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At least 1,189 records · Page 66

How the magnetosphere is driven into the substorm

This paper puts together several aspects of the substorm phenomena into a scenario subject to quantitative analysis, based on Ampere's law, magnetic stresses, and the effect of the parallel electric field. As the magnetospheric convection continuously shears the magnetic field, the parallel electric field suddenly switches on when the shear reaches a critical value. The parallel electric field not only accelerates the charged particles to cause the auroral display but also partially decouples the ionosphere from the magnetosphere so that the magnetospheric convection is enhanced significantly, causing the substorm expansion phase. Pi 2 pulsations are excited by the change of the magnetosphere-ionosphere coupling. We show a direct relationship between the parallel potential drop, the enhanced convection rate, and the amplitude of the Pi 2 pulsations. With no adjustable parameter, the relationship shows quantitative agreement with the diverse observations.

Zhu, Xiaoming↗

Geomagnetic Field Distortion by a Solar Stream as a Mechanism for the Production of Polar Aurora and Electrojets

This paper describes a mechanism for charge separation in the geomagnetically trapped radiation which may account for some observed phenomena associated with the polar aurora and the electrojet current systems. The following development is proposed: given that there exist eastward or westward longitudinal gradients in the geomagnetic field resulting from distortion of the geomagnetic field by solar streams, if the trapped radiation is adiabatic in character, radial drift separation of positive and negative charged particles must occur. It follows that, for bounded or irregular distributions of plasma number density in such an adiabatic - drift region, electric fields will arise. The origin of such electric fields will not arrest the drift separation of the charged particles, but will contribute to exponential growth of irregularities in the trapped plasma density. An adiabatic acceleration mechanism is described, which is based on incorporating the electrostatic energy of the particle in the energy function for the particle. Direct consequences of polarization of the geomagnetically trapped radiation will be the polar electrojet current systems and the polar aurora.

Kern, J. W.↗

Observation of reconnection phenomena at synchronous orbit

SCATHA satellite observations of large-amplitude magnetic field oscillations in the magnetosheath and in the associated plasma are studied. Large-amplitude variations in the magnetosheath magnetic field intensity with a quasi-period of 10 s were observed. Nearly static structures of high-beta plasma associated with the magnetic field minima and low-beta plasma associated with the magnetic field maxima were observed convecting toward the earth. The morphology of charged particle data for the transition between the magnetosphere and the magnetosheath for a northward magnetosheath magnetic field is presented. A convection electric field of about 9 mV/m was inferred from the spectral difference between solar and antisolar drifting ions in the magnetosheath near a magnetopause rotational discontinuity. A trapped component was observed in the magnetosheath plasma during both northward and southward magnetosheath magnetic fields. It is concluded that flux transfer events arise from the interaction of the earthward convecting plasma filaments with the magnetospheric magnetic field at the magnetopause.

Croley, D. R., Jr.↗

Quantum interference of currents in an atomtronic SQUID

Quantum interference of currents is the most important and well known quantum phenomenon in a conventional superconducting quantum interference device (SQUID). Here, we report the observation of quantum interference of currents in an atomtronic SQUID. Analogous to a conventional SQUID, currents flowing through two junctions in an atomtronic SQUID interfere due to the phase difference from rotation. This interference results in modulation of critical currents. This modulation was observed for three different radii with clear modulation periods which were measured to be consistent with fundamental rotation rates. This observation shows the possibility of studying various interesting SQUID physics with an atomtronic SQUID and especially, macroscopic quantum phenomena with currents may be realized with an atomtronic SQUID toward the goal of quantum metrology of rotation sensing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Coherence in Chemistry: Foundations and Frontiers

Coherence refers to correlations in waves. Because matter has a wave-particle nature, it is unsurprising that coherence has deep connections with the most contemporary issues in chemistry research (e.g., energy harvesting, femtosecond spectroscopy, molecular qubits and more). But what does the word "coherence" really mean in the context of molecules and other quantum systems? We provide a review of key concepts, definitions, and methodologies, surrounding coherence phenomena in chemistry, and we describe how the terms "coherence" and "quantum coherence" refer to many different phenomena in chemistry. Moreover, we show how these notions are related to the concept of an interference pattern. Coherence phenomena are indeed complex, and ambiguous definitions may spawn confusion. By describing the many definitions and contexts for coherence in the molecular sciences, we aim to enhance understanding and communication in this broad and active area of chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Report from the Inaugural Meeting on the Opportunities at the SEEMS Facility

An Inaugural Meeting on the Opportunities at the SEEMS Facility was held at the Spallation Neutron Source (SNS) on June 11 - 12, 2019. It focused on the second of the user communities - industrial and academic researchers. Indeed, the SEEMS design concept started with a Spallation Neutron Source (SNS) study conducted for the Federal Aviation Administration (FAA) that examines test facility options for providing neutron radiation simulating that in the atmosphere originating from cosmic rays and solar particles. The study was stimulated by earlier work calling for neutron radiation facilities with increased capacity and capabilities to meet current and future needs. Regulators, aircraft producers and avionics equipment suppliers recognize the growing urgent need for SEE testing in prototypical radiation fields. Industry standards formalizing procedures to assure that critical systems are robust against SEE phenomena have been issued. Regulatory bodies including the Federal Aviation Administration (FAA) and the European Union Aviation Safety Agency (EASA) now requiring that updated standards are met for aircraft certification.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Collaborative Research: Enabling multi-scale studies of magnetic reconnection with interpretable data-driven models

The development of accurate reduced descriptions and improved closures for magnetic reconnection is an important and a long‐standing challenge in plasma physics. The four‐fluid approach, and associated closures, that were investigated have the potential to improve the accuracy of plasma fluid models, capturing physical effects which would otherwise require a kinetic description. If successful, this approach could have an important impact for the modeling of laboratory and space plasmas. The major goals of this project were to develop new machine learning (ML) tools based on sparse and symbolic regression techniques, and to extract interpretable and generalizable reduced models (e.g., in the form of partial differential equations - PDEs) from data generated by first principles plasma simulations. Preserving interpretability of such data‐driven models is key to addressing the long‐standing theoretical and numerical challenges. Prior proof‐of‐principle studies have demonstrated the enormous potential of this approach, by recovering the well‐established hierarchy of plasma equations (from Vlasov to MHD) from data produced by particle‐in‐cell (PIC) simulations. Our goal in this project was to extend and apply these new tools to construct better kinetic closures for magnetic reconnection; to derive better models of particle injection and acceleration by this fundamental plasma process; and to use this understanding to accelerate the development of multi‐scale plasma algorithms. While our immediate focus was on the problem of magnetic reconnection, the tools that were will developed are general and applicable to other areas of plasma physics, and more broadly to many‐body phenomena. We anticipate that the development of these multi‐scale models will have a significant impact across different areas of plasma science, from fusion to space and astrophysical plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Thermochemical nonequilibrium in atomic hydrogen at elevated temperatures

A numerical study of the nonequilibrium flow of atomic hydrogen in a cascade arc was performed to obtain insight into the physics of the hydrogen cascade arc. A rigorous mathematical model of the flow problem was formulated, incorporating the important nonequilibrium transport phenomena and atomic processes which occur in atomic hydrogen. Realistic boundary conditions, including consideration of the wall electrostatic sheath phenomenon, were included in the model. The governing equations of the asymptotic region of the cascade arc were obtained by writing conservation of mass and energy equations for the electron subgas, an energy conservation equation for heavy particles and an equation of state. Finite-difference operators for variable grid spacing were applied to the governing equations and the resulting system of strongly coupled, stiff equations were solved numerically by the Newton-Raphson method.

Scott, R. K.↗

Post-irradiation examination of legacy high burnup fuel to support safety testing

Safety/transient testing to evaluate performance under off-normal conditions is an essential pillar for both the development of Accident Tolerant Fuels (ATF) and the optimization of fuel operation economics beyond current discharge burnups. Among other factors, the successful interpretation of the transient testing results relies upon the knowledge of the initial conditions of the test, including the characteristics of the fuel system under scrutiny. When testing pre-irradiated material, the assumptions that the fuel and the cladding still have the same properties as in the pre-irradiation stage is obviously wrong and could affect the results of the test. This is particularly true the more burnup accumulates in the fuel rod and irradiation progresses. The knowledge of the initial microstructure of both fuel and cladding allows a clearer interpretation of the subsequent transient testing results, provides validation of the physical phenomena underlying the model predictions and eliminates the uncertainties related to the limited knowledge of the sample status before the test. One example is the phenomenon of fine fragmentation that occurs in Light Water reactor (LWR) fuel. During a Loss of Coolant Accident (LOCA) or Reactivity Initiated Transient (RIA) the fuel can severely fragment. During LOCA, high burnup fuel tend to finely fragment, which has raised safety concerns due to the increased likelihood of dispersal of such small particles once the cladding has burst and due to the increased fission gas release. Therefore, efforts have been devoted to the assessment of a pulverization threshold that could determine the conditions under which fine fragmentation is predominant. However, the lack of information regarding the initial conditions of the fuel, and the connections between those conditions and the pre-transient irradiation history, have hindered the development of a fully mechanistic fragmentation and pulverization criterion. The empirical relationships rely on conservative estimations, due to the lack of information on critical material properties and characteristics. More generally, experimental evidence of the irradiation-induced modifications at microstructural scale are necessary to determine the behavior of the material at the macroscopic scale, with the latter being the one of technological interest. Significant progress has been made in the last two decades in the developments of analytical materials science techniques that can be applied to highly radioactive materials, such as high burnup fuels. The availability of new techniques and the improvement of existing ones has enabled investigations previously not possible that can deepen the understanding of the fuel characteristics and properties at high burnup. The better knowledge of material behavior and irradiation-induced phenomena could help the prediction of its performance. In this context, the scope of the present work is to apply a wide portfolio of advanced characterization techniques to determine properties that are relevant for safety and performance. The results are interpreted in the context of engineering scale post-irradiation examinations and available information on the irradiation conditions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Formation and Diagnostics of Collisionless Shocks in Laser-Produced Plasmas (Final Report)

Collisions of supersonic flows occur frequently in astrophysics, and the resulting shock waves are responsible for the properties of many astrophysical phenomena, such as supernova remnants, Gamma Ray Bursts and jets from Active Galactic Nuclei. Because of the low density of astrophysical plasmas, the mean free path due to Coulomb collisions is typically very large; therefore, most shock waves in astrophysics are “collisionless” and form due to plasma instabilities and self-generated magnetic fields. Laboratory experiments at DOE high energy density (HED) facilities can achieve the conditions necessary for the formation of collisionless shocks and will provide a unique avenue for studying the nonlinear physics of shock waves. This project investigates the parameters and experimental configurations needed for the creation of collisionless shocks in the laboratory experiments. This study is being performed with state of the art 3D kinetic plasma simulations. Recent advances in ab-initio particle-in-cell (PIC) simulations of astrophysical shocks enable us to simulate shock formation on timescales and in geometries relevant to the laboratory experiments. The main goal of the proposal is to ascertain which signatures of shock physics can be extracted from the realistic experiments, accounting for limitations imposed by finite spatial and time scales in the lab. To aid the interpretation of current and future experimental data, PIC simulation data have been analyzed using the same diagnostic techniques as used in the laboratory, such as proton radiography and neutronics, to unambiguously predict the experimental signatures of relevant collisionless shock phenomena.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Open associahedra and scattering forms

We continue the study of open associahedra associated with bi-color scattering amplitudes initiated in ref. [1]. We focus on the facet geometries of the open associahedra, uncovering many new phenomena such as fiber-product geometries. We then provide novel recursion procedures for calculating the canonical form of open associahedra, generalizing recursion relations for bounded polytopes to unbounded polytopes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Modeling DC electrical breakdown using a truncated emission spectrum for trapped radiation

Spontaneously emitted radiation from excited atoms can be of principle importance in certain modes of electrical breakdown, especially positive streamers and some regimes of Townsend breakdown. The electrostatic particle-in-cell code Aleph utilizes the direct simulation Monte Carlo method to compute radiation transport. When there is strong radiation trapping, this approach is limited in that it must resolve the timescale associated with self-absorption. This renders many cases computationally intractable as sub-femtosecond time steps can be required to compute solutions for phenomena that occur over nanoseconds or microseconds. For two specific cases which exhibit strong radiation trapping, we find that spontaneous emissions having a frequency near the line center are inactive in the breakdown process and can be neglected. This enables larger time steps and a computational speedup of up to two orders of magnitude is observed. Some considerations for determining the validity of making such an approximation for Townsend breakdown problems and positive ionization wave problems are presented.

Roberds, N. A.↗

On the precipitation of relativistic electrons from the outer belt

A model in which a partially filled drift loss cone plays a prominent role is presently used to investigate relativistic electron data obtained by the Defense Meteorological Satellite Program spacecraft in the outer belt region. The good agreement obtained between model predictions and observations indicates that electron drift in the drift loss cone, which is known to dominate electron precipitation phenomena at lower latitudes, is also important at outer beta latitudes. In conjunction with the degree of partial filling of the drift loss cone, this effect indicates that slow pitch angle diffusion dominates the morphology of outer belt electrons. It is concluded that half of the electron precipitation from the outer belt is due to wave-particle interactions, and the other half by auroral activity and electron drift in the drift loss cone.

Sheldon, W. R.↗

Fun Times with Cosmic Rays

Who would have thought cosmic rays could be so hip? Although discovered 90 years ago on death-defying manned balloon flights hip even by twenty-first-century extremesport standards cosmic rays quickly lost popularity as way-cool telescopes were finding way-too-cool phenomena across the electromagnetic spectrum. Yet cosmic rays are back in vogue, boasting their own set of superlatives. Scientists are tracking them down with new resolve from the Arctic to Antarctica and even on the high western plains of Argentina. Theorists, too, now see cosmic rays as harbingers of funky physics. Cosmic rays are atomic and subatomic particles - the fastest moving bits of matter in the universe and the only sample of matter we have from outside the solar system (with the exception of interstellar dust grains). Lower-energy cosmic rays come from the Sun. Mid-energy particles come from stellar explosions - either spewed directly from the star like shrapnel, or perhaps accelerated to nearly the speed of light by shock waves. The highest-energy cosmic rays, whose unequivocal existence remains one of astronomy's greatest mysteries, clock in at a staggering 10(exp 19) to 10(exp 22) electron volts. This is the energy carried in a baseball pitch; seeing as how there are as many atomic particles in a baseball as there are baseballs in the Moon, that s one powerful toss. No simple stellar explosion could produce them. At a recent conference in Albuquerque, scientists presented the first observational evidence of a possible origin for the highest-energy variety. A team led by Elihu Boldt at NASA s Goddard Space Flight Center found that five of these very rare cosmic rays (there are only a few dozen confirmed events) come from the direction of four 'retired' quasar host galaxies just above the arm of the Big Dipper, all visible with backyard telescopes: NGC 3610, NGC 3613, NGC 4589, and NGC 5322. These galaxies are billions of years past their glory days as the brightest beacons in the universe. Yet they still harbor central, supermassive black holes, which could generate energetic particles if they are spinning.

Wanjek, Christopher↗

Satellite Contributions to the Quantitative Characterization of Biomass Burning for Climate Modeling

Characterization of biomass burning from space has been the subject of an extensive body of literature published over the last few decades. Given the importance of this topic, we review how satellite observations contribute toward improving the representation of biomass burning quantitatively in climate and air-quality modeling and assessment. Satellite observations related to biomass burning may be classified into five broad categories: (i) active fire location and energy release, (ii) burned areas and burn severity, (iii) smoke plume physical disposition, (iv) aerosol distribution and particle properties, and (v) trace gas concentrations. Each of these categories involves multiple parameters used in characterizing specific aspects of the biomass-burning phenomenon. Some of the parameters are merely qualitative, whereas others are quantitative, although all are essential for improving the scientific understanding of the overall distribution (both spatial and temporal) and impacts of biomass burning. Some of the qualitative satellite datasets, such as fire locations, aerosol index, and gas estimates have fairly long-term records. They date back as far as the 1970s, following the launches of the DMSP, Landsat, NOAA, and Nimbus series of earth observation satellites. Although there were additional satellite launches in the 1980s and 1990s, space-based retrieval of quantitative biomass burning data products began in earnest following the launch of Terra in December 1999. Starting in 2000, fire radiative power, aerosol optical thickness and particle properties over land, smoke plume injection height and profile, and essential trace gas concentrations at improved resolutions became available. The 2000s also saw a large list of other new satellite launches, including Aqua, Aura, Envisat, Parasol, and CALIPSO, carrying a host of sophisticated instruments providing high quality measurements of parameters related to biomass burning and other phenomena. These improved data products have enabled significant progress in the study of biomass burning from space. However, appreciable uncertainty remains in many of the measurements that still needs to be addressed. Nevertheless, climate and other atmospheric models are

Ichoku, Charles↗

The Evolution of Icelandic Volcano Emissions, as Observed From Space in the Era of NASA's Earth Observing System (EOS)

Volcanoes are natural phenomena that have global environmental impacts. Satellite remote sensing can help classify volcanic eruptions and track the dispersion of emissions. We assess multiple volcanic eruptions in Iceland (Eyjafjallajökull 2010, Grímsvötn 2011 and Holuhraun 2014-2015), using space-borne observations to infer information about the geological dynamics of each volcano and the properties and evolution of plume particles. We derive qualitative constraints on plume particle size, shape and light-absorption characteristics from Multi-angle Imaging SpectroRadiometer (MISR) space-borne imagery. With the MISR Research Algorithm (RA), we distinguish sulfate/water-dominated volcanic plumes from Holuhraun and ash-dominated plumes from Eyjafjallajökull and Grímsvötn, and even identify subtler changes in ash particle size and light-absorption within plumes. Additionally, plume heights are retrieved geometrically from MISR. These are combined with surface thermal anomalies from the MODerate resolution Imaging Spectroradiometer (MODIS) and SO2 concentrations derived from the Ozone Monitoring Instrument (OMI) to synthesize eruption remote-sensing chronologies. Signals related to differences in particle properties are identified and linked to evolving magma composition at Eyjafjallajökull. The results illustrate the potential to distinguish qualitative differences in eruptive magma composition based on particle light absorption and plume profile from remote-sensing. For the sulfate-rich Holuhraun plumes, the influence of aerosol hygroscopic growth during transport is inferred from such data. Three processes appear to dominate plume evolution in Iceland: downwind aerosol formation; particle hydration; and particle deposition. This work demonstrates enhanced MISR capabilities, and more generally, remote-sensing analysis that can be applied globally, especially where suborbital volcano observations are limited or entirely absent.

remote sensting↗

Chapter 10 - Remote Sensing Measurements of Aerosol Properties

Satellite instruments have proven especially capable at monitoring the quantity of airborne particles in columns of atmosphere, globally. This chapter describes the principles of satellite measurements and retrieval algorithms, and surveys current instruments and their capabilities. We outline the issues associated with retrieval algorithms, such as surface characterization and aerosol proximity to clouds, and the challenges with interpretation of the results. The relationship between measured aerosol properties and climate-relevant aerosol properties simulated in models is outlined, as well as how measurements are used to evaluate models. Most space-based aerosol instruments are passive sensors that measure reflected sunlight at multiple wavelengths, some at multiple viewing angles. A few are active sensors that send out their own laser light and measure the returned signal. Except when clouds are present, the excess amount of light scattered back to space, beyond that expected from the surface and atmospheric gas, is attributed to aerosol. Satellite measurements are used in many ways in aerosol research. They often provide the only method for monitoring hazardous phenomena such as major wildfire and volcanic eruption plumes, especially in remote areas. Stable, long-term, near-global-scale satellite data records make it possible to identify regional and global aerosol trends. Aerosol radiative effects on climate can be quantified on a near-global scale and used to estimate the strength of aerosol–radiation and aerosol–cloud interactions as well as to evaluate climate model simulations of these interactions. Aerosol-type mapping from satellite imagery is helpful for source attribution, model validation, and to constrain particle light-absorption properties that are essential for radiative forcing calculations. The range of aerosol properties retrieved from satellite observations has grown considerably since the first global estimates of aerosol optical depth (τ a) over ocean were made in the late 1970s. Methods for retrieving particle size and light-absorption properties were explored in the 1990s using multispectral, multi-angle observations, and polarization in visible and near-infrared wavelengths. Sensitivity to particle light absorption, primarily from black or brown carbon content, improved with the inclusion of UV channels, and sensitivity to very thin aerosol layers in the upper troposphere and lower stratosphere was advanced with the use of limb-sounding instruments and active sensors. There are limitations to every measurement technique, including satellite aerosol remote sensing. For wide-swath, passive instruments, aerosol retrievals near clouds can present substantial challenges as far as 15 km away due to cloud-scattered light contaminating the signal. In nearly all cases, retrievals over bright snow and ice surfaces are precluded because surface reflectance uncertainties can overwhelm the aerosol signal. Similarly, meteorological cloud is identified and masked out where possible. Data from passive sensors also lack vertical resolution except those that view toward the limb or where multi-angle imagery is acquired over plumes from wildfires, erupting volcanoes, and wind-blown dust. Yet, passive sensors provide vastly more coverage than the active instruments that mitigate these issues. Particle microphysical information is qualitative from all remote sensing techniques, relying on proxies to infer particle composition, hygroscopicity, and the amount of light-absorbing material. Further, particles smaller than about 200 nm diameter cannot be distinguished from atmospheric gas molecules with remote sensing, which hinders studies of cloud condensation nuclei and their effects on clouds. Most satellite instruments dedicated to aerosol observations are in low-Earth, near-polar, sun-synchronous orbits, which means they cross the equator at the same local time each day. Most are set on cycles that repeat approximately every 16 days, which makes it difficult to monitor aerosol evolution locally. Geostationary satellites make it possible to observe changes occurring from minutes to hours over regions up to 8000 km in size, but lack coverage of high latitudes, and often provide more limited constraints on aerosol properties. Ground-truth data are vital for satellite aerosol-retrieval validation. The AErosol RObotic NETwork (AERONET) of sun photometers was created in 1993 and has become an established global network of over 350 instruments for validating satellite measurements. The network, as well as global networks of ground-based lidars, solar flux radiometers and other sun photometers, are widely used for evaluating global satellite retrievals and model simulations. NASA's Earth Observing System (EOS) program beginning in 1999 led to improvements in reliability, spatial resolution, and spectral resolution (and hence, to improved particle size discrimination and light absorption properties). Satellite payloads include advanced broad-swath and multi-angle imagers, along with the first space-based active sensor focused largely on long-term aerosol monitoring. Since about 2002, Europe's SENTINEL and operational meteorological satellite fleets are also providing sustained aerosol observations, with planned continuation until at least 2030. Satellite remote sensing instruments offer valuable data for evaluating aerosol representations in global climate models. They have been used to assess aerosol optical and physical properties, trends and distributions, and are applied increasingly as direct model constraints in data assimilation to create global aerosol reanalysis products. Aerosol optical depth is the most common quantity adopted for routine model evaluation, including multiwavelength data to loosely constrain particle-size distributions. These evaluations of multiple models have revealed general biases in their regional aerosol amounts and seasonal patterns of transport and removal. Although satellite measurements have near-global coverage, substantial errors can be introduced into the model observation comparison unless attention is paid to spatial and temporal collocation, cloud screening, subgrid-scale variability, and measurement uncertainties that vary with retrieval conditions.

aerosol properties↗

Investigating two-dimensional adjoint QCD on the lattice

We present our investigations of SU(N) adjoint QCD in two dimensions with one Majorana fermion on the lattice. We determine the relevant parameter range for the simulations with Wilson fermions and present results for Polyakov loop, chiral condensate, and string tension. In the theory with massive fermions, all observables we checked show qualitative agreement between numerical lattice data and theory, while the massless limit is more subtle since chiral and non-invertible symmetry of the continuum theory are explicitly broken by lattice regularization. In thermal compactification, we observe N perturbative vacua for the holonomy potential at high-T with instanton events connecting them, and a unique vacuum at low-T. At finite-N, this is a cross-over and it turns to a phase transition at large-N thermodynamic limit. In circle compactification with periodic boundary conditions, we observe a unique center-symmetric minimum at any radius. In continuum, the instantons in the thermal case carry zero modes (for even N) and indeed, in the lattice simulations, we observe that chiral condensate is dominated by instanton centers, where zero modes are localized. We present lattice results on the issue of confinement vs. screening in the theory and comment on the roles of chiral symmetry and non-invertible symmetry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗