications. Here, we use in situ environmental transmission electron microscopy to elucidate atomistic structural changes in mechanically exfoliated few-layered BP during exposure to varying partial pressures of oxygen. An amorphous oxide layer is seen on the actively etching BP edges, and the thickness of this layer increases with increasing oxygen partial pressure, indicating that oxidation proceeds via initial formation of amorphous P x O y species which sublime to result in the etching of the BP crystal. We observe that while few-layered BP is stable under the 80 kV electron beam (e-beam) in vacuum, the lattice oxidizes and degrades at room temperature in the presence of oxygen only in the region under the e-beam. The oxidative etch rate also increases with increasing e-beam dosage, suggesting the presence of an energy barrier for the oxidation reaction. Preferential oxidative etching along the [0 0 1] and [0 0 1] crystallographic directions is observed, in good agreement with density functional theory calculations showing favorable thermodynamic stability of the oxidized BP (0 0 $\bar{1}$) planes compared to the (1 0 0) planes. Finally, we expect the atomistic insights and fundamental understanding obtained here to aid in the development of novel approaches to integrate BP in future applications.

2D materials↗

DOE OSTI2025

Quench Analysis of EIC Central Detector (ePIC) Solenoid Magnet (MARCO)

The 2.0 T superconducting solenoid magnet (MARCO) being designed to be built for the EIC central detector (ePIC). Here, the magnet consists of three set of coil in a vacuum impregnated coil pack. Each coil pack consists of a total 554 turns winding wrapped with 6 layers of winding per coil. The coil case assembly is cooled by supercritical helium at 4.6 K. This manuscript presents quench analysis carried out on the magnet system along with the conductor stability. For the normal operation the magnet at 4.6 K and at normal operating current, the quench evaluation is carried out at 4.7 K for design assessment. The quench analysis carried out using commercial multi-physics FEA tool along an equivalent single coil quench model and the requirements for the magnet protection is also presented.

Ghoshal, Probir K. [Thomas Jefferson National Acce↗

DOE OSTI2021

Ionizing-radiation beamline monitoring system

Embodiments are directed generally to an ionizing-radiation beamline monitoring system that includes a vacuum chamber structure with vacuum compatible flanges through which an incident ionizing-radiation beam enters the monitoring system. Embodiments further include at least one scintillator within the vacuum chamber structure that can be at least partially translated in the ionizing-radiation beam while oriented at an angle greater than 10 degrees to a normal of the incident ionizing-radiation beam, a machine vision camera coupled to a light-tight structure at atmospheric/ambient pressure that is attached to the vacuum chamber structure by a flange attached to a vacuum-tight viewport window with the camera and lens optical axis oriented at an angle of less than 80 degrees with respect to a normal of the scintillator, and at least one ultraviolet (“UV”) illumination source facing the scintillator in the ionizing-radiation beam for monitoring a scintillator stability comprising scintillator radiation damage.

Friedman, Peter S.↗

DOE OSTI2023

Ionizing-radiation beamline monitoring system

Friedman, Peter S.↗

DOE OSTI2023

Evolution of nanopores in hexagonal boron nitride

Abstract The engineering of atomically-precise nanopores in two-dimensional materials presents exciting opportunities for both fundamental science studies as well as applications in energy, DNA sequencing, and quantum information technologies. The exceptional chemical and thermal stability of hexagonal boron nitride (h-BN) suggest that exposed h-BN nanopores will retain their atomic structure even when subjected to extended periods of time in gas or liquid environments. Here we employ transmission electron microscopy to examine the time evolution of h-BN nanopores in vacuum and in air and find, even at room temperature, dramatic geometry changes due to atom motion and edge contamination adsorption, for timescales ranging from one hour to one week. The discovery of nanopore evolution contrasts with general expectations and has profound implications for nanopore applications of two-dimensional materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Bead–Spring Simulation of Ionomer Melts—Studying the Effects of Chain-Length and Associating Group Fraction on Equilibrium Structure and Extensional Flow Behavior

Ionomers are associative polymers with diverse applications ranging from selective membranes and high-performance adhesives to abrasion- and chemical-resistant coatings, insulation layers, vacuum packaging, and foamed sheets. Within equilibrium melt, the ionic or associating groups are known to form thermally reversible, associative clusters whose presence can significantly affect the system’s mechanical, viscoelastic, and transport properties. It is, thus, of great interest to understand how to control such clusters’ size distribution, shape, and stability through the designed choice of polymer architecture and the ionic groups’ fraction, arrangement, and interaction strength. In this work, we represent linear associating polymers using a Kremer–Grest type bead–spring model and perform large-scale MD simulations to explore the effect of polymer chain-length (l) and fraction (f s ) of randomly placed associating groups on the size distribution and stability of formed clusters. We consider different chain-lengths (below and above entanglement), varying fractions of associating groups (represented by ‘sticky’ beads) between 5 and 20%, and a fixed sticky–sticky nonbond interaction strength of four times that between regular non-associating beads. For all melts containing associating groups the equilibrium structure factor S(q) displays a signature ionomer peak at low wave vector q whose intensity increases with increasing f s and l. The average cluster size Nc increases with f s . However, the effect of chain-length on Nc appears to be pronounced only at higher values of f s . Under extensional flows, the computed stress (and viscosity) is higher at higher f s and l regardless of strain rate. Beyond a critical strain rate, we observe fragmentation of the associative clusters, which has interesting effects on the stress/viscous response.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Entanglement and correlations in fast collective neutrino flavor oscillations

Collective neutrino oscillations play a crucial role in transporting lepton flavor in astrophysical settings like supernovae and neutron star binary merger remnants, which are characterized by large neutrino densities. In these settings, simulations in the mean-field approximation show that neutrino-neutrino interactions can overtake vacuum oscillations and give rise to fast collective flavor evolution on time-scales t ∝ μ –1 , with μ proportional to the local neutrino density. In this work, we study the full out-of-equilibrium flavor dynamics in simple multi-angle geometries displaying fast oscillations in the mean field linear stability analysis. Focusing on simple initial conditions, we analyze the production of pair correlations and entanglement in the complete many-body-dynamics as a function of the number N of neutrinos in the system, for up to thousands of neutrinos. Similarly to simpler geometries with only two neutrino beams, we identify three regimes: stable configurations with vanishing flavor oscillations, marginally unstable configurations with evolution occurring on long time scales τ ≈ µ –1 $\sqrt{N}$, and unstable configurations showing flavor evolution on short time scales τ ≈ μ –1 log(N). Here, we present evidence that these fast collective modes are generated by the same dynamical phase transition which leads to the slow bipolar oscillations, establishing a connection between these two phenomena and explaining the difference in their time scales. We conclude by discussing a semi-classical approximation which reproduces the entanglement entropy at short to medium time scales and can be potentially useful in situations with more complicated geometries where classical simulation methods starts to become inefficient.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗