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At least 199 records · Page 11

Effects of Heating on Teflon(Registered Trademark) FEP Thermal Control Material from the Hubble Space Telescope

Metallized Teflon(Registered Trademark) FEP (fluorinated ethylene propylene) thermal control material on the Hubble Space Telescope (HST) is degrading in the space environment. Teflon(Registered Trademark) FEP thermal control blankets (space-facing FEP) retrieved during the first servicing mission (SM1) were found to be embrittled on solar facing surfaces and contained microscopic cracks. During the second servicing mission (SM2) astronauts noticed that the FEP outer layer of the multi-layer insulation (MLI) covering the telescope was cracked in many locations around the telescope. Large cracks were observed on the light shield, forward shell and equipment bays. A tightly curled piece of cracked FEP from the light shield was retrieved during SM2 and was severely embrittled, as witnessed by ground testing. A Failure Review Board (FRB) was organized to determine the mechanism causing the MLI degradation. Density, x-ray crystallinity and solid state nuclear magnetic resonance (NMR) analyses of FEP retrieved during SM1 were inconsistent with results of FEP retrieved during SM2. Because the retrieved SM2 material curled while in space, it experienced a higher temperature extreme during thermal cycling, estimated at 200 C, than the SM1 material, estimated at 50 C. An investigation on the effects of heating pristine and FEP exposed on HST was therefore conducted. Samples of pristine. SM1, and SM2 FEP were heated to 200 C and evaluated for changes in density and morphology. Elevated temperature exposure was found to have a major impact on the density of the retrieved materials. Characterization of polymer morphology of as-received and heated FEP samples by NMR provided results that were consistent with the density results. These findings have provided insight to the damage mechanisms of FEP in the space environment.

deGroh, Kim↗

Electrical Ground Support Equipment for the Sampling Caching System of the Mars 2020 Rover

In this work we describe in detail the architecture, design, testing and operation of the Electrical Ground Support Equipment (EGSE) “Blue Box” used to test and validate the Sampling Caching System (SCS) of the Mars 2020 Perseverance rover. The Blue Box architecture is centered around COTS motor controllers and COTS input-output modules communicating over an EtherCAT bus. A custom, low-level safety subsystem ensures no harm can be done to the flight articles. The modular architecture of the EGSE reduces cost and complexity while expediting assembly time. The Blue Box drives the 19 actuators of the SCS which span the main robotic arm, the corer system, the internal sample handling arm, the sample tube sealing system and the gas dust removal tool; mimicking the Rover Motor Control Assembly (RMCA). Due to the limited availability of RMCA’s, the EGSE enabled and performed the bulk of testing activities for SCS. The majority of the SCS actuators are composed of a 3-phase DC brushless motors, hall sensors for commutation, dual resolvers for output angular measurement, brakes, heaters and platinum thermistors. Additionally, the EGSE read 12 strain gauges forming part of a force torque sensor, and switches used for external positioning references. Over the 3-year span of the V&V campaign for the SCS, over 32 EGSE systems were built, tested and deployed to test venues at JPL and externally. The EGSE tested several families of the SCS subsystem, ranging from engineering units, life test units and two flight units. Test venues that this EGSE supported included lab benches, ultra-clean cleanrooms, ATLO facilities, and thermal vacuum chambers. Together with the test software systems, SSDEV and SSDEV-ECAT, the Blue Box EGSE enabled the team to efficiently test flight hardware and flight software together. We go over the safety features and fault management techniques employed to protect flight hardware. The effects of the long, 50-feet, EGSE harnesses on motor performance, EMI, electrical noise, and motor control performance are explained. Mitigations to these unwanted effects, including shielding strategy and inductance compensation, are summarized. We go over an excerpt of notable anomalies that this EGSE suffered through its operation, along with investigations and resolutions. Lessons learned, areas of improvement as part of future work, and recommendations for future implementations for similar EGSE’s, are shared.

Levine, Dan↗

Topological order in interacting semimetals

It has recently been demonstrated that it is possible to open a gap in a magnetic Weyl semimetal, while preserving the chiral anomaly along with the charge conservation and translational symmetries, which all protect the gapless nodes in a weakly interacting semimetal. The resulting state was shown to be a nontrivial generalization of a non-Abelian fractional quantum Hall liquid to three dimensions. Here we point out that a second fractional quantum Hall state exists in this case. This state has exactly the same electrical and thermal Hall responses as the first, but a distinct (fracton) topological order. Moreover, the existence of this second fractional quantum Hall state necessarily implies a gapless phase, which has identical topological response to a noninteracting Weyl semimetal, but is distinct from it. Here, this may be viewed as a generalization (in a weaker form) of the known duality between a noninteracting two-dimensional Dirac fermion and QED 3 to 3+1 dimensions. In addition we discuss a (3+1)-dimensional topologically ordered state, obtained by gapping a nodal line semimetal without breaking symmetries.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Integrity of the Plasma Magnetic Nozzle

This report examines the physics governing certain aspects of plasma propellant flow through a magnetic nozzle, specifically the integrity of the interface between the plasma and the nozzle s magnetic field. The injection of 100s of eV plasma into a magnetic flux nozzle that converts thermal energy into directed thrust is fundamental to enabling 10 000s of seconds specific impulse and 10s of kW/kg specific power piloted interplanetary propulsion. An expression for the initial thickness of the interface is derived and found to be approx.10(exp -2) m. An algorithm is reviewed and applied to compare classical resistivity to gradient-driven microturbulent (anomalous) resistivity, in terms of the spatial rate and time integral of resistive interface broadening, which can then be related to the geometry of the nozzle. An algorithm characterizing plasma temperature, density, and velocity dependencies is derived and found to be comparable to classical resistivity at local plasma temperatures of approx. 200 eV. Macroscopic flute-mode instabilities in regions of "adverse magnetic curvature" are discussed; a growth rate formula is derived and found to be one to two e-foldings of the most unstable Rayleigh-Taylor (RT) mode. After establishing the necessity of incorporating the Hall effect into Ohm s law (allowing full Hall current to flow and concomitant plasma rotation), a critical nozzle length expression is derived in which the interface thickness is limited to about 1 ion gyroradius.

Gerwin, Richard A.↗

Boundary-layer development and transition due to free-stream exothermic reactions in shock-induced flows

A study of the effect of free-stream thermal-energy release from shock-induced exothermic reactions on boundary-layer development and transition is presented. The flow model is that of a boundary layer developing behind a moving shock wave in two-dimensional unsteady flow over a shock-tube wall. Matched sets of combustible hydrogen-oxygen-nitrogen mixtures and inert hydrogen-nitrogen mixtures were used to obtain transition data over a range of transition Reynolds numbers from 1,100,000 to 21,300,000. The heat-energy is shown to significantly stabilize the boundary layer without changing its development character. A method for application of this data to flat-plate steady flows is included.

Hall, J. L.↗

Characterization of Hollow Cathode Performance and Thermal Behavior

Hollow cathodes are one of the main life-limiting components in ion engines and Hall thrusters. Although state-of-the-art hollow cathodes have demonstrated up to 30,352 hours of operation in ground tests with careful handling, future missions are likely to require longer life, more margin and greater resistance to reactive contaminant gases. Three alternate hollow cathode technologies that exploit different emitter materials or geometries to address some of the limitations of state-of-the-art cathodes are being investigated. Performance measurements of impregnated tungsten-iridium dispenser cathodes at discharge currents of 4 to 15 A demonstrated that they have the same operating range and ion production efficiency as conventional tungsten dispenser cathodes. Temperature measurements indicated that tungsten-iridium cathodes also operate at the same emitter temperatures. They did not exhibit the expected reduction in work function at the current densities tested. Hollow cathodes with lanthanum hexaboride emitters operated over a wide current range, but suffered from lower ion production efficiency at currents below about 12.4 A because of higher insert heating requirements. Differences in operating voltages and ion production rates are explained with a simple model of the effect of cathode parameters on discharge behavior.

ion engines↗

Synthesis of nanograined zirconium diboride microsphere powder feedstock via emulsification of suspensions

Ceramic nanograined materials have desirable characteristics compared to their macroparticle counterparts but are rarely used in industrial applications due to issues with poor handleability and health hazards. Due to interparticle forces that become more dominant as the particle size decreases, it is difficult to use nanomaterials to fill dies, spread on surfaces, or flow through hoppers found in various manufacturing processes. In this work, we report a scalable gelcasting solution and unique emulsification process to create microspheres composed of nanoscale powders to enhance the flowability and handleability of nanomaterials. The gelcasting solution and emulsification process can be used with any nanoparticle composition that can be suspended in a liquid phase. This paper reports the effects of various parameters on zirconium diboride microsphere formation, such as surfactant content and mixing conditions. The microspheres maintain the nano-scale characteristics of the powder but improve its flowability by using cross-linked polyvinyl alcohol to combine irregularly shaped zirconium diboride nanoparticles with a particle diameter of 60 nm into larger spherical particles with a d 50 ~25 μm. This hierarchical feedstock engineering design combine the positive characteristics of materials across both length scales and improve the flowability of the feedstock from a Hausner Ratio of 1.56 to 1.19. The materials produced using this technique can be used in thermal plasma spray, die filling for hot pressing or spark plasma sintering, and binder jet printing applications.

36 MATERIALS SCIENCE↗

Investigations of Spot-to-plume Mode Transition in a Hollow Cathode Discharge Using 2-D Axisymmetric Plasma Simulations

After decades of laboratory investigations that provided invaluable measurements and insight, the physics behind the transition from spot to plume modes in hollow cathodes remains one of the longest standing theoretical problems in electric propulsion. This has prohibited the development of ab initio models that allow for the prediction of the transition across different cathodes and operating conditions. Since the beginning of its development over a decade ago, simulations with the 2-D axisymmetric Orificed Cathode (OrCa2D) code have helped elucidate a wide range of processes in hollow cathode discharges. However, the code has never been used to investigate the onset of plume mode. We present results from the first OrCa2D simulations of a 25-A LaB6 cathode for a range of flow rates (5-20 sccm) in which transition from spot to plume modes is known to occur. The cathode in this study was one of the two technologies considered for the 12.5 kW Hall Effect Rocket with Magnetic Shielding (HERMeS) and operates nominally at 21 A and 14.8 sccm. The simulations capture the characteristic rise of the peak-to-peak amplitude in the keeper voltage oscillations and underscore the significance of the plume neutral gas in the transition. The plasma inside the cathode is found to be relatively quiescent throughout the transition, in agreement with previous experimental observations. The computed keeper voltage fluctuations at low flow rates (<8 sccm) are found to be driven by oscillations of the same frequency in the plasma plume with the following main characteristics: (1) they are of low frequency (<10 kHz), and associated with small longitudinal motion in the direction of the applied magnetic field, (2) they occur in a region of the plume where the neutral gas provided by the cathode has been fully depleted, and (3) they have a (small) wave velocity of about 100 m/s, which is at least ~10 smaller than the drift, thermal and acoustic speeds of the ions. At 8 sccm, when the transition to the large-amplitude oscillations begins, the ionization frequency in the neutral-depleted plume region ranges ~2-100 kHz. The frequency of the oscillations in the plasma (and keeper voltage) is found to be equal to the ionization frequency (~5 kHz) at the center of this region. The findings suggest that the transition to plume mode is driven by ionization processes in the near-plume of the cathode, in line with previous conjectures that were based solely on laboratory observations.

Polk, James E.↗

Modeling Cyclic Phase Change and Energy Storage in Solar Heat Receivers

Numerical results pertaining to cyclic melting and freezing of an encapsulated phase change material (PCM), integrated into a solar heat receiver, have been reported. The cyclic nature of the present melt/freeze problem is relevant to latent heat thermal energy storage (LHTES) systems used to power solar Brayton engines in microgravity environments. Specifically, a physical and numerical model of the solar heat receiver component of NASA Lewis Research Center's Ground Test Demonstration (GTD) project was developed and results compared with available experimental data. Multi-conjugate effects such as the convective fluid flow of a low-Prandtl-number fluid, coupled with thermal conduction in the phase change material, containment tube and working fluid conduit were accounted for in the model. A single-band thermal radiation model was also included to quantify reradiative energy exchange inside the receiver and losses through the aperture. The eutectic LiF-CaF2 was used as the phase change material (PCM) and a mixture of He/Xe was used as the working fluid coolant. A modified version of the computer code HOTTube was used to generate results for comparisons with GTD data for both the subcooled and two-phase regimes. While qualitative trends were in close agreement for the balanced orbit modes, excellent quantitative agreement was observed for steady-state modes.

Hall, Carsie A., III↗

Anomalous magnetothermoelectric behavior in massive Dirac materials

Extensive studies of electron transport in Dirac materials have shown positive magnetoresistance (MR) and positive magnetothermopower (MTP) in a magnetic field perpendicular to the excitation current or thermal gradient. In contrast, measurements of electron transport often show a negative longitudinal MR and negative MTP for a magnetic field oriented along the excitation current or thermal gradient; this is attributed to the chiral anomaly in Dirac materials. In this paper, we report a very different magnetothermoelectric transport behavior in the massive Dirac material ZrTe5. Although thin flakes show a commonly observed positive MR in a perpendicular magnetic field, distinct from other Dirac materials, we observe a sharp negative MTP. In a parallel magnetic field, we still observe a negative longitudinal MR, however, a remarkable positive MTP is observed for the fields parallel to the thermal gradients. Our theoretical calculations suggest that this anomalous magnetothermoelectric behavior can be attributed to the screened Coulomb scattering. This work demonstrates the significance of impurity scattering in the electron transport of topological materials and provides deep insight into the magnetotransport phenomena in Dirac materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DME-to-Propane Mixture Effects on a Light Duty Compression Ignition Engine

Fuels that can be produced in a sustainable manner are of high interest because they can provide an essential step toward net zero emissions vehicles. This study examines the combustion of two such fuels, Dimethyl Ether (DME) and propane, in a compression ignition, 4-cylinder, 2.2L engine running with mixtures of DME-to-Propane ranging of 100%-0%, 85%-15%, 75%-25%, and 65%-35% by weight. Testing was conducted at 2000rpm - 100Nm, an important representative point in the FTP certification cycle. For each fuel mixture, conditions tested include sweeps of boost, EGR and injection pressure. Here, tests are mainly conducted at a constant combustion timing with CA10 of -1 deg with respect to TDC, with an engine controller combustion feedback system based on in-cylinder sampling of pressure. Trends of NOx, HC, and CO are similar for the range of DME-to-propane, from 100%-0% to 75%-25%. Boost and injection pressures had the most notable impact on the heat release traces. Higher boost, from stoichiometric to lean resulted in approximately a 3-5% increase on cycle efficiency. Fuel injection pressures resulted in about 1% gain per 200bar. Results also illustrated that EGR is effective in reducing NOx but causes notable degradation of cycle efficiency. The emissions for DME-propane mixtures with 65%-35% had a different trend, with CO and HC exceeding the runs with lower propane content by 2 to 3-fold. As propane content increases, the pressure rise rates become higher, and with 65%-35% mixtures, rates easily exceed 12bar/deg. The increased rise rates correlate with early injection timings but the rates can be reduced, with higher boost and lower injection pressures. The result of the approach, however, leads to lower thermal efficiencies, decreasing efficiency by over 5% between neat DME and the highest propane ratios.

Combustion and combustion processes↗

Effects of cesium ions and cesium vapor on selected ATS-F samples

Thermal control coating samples were subjected to cesium ion beam and vapor exposures. Degradation of solar absorptance and infrared emittance were measured. Solar cells and samples selected from surfaces on the ATS-F spacecraft likely to experience ion or vapor impingement were bombarded by 10-volt cesium ions. Other samples were subjected to high levels of cesium vapor. Aluminum and white paint were backsputtered by 550-volt cesium ions onto selected samples. For direct bombardment, the threshold for ion-induced property changes was above five-thousand trillion ions/sq cm. With material sputtered from a 450-sq cm target onto samples 36 cm distant, the threshold for noticeable effects was above 5 times 10 to the 17-th power ions/sq cm.

Kemp, R. F.↗

Effects of electrostatic rocket material deposited on solar cells.

If solar arrays on solar-electric spacecraft protrude into the exhaust hemisphere of the electric thrusters, they will receive fluxes (usually small) of both propellant and accelerator grid atoms. Unlike propellants, grid materials have low vapor pressures and will not reevaporate. An analysis is presented of degradation in the optical, thermal, and electrical performance of solar cells resulting from thin deposits of grid material (aluminum and molybdenum) on various array surfaces. The classical optical theory of thin films, heat balance equations, and a typical relationship for solar cell efficiency vs temperature are used to compute curves showing optical properties, temperature, and power output as functions of film thickness. The results compare favorably with available experimental data. It is shown that a few monolayers of metal deposition on the illuminated surface will seriously degrade cell performance. A means of estimating the arrival rate of these materials is provided.

Kemp, R. F.↗

Synthesis, Stability, and Magnetic Properties of Antiperovskite Co 3 PdN

Experimental synthesis and characterization of theoretically predicted compounds are important steps in the materials discovery pipeline. Here, we report on the synthesis of Co 3 PdN, which was recently predicted to be a stable magnetic antiperovskite. The Co 3 PdN thin films were grown by reactive sputtering and were confirmed to form in an antiperovskite crystal structure. The thermal stability of the compound is demonstrated up to 600 K by in situ X-ray diffraction, though the phase persists at slightly higher temperatures (700 K) in an air-free magnetometer. Both ab initio calculations and magnetization measurements find Co 3 PdN to be ferromagnetic with an experimentally determined Curie temperature of T C = 560 ± 5 K. The saturation magnetization of 1.2 μ B /Co found in the experiment is slightly lower than the 1.7 μ B /Co value expected by theory. A narrow magnetic hysteresis loop with a coercive field of 100 Oe at low temperature suggests that Co 3 PdN might be useful in electronic applications requiring fast switching of the magnetization vector. While prior prediction of Co 3 PdN showed a gapped electronic band structure for each spin channel, we show that this was due to incomplete sampling of Brillouin zone paths and that band crossings exist along R-X|M and X|M-R paths. The metallic nature of Co 3 PdN is further confirmed by temperature-dependent transport measurements, which also show a considerable anomalous Hall effect. Altogether, this work represents an appreciable step toward understanding the synthesis, structure, stability, and properties of a new magnetic material.

14 SOLAR ENERGY↗

exoALMA. V. Gaseous Emission Surfaces and Temperature Structures

An analysis of the gaseous component in protoplanetary disks can inform us about their thermal and physical structure, chemical composition, and kinematic properties, all of which are crucial for understanding various processes within the disks. By exploiting the asymmetry of the line emission, or via line profile analysis, we can locate the emitting surfaces. Here, we present the emission surfaces of the exoALMA sources in 12 CO J = 3–2, 13 CO J = 3–2, and CS J = 7–6. We find that 12 CO traces the upper disk atmosphere, with mean $\langle$ z/r $\rangle$ values of ≈0.28, while 13 CO and CS trace lower regions of the disk with mean $\langle$ z/r $\rangle$ values of ≈0.16 and ≈0.18, respectively. We find that 12 CO $\langle$ z/r $\rangle$ and the disk mass are positively correlated with each other; this relationship offers a straightforward way to infer the disk mass. We derive 2D r – z temperature distributions of the disks. Additionally, we search for substructure in the surfaces and radial intensity profiles; we find evidence of localized substructure in the emission surfaces and peak intensity profiles of nearly every disk, with this substructure often being coincident between molecular tracers, intensity profiles, and kinematic perturbations. Four disks display evidence of potential photodesorption, implying that this effect may be common even in low far-ultraviolet star-forming regions. For most disks, we find that the physical and thermal structure is more complex than analytical models can account for, highlighting a need for more theoretical work and a better understanding of the role of projection effects on our observations.

79 ASTRONOMY AND ASTROPHYSICS↗

Development of an All-Aqueous Thermally Regenerative Redox Flow Battery to Support Fossil Fuel Assets

Low-temperature thermal energy, a largely untapped resource, holds significant promise for large-scale electrical power generation globally. Various stationary sources, including industrial entities and thermal power plants, emit considerable low-temperature heat that currently remains unutilized. This energy is often overlooked because its low temperature renders it unsuitable for efficient power generation using conventional methods. However, current research is exploring diverse technologies capable of converting low-temperature heat into grid-scale power, aiming to enhance grid efficiency, further decarbonization initiatives, and facilitate a shift toward more decentralized power systems. One such innovative technology is the thermally regenerative battery (TRB), noted for its high power and energy densities compared to similar technologies, positioning it as a potential game-changer in power generation. TRBs integrate two scalable and well-established unit operations: a redox flow battery and a distillation column. This integration suggests that once an effective TRB chemistry is established, the pathway to commercialization could be expedited. The copper-based thermally regenerative ammonia battery (Cu aq -TRAB) stands out as the first TRB that circumvents electrodeposition/dissolution reactions, stabilizing Cu(I) and Cu(II) within the electrolyte and maintaining stability of all electroactive species in an aqueous phase. This stabilization has led to improvements in coulombic efficiency, open circuit potential, and copper solubility, thereby enhancing power density, energy density, and overall energy efficiency. Preliminary tests were conducted to determine the effects of various electrolyte species on the performance metrics of the battery, both theoretically and experimentally. These tests revealed that the solubility of copper in the Cu aq -TRAB electrolyte was constrained by the Cu(I)-NH 3 complex. Adjusting the background electrolyte to 5 M NH4Br and the ligand concentration to 4 M NH 3 enabled the copper concentration to reach a maximum of 0.6 M. This modification led to an estimated theoretical maximum energy density of 9.5 Wh L -1 for the Cu aq -TRAB. Additionally, full cell testing indicated a tradeoff between peak power and energy density with varying copper and ammonia concentrations. Increasing the applied current density during discharge linearly raised the average power output, with a minimal reduction in energy density due to a balance between higher ohmic overpotential and reduced time for undesirable ammonia crossover. Furthermore, a comprehensive numerical sensitivity analysis of the complete Cu aq -TRAB system was performed. This analysis aimed to assess how the battery and the distillation column responded to changes in system input parameters, providing insights into optimal research directions for enhancing system performance. The analysis revealed that at room temperature, battery power was significantly more sensitive to ohmic losses than to mass transfer, with reaction rates having minimal impact. This trend continued even at higher temperatures. Also, the thermal energy required for ammonia separation was studied, showing that increased temperatures generally reduced energy requirements, except in low-pressure scenarios above 65 °C. An investigation into membrane performance in the Cu aq -TRAB was undertaken, given the significant impact of ammonia transport control and ohmic losses on system performance. Various membranes were evaluated to identify key performance metrics. Among the tested membranes, Selemion CMVN exhibited the highest performance, with a peak power density of 84 mW cm -2 and average values of 26 ± 6.8 mW cm -2 for power density and 2.9 Wh L -1 for energy density at an applied current density of 50 mA cm -2 . An economic assessment indicated a levelized cost of storage at $410 per MWh under optimal conditions, highlighting the commercial potential of the Cu aq -TRAB when utilizing cost-effective, readily available materials.

25 ENERGY STORAGE↗

Neutron Transmission Imaging with a Portable D-T Neutron Generator

Fast-neutron transmission imaging provides complementary information to x-ray transmission imaging. While fast neutron imaging resolution is generally below x-ray imaging, 14-MeV neutrons have an advantage over portable x-ray systems. Neutrons have higher transmission through high-Z materials due to a more uniform attenuation as a function of material atomic number Z compared to X-rays, and can therefore image low-Z materials inside high-Z materials. As a result, portable neutron transmission imaging has many applications, including inspection of concrete and welds for corrosion in vehicles, bridges, and other infrastructure, measurement of material levels in containers, and inspection of suspicious packages. Fast-neutron imaging is also more practical for field use than thermal-neutron imaging due to the size and shielding requirements typical of thermal-imaging systems compared to the availability of small 14.1 MeV D-T neutron generators. However, there are limitations in portable fast-neutron imaging systems, including limited neutron output, limited light produced by neutron scintillators, and lower resolution due to neutron source spot size and 2-3 mm scintillator thickness. In addition, digital-panel dark-noise is roughly 100x higher than neutron scintillator light, and variations in noise across the panel and in time is comparable to the imaging signal. Here we discuss recent efforts in developing a portable fast-neutron radiography system, including an improved neutron scintillator, mitigation of panel noise, and new commercial portable D-T neutron generators. We also present MCNP efforts to model neutron imaging, including scintillator resolution and the effects of neutron scattering from the object and surrounding materials.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Topological orders of monopoles and hedgehogs: From electronic and magnetic spin-orbit coupling to quarks

Topological states of matter are, generally, quantum liquids of conserved topological defects. We establish this by constructing and analyzing topological field theories which introduce gauge fields to describe the dynamics of singularities in the original field configurations. In this work, homotopy groups are utilized to identify topologically protected singularities, and the conservation of their protected number is captured by a topological action term that unambiguously obtains from the given set of symmetries. Stable phases of these theories include quantum liquids with emergent massless Abelian and non-Abelian gauge fields, as well as topological orders with long-range quantum entanglement, fractional excitations, boundary modes, and unconventional responses to external perturbations. This paper focuses on the derivation of topological field theories and basic phenomenological characterization of topological orders associated with homotopy groups π n (S n ), n ≥ 1 . These homotopies govern monopole and hedgehog topological defects in d = n + 1 dimensions, and enable the generalization of both weakly interacting and fractional quantum Hall liquids of vortices to d > 2 . Hedgehogs have not been in the spotlight so far, but they are particularly important defects of magnetic moments because they can be stimulated in realistic systems with spin-orbit coupling, such as chiral magnets and d = 3 topological materials. We predict topological orders in systems with U(1) × Spin(d) symmetry in which fractional electric charge attaches to hedgehogs. Monopoles, the analogous defects of charge or generic U(1) currents, may bind to hedgehogs via Zeeman effect, or effectively emerge in purely magnetic systems. The latter can lead to spin liquids with different topological orders than that of the resonant valence bond spin liquid. Charge fractionalization of quarks in atomic nuclei is also seen as possibly arising from the charge-hedgehog attachment.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗