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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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At least 127 records · Page 7

Investigation of ion-beam machining methods for replicated x-ray optics

The final figuring step in the fabrication of an optical component involves imparting a specified contour onto the surface. This can be expensive and time consuming step. The recent development of ion beam figuring provides a method for performing the figuring process with advantages over standard mechanical methods. Ion figuring has proven effective in figuring large optical components. The process of ion beam figuring removes material by transferring kinetic energy from impinging neutral particles. The process utilizes a Kaufman type ion source, where a plasma is generated in a discharge chamber by controlled electric potentials. Charged grids extract and accelerate ions from the chamber. The accelerated ions form a directional beam. A neutralizer outside the accelerator grids supplies electrons to the positive ion beam. It is necessary to neutralize the beam to prevent charging workpieces and to avoid bending the beam with extraneous electro-magnetic fields. When the directed beam strikes the workpiece, material sputters in a predicable manner. The amount and distribution of material sputtered is a function of the energy of the beam, material of the component, distance from the workpiece, and angle of incidence of the beam. The figuring method described here assumes a constant beam removal, so that the process can be represented by a convolution operation. A fixed beam energy maintains a constant sputtering rate. This temporally and spatially stable beam is held perpendicular to the workpiece at a fixed distance. For non-constant removal, corrections would be required to model the process as a convolution operation. Specific figures (contours) are achieved by rastering the beam over the workpiece at varying velocities. A unique deconvolution is performed, using series-derivative solution developed for the system, to determine these velocities.

Drueding, Thomas W.↗

Development of Advanced, Radiation Resistant, Optical-based Detector Technology for Future Experiments.

The primary objective of this project has been to advance the design of high-performance electromagnetic (EM) calorimeters for future particle physics experiments, to identify and measure the timing, position and energy of electrons, positrons and gamma rays, particularly in high-luminosity environments with intense radiation and pileup conditions. To meet such challenges, the proposed research has focused on the development of ultra-compact, radiation-hard calorimeter modules, to provide excellent timing, spatial, and energy resolution. The work aligns with the DOE’s Basic Research Needs (BRN) for High Energy Physics (HEP) Instrumentation and the research team contributes actively to the Coordinating Panel on Advanced Detectors (CPAD) RDC9 calorimetry collaboration in the USA and the European Committee on Future Accelerators (ECFA) DRD-CALO calorimetry collaboration at CERN, the European Laboratory for Particle Physics located in Geneva, Switzerland. The research builds on the RADiCAL (radiation-hard, ultra-compact) modular sampling calorimeter approach, developed by the research team, which employs dense and very bright optical materials such as LYSO:Ce scintillator plates that are interleaved with very dense tungsten plates to minimize detector size while optimizing performance. The modules are comparable in size to a human index finger, dimensionally 14 mm x 14 mm in cross section and 135 mm in length. And despite the small size, the structure is capable of providing excellent timing and energy resolution. This is facilitated through the use of specialized quartz capillaries filled with wavelength-shifting filaments, positioned at various depths along the length of a module, to collect and guide light signals to silicon photomultipliers (SiPMs) which detect and convert the optical signals to electronic signals for analysis. The primary goals of this project have been: (1) Achieve a timing resolution to σ t ≤ 30 ps for high-energy electrons and photons, important for their association with specific events produced in colliding-beam experiments and for the detection of decays-in-flight of long-lived particles. The project has achieved this goal in beam tests of a single RADiCAL module at CERN, during which a timing resolution of σ t = 27 ps was measured for electrons of energy E = 150 GeV. Based upon a mathematical fit to the data measured over a broad energy range from low energy to high energy, a resolution of σ t ≤ 18 ps has been estimated for electrons of very high (TeV) energy. From these measurements and with further expected technical improvements, the timing resolution should reach σ t ≤ 10 ps, important for searches for discovery physics in upcoming and future experiments. (2) Achieve an energy resolution of σ E / E ≤ 10% / $\sqrt{E}$. The project has yet to achieve this goal, but is close to it, having measured a value of σ E / E ≤ 15.9% / $\sqrt{E}$ using a modular array. Ultimately, the resolution goal is expected to be reached by adjustments to material thicknesses within the modules, which will improve the sampling fraction to measure more precisely the shower energy for lower energy particles. The versatility of the modular RADiCAL approach enables the testing of advanced materials, photosensors and electronics, developed in collaboration with CPAD RDC and ECFA DRD-CALO groups. The structure can distinguish electrons, positrons and gamma rays from hadrons and muons and beam-induced backgrounds, making it a valuable tool in a variety of detector environments, including future circular colliders (FCC-ee, FCC-hh) proposed for the European Laboratory for Particle Physics (CERN), the muon-collider proposed for Fermi National Accelerator Laboratory (Fermilab), and searches for new physics in beam-dump, fixed target and forward-physics experiments. And, while designed with particle physics applications in mind, the technologies developed in this project have the potential for application more broadly in particle and nuclear physics, materials science, and medical physics, underscoring the far-reaching potential of this line of instrumentation research and development.

47 OTHER INSTRUMENTATION↗

Effect of g-jitter on Directional Solidification of a Binary Alloy

A study of directional solidification of a weak binary alloy (specifically, Bi - 1 at% Sn) based on the fixed grid single domain approach is being undertaken. The enthalpy method is used to solve for the temperature field over the computational domain including both the solid and liquid phases; latent heat evolution is treated with the aid of an effective specific heat coefficient. A source term accounting for the release of solute into the liquid during solidification has been incorporated into the solute transport equation. The vorticity-stream function formulation is used to describe thermosolutal convection in the liquid region. In this paper we present a numerical simulation of g-jitter: the small, rapid fluctuations in gravitational acceleration which may be experienced in an orbiting space vehicle. A background gravity of 1 micro-g has been assumed, and new results for the effects of orientation angle of the periodic disturbances over a range of amplitudes and frequencies on solute field and segregation have been presented.

Santiviriyapanich, P.↗

Independent pixel and Monte Carlo estimates of stratocumulus albedo

Monte Carlo radiative transfer methods are employed here to estimate the plane-parallel albedo bias for marine stratocumulus clouds. This is the bias in estimates of the mesoscale-average albedo, which arises from the assumption that cloud liquid water is uniformly distributed. The authors compare such estimates with those based on a more realistic distribution generated from a fractal model of marine stratocumulus clouds belonging to the class of 'bounded cascade' models. In this model the cloud top and base are fixed, so that all variations in cloud shape are ignored. The model generates random variations in liquid water along a single horizontal direction, forming fractal cloud streets while conserving the total liquid water in the cloud field. The model reproduces the mean, variance, and skewness of the vertically integrated cloud liquid water, as well as its observed wavenumber spectrum, which is approximately a power law. The Monte Carlo method keeps track of the three-dimensional paths solar photons take through the cloud field, using a vectorized implementation of a direct technique. The simplifications in the cloud field studied here allow the computations to be accelerated. The Monte Carlo results are compared to those of the independent pixel approximation, which neglects net horizontal photon transport. Differences between the Monte Carlo and independent pixel estimates of the mesoscale-average albedo are on the order of 1% for conservative scattering, while the plane-parallel bias itself is an order of magnitude larger. As cloud absorption increases, the independent pixel approximation agrees even more closely with the Monte Carlo estimates. This result holds for a wide range of sun angles and aspect ratios. Thus, horizontal photon transport can be safely neglected in estimates of the area-average flux for such cloud models. This result relies on the rapid falloff of the wavenumber spectrum of stratocumulus, which ensures that the smaller-scale variability, where the radiative transfer is more three-dimensional, contributes less to the plane-parallel albedo bias than the larger scales, which are more variable. The lack of significant three-dimensional effects also relies on the assumption of a relatively simple geometry. Even with these assumptions, the independent pixel approximation is accurate only for fluxes averaged over large horizontal areas, many photon mean free paths in diameter, and not for local radiance values, which depend strongly on the interaction between neighboring cloud elements.

Cahalan, Robert F.↗

An Experimental Study of Richtmyer-Meshkov Instability

Richtmyer-Meshkov (RM) instability occurs when a planar interface separating two fluids of different density is impulsively accelerated In the direction of its normal. It is one of the most fundamental of fluid instabilities and is of importance in fields ranging from astrophysics to materials processing. Because RM instability experiments are normally carried out in shock tubes, where the generation of a sharp well controlled interface between gases is difficult, there is a scarcity of good experimental results. The experiments presented here utilize a novel technique which circumvents many of the experimental difficulties that have previously limited the study of RM instability. In this system, the instability is generated by bouncing a thin rectangular tank containing two liquids off of a fixed spring. Results obtained from these experiments yield particularly well visualized images of the nonlinear development of the instability. However, because the run time in these experiments is limited, new experiments capable of achieving longer run times are planned.

Jacobs, Jeffrey W.↗

Proposal for a Proton-Bunch Compression Experiment at IOTA in the Strong Space-Charge Regime

The longitudinal compression of intense proton bunches with strong space-charge force is an essential component of a proton-based muon source for a muon collider. This paper discusses a proton-bunch compression experiment at the Integrable Optics Test Accelerator (IOTA) storage ring at Fermilab to explore optimal radio frequency (RF) cavity and lattice configurations. IOTA is a compact fixed-energy storage ring that can circulate a 2.5-MeV proton beam with varying beam parameters and lattice configurations. The study will aim to demonstrate a bunch-compression factor of at least 2 in the IOTA ring while examining the impact of intense space-charge effects on the compression process.

43 PARTICLE ACCELERATORS↗

Improved Modelling of SEP Event Onset Within the WSA–Enlil–SEPMOD Framework

Multi-spacecraft observations of solar energetic particle (SEP) events not only enable a deeper understanding and development of particle acceleration and transport theories but also provide important constraints for model validation efforts. However, because of computational limitations, a given physics-based SEP model is usually best suited to capture a particular phase of an SEP event, rather than its whole development from onset through decay. For example, magnetohydrodynamic (MHD) models of the heliosphere often incorporate solar transients only at the outer boundary of their so-called coronal domain – usually set at a heliocentric distance of 20–30 R⊙. This means that particle acceleration at coronal mass ejection (CME)-driven shocks is also computed from this boundary onwards, leading to simulated SEP event onsets that can be many hours later than observed, since shock waves can form much lower in the solar corona. In this work, we aim to improve the modelled onset of SEP events by inserting a “fixed source” of particle injection at the outer boundary of the coronal domain of the coupled WSA–Enlil 3D MHD model of the heliosphere. The SEP model that we employ for this effort is Solar Energetic Particle MODel (SEPMOD), a physics-based test-particle code based on a field line tracer and adiabatic invariant conservation. We apply our initial tests and results of SEPMOD’s fixed-source option to the 2021 October 9 SEP event, which was detected at five well-separated locations in the inner heliosphere – Parker Solar Probe, STEREO-A, Solar Orbiter, BepiColombo, and near-Earth spacecraft.

Solar eruptions↗

Comparison Between MAD-IPA Thrust Stand Measurements and Performance Modeling

The high specific impulse values associated with electric propulsion (EP) that allow for higher payload fractions than conventional, chemical propulsion are achieved by the acceleration of ionized propellant (plasma) by electromagnetic body forces. The lifetime of many EP devices is limited by electrode erosion caused by direct plasma-electrode interaction, while the efficiency is often limited by, among other thruster-specific factors, the available power in space. The efficiency can be increased during higher power operation since the amount of power required to ionize the propellant is fixed and decreases as a percentage of the increased input power. Pulsed inductive plasma accelerators [1-3] are a potentially elegant solution to the problems of high power demands and electrode erosion. The former is addressed in the pulsed nature of these devices, which allows for instantaneous operation on the order of megawatts while requiring a continuous supply on the order of only kilowatts, while the latter is addressed by inductive coupling of the thruster to ionized propellant. These devices operate by rapidly (on the order of microseconds) discharging stored energy at a given pulse repetition rate through a coil creating time-varying magnetic and electric fields that cause ionization, current formation and acceleration of propellant away from the coil. While the inductive (contact-less) nature of the energy transfer from the thruster to the propellant alleviates the problem of erosion and enables the use of in-situ and storable propellants incompatible with metallic electrodes, it places high voltage demands (on the order of tens of kilovolts) on the energy storage system to achieve propellant ionization.

Hallock, Ashley K.↗

Towards Improving luminosity using optics tuning and data-driven methods

The results of Run 24 experiments at Relativistic Heavy Ion Collider (RHIC) for improving luminosity using optics tuning are presented in this study. In the first experiment, MADx matching was used to output magnet strengths corresponding to specific s star movements around Interaction Region 8 (IR8). The corresponding Zero Degree Calorimeter (ZDC) signal was measured in place of luminosity, and Bayesian Optimization aids search of optimal movements. It was found that values retrieved from matching were inaccurate, resulting in negative feedback loops. The second experiment focused on calculating accurate s star movements. The matching method was replaced with a linear sensitivity matrix, directly relating optics to power supply, and its null space was used to fit constraints such as hysteresis effects. At the experiment, beam losses were observed at collimators around boundary of IR8, which were fixed for the third experiment. Dynamic mode decomposition was also introduced to improve quality of turn-by-turn (TBT) data as well as accuracy and consistency of optics measurements at IR8. These improvements will be tested in the experiment of next RHIC run for luminosity optimization.

Accelerator Physics↗

Polar Rain Gradients and Field-Aligned Polar Cap Potentials

ACE SWEPAM measurements of solar wind field-aligned electrons have been compared with simultaneous measurements of polar rain electrons precipitating over the polar cap and detected by DMSP spacecraft. Such comparisons allow investigation of cross-polar-cap gradients in the intensity of otherwise-steady polar rain. The generally good agreement of the distribution functions, f, from the two data sources confirms that direct entry of solar electrons along open field lines is indeed the cause of polar rain. The agreement between the data sets is typically best on the side of the polar cap with most intense polar rain but the DMSP f's in less intense regions can be brought into agreement with ACE measurements by shifting all energies by a fixed amounts that range from tens to several hundred eV. In most cases these shifts are positive which implies that field-aligned potentials of these amounts exist on polar cap field lines which tend to retard the entry of electrons and produce the observed gradients. These retarding potentials undoubtedly appear in order to prevent the entry of low-energy electrons and maintain charge quasi-neutrality that would otherwise be violated since most tailward flowing magnetosheath ions are unable to follow polar rain electrons down to the polar cap. In more limited regions near the boundary of the polar cap there is sometimes evidence for field-aligned potentials of the opposite sign that accelerate polar rain electrons. A solar electron burst is also studied and it is concluded that electrons from such bursts can enter the magnetotail and precipitate in the same manner as polar rain.

Fairfield, D. H.↗

Polar Rain Gradients and Field-Aligned Polar Cap Potentials

ACE SWEPAM measurements of solar wind field-aligned electrons have been compared with simultaneous measurements of polar rain electrons precipitating over the polar cap and detected by DMSP spacecraft. Such comparisons allow investigation of cross-polarcap gradients in the intensity of otherwise-steady polar rain. The generally good agreement of the distribution functions, f, from the two data sources confirms that direct entry of solar electrons along open field lines is indeed the cause of polar rain. The agreement between the data sets is typically best on the side of the polar cap with most intense polar rain but the DMSP f's in less intense regions can be brought into agreement with ACE measurements by shifting all energies by a fixed amounts that range from tens to several hundred eV. In most cases these shifts are positive which implies that field-aligned potentials of these amounts exist on polar cap field lines which tend to retard the entry of electrons and produce the observed gradients. These retarding potentials undoubtedly appear in order to prevent the entry of low-energy electrons and maintain charge quasi-neutrality that would otherwise be violated since most tailward flowing magnetosheath ions are unable to follow polar rain electrons down to the polar cap. In more limited regions near the boundary of the polar cap there is sometimes evidence for field-aligned potentials of the opposite sign that accelerate polar rain electrons. A solar electron burst is also studied and it is concluded that electrons from such bursts can enter the magnetotail and precipitate in the same manner as polar rain.

Fairfield, D. H.↗

Comparison of URANS and LES predictions for the open phase of the OECD NEA CSNI fluid structure interaction CFD benchmark

The OECD NEA CSNI WGAMA CFD Task Group ran a benchmark in 2020 and 2021 to assess the predictive capabilities of coupled fluid structure interaction (FSI) CFD analysis methods. This paper presents the predictions made for the open phase of the benchmark using URANS and LES turbulence modelling approaches, and a comparison of the results to the experimental data. The benchmark comprised a channel containing two inline cylinders in cross-flow. The cylinders were fixed at one end, free at the other, and had measured resonant frequencies and damping properties. The URANS modelling used ANSYS Fluent 2-way coupled to ANSYS Mechanical. The LES modelling used Nek5000, 1-way coupled to Diablo. Comparisons with cross-channel velocity profiles are presented, both for the mean flow and its RMS. Comparisons are also made to the frequency spectra for point measurements of fluid velocity and pressure, and for the accelerations of the free end of each cylinder. URANS predicts the average velocity profiles relatively well, and is able to predict the velocity and acceleration spectra at the shedding frequency. However, the frequency content at the 4th harmonic of the shedding frequency is low in the URANS flow fields, and so does not excite accelerations at the resonant frequency of the cylinders. LES makes better predictions of the average profiles, and the velocity spectra agree well at both the shedding frequency and at higher frequencies. In conclusion, the 1-way coupled LES results show good agreement for acceleration spectra.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Training the Powered-Lift Evaluation Pilot

This poster describes a project to prepare pilots for a study assessing novel aircraft automation concepts for electric Vertical Takeoff and Landing (eVTOL) aircraft using NASA’s Vertical Motion Simulator (VMS). By exploring the operational and learning challenges related to transitioning between forward flight and vertical landing, we seek to establish baselines of pilot workload and aircraft handling qualities across varying atmospheric conditions and automation states. The simulated eVTOL design differentiates flight control allocations as a function of airspeed across four speed ranges as the vehicle transitions between fully thrust-borne lift and wing-borne lift. As speed increases, side stick controls command: translational ground speeds, vertical and lateral acceleration, vertical rate, vertical flight path angle, and bank angle. This novel approach to flight control allocation creates a significant learning challenge for pilots. Since initial eVTOL aircraft may have limitations on hover capabilities, automation and flight guidance cues also vary with airspeed to provide efficient landing profiles while still providing cues suitable for cruise flight. The NASA team prepared the study pilots to follow these flight guidance cues along curved Required Navigation Performance (RNP) approaches and along 6o and 12o glide paths to energy-efficient assistive-hover landing and goarounds. The pre-VMS preparation sought to prepare pilots from diverse levels of experience and background. To do this, NASA researchers designed and developed a fixed-based, large field-ofview simulator with terrain, structures, and air traffic. With one day of combined classroom learning and skill development in the fixedbase simulator, pilots were largely able to fly the simulated eVTOL in the VMS with sufficient mastery to provide handling quality assessments using the Cooper-Harper Handling Qualities Rating and workload assessments through the Bedford Workload Scale.

AAM↗

Quantum computation of SU(2) lattice gauge theory with continuous variables

We present a quantum computational framework for pure SU(2) lattice gauge theory, using continuous variables instead of discrete qubits to represent the infinite-dimensional Hilbert space of the gauge fields. We consider a ladder as well as a two-dimensional grid of plaquettes, detailing the use of gauge fixing to reduce the degrees of freedom and simplify the Hamiltonian. We demonstrate how system dynamics, ground states, and energy gaps can be computed using the continuous-variable approach to quantum computing. Our results indicate that it is feasible to study non-Abelian gauge theories with continuous variables, providing new avenues for understanding the real-time dynamics of quantum field theories.

Gauge Symmetry↗

Concept of Very-Asymmetric lepton Collider for dark matter search

Accelerator-based searches for dark matter are aiming for high sensitivity and need an experimental setup with high luminosity. This field of research is often called intensity frontier physics. One of the best motivated portals of interaction between dark matter and ordinary matter is a dark photon which could be observed as a resonance in the invariant mass of the decay products. Electron–positron collisions are known to be the cleanest interaction for such a study. In this paper we propose a scheme for a collider which allows for a luminosity of a few orders of magnitude higher than could be obtained in a conventional symmetric collider and with a few times higher accessible mass than is possible using a positron beam and a fixed target approach. The key concept is based on asymmetric energies: a high-energy circulating positron beam and a low-energy high-intensity electron beam, and optimization of the beam interaction region. We present here a configuration of a collision region of 10 MeV electron and 4 GeV positron beams.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Optical Strain Sensing for Particle Detection

Optomechanical strain sensing provides attractive opportunities for novel particle detection schemes, as well as studying stress-induced (i.e. non-radiogenic) phonon bursts, which have been demonstrated to limit the coherence times of superconducting qubits and are a suspected culprit in the low energy excesses observed by many dark matter direct detection experiments. We are investigating SiN microring optical resonator strain sensors, developed at Purdue University, for applications in fundamental particle sensing and QIS. These sensors can be embedded in the substrate upon which superconducting qubits are patterned, providing a handle to distinguish decoherence events of radiogenic origin from those due to crystal stress. In a similar way, these sensors can be operated in conjunction with superconducting detectors (e.g., MKIDs, TES) to enable multi-channel readout of particle interactions in the device substrate or serve as anticoincidence detectors, which may be required to ident ify low-energy interactions from dark matter particles down to the fermionic thermal relic mass limit of a few keV. Such sensors can potentially be used to directly observe resonant scattering processes of gamma rays (and perhaps neutrinos) where no detectable quanta are produced in the target, via the microscopic stress induced by the momentum transfer to the (fixed-in-place) crystal lattice as a whole. These strain sensors have so far found application in photonics and communications, but have yet to be adopted for HEP uses, where they can provide unique capabilities in the search for dark matter as well as understanding and improving the coherence times of superconducting qubits.

43 PARTICLE ACCELERATORS↗

Design Progress for the 22 GeV CEBAF Energy Upgrade

Extending the energy reach of CEBAF up to 22 GeV within the existing tunnel is being explored. Proposed energy upgrade can be achieved by increasing the number of recirculations, while using the existing CEBAF SRF cavity system. A proposal was formulated to raise CEBAF energy by replacing the highest-energy arcs with FFA arcs. The new pair of arcs configured with FFA (Fixed Field Alternating Gradient) lattice would support simultaneous transport of additional 6 passes with energies spanning a factor of two, using the non-scaling FFA principle implemented with Halbach-derived permanent magnets - a novel magnet technology that significantly saves energy and lowers operating costs. The design involves new optics for the linacs and remaining electromagnetic arcs, as well as new electromagnetic switchyard. These feed into the permanent magnet FFA arcs. We also report on ongoing beam dynamics studies and mitigating measures to alleviate energy loss and emittance dilution due to synchrotron radiation.

Bogacz, Alex [Thomas Jefferson National Accelerato↗

Sensitivities to neutrino non-standard interactions from the disappearance of muon (anti)neutrinos at the NOvA experiment

The experimental confirmation of the phenomenon of neutrino oscillations provided evidence for a non-zero value for the mass of neutrinos, a property not initially predicted by the Standard Model of Physics. Investigations of the existence of the so called Physics Beyond the Standard Model is a subject of growing interest and effort in the field of particle physics. Interactions of neutrinos with matter are well described by the Standard Model, however in the presence of new Physics, additional phenomena regarding neutrino properties would be possible, including non-standard interactions of neutrinos with matter. The NOvA experiment, at Fermilab, has been investigating neutrino oscillations through studies of ν µ produced at the Fermilab accelerator facilities, and also comprise a suitable environment for investigation of additional phenomena taking part in the neutrino oscillation framework. We show in this thesis the results of the sensitivity studies to neutrino non standard interactions in the NOvA experiment through investigation of the disappearance of muon (anti)neutrinos during their evolution in the NOvA 810 km baseline. We investigate the effect of the NSI parameters, |ε µτ | and δ µτ , on the determination of the standard oscillation parameters sin 2 (θ 23 ) and Δ$m^2_{32}$, as well as the relation between each parameter, for both neutrino mass hierarchies. This study makes use of an exposure of 9.48 × 10 20 POT for neutrino beam (FHC), and 12.33 × 10 20 POT for antineutrino beam (RHC). No deviations from the standard oscillation scenario is found at the 90% CL limit. The joint neutrino and antineutrino fit yields a limit of |ε µτ | ≤ 0.086 (0.085) for a fixed value of δ µτ = 0, and |ε µτ | ≤ 1.054 (1.053) for the case where both NSI parameters are fitted, for the normal (inverted) neutrino mass hierarchy, at the 90% CL. In the current sensitivity, all values of δ µτ are found to be allowed. The 90% CL interval for the standard oscillation parameters are Δ$m^2_{32}$ ϵ [2.379, 2.580] and sin 2 (θ 23 ) ϵ [0.420, 0.602] for the normal hierarchy scenario, and Δ$m^2_{32}$ ϵ [-2.639, - 2.438] and sin 2 (θ 23 ) ϵ [0.418, 0.602] for the inverted hierarchy scenario.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗