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At least 1,747 records · Page 97

Enhancement of 2D topological semimetal transport properties by current annealing

Observation of intrinsic quantum transport properties of two-dimensional (2D) topological semimetals can be challenging due to suppression of high mobility caused by extrinsic factors introduced during fabrication. We demonstrate current annealing as a method to substantially improve electronic transport properties of 2D topological semimetal flakes. Contact resistance and resistivity were improved by factors up to 2 × 10 6 and 2 × 10 4 , respectively, in devices based on exfoliated flakes of two topological semimetals, ZrSiSe and BaMnSb 2 . Using this method, carrier mobility in ZrSiSe was improved by a factor of 3800, resulting in observation of record-high mobility for exfoliated ZrSiSe. Quantum oscillations in annealed ZrSiSe appeared at magnetic fields as low as 5 T, and magnetoresistance increased by a factor of 10 4 . We argue that a thermal process underlies this improvement. Finally, Raman spectroscopy and analysis of quantum oscillations in ZrSiSe indicate that the phonon modes and Fermi surface area are unchanged by current annealing.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Mechanism of enhanced critical fields and critical current densities of MgB2 wires with C/Dy$^{2}$O3 co-additions

A series of monofilamentary powder-in-tube MgB2 wires were fabricated with 2 mol. % C doping and co-additions of 0–3 wt. % Dy2O3. Irreversibility fields (μ0Hirr), upper critical fields (μ0Hc2), and transport critical currents were measured, and from these quantities, anisotropies (γ) and electronic diffusivities (Dπ,σ) were estimated. The addition of 1 wt. % Dy2O3 to already optimally C-doped MgB2 wires produced higher Hc2//ab, Hc2//c, and Hirr values at 4.2 K. In addition, the critical current density, Jc, increased with Dy2O3 concentration up to 1 wt. % where non-barrier Jc reached 4.35 × 104 A/cm2 at 4.2 K, 10 T. At higher temperatures, for example, 20 K and 5 T, co-additions of 2 mol. % C and 2 wt. % Dy2O3 improved non-barrier Jc by 40% and 93% compared to 2 and 3 mol. % C doping, respectively. On the other hand, measurements of Tc showed that C/Dy2O3 co-additions increase interband scattering rates at a lower rate than C doping does (assuming C doping levels giving similar levels of low-T μ0Hc2 increase as co-addition). Comparisons to a two-band model for μ0Hc2 in MgB2 allowed us to conclude that the increases in Hc2//ab, Hc2//c, and Hirr (as well as concomitant increases in high-field Jc) with Dy2O3 addition are consistent with increases primarily in intraband scattering. This suggests C/Dy2O3 co-addition to be a more promising candidate for improving non-barrier Jc of MgB2 at temperatures above 20 K.

36 MATERIALS SCIENCE↗

Disruption halo current rotation scaling on Alcator C-Mod and HBT-EP

Asymmetric halo currents (HCs) can exert large net forces on the vacuum vessel and other components during disruptions on tokamaks. The displacements caused by these forces can then be amplified if these asymmetric forces rotate at frequencies resonant with the vessel. This paper reports on the investigation of a recently proposed scaling law for the disruption HC rotation frequency [Saperstein et al., “Halo current rotation scaling in post-disruption plasmas,” Nucl. Fusion 62, 026044 (2022)] that combines measurements on Alcator C-Mod with those on HBT-EP. We find that a new non-circular version of the scaling law [ ⟨ f rot ⟩ m / ⟨ m ⟩ ∝ 1 B T ( S / π )] takes into consideration the dependence of frot on the poloidal structure of the MHD instability (m) driving the asymmetry and describes the disruption-averaged rotation frequency on C-Mod. Disruption rotation is also found to be insensitive to the vertical position and impurity content of the plasma at the onset of the disruption. However, a stagnation in the time evolution of frot is occasionally observed. In conclusion, observations are consistent with the dominance of poloidal rotation during the disruption, which is motivated by the poloidal drift nature of the scaling law.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Defects of perovskite semiconductor CsPbBr3 investigated via photoluminescence and thermally stimulated current spectroscopies

Halide perovskites are essential materials for hard radiation detectors at ambient temperature. To improve detector performance, charge transport must be investigated and optimized. Using photoluminescence (PL) and thermally stimulated current (TSC) spectroscopies, we investigate photogenerated charge carriers in Bridgman-grown CsPbBr3 single crystals to understand the nature of charge transport. PL spectroscopy of these halide perovskites revealed the presence of strong emission bands at the band edge, which were attributed to free or bound excitons. It is shown that a wide broadening of the excitonic linewidth in these halide perovskites arises from strong exciton–phonon coupling, which is substantially dominated by longitudinal optical phonons via Fröhlich interaction. An additional contribution due to the presence of ionized impurities was also observed. Crystals with a detectable sensitivity to high-energy gamma radiation are characterized by a higher intensity and a narrower linewidth of the principal PL peak at 2.326 eV. Defect states beyond 2.214 eV have a negative impact on detector sensitivity to high-energy gamma radiation. TSC spectroscopy reveals an array of trap levels spanning 0.15–0.70 eV, attributed to intrinsic point defects and multiple extrinsic defects involving dopants or impurities. Defects identified included Cs and Br vacancies, as well as Pb interstitials with concentrations in the 1011–1016 cm−3 range. Understanding how the synthesis process impacts the types and concentrations of the defects present is currently under investigation. Elimination or suppression of the defect/trap states should result in halide perovskite materials with longer carrier diffusion lengths and improved detector characteristics.

Physics↗

Parameterized anomalous transport model for current-carrying collisionless plasmas in pulsed power inertial confinement fusion

Current delivery in pulsed power inertial confinement fusion is influenced by collisionless current-carrying microturbulent plasmas, which are sourced from electrode surfaces. In this setting, the lower hybrid drift instability—triggered by plasma acceleration—is a leading candidate driver of difficult-to-predict momentum and energy transport. To characterize the nonlinear state of the microturbulent plasma, a parameterized anomalous transport model is developed for the instability, with analytic formulas for anomalous collision frequency, resistivity, and species heating rates. The formulas are expressed in terms of linear-theory variables and four dimensionless parameters that characterize the macroscopic plasma state. The model is built on linear theory analysis, power law analysis, and quasilinear theory analysis, and is validated using a series of nonlinear continuum kinetic Vlasov–Poisson simulations. The theoretical and computational investigation demonstrates that the anomalous collision frequency associated with the instability can be reliably approximated, within about a factor of five or better, by the unscaled linear theory growth rate of the fastest-growing wavenumber mode. This finding enables efficient calculation of anomalous resistivity and species heating rates over a wide range of plasma conditions, resulting in improved predictive capabilities.

Complex functions↗

Pressure Response Optimization of an Eddy Current-Driven Flyer Plate Valve for the ITER Shattered Pellet Injection System

One technique for mitigating disruptions in a tokamak is shattered pellet injection (SPI). SPI is a process in which a large solid pellet consisting of deuterium, neon, or argon is desublimated in a pipe gun barsrel and launched downstream. Pellets are shattered just before entering the plasma by an impact with an angled tube. Injection of these materials into the plasma radiates stored thermal energy, limits current decay rates, suppresses the generation of runaway electrons, and dissipates runaway electrons if necessary. A critical element of the SPI system is a fast-acting valve that releases high-pressure gas to dislodge and accelerate pellets directly, or indirectly via a mechanical punch. A prototype valve sized for the ITER SPI system has been designed and fabricated. A pulsed high-voltage power supply energizes the valve’s internal magnetic coil, which induces eddy currents in the adjacent flyer plate resulting in a repulsive force between the flyer plate and the coil. The flyer plate action lifts a valve seat, allowing high-pressure gas to flow from the valve plenum to the downstream (breech) location of the pellet or mechanical punch. All of the valve’s internal components are designed to operate in ITER-level static background magnetic fields. Here, a study was conducted to optimize the downstream pressure response for a range of valve sizes and operating pressures. In particular, the study analyzes the breech pressure response associated with varying plenum pressures as well as varying breech volumes. A computational fluid dynamics simulation was built in STAR-CCM+ and validated against data from laboratory experiments. The resulting simulation outputs, in the form of downstream responses for a variety of initial plenum pressures and breech volumes, will be used as a complement to experimental data to ensure the pressure pulse is suitable for pellet survivability. These data, combined with studies on pellet shear strength and shock response, will be applied to optimization of overall operating parameters of the ITER SPI system.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The MIST-1 and MIST-2 multicusp ion sources for high-current $H$$^{+}_{2}$ beams

We present two iterations of the Multicusp Ion Source Technology at MIT (MIST) sources, designed to fulfill the requirements of the HCHC-XX cyclotron design. The HCHC-XX is a novel compact cyclotron accelerating $H$$^{+}_{2}$. Beam is injected through a radio-frequency quadrupole buncher-accelerator (embedded in the cyclotron yoke) and utilizes so-called vortex motion during acceleration. If successful, it will deliver 10 mA of protons at 60 MeV in CW mode. This scheme requires a low-emittance, high-current initial beam with high $H$$^{+}_{2}$ purity. We briefly summarize the design and previous results of the MIST-1 ion source and, for the first time, the detailed design of the new and improved MIST-2, including the mechanical, electrical, and control system design. We further show experimental results of using the MIST-2 backplate on the MIST-1 body, present a study using different types of permanent magnets for confinement (including no magnets), and finally, we present first results of the MIST-2 in full operation. In this first commissioning run, we were able to increase the total extracted current from the MIST-2 to 7 mA—a factor of 2 over the MIST-1.

Winklehner, D. [Massachusetts Institute of Technol↗

Elimination of MHD current sheets by modifications to the plasma wall in a fixed boundary model

Models of magnetohydrodynamic (MHD) equilibia that for computational convenience assume the existence of a system of nested magnetic flux surfaces tend to exhibit singular current sheets. These sheets are located on resonant flux surfaces that are associated with rational values of the rotational transform. We study the possibility of eliminating these singularities by suitable modifications of the plasma boundary, which we prescribe in a fixed boundary setting. We find that relatively straightforward iterative procedures can be used to eliminate weak current sheets that are generated at resonant flux surfaces by the nonlinear interactions of resonating wall harmonics. These types of procedures may prove useful in the design of fusion devices with configurations that enjoy improved stability and transport properties.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Self-organization in 1 atm DC glows with liquid anodes: current understanding and potential applications

Self-organization refers to the spontaneous generation of spatially or temporally organized patterns in an otherwise disordered system. Self-organization is ubiquitous in plasma physics particularly in the low-pressure regime as observed in astrophysical jets or plasma loaded flux loops that form on the surface of the Sun. In recent times, self-organization in atmospheric pressure plasmas has captured the attention of researchers. Its occurrence has been observed in DBD discharges as well as DC 1 atm glows with liquid electrodes. The mechanism of pattern formation is still not well understood. In this work, we briefly review the current understanding of pattern formation in DC glows with liquid anode, surveying past work, application areas, theories on mechanisms of formation from the context of reaction diffusion systems, current experimental work and computational progress towards predicting pattern formation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

W7-X and the sawtooth instability: towards realistic simulations of current-driven magnetic reconnection

Magnetic reconnection in W7-X is studied by means of global numerical simulations in a series of models of increasing complexity. The magnetic geometry ranges from that of a cylinder to the full three-dimensional field of W7-X, and the equations solved range from ideal magnetohydrodynamics (MHD) to gyrokinetics. We simulate plasmas from the first operation phase with electron cyclotron current drive (ECCD). These are characterized by an equilibrium magnetic field featuring an ECCD-distorted 'humped' profile of the rotational transform ι, with ι = 1 in two radial locations. Such plasmas generally show sawtooth activity, hence motivating the present study. We pay particular attention to the role of equilibrium current density gradients in the destabilization of reconnecting modes. When the equilibrium temperature and density gradients are artificially suppressed (to eliminate the pressure gradient drive), the perturbed electrostatic potential is radially localized between the locations at which ι = 1. This is shown with a purely collisionless gyrokinetic model, in cylindrical geometry. In the real toroidal geometry of W7-X, for a non-ideal MHD model including a uniform resistivity, electron inertia and (numerical) viscosity, the same qualitative behaviour is observed. In particular, even if a resonant (m, n) = (1, -1) perturbation is initialized, the most unstable mode is the (m, n) = (-4, 4), where m and n are the poloidal and toroidal mode numbers, respectively. Other modes are destabilized due to geometric coupling. The growth rate of this instability scales as η 1/3 , where η is the plasma resistivity, thus suggesting that ECCD drives ideal MHD stable W7-X plasmas towards non-ideal marginality. An ideal magnetohydrodynamic analysis confirms the result. A fluid-kinetic hybrid version of the EUTERPE code shows that gyrokinetic ions have a stabilizing effect on these modes. For W7-X relevant collisionalities, the growth rate scales linearly with the electron skin depth, d e . Implications of our results for sawtoothing W7-X operation are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Spectral broadening from turbulence in multiscale lower hybrid current drive simulations

Abstract The scattering of lower hybrid (LH) waves due to scrape-off layer filaments is investigated. It is revealed that scattering can account for the LH spectral gap without any ad hoc modification to the wave-spectrum. This is shown using a multiscale simulation approach which allows, for the first time, the inclusion of full-wave scattering physics in ray-tracing/Fokker–Planck calculations. In this approach, full-wave scattering probabilities are calculated for a wave interacting with a statistical ensemble of filaments. These probabilities are coupled to ray-tracing equations using radiative transfer theory. This allows the modeling of scattering along the entire ray-trajectory, which can be important in the multi-pass regime. Simulations are conducted for LH current drive (LHCD) in Alcator C-Mod, resulting in excellent agreement with experimental current and hard x-ray profiles. A region in filament parameter space is identified in which the impact of scattering on LHCD is saturated. Such a state coincides with experimental LHCD measurements, suggesting saturation indeed occurs in C-Mod, and therefore the exact statistical properties of the filaments are not important.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Simultaneous access to high normalized density, current, pressure, and confinement in strongly-shaped diverted negative triangularity plasmas

Strongly-shaped diverted negative triangularity (NT) plasmas in the DIII-D tokamak demonstrate simultaneous access to high normalized density, current, pressure, and confinement. NT plasmas are shown to exist across an expansive parameter space compatible with high fusion power production, revealing surprisingly good core stability properties that compare favorably to conventional positive triangularity plasmas in DIII-D. Non-dimensionalizing the key parameters, expanded operating spaces featuring edge safety factors below 3, normalized betas above 3, Greenwald density fractions above 1, and high-confinement mode (H-mode) confinement qualities above 1 are observed, even simultaneously, and all with a robustly stable edge free from deleterious edge-localized mode instabilities. Scaling of the confinement time with engineering parameters reveals at least a linear dependence on plasma current although with significant power degradation, both in excess of expected H-mode scalings. These results increase confidence that NT plasmas are a viable approach to realize fusion power and open directions for future detailed study.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Achievement of a high-density, high-confinement, and high-beta tokamak plasma regime in DIII-D, and implications for a lower-current path for ITER and FPP

Experiments on DIII-D have demonstrated a density-confinement synergy that enables sustainment of high performance in a previously unattained parameter regime of simultaneous very high energy confinement quality (H 98y2 ≥ 1.5), very high line-average density Greenwald fraction (ƒ Gr = πa 2 < n >/I P ≥ 1.4), and high toroidal beta (β T ≥ 3%). Tokamak operation in this regime is essential for a compact steady-state FPP, as well as for Q=10 with 500 MW of fusion power in ITER at I P << 15 MA. These experiments leveraged the knowledge that, in the high-poloidal-beta (β P ) regime, impurity and density gradients can enhance turbulence stabilization caused by high α MHD (α MHD ~(dβ P )⁄dr). This was described by theoretical predictions and gyrokinetic transport simulations [M.T. Kotschenreuther et al, 2024 Nucl. Fusion, 64 076033], and later confirmed by experiments on DIII-D [S. Ding et al, 2024 Nature 629 555]. To increase both β P and β T , the new experiments increased the ideal-wall stability β N -limit by using a smaller plasma-outer wall distance and higher triangularity in the plasma cross section (top/bottom average δ~0.9), enabled by the recent “shape & volume rise” (SVR) modification to the DIII-D divertor. The higher triangularity also contributed to achieving higher ƒ Gr by enabling higher pedestal density. At high density, the pedestal is ballooning limited and exhibits small and frequent ELMs, while the divertor is near detachment even without any impurity seeding. High plasma performance was attained and sustained reproducibly, with the eventual terminations brought about by an MHD mode destabilized as the current profile slowly continued to evolve. A path to stationary fully noninductive operation might include ECH injection to reduce both core impurity accumulation and the electron collisionality, thus increasing the bootstrap current. These experiments provide the first experimental demonstration of the ƒ Gr , H 98y2 , and β T values required simultaneously for ITER Q = 10 at I P < 10 MA, pointing to practical ways to improve the energy confinement in a fusion reactor.

Garofalo, Andrea M. [General Atomics, San Diego, C↗

Machine learning models inaccurately predict current and future high-latitude C balances

The high-latitude carbon (C) cycle is a key feedback to the global climate system, yet because of system complexity and data limitations, there is currently disagreement over whether the region is a source or sink of C. Recent advances in big data analytics and computing power have popularized the use of machine learning (ML) algorithms to upscale site measurements of ecosystem processes, and in some cases forecast the response of these processes to climate change. Due to data limitations, however, ML model predictions of these processes are almost never validated with independent datasets. To better understand and characterize the limitations of these methods, we develop an approach to independently evaluate ML upscaling and forecasting. We mimic data-driven upscaling and forecasting efforts by applying ML algorithms to different subsets of regional process-model simulation gridcells, and then test ML performance using the remaining gridcells. In this study, we simulate C fluxes and environmental data across Alaska using ecosys, a process-rich terrestrial ecosystem model, and then apply boosted regression tree ML algorithms to training data configurations that mirror and expand upon existing AmeriFLUX eddy-covariance data availability. We first show that a ML model trained using ecosys outputs from currently-available Alaska AmeriFLUX sites incorrectly predicts that Alaska is presently a modeled net C source. Increased spatial coverage of the training dataset improves ML predictions, halving the bias when 240 modeled sites are used instead of 15. However, even this more accurate ML model incorrectly predicts Alaska C fluxes under 21st century climate change because of changes in atmospheric CO 2 , litter inputs, and vegetation composition that have impacts on C fluxes which cannot be inferred from the training data. Our results provide key insights to future C flux upscaling efforts and expose the potential for inaccurate ML upscaling and forecasting of high-latitude C cycle dynamics.

54 ENVIRONMENTAL SCIENCES↗

The microbial rare biosphere: current concepts, methods and ecological principles

ABSTRACT Our ability to describe the highly diverse pool of low abundance populations present in natural microbial communities is increasing at an unprecedented pace. Yet we currently lack an integrative view of the key taxa, functions and metabolic activity which make-up this communal pool, usually referred to as the ‘rare biosphere’, across the domains of life. In this context, this review examines the microbial rare biosphere in its broader sense, providing an historical perspective on representative studies which enabled to bridge the concept from macroecology to microbial ecology. It then addresses our current knowledge of the prokaryotic rare biosphere, and covers emerging insights into the ecology, taxonomy and evolution of low abundance microeukaryotic, viral and host-associated communities. We also review recent methodological advances and provide a synthetic overview on how the rare biosphere fits into different conceptual models used to explain microbial community assembly mechanisms, composition and function.

Pascoal, Francisco↗

Measurements of $\overline{\nu}_{\mu}$ and $\overline{\nu}_{\mu} + \nu_{\mu}$ charged-current cross-sections without detected pions or protons on water and hydrocarbon at a mean anti-neutrino energy of 0.86 GeV

We report measurements of the flux-integrated $\overline{\nu}_\mu$ and $\overline{\nu}_\mu+\nu_\mu$ charged-current cross-sections on water and hydrocarbon targets using the T2K anti-neutrino beam with a mean beam energy of 0.86 GeV. The signal is defined as the (anti-)neutrino charged-current interaction with one induced $\mu^\pm$ and no detected charged pion or proton. These measurements are performed using a new WAGASCI module recently added to the T2K setup in combination with the INGRID Proton Module. The phase space of muons is restricted to the high-detection efficiency region, $p_{\mu}>400~{\rm MeV}/c$ and $\theta_{\mu}<30^{\circ}$, in the laboratory frame. An absence of pions and protons in the detectable phase spaces of $p_{\pi}>200~{\rm MeV}/c$, $\theta_{\pi}<70^{\circ}$ and $p_{\rm p}>600~{\rm MeV}/c$, $\theta_{\rm p}<70^{\circ}$ is required. In this paper, both the $\overline{\nu}_\mu$ cross-sections and $\overline{\nu}_\mu+\nu_\mu$ cross-sections on water and hydrocarbon targets and their ratios are provided by using the D’Agostini unfolding method. The results of the integrated $\overline{\nu}_\mu$ cross-section measurements over this phase space are $\sigma_{\rm H_{2}O}=(1.082\pm0.068(\rm stat.)^{+0.145}_{-0.128}(\rm syst.)) \times 10^{-39}\,{\rm cm^{2} / nucleon}$, $\sigma_{\rm CH}=(1.096\pm0.054(\rm stat.)^{+0.132}_{-0.117}(\rm syst.)) \times 10^{-39}\,{\rm cm^{2} / nucleon}$, and $\sigma_{\rm H_{2}O}/\sigma_{\rm CH} = 0.987\pm0.078(\rm stat.)^{+0.093}_{-0.090}(\rm syst.)$. The $\overline{\nu}_\mu+\nu_\mu$ cross-section is $\sigma_{\rm H_{2}O} = (1.155\pm0.064(\rm stat.)^{+0.148}_{-0.129}(\rm syst.)) \times 10^{-39}\,{\rm cm^{2} / nucleon}$, $\sigma_{\rm CH}=(1.159\pm0.049(\rm stat.)^{+0.129}_{-0.115}(\rm syst.)) \times 10^{-39}\,{\rm cm^{2} / nucleon}$, and $\sigma_{\rm H_{2}O}/\sigma_{\rm CH}=0.996\pm0.069(\rm stat.)^{+0.083}_{-0.078}(\rm syst.)$.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Measurement of muon neutrino charged-current quasielasticlike cross section using off-axis NuMI beam at ICARUS

This paper presents the first neutrino cross-section measurement from the ICARUS detector at Fermilab, using Neutrinos at the Main Injector (NuMI) beam data collected from two beam operation periods corresponding to 2.5 × 10 20 protons-on-target in neutrino beam mode. The signal is defined by events with no pions produced in the final state, a topology dominated by charged-current quasielasticlike signatures. The measurement is reported as flux-averaged differential cross sections as functions of kinematic variables that provide sensitivity to the complex nuclear effects that often dominate the systematic uncertainty budgets of neutrino oscillation measurements. Specifically, this work reports cross sections in two angular variables—the angle of the outgoing lepton and the opening angle between the lepton and leading proton—and two variables characterizing the kinematic imbalance between the muon and proton in the plane transverse to the incoming neutrino. These results are compared against predictions from a variety of neutrino event generators, with p values calculated between the extracted cross sections and each prediction. Overall, the predictions agree with the data; however, the current budget of uncertainties does not yet provide sufficient discriminating power to favor a specific model.

Abd Alrahman, F. [Houston U.]↗

Measurement of magnetic dipole strength in 40 Ar between 9.3 and 10.3 MeV excitation energy and impact on neutral current neutrino interaction

The magnetic dipole strength 𝐵⁡(𝑀⁢1 ↑) of 40 Ar was measured in the excitation energy range between 9.3 and 10.3 MeV. The nuclear resonance fluorescence technique was used with monoenergetic, linearly polarized incident photon beams. The new data increase the known 𝐵⁡(𝑀⁢1 ↑) strength in this important excitation energy range by a factor of 2, resulting in an equivalent increase of the calculated neutral current neutrino cross section of 40 Ar . This observation is of special interest for liquid-argon (LAr)-based neutrino detectors. 𝐵⁡(𝑀⁢1 ↑) strength has not been found between 10.3 and 11.7 MeV excitation energy. In conclusion, with the new data, a more reliable detection capability of the large Deep Underground Neutrino Experiment LAr detectors can be derived for potential core-collapse supernova neutrinos via the neutral current interaction.

Energy levels↗