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Explaining the structure sensitivity of Pt and Rh for aqueous-phase hydrogenation of phenol

Phenol is an important model compound to understand the thermocatalytic (TCH) and electrocatalytic hydrogenation (ECH) of biomass to biofuels. Although Pt and Rh are among the most studied catalysts for aqueous-phase phenol hydrogenation, the reason why certain facets are active for ECH and TCH is not fully understood. Herein, we identify the active facet of Pt and Rh catalysts for aqueous-phase hydrogenation of phenol and explain the origin of the size-dependent activity trends of Pt and Rh nanoparticles. Phenol adsorption energies extracted on the active sites of Pt and Rh nanoparticles on carbon by fitting kinetic data show that the active sites adsorb phenol weakly. We predict that the turnover frequencies (TOFs) for the hydrogenation of phenol to cyclohexanone on Pt(111) and Rh(111) terraces are higher than those on (221) stepped facets based on density functional theory modeling and mean-field microkinetic simulations. The higher activities of the (111) terraces are due to lower activation energies and weaker phenol adsorption, preventing high coverages of phenol from inhibiting hydrogen adsorption. We measure that the TOF for ECH of phenol increases as the Rh nanoparticle diameter increases from 2 to 10 nm at 298 K and -0.1 V vs the reversible hydrogen electrode, qualitatively matching prior reports for Pt nanoparticles. The increase in experimental TOFs as Pt and Rh nanoparticle diameters increase is due to a larger fraction of terraces on larger particles. These findings clarify the structure sensitivity and active site of Pt and Rh for the hydrogenation of phenol and will inform the catalyst design for the hydrogenation of bio-oils.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Global Aspects of Heliosphere-Geosphere Coupling

The magnetosphere serves both to hold off the solar wind and to couple it selectively to the Earth through the auroral zones. It has long been understood that the plasmasphere consists of geogenic plasmas that expand out of the sunlit low latitude ionosphere, but it was initially assumed that the hot low density plasma beyond the plasmasphere is largely of solar wind origin with a minor admixture of ionospheric plasmas, discovered via mass spectrometric observations in the early 70's. Since then, elaborate simulation models have been developed that have taken us from an era of cartoon physics to a new era of quantitative global comparisons between observations and theory. In most current global circulation models of the magnetosphere, the ionospheric load on the system is taken to lie exclusively in the thin F layer of the ionosphere. This layer is coupled with solar wind and magnetospheric plasmas via Maxwell stresses communicated by field aligned current systems, and with the thermosphere via ion-neutral charge exchange and Coulomb collisions. However, recent observations have shown us that ionospheric plasmas flow sporadically in various forms into the plasmasphere and up into the high latitude circulation cells of the outer magnetosphere, as driven by the solar wind and its variable intensity and magnetic field. Under some conditions, ionospheric material is observed to be the principal component of plasmas at the dayside magnetopause and in the plasma sheet and ring current regions. Given a global model of magnetospheric circulation, it is relatively straightforward to investigate the behaviors of ionospheric plasmas in response to solar wind drivers, and we report the results of such efforts here. We find that ionospheric plasmas dominate the plasma pressure in the magnetosphere in some regions, particularly when the solar wind is especially intense and-or southward directed. This result violates the assumption that the ionospheric load is confined to the F layer, and shows that the ionosphere is often an important dynamic element of the solar wind-ionosphere system throughout the magnetosphere, especially during larger geospace storms. This means that future global circulation models must account for ionospheric plasma inertia, heat capacity, and pressure, to be quantitatively credible.

Moore, Thomas E.↗

Variational nonlinear WKB in the Eulerian frame

Nonlinear WKB is a multiscale technique for studying locally plane-wave solutions of nonlinear partial differential equations (PDEs). Its application comprises two steps: (1) replacement of the original PDE with an extended system separating the large scales from the small and (2) reduction of the extended system to its slow manifold. In the context of variational fluid theories with particle relabeling symmetry, nonlinear WKB in the mean Eulerian frame is known to possess a variational structure. This much has been demonstrated using, for instance, the theoretical apparatus known as the generalized Lagrangian mean. On the other hand, the variational structure of nonlinear WKB in the conventional Eulerian frame remains mysterious. By exhibiting a variational principle for the extended equations from step (1) above, here we demonstrate that nonlinear WKB in the Eulerian frame is in fact variational. Remarkably, the variational principle for the extended system admits loops of relabeling transformations as a symmetry group. Noether’s theorem therefore implies that the extended Eulerian equations possess a family of circulation invariants parameterized by S 1 . As an illustrative example, we use our results to systematically deduce a variational model of high-frequency acoustic waves interacting with a larger-scale compressible isothermal flow.

97 MATHEMATICS AND COMPUTING↗

QCD Theory and Transverse Momentum Dependent Physics

A major challenge for QCD theorists is to understand how to different categories of QCD physics contribute to a single observable. This is the goal of QCD factorization theory. Today, QCD physicists are tasked with describing increasingly detailed properties of transverse momentum dependent particle distributions, including their shapes and normalizations, their variation with energy and other kinematical variables, the identity of particles involved, correlations with spin, and the relationship between transverse momentum distributions in different processes. Embedded within that broad effort are specific fundamental questions at the heart of QCD theory. Namely, how does one give precise, quantitative meaning to quark and gluon concepts in hard scattering events, and what are the limits of those concepts? In the past two decades, there has been a renaissance in TMD QCD, with a broad spectrum of motivations driving the study of TMD observables. TMD QCD studies are in a transformative stage; subfields that traditionally progressed nearly independently of one other, such as hadronic structure studies and the study of perturbative QCD gluon radiation in high-energy collisions, are becoming intertwined. It is thus becoming increasingly clear that unified approaches -- those that incorporate all the relevant phenomena into a single formalism rooted in QCD fundamentals -- will be critical to the mission to expand the current understanding of QCD nuclear/hadronic dynamics. TMD QCD factorization theorems and their generalizations will be central to these efforts. The factorization theorems, in addition, provide the practical prescription for applying specific calculations to phenomenology. The goal of this project was to unify and push the boundaries of traditional TMD research and prepare it for use in future phenomenological applications.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Solitons in lattice field theories via tight-binding supersymmetry

Reflectionless potentials play an important role in constructing exact solutions to classical dynamical systems (such as the Korteweg-de Vries equation), non-perturbative solutions of various large-N field theories (such as the Gross-Neveu model), and closely related solitonic solutions to the Bogoliubov-de Gennes equations in the theory of superconductivity. These solutions rely on the inverse scattering method, which reduces these seemingly unrelated problems to identifying reflectionless potentials of an auxiliary one-dimensional quantum scattering problem. There are several ways of constructing these potentials, one of which is quantum mechanical supersymmetry (SUSY). In this paper, motivated by recent experimental platforms, we generalize this framework to develop a theory of lattice solitons. We first briefly review the classical inverse scattering method in the continuum limit, focusing on the Korteweg-de Vries (KdV) equation and SU(N) Gross-Neveu model in the large N limit. We then generalize this methodology to lattice versions of interacting field theories. Our analysis hinges on the use of trace identities, which are relations connecting the potential of an equation of motion to the scattering data. For a discrete Schrödinger operator, such trace identities had been known as far back as Toda; however, we derive a new set of identities for the discrete Dirac operator. We then use these identities in a lattice Gross-Neveu and chiral Gross-Neveu (Nambu-Jona-Lasinio) model to show that lattice solitons correspond to reflectionless potentials associated with the discrete scattering problem. These models are of significance as they are equivalent to a mean-field theory of a lattice superconductor. To explicitly construct these solitons, we generalize supersymmetric quantum mechanics to tight-binding models. We show that a matrix transformation exists that maps a tight-binding model to an isospectral one which shares the same structure and scattering properties. The corresponding soliton solutions have both modulated hopping and onsite potential, the former of which has no analogue in the continuum limit. We explicitly compute both topological and non-topological soliton solutions as well as bound state spectra in the aforementioned models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Self-consistently renormalized spin-wave theory of layered ferromagnets on the honeycomb lattice

We develop a self-consistently renormalized spin-wave theory, within a mean-field approximation, for the two-dimensional Heisenberg ferromagnet with perpendicular easy-axis anisotropy on the honeycomb lattice, as well as its few-layer and bulk extensions. In this method, the magnetization dependence on temperature is found as the solution of the self-consistency equation. Furthermore, we account for the physical difference of surface and bulk layers by treating the layers as separate sublattices. Thus the method can be readily generalized to study various magnetic phenomena in a broad range of systems, including those comprising magnetically inequivalent sublattices. Using our theory, we calculate the temperature-dependent magnetization for two chromium-based layered van der Waals insulating magnets, Cr 2 Ge 2 Te 6 and CrI 3 , employing various sets of Heisenberg exchange and single-ion anisotropy values reported for these materials in the existing literature. As expected, we observe a strong dimensionality effect where the ordering temperature is reduced and its sensitivity on the anisotropy is enhanced with the decrease of dimensionality.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Amplification of turbulence through multiple planar shocks

We study the amplification of isotropic, incompressible turbulence through multiple planar, collisional shocks, using analytical linear theory. There are two limiting cases we explore. The first assumes shocks occur rapidly in time such that the turbulence does not evolve between shocks. Whereas the second case allows enough time for turbulence to isotropize between each shock. For the latter case, through a quasi-equation-of-state, we show that the weak multishock limit is agnostic to the distinction between thermal and vortical turbulent pressures, like an isotropic volumetric compression. When turbulence does not return to isotropy between shocks, the generated anisotropy—itself a function of shock strength—can feedback on amplification by further shocks, altering choices for maximal or minimal amplification. In addition for this case, we find that amplification is sensitive to the shock ordering. As a result, we map how choices of shock strength can impact these amplification differences due to ordering, finding, for example, shock pairs which lead to identical mean postshock fields (density, temperature, pressure) but maximally distinct turbulent amplification.

Astrophysical fluid dynamics↗

Learning effective stochastic differential equations from microscopic simulations: Linking stochastic numerics to deep learning

We identify effective stochastic differential equations (SDEs) for coarse observables of fine-grained particle- or agent-based simulations; these SDEs then provide useful coarse surrogate models of the fine scale dynamics. We approximate the drift and diffusivity functions in these effective SDEs through neural networks, which can be thought of as effective stochastic ResNets. The loss function is inspired by, and embodies, the structure of established stochastic numerical integrators (here, Euler–Maruyama and Milstein); our approximations can thus benefit from backward error analysis of these underlying numerical schemes. They also lend themselves naturally to “physics-informed” gray-box identification when approximate coarse models, such as mean field equations, are available. Existing numerical integration schemes for Langevin-type equations and for stochastic partial differential equations can also be used for training; we demonstrate this on a stochastically forced oscillator and the stochastic wave equation. Our approach does not require long trajectories, works on scattered snapshot data, and is designed to naturally handle different time steps per snapshot. We consider both the case where the coarse collective observables are known in advance, as well as the case where they must be found in a data-driven manner.

97 MATHEMATICS AND COMPUTING↗

Tensor-polarized parton density in the 𝑁 → Δ transition from the large-𝑁 𝑐 light-cone wave function

The tensor-polarized parton density is defined by the forward matrix element of a partonic operator in the 𝑁 → Δ transition. In this work, we investigate it by employing the large-𝑁 𝑐 light-cone wave function derived from the mean-field approach. The mean-field picture is based on low-energy effective dynamics in the large-𝑁 𝑐 limit, where the baryon wave function is formulated in the rest frame. By exploiting the covariance of the mean-field solution, we derive the corresponding large-𝑁 𝑐 light-cone wave function—decomposed unambiguously into 3⁢𝑄 , 5⁢𝑄 , 7⁢𝑄 , and higher Fock components—in the infinite momentum frame. Evaluating the overlap of these wave functions, we derive an overlap representation of the tensor-polarized parton density in the 𝑁 → Δ transition and find that the leading contribution arises from the 5⁢𝑄 Fock sector. This indicates that the tensor-polarized parton density directly probes the genuine 5⁢𝑄 component and is governed by chiral dynamics. Our numerical analysis shows that the 𝑁 → Δ tensor-polarized parton density is suppressed, consistent with standard large-𝑁 𝑐 expectations. Finally, we establish connections among the tensor-polarized parton density, the generalized parton distribution 𝐻 𝑋 , and the energy-momentum tensor form factor 𝐹 4 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Magnetic Field Strength from Turbulence Theory. I. Using Differential Measure Approach

The mean plane-of-sky magnetic field strength is traditionally obtained from the combination of polarization and spectroscopic data using the Davis–Chandrasekhar–Fermi (DCF) technique. However, we identify the major problem of the DCF technique to be its disregard of the anisotropic character of MHD turbulence. On the basis of the modern MHD turbulence theory we introduce a new way of obtaining magnetic field strength from observations. Unlike the DCF technique, the new technique uses not the dispersion of the polarization angle and line-of-sight velocities, but increments of these quantities given by the structure functions. To address the variety of astrophysical conditions for which our technique can be applied, we consider turbulence in both media with magnetic pressure higher than the gas pressure, corresponding, e.g., to molecular clouds, and media with gas pressure higher than the magnetic pressure, corresponding to the warm neutral medium. We provide general expressions for arbitrary admixtures of Alfvén, slow, and fast modes in these media and consider in detail particular cases relevant to diffuse media and molecular clouds. We successfully test our results using synthetic observations obtained from MHD turbulence simulations. We demonstrate that our differential measure approach, unlike the DCF technique, can be used to measure the distribution of magnetic field strengths, can provide magnetic field measurements with limited data, and is much more stable in the presence of induced large-scale variations of nonturbulent nature. Furthermore, our study uncovers the deficiencies of earlier DCF research.

79 ASTRONOMY AND ASTROPHYSICS↗

On the Effect of Beating during Nonlinear Frequency Chirping

Spectroscopic analyses of energetic particle (EP) driven bursts of MHD fluctuations in magnetically confined plasmas often exhibit chirps that occur simultaneously in groups of two or more. While the superposition of oscillations at multiple frequencies necessarily causes beating in the signal acquired by a localized external probe, self-consistent hybrid simulations of chirping EP modes in a JT-60U tokamak plasma have demonstrated the possibility of global beating, where the mode's electromagnetic field vanishes globally between beats and reappears with opposite phase [Bierwage et al., Nucl. Fusion 57, 016036 (2017)]. This implies that there can be a single coherent field mode that oscillates at multiple frequencies simultaneously when it is resonantly driven by multiple density waves in EP phase space. Conversely, this means that the EP density waves are mutually coupled and interfere with each other via the jointly driven field, a mechanism ignored in some theories of chirping. In this thesis-style treatise, we study the role of field pulsations in general and beating in particular using the Hamiltonian guiding center orbit-following code ORBIT with a reduced wave-particle interaction model in realistic geometry. Beating is found to drive the evolution of EP phase space structures. Additionally, a key mechanism is the pulsation of effective phase space islands combined with the alternation of their effective O- and X-points due to phase jumps between each beat. Observations: (1) Beating causes density wave fronts to advance radially in a pulsed manner and the resulting chirps become staircase-like. (2) The pulsations facilitate convective transfer of material between neighboring layers of phase space density waves. On the one hand, this may inhibit the early detachment of solitary phase space vortices. On the other hand, it facilitates the accumulation of hole and clump fragments into larger structures. (3) Long-range chirping is observed when massive holes or clumps detach and drift away from the turbulent belt around the seed resonance. It is remarkable that the detached vortices remain robust and,on average, maintain their concentric nested layers while being visibly perturbed by the field's continued beating.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Role of the isovector spin-orbit potential in mitigating the CREX-PREX dilemma

Pioneering electroweak measurements of the neutron skin thickness in lead-208 and calcium-48 are challenging our understanding of nuclear dynamics. Many theoretical models suggest that the slope of the symmetry energy controls the development of a neutron skin in neutron-rich nuclei. This led to the expectation that if lead-208 exhibits a large neutron skin, calcium-48 should as well. Given that the PREX Collaboration reported a relatively thick neutron skin in lead, we anticipated that calcium would also have a significant neutron skin. Instead, the CREX Collaboration reported a thin neutron skin in calcium. Although many suggestions have been proposed, the “CREX-PREX dilemma” remains unsolved. Recently, an intriguing scenario has emerged, suggesting that an enhanced isovector spin-orbit interaction could simultaneously account for both results. Following this approach, we performed relativistic mean-field calculations with an increased isovector spin-orbit potential. Our findings indicate that, while this modification significantly affects the structure of calcium-48, it has only a marginal impact on lead-208, thereby bringing the results into better agreement with experiment. Furthermore, the strong enhancement required to mitigate the CREX-PREX dilemma destroys the agreement with a successful spin-orbit phenomenology, primarily by modifying the well-known ordering of spin-orbit partners.

Neutron skin thickness↗

Quantum dynamics of a nucleon in the Fermi accelerator

Highlights: • In nuclear physics, the Fermi accelerator is a coherent open quantum system. • There is not a true equilibrium for a nucleon‘s mean-energy in the Fermi accelerator. • Occupation of higher energy eigen-states remains even after the mean-energy plateaus. • This work paves the way for work on quantum tunnelling in the Fermi accelerator. The quantum dynamics of a particle in a one-dimensional box with an oscillating wall (the Fermi accelerator) is investigated. The model is applied to the motion of a single nucleon in the mean-field potential of a heavy atomic nucleus whose surface vibrates. By directly solving the time-dependent Schrödinger equation, both the state of the particle and its mean-energy are studied. The effects of the frequency of the wall oscillation on the nucleon’s energy are addressed. Its energy oscillates in phase with the moving wall for all frequencies, showing no chaotic behaviour. There is a large initial peak of the nucleon’s energy as the particle adjusts to the sudden change in the size of the box and a varying relaxation time as it plateaus towards lower energy and a partial equilibrium. Small oscillations in energy continue, since there cannot be a true equilibrium while the wall is moving. The quantum coherence between the different parts of the nucleon’s wave-function in real space is very much preserved. This research lays the foundation for future investigations into quantum tunnelling in the Fermi accelerator.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The Dynamic of Complex Two-Phase Mixtures During Coarsening: From Dendritic to Bicontinuous Mixtures

Dendrites are tree-like crystals that frequently form during the solidification of castings. In systems with nearly isotropic interfacial energy, these dendrites possess secondary and sometimes even tertiary arms, and lead to morphologically complex two-phase mixtures. Dealloying, in which one component is selectively leached, leads to nanoporous structures that have proven useful for many technological applications. These bicontinuous two-phase mixtures are topologically and morphologically complex with spatially varying mean and Gaussian curvatures. The evolution of these structures during coarsening is of considerable technological importance since the morphology of the dendrites and nanoporous structure sets the properties of the resulting material. During coarsening, the total surface area per volume of the mixture decreases, thus resulting in an increase in the size-scale of the two-phase mixture. The evolution of interfacial morphology of these interconnected two-phase mixtures is being studied using large-scale computer simulations. The simulations are used to develop a theory of coarsening in these systems that will elucidate the impact of the complicated morphology found in dendritic and nanoporous systems on the coarsening process. The experiments employ four-dimensional X-ray microtomography, which enables the morphology of the two-phase mixture to be followed in three dimensions and time (an additional dimension). The experiments also serve as a test of simulations and theory of the coarsening process, as well as to provide initial conditions for the simulations. Through these experiments and theory, we aim to develop a comprehensive description of coarsening in these complex and technologically important two-phase mixtures.

36 MATERIALS SCIENCE↗

Semianalytical Propagation of Satellite Orbits about an Arbitrary Central Body

Precision mean element (PME) satellite theories play a key role in orbit dynamics analyses. These theories employ: nonsingular orbital elements comprehensive force models Generalized Method of Averaging Numerical interpolation concepts The Draper Semianalytical Satellite Theory (DSST) (Refs. 1 - 6), whose development was led by the author, and the independently-developed Universal Semianalytical Method (USM) (Ref. 7) are examples of such theories. These theories provide the capability to tailor the force modeling to meet the desired computational speed vs. accuracy trade-off. The flexibility of such theories is demonstrated by their ability to include complicated atmosphere density models and spacecraft models in the perturbation theory context. The value of high speed satellite theories, in this era of computational plenty, is that they allow new ways of looking at astrodynamical problems such as orbit design (Refs. 8, 9) and atmosphere density updating (Refs. 10, 11). In the mid to late-1980 s, the geodynamics community led the development of very precise geopotential models such as GEM T2 and GEM T3 (Ref. 12), and with the subsequent analysis of the TOPEX flight data, JGM-2 and JGM-3 (Ref. 13). These were high degree and order geopotentials, at least 50 x 50. In 1993, the DSST implementation in the GTDS program was extended to include the 50 x 50 geopotential models (Ref. 14). The 50 x 50 geopotential, J2000 integration coordinate system, and solid Earth tide capabilities were integrated in GTDS by Scott Carter (Ref. 15). This capability demonstrated 1 m accuracy versus the TOPEX Precise Orbit Ephemerides. Subsequently the DSST Standalone program was also extended to include high degree and order geopotential models (Ref. 5). More recently GTDS has been hosted in the Linux PC environment. However, all of these efforts have been limited to modeling the motion of an artificial Earth satellite. They did not consider the additional complexities associated with lunar, planetary, or other natural satellite orbiters. Such complexities include: additional coordinate systems (associated with the direction of the north pole of rotation and the prime meridian of the new central bodies) (Ref. 16) normalized gravity model coefficients (desirable for high degree and order fields) (Ref. 17) indirect oblateness

Cefola, Paul J.↗

Turbulence Modeling Verification and Validation

Computational fluid dynamics (CFD) software that solves the Reynolds-averaged Navier-Stokes (RANS) equations has been in routine use for more than a quarter of a century. It is currently employed not only for basic research in fluid dynamics, but also for the analysis and design processes in many industries worldwide, including aerospace, automotive, power generation, chemical manufacturing, polymer processing, and petroleum exploration. A key feature of RANS CFD is the turbulence model. Because the RANS equations are unclosed, a model is necessary to describe the effects of the turbulence on the mean flow, through the Reynolds stress terms. The turbulence model is one of the largest sources of uncertainty in RANS CFD, and most models are known to be flawed in one way or another. Alternative methods such as direct numerical simulations (DNS) and large eddy simulations (LES) rely less on modeling and hence include more physics than RANS. In DNS all turbulent scales are resolved, and in LES the large scales are resolved and the effects of the smallest turbulence scales are modeled. However, both DNS and LES are too expensive for most routine industrial usage on today's computers. Hybrid RANS-LES, which blends RANS near walls with LES away from walls, helps to moderate the cost while still retaining some of the scale-resolving capability of LES, but for some applications it can still be too expensive. Even considering its associated uncertainties, RANS turbulence modeling has proved to be very useful for a wide variety of applications. For example, in the aerospace field, many RANS models are considered to be reliable for computing attached flows. However, existing turbulence models are known to be inaccurate for many flows involving separation. Research has been ongoing for decades in an attempt to improve turbulence models for separated and other nonequilibrium flows. When developing or improving turbulence models, both verification and validation are important steps in the process. Verification insures that the CFD code is solving the equations as intended (no errors in the implementation). This is typically done either through the method of manufactured solutions (MMS) or through careful step-by-step comparisons with other verified codes. After the verification step is concluded, validation is performed to document the ability of the turbulence model to represent different types of flow physics. Validation can involve a large number of test case comparisons with experiments, theory, or DNS. Organized workshops have proved to be valuable resources for the turbulence modeling community in its pursuit of turbulence modeling verification and validation. Workshop contributors using different CFD codes run the same cases, often according to strict guidelines, and compare results. Through these comparisons, it is often possible to (1) identify codes that have likely implementation errors, and (2) gain insight into the capabilities and shortcomings of different turbulence models to predict the flow physics associated with particular types of flows. These are valuable lessons because they help bring consistency to CFD codes by encouraging the correction of faulty programming and facilitating the adoption of better models. They also sometimes point to specific areas needed for improvement in the models. In this paper, several recent workshops are summarized primarily from the point of view of turbulence modeling verification and validation. Furthermore, the NASA Langley Turbulence Modeling Resource website is described. The purpose of this site is to provide a central location where RANS turbulence models are documented, and test cases, grids, and data are provided. The goal of this paper is to provide an abbreviated survey of turbulence modeling verification and validation efforts, summarize some of the outcomes, and give some ideas for future endeavors in this area.

Rumsey, Christopher L.↗

The 2022 magneto-optics roadmap

Abstract Magneto-optical (MO) effects, viz. magnetically induced changes in light intensity or polarization upon reflection from or transmission through a magnetic sample, were discovered over a century and a half ago. Initially they played a crucially relevant role in unveiling the fundamentals of electromagnetism and quantum mechanics. A more broad-based relevance and wide-spread use of MO methods, however, remained quite limited until the 1960s due to a lack of suitable, reliable and easy-to-operate light sources. The advent of Laser technology and the availability of other novel light sources led to an enormous expansion of MO measurement techniques and applications that continues to this day (see section 1). The here-assembled roadmap article is intended to provide a meaningful survey over many of the most relevant recent developments, advances, and emerging research directions in a rather condensed form, so that readers can easily access a significant overview about this very dynamic research field. While light source technology and other experimental developments were crucial in the establishment of today’s magneto-optics, progress also relies on an ever-increasing theoretical understanding of MO effects from a quantum mechanical perspective (see section 2), as well as using electromagnetic theory and modelling approaches (see section 3) to enable quantitatively reliable predictions for ever more complex materials, metamaterials, and device geometries. The latest advances in established MO methodologies and especially the utilization of the MO Kerr effect (MOKE) are presented in sections 4 (MOKE spectroscopy), 5 (higher order MOKE effects), 6 (MOKE microscopy), 8 (high sensitivity MOKE), 9 (generalized MO ellipsometry), and 20 (Cotton–Mouton effect in two-dimensional materials). In addition, MO effects are now being investigated and utilized in spectral ranges, to which they originally seemed completely foreign, as those of synchrotron radiation x-rays (see section 14 on three-dimensional magnetic characterization and section 16 on light beams carrying orbital angular momentum) and, very recently, the terahertz (THz) regime (see section 18 on THz MOKE and section 19 on THz ellipsometry for electron paramagnetic resonance detection). Magneto-optics also demonstrates its strength in a unique way when combined with femtosecond laser pulses (see section 10 on ultrafast MOKE and section 15 on magneto-optics using x-ray free electron lasers), facilitating the very active field of time-resolved MO spectroscopy that enables investigations of phenomena like spin relaxation of non-equilibrium photoexcited carriers, transient modifications of ferromagnetic order, and photo-induced dynamic phase transitions, to name a few. Recent progress in nanoscience and nanotechnology, which is intimately linked to the achieved impressive ability to reliably fabricate materials and functional structures at the nanoscale, now enables the exploitation of strongly enhanced MO effects induced by light–matter interaction at the nanoscale (see section 12 on magnetoplasmonics and section 13 on MO metasurfaces). MO effects are also at the very heart of powerful magnetic characterization techniques like Brillouin light scattering and time-resolved pump-probe measurements for the study of spin waves (see section 7), their interactions with acoustic waves (see section 11), and ultra-sensitive magnetic field sensing applications based on nitrogen-vacancy centres in diamond (see section 17). Despite our best attempt to represent the field of magneto-optics accurately and do justice to all its novel developments and its diversity, the research area is so extensive and active that there remains great latitude in deciding what to include in an article of this sort, which in turn means that some areas might not be adequately represented here. However, we feel that the 20 sections that form this 2022 magneto-optics roadmap article, each written by experts in the field and addressing a specific subject on only two pages, provide an accurate snapshot of where this research field stands today. Correspondingly, it should act as a valuable reference point and guideline for emerging research directions in modern magneto-optics, as well as illustrate the directions this research field might take in the foreseeable future.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Visualization of High Latitude Ion Upflow in Support of the Image Mission

The study of the magnetosphere is a 400 year old science that began with the publication by Gilbert, in 1600, of his hypotheses that the Earth was a giant magnet. Since then we have learned many things about the magnetosphere, particularly in the last 40 years of the space age, but we still have many unanswered questions. In spite of the many thousands of observations of this system we still lack a global understanding of how it works. This is due to its large size and tenuous nature that mean that any measurement made of the fields or particles involved only give one a knowledge of the local conditions at a given time. To gain a global perspective through such observations would require the simultaneous operation of thousands of satellites spread throughout the magnetospheric system in addition to observations made on the ground. Such a program would be impractical at least from financial considerations. What is needed for the advancement of magnetospheric physics is to develop the same capabilities that astrophysicists, solar physicists and meteorologists have been using for years --- the ability to stand back from the object under study and see it in its entirety. The challenge for doing this for the magnetosphere is that the particle densities are very low and the material is, for the most part, not luminous. In the last 25 years several ideas have been proposed that would allow at least the imaging of certain portions of the magnetosphere. These include imaging of the plasmasphere through the resonant scattering of solar 304 A from He+ ions, imaging of various hot plasma populations (i.e. the ring current, plasmasheet, upflowing ionospheric ions, etc.) from the neutral atoms that result when ions of these populations charge exchange with the hydrogen geocorona, and imaging the aurora at various wavelengths in the far ultraviolet. In addition, a novel technique for probing various boundaries in the magnetosphere by bouncing low frequency radio waves off of them has been extensively studied. Such a technique is analogous to the way the under water world can be probed with sonar. About five years ago NASA convened a science working group to study the possibility of flying a magnetospheric imaging mission. This resulted in a number of proposals for such a mission, one of which was selected to be the first MIDEX mission, to be launched in early 2000. The mission is called IMAGE (Imager for Magnetopause to Aurora Global Exploration) and its P.I. is J. Burch at SwRI. The IMAGE spacecraft will carry imagers to view the plasmasphere, aurora, ring current, inner plasmasheet, and upflowing ionospheric ions as well as a radio sounder to probe the location, shape and dynamics of the magnetopause, plasmapause, etc. Between its selection last April and the non advocacy mission review, which takes place next spring, the IMAGE teams needs to further refine the design of the mission and its instruments. The theory and modeling (T&M) subgroup of this team has the task of demonstrating what kind of images the instruments on IMAGE will see as well as showing that useful scientific information can be extracted from such images. As a central element to the efforts of the T&M subgroup we have decided to simulate and create synthetic images for the magnetic cloud event of October, 1995. In this event a large cloud, with high plasma densities and strong magnetic fields, ejected from the sun collided with the earth's magnetosphere triggering a three day period of intense magnetic storms and substorms. This event was observed from a number of different spacecraft and on the ground so we have a good data set to work with. In our work we will place the IMAGE spacecraft in the magnetosphere on its proposed orbit, with its proposed instruments, to see what it would see had it been there. Existing models of the plasmasphere, ring current and magnetopause will be run for this event to give the structures for the imaging instruments. There are several models which are lacking and which need to be developed. These include a model for the cusp, the inner plasmasheet and the upflowing ions. My task this summer was to develop the upflowing ion model and use it to create synthetic images.

Wilson, Gordon R.↗