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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 595 records · Page 33

Frontogenesis and frontal arrest of a dense filament in the oceanic surface boundary layer

The evolution of upper ocean currents involves a set of complex, poorly understood interactions between submesoscale turbulence (e.g. density fronts and filaments and coherent vortices) and smaller-scale boundary-layer turbulence. Here we simulate the lifecycle of a cold (dense) filament undergoing frontogenesis in the presence of turbulence generated by surface stress and/or buoyancy loss. This phenomenon is examined in large-eddy simulations with resolved turbulent motions in large horizontal domains using ${\sim}10^{10}$ grid points. Steady winds are oriented in directions perpendicular or parallel to the filament axis. Due to turbulent vertical momentum mixing, cold filaments generate a potent two-celled secondary circulation in the cross-filament plane that is frontogenetic, sharpens the cross-filament buoyancy and horizontal velocity gradients and blocks Ekman buoyancy flux across the cold filament core towards the warm filament edge. Within less than a day, the frontogenesis is arrested at a small width, ${\approx}100~\text{m}$ , primarily by an enhancement of the turbulence through a small submesoscale, horizontal shear instability of the sharpened filament, followed by a subsequent slow decay of the filament by further turbulent mixing. The boundary-layer turbulence is inhomogeneous and non-stationary in relation to the evolving submesoscale currents and density stratification. The occurrence of frontogenesis and arrest are qualitatively similar with varying stress direction or with convective cooling, but the detailed evolution and flow structure differ among the cases. Thus submesoscale filament frontogenesis caused by boundary-layer turbulence, frontal arrest by frontal instability and frontal decay by forward energy cascade, and turbulent mixing are generic processes in the upper ocean.

Mechanics↗

Beyond the ponderomotive limit: Direct laser acceleration of relativistic electrons in sub-critical plasmas

We examine a regime in which a linearly polarized laser pulse with relativistic intensity irradiates a sub-critical plasma for much longer than the characteristic electron response time. A steady-state channel is formed in the plasma in this case with quasi-static transverse and longitudinal electric fields. These relatively weak fields significantly alter the electron dynamics. The longitudinal electric field reduces the longitudinal dephasing between the electron and the wave, leading to an enhancement of the electron energy gain from the pulse. The energy gain in this regime is ultimately limited by the superluminosity of the wave fronts induced by the plasma in the channel. The transverse electric field alters the oscillations of the transverse electron velocity, allowing it to remain anti-parallel to laser electric field and leading to a significant energy gain. The energy enhancement is accompanied by the development of significant oscillations perpendicular to the plane of the driven motion, making trajectories of energetic electrons three-dimensional. Proper electron injection into the laser beam can further boost the electron energy gain.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Measuring Local Turbulence Along the Optical Path: Multi-Beam Optical Seeing Sensor

Deflection of light along the optical path is a major source of image degradation for ground-based telescopes. Methods have been developed to measure upper atmospheric seeing based on models of the turbulence in the atmosphere, but due to boundary conditions, transmission within telescope enclosures is more complex. The Multi-beam Optical Seeing Sensor (MOSS) directly measures the component of the image quality degradation from inhomogeneity of the index of refraction within the telescope dome. MOSS outputs four near-parallel beams of light that travel along the optical path and are imaged by the telescope’s detector, landing like starlight on the telescope’s focal plane. By using a strobed light source, we can ‘freeze’ the instantaneous index variations transverse to the optical path. This system captures both ‘dome’ and ‘mirror’ seeing. Through plotting the standard deviation of differential motion between pairs of beams, MOSS enables characterization of the length scale of turbulence within the dome. The temporal coherence of temperature gradients can be probed with different pulse lengths, and the spatial coherence by comparing pairs at different separations across the aperture of the telescope. Optical path turbulence measurements, alongside other telemetry metrics, will guide thermal and airflow management to optimize image quality. A MOSS prototype was installed in the 1.2[Formula: see text]m Auxiliary Telescope (AuxTel) at the Vera C. Rubin Observatory in Chile, and preliminary data constrain the optical path turbulence with a lower bound of 1.4 arcsec. The optical path turbulence varied throughout the night of observing.

Astronomical seeing↗

Giant Nonlinear Optical Response via Coherent Stacking of In-Plane Ferroelectric Layers

Thin ferroelectric materials hold great promise for compact nonvolatile memory and nonlinear optical and optoelectronic devices. Herein, an ultrathin in-plane ferroelectric material that exhibits a giant nonlinear optical effect, group-IV monochalcogenide SnSe, is reported. Nanometer-scale ferroelectric domains with ≈90°/270° twin boundaries or ≈180° domain walls are revealed in physical-vapor-deposited SnSe by lateral piezoresponse force microscopy. Atomic structure characterization reveals both parallel and antiparallel stacking of neighboring van der Waals ferroelectric layers, leading to ferroelectric or antiferroelectric ordering. Ferroelectric domains exhibit giant nonlinear optical activity due to coherent enhancement of second-harmonic fields and the as-resulted second-harmonic generation was observed to be 100 times more intense than monolayer WS 2 . This work demonstrates in-plane ferroelectric ordering and giant nonlinear optical activity in SnSe, which paves the way for applications in on-chip nonlinear optical components and nonvolatile memory devices.

36 MATERIALS SCIENCE↗

Unraveling the dislocation core structure at a van der Waals gap in bismuth telluride

Tetradymite-structured chalcogenides such as bismuth telluride (Bi 2 Te 3 ) are of significant interest for thermoelectric energy conversion and as topological insulators. Dislocations play a critical role during synthesis and processing of such materials and can strongly affect their functional properties. The dislocations among quintuple layers present special interest since their core structure is controlled by the van der Waals interactions between the layers. In this work, using atomic-resolution electron microscopy, we resolve the basal dislocation core structure in Bi 2 Te 3 , quantifying the disregistry of the atomic planes across the core. We show that, despite the existence of a stable stacking fault in the basal plane gamma surface, the dislocation core spreading is mainly due to the weak bonding between the layers, which leads to a small energy penalty for layer sliding parallel to the van der Waals gap. Measurements within a semidiscrete variational Peierls-Nabarro model informed by first-principles calculations support our experimental findings.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Partitioned Coupling for Structural Acoustics

Here, we expand the second-order fluid–structure coupling scheme of Farhat et al. (1998, “Load and Motion Transfer Algorithms for 19 Fluid/Structure Interaction Problems With Non-Matching Discrete Interfaces: Momentum and Energy Conservation, Optimal Discretization and Application to Aeroelasticity,” Comput. Methods Appl. Mech. Eng., 157(1–2), pp. 95–114; 2006, “Provably Second-Order Time-Accurate Loosely-Coupled Solution Algorithms for Transient Nonlinear Computational Aeroelasticity,” Comput. Methods Appl. Mech. Eng., 195(17), pp. 1973–2001) to structural acoustics. The staggered structural acoustics solution method is demonstrated to be second-order accurate in time, and numerical results are compared to a monolithically coupled system. The partitioned coupling method is implemented in the Sierra Mechanics software suite, allowing for the loose coupling of time domain acoustics in SIERRA/SD to structural dynamics ( SIERRA/SD ) or solid mechanics ( SIERRA/SD ). The coupling is demonstrated to work for nonconforming meshes. Results are verified for a one-dimensional piston, and the staggered and monolithic results are compared to an exact solution. Huang, H. (1969, “Transient Interaction of Plane Acoustic Waves With a Spherical Elastic Shell,” J. Acoust. Soc. Am., 45(3), pp. 661–670) sphere scattering problem with a spherically spreading acoustic load demonstrates parallel capability on a complex problem. Our numerical results compare well for a bronze plate submerged in water and sinusoidally excited (Fahnline and Shepherd, 2017, “Transient Finite Element/Equivalent Sources Using Direct Coupling and Treating the Acoustic Coupling Matrix as Sparse,” J. Acoust. Soc. Am., 142(2), pp. 1011–1024).

42 ENGINEERING↗

Simulating the Effect of Fracture Connectivity on Repository Performance with GDSA Framework - 18589

This work examines the possible migration of radionuclides from a deep geologic nuclear waste repository sited in fractured crystalline host rock. The key safety concern is the potential effect on waste isolation of the inter-connectivity of the fracture network, which is primarily established by the temporal evolution of the temperature and stress fields at the time of original rock intrusion and cooling. Two end members are considered in these simulations, one with a high degree of connectivity to the biosphere, such that advective transport through the fracture and fault network controls radionuclide migration, and the other with a low degree of connectivity, such that slow diffusive transport through the crystalline rock matrix is the controlling process for radionuclide migration to the biosphere. Both end members have several areally extensive, high-transmissivity deformation zones, whose distance to the repository is an important factor for waste isolation capability. Uncertainties in fracture properties (transmissivity, orientation, radius) and fracture distribution also give rise to uncertainty in waste isolation capability (i.e., the overall connectivity of the repository with the surface biosphere). These types of natural system uncertainties are generally present in any geologic site-characterization program and thus represent an important factor in assessing repository performance in hard rock environments. The waste considered in these simulations are spent fuel rod assemblies from the U.S. commercial nuclear reactor fleet. Thermal output of the waste must be considered in the simulations and can influence the rate and timing of waste package failure, waste form degradation, and fluid flux due to thermal expansion around the repository horizon. To achieve a high-fidelity representation of radionuclide transport in fractures and rock matrix, combined with thermal energy transport and fluid flow in fractures and matrix, the mathematical model is solved numerically in a parallel high-performance computing (HPC) environment on a finite volume unstructured grid consisting of approximately 5 million cells, using Geologic Disposal Safety Assessment (GDSA) Framework (https://pa.sandia.gov), an open-source performance assessment tool for deep underground disposal of nuclear waste. GDSA Framework uses PFLOTRAN to solve the balance equations on a three-dimensional grid with heterogeneous properties, using multiple processors in a parallel configuration based on domain decomposition. The fracture networks in these simulations are originally generated as discrete fracture networks (DFNs), which are sets of two-dimensional planes distributed in a three-dimensional domain. The method used in GDSA Framework maps the stochastically generated DFN to an equivalent continuous porous medium (ECPM) domain that allows for the simulation of coupled heat flow, fluid flow, and radionuclide transport, including heat conduction through the matrix of the fractured rock, which is a process not easily modeled in a DFN representation. Computational efficiency is also greatly enhanced using the ECPM method, allowing for a realistic representation and analysis of uncertainties in a multi-realization performance assessment of a deep geologic repository. The effect of fracture connectivity on the waste isolation safety function, as brought to light by these GDSA Framework simulations, points to the importance of including a realistic representation of uncertainties in fracture properties and distribution (effectively, uncertainty in spatial heterogeneity) in repository safety assessment simulations. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

3-D Semantic Information Inference from Airborne Video. Final Report

We developed a full 3D modeling pipeline focusing on an important application scenario: city-scale 3D reconstruction from aerial imagery. We propose an approach to solve camera pose estimation and dense reconstruction from Wide Area Aerial Surveillance (WAAS) videos captured by an airborne platform. Our approach solves them in an online fashion: it incrementally updates a sparse 3D map and estimates the camera pose as each new frame arrives; depth maps of selected key frames are computed using a variational method and integrated to produce a full 3D model via volumetric reconstruction. In practice, aerial imagery is usually captured using a multicamera system. We propose an approach for camera pose estimation of multi-camera aerial imagery which is parallelized on multiple GPUs for efficiency. The approach is also extended for progressive 3D model acquisition with a hand-held camera. We also developed an offline approach since online approach is not a necessity and accuracy has higher priority over efficiency in many scenarios. We presented MeshRecon, a mesh-based offline system composed of three modules: a dense point cloud is generated using multi-resolution plane sweep method; an initial mesh model is extracted from the point cloud via global optimization considering visibility information of all images; the mesh model is then iteratively refined to capture structural details by optimizing the photometric consistency and spatial regularization. The major processes are parallelized on GPU for efficiency. For the aerial imagery case, we evaluate our system on several real-world multicamera aerial imagery datasets, each covering an urban scenario of several square kilometers. Quantitative result shows that the reconstructed geometric 3D model is highly accurate with error smaller than 1 meter over the entire city. Besides aerial imagery, we also evaluate its performance on general geometric 3D model acquisition of real-world objects. Result shows that the system is robust and flexible for various types of objects at different scales in both indoor and outdoor environments. Based on city 3D models reconstructed at different times, we present a system for city-scale geometry change detection by performing comparisons at the 3D geometry level. Our system is able to detect geometry changes at different scales, ranging from a building cluster to small-scale vegetation changes, with high accuracy.

97 MATHEMATICS AND COMPUTING↗

Local structure of Sr 2 CuO 3.3 , a 95 K cuprate superconductor without CuO 2 planes

The local structure of the highly “overdoped” 95 K superconductor Sr 2 CuO 3.3 determined by Cu K X-ray absorption fine structure (XAFS) at 62 K in magnetically oriented samples shows that 1) the magnetization is perpendicular to the c axis; 2) at these levels of precision the Cu sublattice is tetragonal in agreement with the crystal structure; the O sublattice has 3) continuous -Cu-O- chains that orient perpendicular to an applied magnetic field; 4) approximately half-filled -Cu-O- chains that orient parallel to this field; 5) a substantial number of apical O vacancies; 6) O ions at some apical positions with expanded Cu-O distances; and 7) interstitial positions that imply highly displaced Sr ions. These results contradict the universally accepted features of cuprates that require intact CuO 2 planes, magnetization along the c axis, and a termination of the superconductivity when the excess charge on the CuO 2 Cu ions exceeds 0.27. These radical differences in charge and structure demonstrate that this compound constitutes a separate class of Cu-O–based superconductors in which the superconductivity originates in a different, more complicated structural unit than CuO 2 planes while retaining exceptionally high transition temperatures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Energy Conversion by Parallel Electric Fields During Guide Field Reconnection in Scaled Laboratory and Space Experiments

Here, we present direct and scaled comparisons between laboratory and in situ space observations of magnetic reconnection with a guide field, comparing results from the Magnetospheric Multiscale Mission and the Magnetic Reconnection eXperiment (MRX). While Magnetospheric Multiscale Mission observations obtain high–resolution and fully kinetic data, MRX observations fully cover the 2–D reconnection plane near the current sheet, removing uncertainties in situating the measurements compared to the reconnection region. Through scaling transformations, we show a quantitative agreement in magnetic field and current density profiles, which agree within a factor of 2 from each other. The introduction of the guide field causes the energy conversion J·E in the current sheet to be dominated by J || E || in both cases. However, parallel electric fields reported by recent spacecraft crossings are significantly (5–10 times) larger than values obtained on MRX, highlighting an important issue for understanding energy conversion by reconnection.

30 DIRECT ENERGY CONVERSION↗

Residual-stress-induced grain growth of twinned grains and its effect on formability of magnesium alloy sheet at room temperature

A magnesium alloy sheet was subjected to in-plane compression along with a vertical load to avoid buckling during compression. Pre-compressed specimens machined from the sheet were annealed at different temperatures and the changes in microstructure and texture were observed using electron back scattered diffraction (EBSD). Twinned grains preferentially grew during annealing at 300 °C, so that a strong texture with the < 0001 > direction parallel to the transverse direction developed. EBSD analysis confirmed that the friction caused by the vertical load induced inhomogeneous distribution of residual stress, which acted as an additional driving force for preferential grain growth of twinned grain during annealing. The annealed specimen showed excellent formability. - Highlights: • A magnesium alloy sheet subjected to in-plane compression under a vertical load • The vertical load induced inhomogeneous distribution of the residual stress. • The residual stress acted as an additional driving force for grain growth. • The annealed specimen with strong non-basal texture showed excellent formability.

36 MATERIALS SCIENCE↗

Dynamic Load Balancing Based on Constrained K-D Tree Decomposition for Parallel Particle Tracing

Particle tracing is a fundamental technique in flow field data visualization. In this work, we present a novel dynamic load balancing method for parallel particle tracing. Specifically, we employ a constrained k-d tree decomposition approach to dynamically redistribute tasks among processes. Each process is initially assigned a regularly partitioned block along with duplicated ghost layer under the memory limit. During particle tracing, the k-d tree decomposition is dynamically performed by constraining the cutting planes in the overlap range of duplicated data. This ensures that each process is reassigned particles as even as possible, and on the other hand the new assigned particles for a process always locate in its block. Result shows good load balance and high efficiency of our method.

Zhang, Jiang↗

Microscopic Nature of Magnetic Ground State in CeAuSb 2

Here, the synergistic investigation of ground-state magnetic correlation in the single-crystal heavy fermion compound CeAuSb 2 using detailed neutron scattering measurements and density functional calculations is reported. Unlike the previous reports of single antiferromagnetic transition at T N ≈ 6 K, three successive transitions with distinct critical exponents at T N = 5.3, 4.46, and 3.76 K, respectively, are detected in CeAuSb. The low-temperature ground-state magnetic correlation is described by the spin density wave order in the basal plane with propagation wave vector $τ$ = (0.135, 0.135, 0.5) rlu. The spin density wave order arises due to the nesting of hole pockets in the Fermi surface, with parallel surfaces being separated by the experimentally found propagation vector τ. The comprehensive investigation of magnetic ground-state properties is expected to provide new insights in understanding the emerging quantum magnetism in this system, including the debated quantum critical state and magnetic field-induced metamagnetic transitions at low temperature.

36 MATERIALS SCIENCE↗

High strain in polycrystalline Ni{sub 48.8}Mn{sub 31.4}Ga{sub 19.8} Heusler alloys under overlapped static and oscillating magnetic fields

Martensitic polycrystalline Ni{sub 48.8}Mn{sub 31.4}Ga{sub 19.8} Heusler alloys, with a stacking period of 14 atomic planes at room temperature, were innovatively processed by combining high-energy ball milling and powder metallurgy. Bulk samples were mechanically coupled to a piezoelectric material in a parallel configuration, and the mechanical deformation of the studied system due to the twin's variant motion was investigated under overlapped static and oscillating magnetic fields. A reversible and high mechanical deformation is observed when the frequency of the oscillating magnetic field is tuned with the natural vibration frequency of this system. In this condition, a linear deformation as a function of the static magnetic field amplitude occurs in the ±4 kOe range, and a mechanical deformation of 2% at 10 kOe is observed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Modeling of hydride precipitation and re-orientation

In this report, we present a thermodynamic-­based model of hydride precipitation in Zr-based claddings. The model considers the state of the cladding immediately following drying, after removal from cooling-pools, and presents the evolution of precipitate formation upon cooling as follows: The pilgering process used to form Zr-based cladding imparts strong crystallographic and grain shape texture, with the basal plane of the hexagonal α-Zr grains being strongly aligned in the rolling-­direction and the grains are elongated with grain size being approximately twice as long parallel to the rolling direction, which is also the long axis of the tubular cladding, as it is in the orthogonal directions.

36 MATERIALS SCIENCE↗

Functional Domain Walls as Active Elements for Energy Technology

In the past five years in the duration of this project (July 2011-July 2016), we have made a wide range of achievements in both basic research and energy applications along the direction planned in the original proposal. These achievements were reflected by 13 articles published in peer-reviewed journals including Nature Communications, Nano Letters, etc., and one currently in revision at Science. These papers have been accumulatively cited for more than 660 times as of October 2016, according to Web of Science statistics. Specifically, we have made impactful discoveries in the following fields. Basic Research. We have investigated in depth the materials physics of the representative quantum material, VO 2 , on which most of our project is anchored. We have discovered that independent diffusion of heat and charge in the absence of quasiparticles in metallic VO 2 leads to an anomalously low electronic thermal conductivity, dramatically violating the Wiedemann-Franz law, which is a robust law governing behavior of normal conductors stating that free electrons transport heat proportionally to the charge they transport. In addition, we have discovered a peculiar thermal rectification effect based on its phase transition, as well as a gating response of the phase transition. In parallel to the work on VO 2 , we have also made breakthroughs in investigation of transition metal dichalcogenides (TMDs): we have experimentally demonstrate a strong anisotropy in in-plane thermal conductivity of black phosphorous, discovered a new, unusual member of the TMDs family, ReS 2 , where the bulk behaves as monolayers due to electronic and vibrational decoupling, unusual interaction between physi-sorbed molecules and 2D semiconductors, and thermally driven crossover from indirect toward direct bandgap in some 2D TMDs. Applications. Based on the understanding and knowledge gained from the basic investigation, we have developed novel tools and devices for energy applications. These include a nanowire based microthermometer for quantitative evaluation of electron beam heating in electron microscopy, giant-amplitude, high-work density microactuators and torsional micromuscles, as well as nanoscale thermometers and powermeters, all based on the VO 2 phase transition.

2D materials↗

Utilization of optical tracking to validate a software-driven isocentric approach to robotic couch movements for proton radiotherapy

Purpose: An optical tracking and positioning system (OTPS) was developed to validate the software-driven isocentric (SDI) approach to control the six-degrees-of-freedom movement of a robotic couch. Methods: The SDI approach to movements rotating around a predefined isocenter, referred to as a GeoIso, instead of a mechanical pivot point was developed by the robot automation industry. With robotic couch-sag corrections for weight load in a traditional SDI approach, movements could be accurately executed for a GeoIso located within a 500 mm cubic volume on the couch for treatments. The accuracy of SDI movement was investigated using the OTPS. The GeoIso was assumed to align with the proton beam isocenter (RadIso) for gantry at the reference angle. However, the misalignment between GeoIso and RadIso was quantitatively investigated by measuring the displacements at various couch angles for a target placed at the RadIso at an initial couch angle. When circular target displacements occur on a plane, a relative isocenter shift (RIS) correction could be applied in the SDI movement to minimize target displacements. Target displacements at a fixed gantry angle without and with RIS correction were measured for 12 robotic couches. Target displacements for various gantry angles were performed on three couches in gantry rooms to study the gantry-induced RadIso shift. The RIS correction can also be applied for the RadIso shift. A new SDI approach incorporating the RIS correction with the couch sag is described in this study. In parallel, the accuracy of SDI translation movements for various weight loads of patients on the couch was investigated during positioning of patients for proton prostate treatments. Results: For a fixed gantry angle, measured target displacements without RIS correction for couch rotations in the horizontal plane varied from 4 to 20 mm. However, measured displacements perpendicular to couch rotation plane were about 2 mm for all couches. Extracted misalignments of GeoIso and RadIso in the horizontal plane were about 10 mm for one couch and within 3 mm for the rest of couches. After applying the RIS correction, the residual target displacements for couch rotations were within 0.5 mm to RadIso for all couches. For various gantry angles, measured target location for each angle was within 0.5 mm to its excepted location by the preset RadIso shift. Measured target displacements for ±30° of couch rotations were within 0.5 mm for gantry angles at 0° and 180°. Overall, nearly 85% of couch movements were within 0.5 mm in the horizontal plane and 0.7 mm vector distance from required displacements. Conclusions: The authors present an optical tracking methodology to quantify for software-driven isocentric movements of robotic couches. By applying proper RIS correction for misaligned GeoIso and RadIso for each couch, and the RadIso shifts for a moving gantry, residual target displacements for isocentric couch movements around the actual RadIso can be reduced to submillimeter tolerance.

60 APPLIED LIFE SCIENCES↗

Parallel pumping of magnons in inhomogeneous spin textures probed through NV spin relaxometry

We combine micromagnetic simulations and nitrogen-vacancy (NV) defect center spin relaxometry measurements to study magnon modes in inhomogeneous spin textures. A thin, micrometer-scale ferromagnetic disk is magnetized in a vortex state in which the magnetization curls around a central core. Micromagnetic simulations show that at zero applied field, the magnetization dynamics of the disk consist of a low frequency gyrotropic mode and higher frequency azimuthal magnon modes, all far detuned from the NV spin transition frequencies. An in-plane static magnetic field breaks the azimuthal symmetry of the vortex state, resulting in the magnon modes transforming in frequency and spatial profile as the field increases. Experimentally, we probe the dynamics of vortex magnetization as a function of applied in-plane static field and ac driving frequency by optically monitoring a nearby NV defect center spin. At certain values of the applied magnetic field, we observe enhanced spin relaxation when driving at twice the frequency of the NV ground state spin transition in optically detected magnetic resonance measurements. We attribute this effect to parallel pumping of a magnon mode in the disk producing magnons at half the excitation frequency. Micromagnetic simulations support this finding, showing spatial and spectral overlap of a confined magnon mode and an NV spin transition, with sufficient interaction strength to explain the observed signal.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗