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At least 361 records · Page 20

An experimental platform for investigating astrophysically relevant magnetized plasma jets on the COBRA facility

A new platform has been developed for the 1-MA COBRA generator to investigate the physical processes affecting the formation, collimation, and stability of high-speed outflows in magnetically driven laboratory plasma jets. Such experiments serve as diagnostically accessible surrogates for astrophysical jets under the assumption that the underlying dynamics are scale invariant. In contrast to previous current driven high energy density laboratory jet experiments that use radial/conical wire arrays or foils, the platform described here uses azimuthally symmetric gas-puff injection. This avoids the ablation phase from a solid target, allowing the jets to develop earlier and be driven longer without depleting their mass source and disrupting. A permanent magnet provides an initial poloidal magnetic field, which links the two concentric electrodes and mimics the boundary conditions of a star-accretion disk system. Extended magnetohydrodynamic effects can be assessed using a polarity convolute, which allows for reversal of the electrode bias. The resulting plasma jets exhibit remarkable stability, persisting for hundreds of nanoseconds and achieving aspect ratios ≳30:1.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Fabric properties and electric efficiency limits of mechanical moisture extraction from fabrics

Residential clothes drying consume about 650 TBtu of primary energy per year in the United States, equivalent to 3% of primary residential energy consumption. There is a strong impetus to reduce the energy consumption of clothes dryers by both improving existing technology and developing alternatives that use fundamentally different drying mechanisms. Clothes drying technologies are broadly classified into either evaporative or mechanical drying. The focus of this paper is on mechanical drying, including vibrational, centrifugal, and press-based methods. In this work, the physical processes involved in these mechanical fabric drying processes were analyzed to develop general theories of mechanical cloth drying energy efficiency. Quantitative evaluation of the theories requires measured fabric properties. To accomplish this, a set of experiments was conducted on samples of a standard test fabric. The fabric was a cotton-polyester blend specified by the US Department of Energy to evaluate the standardized efficiency of all residential clothes dryers in the US. Mercury porosimetry experiments were conducted to determine the fabric pore size distribution, apparent density, and porosity. Elasticity experiments were conducted to determine the fabric’s Young’s modulus. Isostatic press experiments were conducted to establish a relationship between compression force and fabric moisture content. The data resulting from these experiments were combined with mathematical models developed in this work to calculate the theoretical maximum performance limits for mechanical drying of the standard fabric. The results of the analysis are used to make recommendations for the most promising technologies that offer the greatest potential energy savings for residential clothes drying.

36 MATERIALS SCIENCE↗

Partitioned exponential methods for coupled multiphysics systems

Multiphysics problems involving two or more coupled physical phenomena are ubiquitous in science and engineering. This work develops a new partitioned exponential approach for the time integration of multiphysics problems. After a possible semi-discretization in space, the class of problems under consideration is modeled by a system of ordinary differential equations where the right-hand side is a summation of two component functions, each corresponding to a given set of physical processes. The partitioned-exponential methods proposed herein evolve each component of the system via an exponential integrator, and information between partitions is exchanged via coupling terms. Here, the traditional approach to constructing exponential methods, based on the variation-of-constants formula, is not directly applicable to partitioned systems. Rather, our approach to developing new partitioned-exponential families is based on a general-structure additive formulation of the schemes. Two method formulations are considered, one based on a linear-nonlinear splitting of the right hand component functions, and another based on approximate Jacobians. The paper develops classical (non-stiff) order conditions theory for partitioned exponential schemes based on particular families of T-trees and B-series theory. Several practical methods of third order are constructed that extend the Rosenbrock-type and EPIRK families of exponential integrators. Several implementation optimizations specific to the application of these methods to reaction-diffusion systems are also discussed. Numerical experiments reveal that the new partitioned-exponential methods can perform better than traditional unpartitioned exponential methods on some problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Long-pulse high-performance H-mode plasmas achieved on EAST

A record duration of a 310 s H-mode plasma (H 98y2 ~ 1.3, n e /n GW ~ 0.7, f BS > 50%) has been recently achieved on experimental advanced superconducting tokamak (EAST) with metal walls, exploiting the device's improved long-pulse capabilities. The experiment demonstrates good control of tungsten concentration, core/edge MHD stability, and particle and heat exhaust with an ITER-like tungsten divertor and zero injected torque, establishing a milestone on the path to steady-state long-pulse high-performance scenarios in support of ITER and CFETR. Important synergistic effects are leveraged toward this result, which relies purely on radio frequency (RF) powers for heating and current drive (H&CD). On-axis electron cyclotron heating enhances the H&CD efficiency from lower hybrid wave injection, increasing confinement quality and enabling fully non-inductive operation at high density (n e /n GW ~ 70%) and high poloidal beta (β P ~ 2.5). A small-amplitude grassy edge localized mode regime facilitates the RF power coupling to the H-mode edge and reduces divertor sputtering/erosion. The high energy confinement quality (H 98y2 ~ 1.3) is achieved with the experimental and simulated results pointing to the strong effect of Shafranov shift on turbulence. Transport analysis suggests that trapped electron modes dominate in the core region during the record discharge. The detailed physics processes (RF synergy, core-edge integration, confinement properties, etc.) of the steady-state operation will be illustrated in the content. In the future, EAST will aim at accessing more relevant dimensionless parameters to develop long-pulse high-performance plasma toward ITER and CFETR steady-state advanced operation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Validation of SPH code Spheral to model interacting solid bodies in a supersonic flow

Contemporary discussions of planetary defense involve analyzing the risks posed by smaller sized, 20 to 200 m diameter, asteroids which are capable of breaking up in the atmosphere and generating a blast wave. Consequence assessments for this size class of asteroids are performed through fast-running analytic or semi-analytic models which are informed by high-fidelity hydrocode simulations of asteroid entry and breakup. However, insufficient historical data necessitates validating the independent physical processes which dominate airburst events. Here, the Fluid Solid Interface Smoothed Particle Hydrodynamics solver was previously used by Pearl et al. in 2023 to model the Chelyabinsk airburst and is used here to perform a series of validation simulations. The first effort involves modeling a cylinder in a hypersonic flow and comparing the bow shock geometry to that predicted by analytic theory. The second effort involves modeling the separation of two spherical bodies in supersonic flow and validating against experimental footage. Combined, these exercises demonstrate the ability of the code to model the flight-path of interacting solid bodies in a hypersonic flow.

Airburst↗

A Cost-Effective Upgrade Path for the Fermilab Accelerator Complex

The Fermilab Proton Improvement Plan II, or PIP-II, would enable the world's most intense high-energy neutrino beam and would help scientists search for rare particle physics processes. The PIP-II goal is to deliver 1.2 MW of proton beam power from the Fermilab Main Injector, over the energy range 60 - 120 GeV, at the start of operation of the LBNF/DUNE program. PIP-II provides a variety of upgrade paths to higher beam power from the Main Injector, as demanded by the neutrino science program and as recommended by the 2014 P5 report. Delivering more than 2 MW to the LBNF target in the future will require a replacement of the existing Booster. This report outlines a cost-effective Booster replacement option and an upgrade path for the Fermilab Accelerator Complex to attain 2.4-MW beam power on the LBNF target, as well as to retain the capability to provide 8-GeV proton beams to the existing Fermilab Muon Campus via the existing Recycler ring. Its cost-effectiveness is achieved by: (1) using a small-diameter metallic vacuum chamber in the Booster replacement and (2) reusing the existing Recycler ring. Reusing the Recycler ring may be of particular advantage since it is presently employed to deliver 8-GeV beams to the Muon Campus experiments. The present concept also retains such a capability.

43 PARTICLE ACCELERATORS↗

Low-energy physics in neutrino LArTPCs

Here, in this paper, we review scientific opportunities and challenges related to detection and reconstruction of low-energy (less than 100 MeV) signatures in liquid argon time-projection chamber (LArTPC) neutrino detectors. LArTPC neutrino detectors designed for performing precise long-baseline oscillation measurements with GeV-scale accelerator neutrino beams also have unique sensitivity to a range of physics and astrophysics signatures via detection of event features at and below the few tens of MeV range. In addition, low-energy signatures are an integral part of GeV-scale accelerator neutrino interaction final-states, and their reconstruction can enhance the oscillation physics sensitivities of LArTPC experiments. New physics signals from accelerator and natural sources also generate diverse signatures in the low-energy range, and reconstruction of these signatures can increase the breadth of Beyond the Standard Model scenarios accessible in LArTPC-based searches. A variety of experimental and theory-related challenges remain to realizing this full range of potential benefits. Neutrino interaction cross-sections and other nuclear physics processes in argon relevant to sub-hundred-MeV LArTPC signatures are poorly understood, and improved theory and experimental measurements are needed; pion decay-at-rest sources and charged particle and neutron test beams are ideal facilities for improving this understanding. There are specific calibration needs in the low-energy range, as well as specific needs for control and understanding of radiological and cosmogenic backgrounds. Low-energy signatures, whether steady-state or part of a supernova burst or larger GeV-scale event topology, have specific triggering, DAQ and reconstruction requirements that must be addressed outside the scope of conventional GeV-scale data collection and analysis pathways. Novel concepts for future LArTPC technology that enhance low-energy capabilities should also be explored to help address these challenges.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Numerical investigation of liquid wall ablation in inertial fusion energy chambers

This paper presents a novel approach for modeling liquid wall ablation in liquid wall-protected inertial fusion energy (IFE) chambers. These systems are promising candidates for the implementation of fusion technology, yet significant gaps remain in understanding the underlying physical processes and their implications for design. Following target ignition, a portion of the fusion energy is released as x-rays, which deposit their energy into an array of liquid jets, leading to partial vaporization. Accurately modeling this heat deposition and vaporization process remains challenging due to the complex geometries typical of (pre-conceptual) IFE chamber designs. Furthermore, the subsequent expansion of vaporized material into the chamber’s vacuum environment poses difficulties for conventional CFD methods based on continuum assumptions, which can lead to significant inaccuracies. To address some aspects of these challenges, this work introduces a ray-tracing-based methodology to map the spatial distribution of ablated material in liquid wall-protected systems. In addition, a vacuum-tracking scheme is developed to extend the applicability of an OpenFOAM-based solver to gas dynamics in rarefied environments. The proposed approach has been verified through numerical benchmarks and applied to a practical case involving the HYLIFE-II (High Yield Lithium Injection Fusion Energy) chamber. The methodology advances the modeling capabilities for liquid wall-protected IFE systems and provides valuable tools to support their design and optimization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

THz Radiation Generation to Enable Internal Magnetic Field Measurement of Burning Plasmas (Final Scientific Report)

A one-year experimental program was performed using the Multi-TeraWatt (MTW) laser at the Laboratory for Laser Energetics (LLE) to investigate the efficiency and physical process of laser-driven—wire THz generation. This process was evaluated as a potential high-repetition-rate source of powerful THz pulses for use in THz pulsed polarimetry of a moderate-density magnetic-confinement fusion concept developed by TAE. The goal was to develop a source for short pulses in the THz regime (150 μm wavelength) containing 10’s of mJ. The campaign tested the impact of Cu wire diameter (25, 75, 160 μm), length (250 – 750 μm), and laser irradiation orientation on THz production efficiency in comparison to 20-μm thick Cu foils. Of these targets, the 160 µm diameter, 750 µm long wires with sharpened tips and irradiated at the base were found to produce the highest energy and shortest wavelength THz pulses, exceeding 2.5 Joule/sr and meeting the requirements for the polarimetry diagnostic. The brightest THz signal was radiated in the direction of the sharpened wire tip. A combination of two models – a traveling wave antenna combined with coherent transition radiation – describes the emission pattern, pulse energy, and spectrum observed in the experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Plasma Imaging, LOcal Measurement, and Tomographic Experiment (PILOT): A Mission Concept for Transformational Multi-Scale Observations of Mass and Energy Flow Dynamics in Earth’s Magnetosphere

We currently do not understand the fundamental physical processes that govern mass and energy flow through the Earth’s magnetosphere. Knowledge of these processes is critical to understanding the mass loss rate of Earth’s atmosphere, as well as for determining the role that a planetary magnetic field plays in atmospheric retention, and therefore habitability, for Earth-like planets beyond the solar system. Mass and energy flow processes are challenging to determine at Earth in part because Earth’s planetary magnetic field creates a complex “system of systems” composed of interdependent plasma populations and overlapping spatial regions that perpetually exchange mass and energy across a broad range of temporal and spatial scales. Further, the primary mass carrier in the magnetosphere is cold plasma (as cold as ~0.1 eV), which is invisible to many space-borne instruments that operate in the inner magnetosphere. The Plasma Imaging LOcal and Tomographic experiment (PILOT) mission concept, described here, provides the transformational multi-scale observations required to answer fundamental open questions about mass and energy flow dynamics in the Earth’s magnetosphere. PILOT uses a constellation of spacecraft to make radio tomographic, remote sensing, and in-situ measurements simultaneously, fully capturing cold plasma mass dynamics and its impact on magnetospheric systems over an unprecedented range of spatial and temporal scales. This article details the scientific motivation for the PILOT mission concept as well as a potential mission implementation.

79 ASTRONOMY AND ASTROPHYSICS↗

Understanding the Angular Momentum Evolution of T Tauri and Herbig Ae/Be Stars

We investigate a sample of six Herbig Ae/Be stars belonging to the Orion OB1 association, as well as 73 low-mass objects, members of the σ Orionis cluster, in order to explore the angular momentum evolution at early stages of evolution, and its possible connection with main-sequence Ap/Bp magnetic stars. Using FIES and HECTOCHELLE spectra, we obtain projected rotational velocities through two independent methods. Individual masses, radii, and ages are computed using evolutionary models, distance, and cluster extinction. Under the assumption that similar physical processes operate in both T Tauri and Herbig Ae/Be stars, we construct snapshots of the protostar’s rotation against mass during the first 10 Myr with the aid of a rotational model that includes a variable disk lifetime, changes in the stellar moment of inertia, a dipolar magnetic field with variable strength, and angular momentum loss through stellar winds powered by accretion. We use these snapshots, as well as the rotational data, to infer a plausible scenario for the angular momentum evolution. We find that magnetic field strengths of a few kilo-Gauss at 3 Myr are required to match the rotational velocities of both groups of stars. Models with masses between 2 M {sub ⊙} and 3 M {sub ⊙} display larger angular momentum values by a factor of ~3, in comparison to stars of similar spectral types on the main sequence. Even though some quantitative estimates on this dramatic decrease with age for Ap/Bp magnetic main-sequence stars are presented, the results obtained for the angular momentum evolution do not explain their low rotation rates.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A data analytical approach for assessing the efficacy of Operational Technology active defenses against insider threats

In recent years, the need for Operational Technology (OT) defenses has been recognized, serving as an additional line of defense when Information Technology (IT) defenses are bypassed. This is no longer considered an uncommon possibility when dealing with advanced persistent threat (APT) actors expected to be state-sponsored and receiving insider assistance. In these extreme adversarial situations, OT defenses aim to provide another layer of defense for the system, introduced directly at the physical process level, as described by the sensors data, the system model, and control actions. Just like IT defenses, two schools of thought, i.e., passive and active defenses, have emerged to address this challenge. In active defenses, representing the focus of this paper, known signatures, synthesized based on the system's unique characteristics, are inserted into the system. In contradistinction, passive methods rely solely on observing system behavior in search of patterns of normal behavior with deviations thereof representing abnormal behavior. In their most sophisticated implementations, both passive and active defenses rely on the use of data analytics to identify the patterns and synthesize the observed and/or inserted signatures. Past research has shown that passive defenses may be bypassed by APT actors relying on data analytics and their intimate knowledge of the system to evade detection by respecting the patterns identified by the defenders. Here this manuscript explores the use of active defenses under the assumption that the attacker has privileged access to the system, including access to the system's model and sensors data. Specifically, this manuscript assesses the ability of active defenses to remain invisible to the attackers, and discusses the associated challenges that must be addressed to ensure their resiliency against APT actors.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

The role of breakup and coalescence in fine-scale bubble-induced turbulence. I. Dynamics

We study the effect of bubble breakup and coalescence on fine-scale dynamics of bubbly turbulent flows using direct numerical simulations. We perform two different simulations of dilute bubbly flows of void fraction 0.5%: one with bubbles breaking up and coalescing and the other without these physical processes. The volume of the fluid method is used for simulating bubbles undergoing breakup and coalescence while the bubbles are treated as rigid spheres in the immersed boundary method simulation. The energy spectrum in both types of simulation, consistent with previous studies, exhibits a -3 slope. We follow a single infinitesimal fluid element as it evolves to understand velocity gradient dynamics using conditional mean trajectories. We note finite-time divergence when the fluid element evolves under the action of inertial and pressure dynamics. The inertial, pressure, and viscous velocity gradient dynamics, when considered individually, produce the same results for bubble-induced turbulence (BIT) as with the classical homogeneous isotropic turbulence (HIT). Yet when the overall velocity gradient dynamics is considered, BIT results in non-cyclic trajectories moving toward stable node and unstable saddle while classical HIT shows cyclic behavior in their trajectories that move toward the origin. Interestingly, both the volume of fluid and immersed boundary simulations produce similar results. Therefore, there are two main takeaways from this research. First, new velocity gradient models are needed for BIT as their velocity gradients behavior is entirely different from the HIT. Second, we can neglect the bubble topology, breakup, and coalescence while studying or modeling the fine-scale dynamics of BIT.

42 ENGINEERING↗

Anisotropic flow and flow fluctuations of identified hadrons in Pb–Pb collisions at $ \sqrt{s_{\textrm{NN}}}$ = 5.02 TeV

The first measurements of elliptic flow of π ± , K ± , p+$\bar{p}$, K$_{S}^{0}$, Λ+$\bar{Λ}$, $\phi$, Ξ – +$\barΞ$ + , and Ω – +$\barΩ$ + using multiparticle cumulants in Pb–Pb collisions at $\sqrt{s_{NN}}$= 5.02 TeV are resented. Results obtained with two- (v 2 {2}) and four-particle cumulants (v 2 {4}) are shown as a function of transverse momentum, p T , for various collision centrality intervals. Combining the data for both v 2 {2} and v 2 {4} also allows us to report the first measurements of the mean elliptic flow, elliptic flow fluctuations, and relative elliptic flow fluctuations for various hadron species. These observables probe the event-by-event eccentricity fluctuations in the initial state and the contributions from the dynamic evolution of the expanding quark–gluon plasma. The characteristic features observed in previous p T -differential anisotropic flow measurements for identified hadrons with two-particle correlations, namely the mass ordering at low p T and the approximate scaling with the number of constituent quarks at intermediate p T , are similarly present in the four-particle correlations and the combinations of v 2 {2} and v 2 {4}. In addition, a particle species dependence of flow fluctuations is observed that could indicate a significant contribution from final state hadronic interactions. The comparison between experimental measurements and CoLBT model calculations, which combine the various physics processes of hydrodynamics, quark coalescence, and jet fragmentation, illustrates their importance over a wide p T range.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Primordial non-Gaussianities with weak lensing: information on non-linear scales in the Ulagam full-sky simulations

Abstract Primordial non-Gaussianities (PNGs) are signatures in the density field that encode particle physics processes from the inflationary epoch. Such signatures have been extensively studied using the Cosmic Microwave Background, through constraining their amplitudes,f X NL , with future improvements expected from large-scale structure surveys; specifically, the galaxy correlation functions. We show that weak lensing fields can be used to achieve competitive and complementary constraints. This is shown via theUlagamsuite of N-body simulations, a subset of which evolves primordial fields with four types of PNGs. We create full-sky lensing maps and estimate the Fisher information from three summary statistics measured on the maps: the moments, the cumulative distribution function, and the 3-point correlation function. We find that the year 10 sample from the Rubin Observatory Legacy Survey of Space and Time (LSST) can constrain PNGs toσ(f NL eq ) ≈ 110,σ(f NL or, lss ) ≈ 120,σ(f NL loc ) ≈ 40. For the former two, this is better than or comparable to expected galaxy clustering-based constraints from the Dark Energy Spectroscopic Instrument (DESI). The PNG information in lensing fields is on non-linear scales and at low redshifts (z≲ 1.25), with a clear origin in the evolution history of massive halos. The constraining power degrades by ∼60% under scale cuts of ≳ 20 Mpc, showing there is still significant information on scales mostly insensitive to small-scale systematic effects (e.g., baryons). We publicly release theUlagamsuite to enable more survey-focused analyses.

Astronomy & Astrophysics↗

Contribution of Electron Pressure to Ring Current and Ground Magnetic Depression Using RAM-SCB Simulations and Arase Observations During 7–8 November 2017 Magnetic Storm

Understanding the physical processes that control the dynamics of energetic particles in the inner magnetosphere is important for both space-borne and ground-based assets essential to the modern society. The storm time distribution of ring current particles in the inner magnetosphere depends strongly on their transport in the evolving electric and magnetic fields along with particle acceleration and loss. Here, we investigated the ring current particle variations using observations and simulations. We compared the ion (H + , He + , and O + ) and electron flux and plasma pressure variations from Arase observations with the self-consistent inner magnetosphere model: Ring current Atmosphere interactions Model with Self Consistent magnetic field (RAM-SCB) during the 7–8 November 2017 geomagnetic storm. We investigated the contribution of the different species (ions and electrons) to the magnetic field deformation observed at ground magnetic stations (09°–45° MLat) using RAM-SCB simulations. The results show that the ions are the major contributor with ~88% and electrons contribute ~12% to the total ring current pressure. It is also found that the electron contribution is non-negligible (~18%) to the ring current in dawn-side during the main phase of the storm. Thus, the electron contribution to the storm time ring current is important and should not be neglected.

79 ASTRONOMY AND ASTROPHYSICS↗

Temperature and Density on the Forsterite Liquid‐Vapor Phase Boundary

Abstract The physical processes during planet formation span a large range of pressures and temperatures. Giant impacts, such as the one that formed the Moon, achieve peak pressures of 100s of GPa. The peak shock states generate sufficient entropy such that subsequent decompression to low pressures intersects the liquid‐vapor phase boundary. The entire shock‐and‐release thermodynamic path must be calculated accurately in order to predict the post‐impact structures of planetary bodies. Forsterite (Mg 2 SiO 4 ) is a commonly used mineral to represent the mantles of differentiated bodies in hydrocode models of planetary collisions. Here, we performed shock experiments on the Sandia Z Machine to obtain the density and temperature of the liquid branch of the liquid‐vapor phase boundary of forsterite. This work is combined with previous work constraining pressure, density, temperature, and entropy of the forsterite principal Hugoniot. We find that the vapor curves in previous forsterite equation of state models used in giant impacts vary substantially from our experimental results, and we compare our results to a recently updated equation of state. We have also found that due to under‐predicted entropy production on the principal Hugoniot and elevated temperatures of the liquid vapor phase boundary of these past models, past impact studies may have underestimated vapor production. Furthermore, our results provide experimental support to the idea that giant impacts can transform much of the mantles of rocky planets into supercritical fluids.

58 GEOSCIENCES↗

Ionization yield measurement in a germanium CDMSlite detector using photo-neutron sources

Two photo-neutron sources, Y 88 Be 9 and Sb 124 Be 9 , have been used to investigate the ionization yield of nuclear recoils in the CDMSlite germanium detectors by the SuperCDMS collaboration. In this study, we evaluate the yield for nuclear recoil energies between 1 and 7 keV at a temperature of ~ 50 mK . We use a geant4 simulation to model the neutron spectrum assuming a charge yield model that is a generalization of the standard Lindhard model and consists of two energy dependent parameters. We perform a likelihood analysis using the simulated neutron spectrum, modeled background, and experimental data to obtain the best fit values of the yield model. The ionization yield between recoil energies of 1 and 7 keV is shown to be significantly lower than predicted by the standard Lindhard model for germanium. There is a general lack of agreement among different experiments using a variety of techniques studying the low energy range of the nuclear recoil yield, which is most critical for interpretation of direct dark matter searches. This suggests complexity in the physical process that many direct detection experiments use to model their primary signal detection mechanism and highlights the need for further studies to clarify underlying systematic effects that have not been well understood up to this point.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗