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136 records · Page 8

APT Flash Lamps for a New Laser at LLNL Memo

Each flashlamp is supported coaxially within a pyrex water-jacket tube by two identical connector assemblies, one at each end. These connector assemblies not only support the flashlamp mechanically, but also provide source and return pathways for flashlamp DI cooling water and for electrical current. At each end of the flashlamp, the (presumably) tungsten feed-through rod that supports the electrode is attached to a connector assembly through a Multilam fitting. O rings seated on the outside of each connector assembly form a water-tight seal between the connector assembly and the inside of the pyrex water-jacket tube. During operation, DI cooling water enters the tube located at the end of one of the connectors, flows over that connector’s Multilam fitting, flows through a ring of holes in the connector assembly and then flows into the 1-mm gap between the flashlamp and the pyrex water-jacket tube. After passing over the length of the flashlamp, the water flows through the connector assembly at the opposite end of the flashlamp and exits through that connector assembly’s end tube. Electrical pulses are delivered to the flashlamp through the tubes coming out of the connector assemblies.

42 ENGINEERING↗

Technology Demonstration Missions

Technology Demonstration Missions (TDM) is in its third year of execution, being initiated in 2010 and baselined in January of 2012. There are 11 projects that NASA Marshall Space Flight Center (MSFC) has contributed to or led: (1) Evolvable Cryogenics (eCryo): Cyrogenic Propellant Storage and Transfer Engineering Development Unit (EDU), a proof of manufacturability effort, used to enhance knowledge and technology related to handling cryogenic propellants, specifically liquid hydrogen. (2) Composites for Exploration Upper Stage (CEUS): Design, build, test, and address flight certification of a large composite shell suitable for the second stage of the Space Launch System (SLS). (3) Deep Space Atomic Clock (DSAC): Spaceflight to demo small, low-mass atomic clock that can provide unprecedented stability for deep space navigation. (4) Green Propellant Infusion Mission (GPIM): Demo of high-performance, green propellant propulsion system suitable for Evolved Expendable Launch Vehicle (EELV) Secondary Payload Adapter (ESPA)-class spacecraft. (5) Human Exploration Telerobotics (HET): Demonstrating how telerobotics, remote control of a variety of robotic systems, can take routine, highly repetitive, dangerous or long-duration tasks out of human hands. (6) Laser Communication Relay Demo (LCRD): Demo to advance optical communications technology toward infusion into deep space and near Earth operational systems, while growing the capabilities of industry sources. (7) Low Density Supersonic Decelerator (LDSD): Demo new supersonic inflatable decelerator and parachute technologies to enable Mars landings of larger payloads with greater precision at a wider range of altitudes. (8) Mars Science Laboratory (MSL) Entry Descent & Landing Instrumentation (MEDLI): Demo of embedded sensors embedded in the MSL heat shield, designed to record the heat and atmospheric pressure experienced during the spacecraft's high-speed, hot entry in the Martian atmosphere. (9) Solar Electric Propulsion (SEP): 50-kW class spacecraft that uses flexible blanket solar arrays for power generation and an electric propulsion system that delivers payload from low-Earth orbit to higher orbits. (10) Solar Sail Demonstration (SSD): Demo to validate sail deployment techniques for solar sails that are propelled by the pressure of sunlight. (11) Terrestrial HIAD Orbit Reentry (THOR): Demo of a 3.7-m Hypersonic Inflatable Aerodynamic Decelerator (HIAD) entry vehicle to test second generation aerothermal performance and modeling.

McDougal, John↗

Cosmic axions revealed via amplified modulation of the ellipticity of a laser

We propose a new axion dark matter detection strategy that employs optical readout of laser beam ellipticity modulations caused by axion-induced electric fields in a microwave cavity, using electro-optic (EO) crystals, enhanced by externally injected radio-frequency (rf) power. Building upon the variance-based probing method [Phys. Rev. D 107, 103005 (2023).], we extend this concept to the optical domain: A weak probe laser interacts with an EO crystal coupled to the resonant microwave cavity field at cryogenic temperatures, and the axion-induced electric field is revealed through induced ellipticity. The injected rf signal coherently interferes with that of the axion field, amplifying the optical response and significantly improving sensitivity. While our EO-based method employs a Fabry-Pérot resonator, we do not require Michelson interferometers. Our method, hence, enables compact, high-frequency axion searches, across the 0.5–50 GHz range. Operating at cryogenic temperatures not only suppresses thermal backgrounds, but, critically, allows the probing method to mitigate the quantum noise. This approach offers a scalable path forward for axion detection over the ∼(few−200) μ⁢eV mass range—covering the preferred parameter space for the postinflationary Peccei-Quinn axion dark matter—using compact, tunable systems.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Advanced Space Propulsion

This presentation describes a number of advanced space propulsion technologies with the potential for meeting the need for dramatic reductions in the cost of access to space, and the need for new propulsion capabilities to enable bold new space exploration (and, ultimately, space exploitation) missions of the 21st century. For example, current Earth-to-orbit (e.g., low Earth orbit, LEO) launch costs are extremely high (ca. $10,000/kg); a factor 25 reduction (to ca. $400/kg) will be needed to produce the dramatic increases in space activities in both the civilian and government sectors identified in the Commercial Space Transportation Study (CSTS). Similarly, in the area of space exploration, all of the relatively 'easy' missions (e.g., robotic flybys, inner solar system orbiters and landers; and piloted short-duration Lunar missions) have been done. Ambitious missions of the next century (e.g., robotic outer-planet orbiters/probes, landers, rovers, sample returns; and piloted long-duration Lunar and Mars missions) will require major improvements in propulsion capability. In some cases, advanced propulsion can enable a mission by making it faster or more affordable, and in some cases, by directly enabling the mission (e.g., interstellar missions). As a general rule, advanced propulsion systems are attractive because of their low operating costs (e.g., higher specific impulse, ISD) and typically show the most benefit for relatively 'big' missions (i.e., missions with large payloads or AV, or a large overall mission model). In part, this is due to the intrinsic size of the advanced systems as compared to state-of-the-art (SOTA) chemical propulsion systems. Also, advanced systems often have a large 'infrastructure' cost, either in the form of initial R&D costs or in facilities hardware costs (e.g., laser or microwave transmission ground stations for beamed energy propulsion). These costs must then be amortized over a large mission to be cost-competitive with a SOTA system with a low initial development and infrastructure cost and a high operating cost. Note however that this has resulted in a 'Catch 22' standoff between the need for large initial investment that is amortized over many launches to reduce costs, and the limited number of launches possible at today's launch costs. Some examples of missions enabled (either in cost or capability) by advanced propulsion include long-life station-keeping or micro-spacecraft applications using electric propulsion or BMDO-derived micro-thrusters, low-cost orbit raising (LEO to GEO or Lunar orbit) using electric propulsion, robotic planetary missions using aerobraking or electric propulsion, piloted Mars missions using aerobraking and/or propellant production from Martian resources, very fast (100-day round-trip) piloted Mars missions using fission or fusion propulsion, and, finally, interstellar missions using fusion, antimatter, or beamed energy. The NASA Advanced Propulsion Technology program at the Jet Propulsion Laboratory (JPL) is aimed at assessing the feasibility of a range of near-term to far term advanced propulsion technologies that have the potential to reduce costs and/or enable future space activities. The program includes cooperative modeling and research activities between JPL and various universities and industry; and directly supported independent research at universities and industry. The cooperative program consists of mission studies, research and development of ion engine technology using C60 (Buckminsterfullerene) propellant, and research and development of lithium-propellant Lorentz-force accelerator (LFA) engine technology. The university/industry-supported research includes modeling and proof-of-concept experiments in advanced, high-lsp, long-life electric propulsion, and in fusion propulsion.

Frisbee, Robert H.↗

Manufacturing Supply Chain Development for Modular Solar-Thermochemical Conversion Platform - CRADA 387 (Final Report)

Modular chemical process intensification (MCPI) is an emerging field where chemical processing is performed using small-scale modular equipment instead of conventional large centralized chemical plants. Conventional chemical plants benefit from economies of scale that encourage scale-up to ever larger plants. A goal of MCPI is to develop technology that intensifies processing so that equipment can be dramatically smaller and integrated into modular systems. Scale-up occurs by adding more modules in parallel rather than making the equipment larger. A key concept is that equipment and modules can ultimately be cheaper by leveraging economies of mass production, analogous to the automotive industry, in manufacturing the equipment. This project made significant progress toward this outcome by meeting the RAPID institute metric to reduce equipment cost by 20% for each doubling in manufacturing volume. The MCPI application was thermochemical technology that is being commercialized by STARS Technology Corporation, one of the CRADA partners. The technology converts solar and renewable power to chemical energy to produce renewable hydrogen, fuels, and chemicals. The benefit to the public is reduction in greenhouse gases that are contributing to climate change. The project transitioned the steam methane reforming (SMR) reactor from conventional fabrication methods to additive manufacturing (AM) direct metal laser sintering (DMLS) process. This is projected to reduce the cost of making a reactor by 58% when producing 100 reactors per year. Innovations in the DMLS process produced a patented design that reduces reactor weight by 60%. Reductions in material costs and processing time extend the DMLS advantage to higher production volumes. The new design promises to be 38% cheaper than the conventional processes at 1000 units per year. The resulting 87% reduction in the steam methane reforming (SMR) module cost in scaling from current costs meets the RAPID metric. The project was successful in producing and testing the first ever additively manufactured SMR reactors. A reactor achieved over 82% efficiency in converting electric power to chemical energy, which is a world record for an inductively heated SMR. The project has contributed to the design and assembly of a first demonstration plant that is headed to a hydrogen bus filling station in Thousand Palms, CA.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Diagnostics: Chapter 8 of the special issue: on the path to tokamak burning plasma operation

This chapter presents the activity conducted by the ITPA topical group (TG) on Diagnostics over about the last 15 years. Following a general introduction of the ITER Diagnostics led by their measurement roles, the document is organized in several subchapters detailing the design support, research and development activity conducted by each of the specialist working groups (WGs) of the TG. Please note that the magnetic diagnostics were supported at the TG without a specific WG. Their status is included in the general introduction. In the following some highlights of the subchapter’s contents are provided. Recent advances in ITER first wall (FW) diagnostics for the measurements of plasma-metallic wall interaction in support of the ITER research plan are reported. An InfraRed imaging Video Bolometer for ITER has been developed and tested on several tokamaks to measure the radiated power loss. A laser-induced breakdown spectroscopy (LIBS) technique which utilizes a pulsed laser beam to ablate locally by forming a crater, will measure local tritium inventory in the FW material. Real-time Residual Gas Analyzers will measure the neutral gas composition in a divertor port and an equatorial port during plasma operation. Due to the full metallic FW environment, the plasma-wall interaction in ITER will face several challenges such as the compromised radiated power and divertor heat flux measurements by reflection. Ray tracing and analysis codes have been developed to eliminate and correct the effects of reflection in the measurements. The characteristics of the reflecting surfaces depending on the roughness and angle of the incidence have been measured by dedicated experiments, and the results were applied to the reflection elimination. For the measurement of the metallic impurity radiation induced by eroded metallic atoms, a vacuum ultraviolet spectrometer has been developed and tested. An extensive thermonuclear diagnostic suite will be required to support the operation of ITER and the planned experimental program for future burning plasma experiments. Due to the harsh environmental conditions, the implementation of diagnostic systems in ITER is a major challenge. These conditions include high levels of neutron and gamma fluxes, neutron heating, particle bombardment. Therefore, the selection and design of diagnostic systems must take into account a number of phenomena previously unseen in diagnostic design. For this reason, the measurement of neutrons and confined or lost fast ions, with particular emphasis on alpha particles, is critical to ITER. The diagnostics associated with these measurements will be important for future plasma-burning experiments at ITER. The high neutron emission and very large plasma size in ITER make neutron diagnostics the main diagnostic method used to measure plasma parameters such as fusion power, fusion power density, ion temperature, energy of fast ions and their spatial distributions in the plasma core. Active spectroscopy techniques are methods where a neutral particle beam is injected into the plasma and information on plasma parameters is extracted from the measurement of line emission resulting from the beam-plasma interaction, either by plasma ions or by beam atoms. Spatial localization is achieved by crossing the beamline and multiple observation lines. The ITER plasma will be a high temperature, moderately dense, fully ionized collisional plasma. The plasma facing surfaces are principally metallic being fashioned from beryllium or tungsten but many other elements, arising from either structural or from operational needs, may enter this plasma. The energy range of the emitted photons range from meV (infra-red) to multi keV (x-rays) and originate from all areas of the plasma volume. The primary role of passive emission diagnostics is to identify what is in the plasma from spectral signatures. Extracting quantitative information from these measurements such as impurity content, ion temperature, rotation, degree of detachment and radiated power depends on calibrated instruments, a physics model of the atomic and molecular processes and plasma transport and an analysis workflow that takes into account environmental effects such as reflections. The particular needs for ITER have prompted a multi-machine, many-year effort to address all these aspects and this chapter reviews the work on diagnostic design, experiments and new analysis techniques. An overview of the laser diagnostics to be implemented on ITER is also provided in this paper. This includes descriptions of the Thomson scattering in the core, edge and divertor regions, polarimetry and interferometry diagnostics used for measuring plasma density and also measurements of helium density in the divertor using Laser Induced Flourescence. Techniques which can allow improvements on current measurements are also addressed in particular expanding poloidal polarimetry measurements to measure field fluctuations and proposed use of dispersion interferometery which has a number of advantages over existing methods. This paper identifies particular areas where further research and testing on existing tokamaks is useful even at this advanced stage to inform the design of diagnostics for ITER. Outstanding areas of concern for the implementation of laser diagnostics, in particular with a view to reliable operation are identified. An overview of the latest developments of microwave diagnostic systems and techniques is given. The primary focus is the contributions for ITER—the next step burning plasma experiment—which is supplemented by describing recent progress of techniques applicable for fusion experiments beyond ITER. The contributions are intentionally kept concise, and are being supplemented by a rich list of references for further studies. Radiation induced effects are receiving continuous and well-deserved attention of the ITER diagnostic community and they are in many cases one of the primary design drivers of the ITER diagnostic systems. The paper summarizes recent progress in this area focusing primarily on the ITER diagnostics but in some cases provides also outlook for the possible solutions for even more demanding radiation environment of fusion reactors beyond ITER. Despite advancements in the area of modeling and simulation of various radiation induced effects, experimental testing in a nuclear environment as close as possible to the target one is still seen as unavoidable for proper qualification of particular diagnostic functional elements. Recent advancement within three diagnostic areas: optical diagnostics, magnetics and bolometers is covered. Encouraging results on qualification of silica glass vacuum window assemblies are presented. In the area of magnetic sensors, progress of irradiation tests performed on ITER in-vessel LTCC inductive sensors is presented with outlook for novel technological approaches to inductive sensors utilizing thick printing and photolithography technologies being highlighted. Summary of advancements in the area of steady state magnetic field sensors based on Hall effect is given. New results of neutron irradiation test of the ITER borosilicate glass inserts for vacuum electrical feedthroughs are summarized finding negligible swelling at target level of neutron fluence. Off-line irradiation tests of fiber optic current sensors for plasma current measurement demonstrated that both for gamma doses up to 5 MGy and a total neutron fluence up to 10 15 cm −2 , radiation induced changes are still compatible with required measurement accuracy on ITER. The ITER bolometers are given as an example how considering radiation effects may influence the diagnostic design. Finally, outlook for future main R&D directions is outlined. All optical and laser-based diagnostics in ITER will be using mirrors to guide plasma radiation toward detectors, cameras and sensors. In the hostile plasma, radiation and particle environment the optical characteristics of diagnostic mirrors will degrade directly affecting the entire performance of involved diagnostic systems. An assessment of factors affecting mirror performance is provided. Among the prime adverse factors are deposition of plasma impurities, sputtering of mirror surface and steam ingress in the vicinity of mirrors. Within the International Tokamak Physics Activity with active support by ITER central team and domestic agencies, the structured research and development (R&D) program on mitigation of risks for diagnostic mirrors is underway. Within this program the mirror material development, the passive mitigation of mirror degradation by using diagnostic ducts and shutters along with an active mirror recovery program comprising the in-situ mirror cleaning and calibration is underway. Recent developments in diagnostic mirror R&D are described in this Chapter along with an example of their implementation of R&D solutions in ITER Infrared Thermography diagnostic. An assessment of still open engineering and physics questions, considerations on mirror risks during an early phase of ITER operation are given along with an overview of diagnostic mirror evolution in the late ITER operation stage toward the demonstration fusion power plant. Several crucial areas of diagnostic R&D outlined in ITER Research Plan are addressed. The basic control groups in a fusion reactor can be broken-down in five categories: (1) plasma position, magnetic configuration, and plasma current control, (2) profile control and confinement optimization, (3) MHD control and suppression, (4) edge dissipation control, radiation and plasma exhaust control and (5) break-down optimization. These categories are coupled via the physics (a control action in one domain will affect the other domains) and via shared actuators (e.g. ECRH for impurity accumulation avoidance, current density distribution control and MHD suppression). Consequently, a supervisory control system should determine the priority of the various control tasks, their couplings, and the interfaces with the safety and interlock system. For the systematic development of the various controllers taking the complexity of the plasma and the control system into account, a model-based approach is required. A short historical overview is given of the developments in systems and control theory and control engineering with special emphasis on those developments that are most relevant for Nuclear Fusion research and operation. An overview is given of the state of the field of fusion plasma control for the control categories. It will be shown how synthetic diagnostics are being developed in ITER and how they are used in diagnostic design and design validation and how they can be in model-based controller synthesis using relatively simple models. In modern control methods, multiple diagnostics are used to constrain relatively simple models. The constrained models provide an estimate for the state. This opens the route to state controllers, such as model predictive control. A major challenge in nuclear fusion research is the coherent combination of data from heterogeneous diagnostics and modeling codes for machine control and safety as well as physics studies. Measured data from different diagnostics often provide information about the same subset of physical parameters. Additionally, information provided by some diagnostics might be needed for the analysis of other diagnostics. A joint analysis of complementary and redundant data allows, e.g. to improve the reliability of parameter estimation, to increase the spatial and temporal resolution of profiles, to obtain synergistic effects, to consider diagnostics interdependencies and to find and resolve data inconsistencies. Physics-based modeling and parameter relationships provide additional information improving the treatment of ill-posed inversion problems. A coherent combination of all kind of available information within a probabilistic framework allows for improved data analysis results. The concept of integrated data analysis (IDA) in the framework of Bayesian probability theory is outlined and contrasted with conventional data analysis. Components of the probabilistic approach are summarized and specific ingredients beneficial for data analysis at fusion devices are discussed.

ITER↗

Structural and Electrocatalytic Studies of Pulsed Laser Deposited Epitaxial RuO 2 Thin Films

Two sets of high-quality epitaxial ruthenium oxide (RuO 2 ) thin films with different thicknesses were synthesized in situ on cost-competitive sapphire substrates by using a pulsed laser deposition technique. The first set of films, with a thickness of 40 nm and a sheet resistance of 15.7 Ω/□, was prepared using 2100 laser pulses, while the second set of films, with a thickness of 87 nm and a sheet resistance of 6.7 Ω/□, was prepared using 4800 laser pulses. All other deposition parameters were kept the same. The post-deposition structural and morphological measurements showed that both sets of films grew at the same growth rate, had the same crystallinity, similar grain boundary density, and slightly different surface roughness. The thicker RuO 2 films achieved an overpotential of 280 mV for the oxygen evolution reaction at a current density of 100 μA/cm 2 , comparable to or exceeding the performance of films grown on more expensive substrates. Comparatively, the thinner RuO 2 films, which have a significantly higher charge transfer resistance (250 Ω versus 100 Ω for thick films), display a higher overpotential of 320 mV. These results indicate that the lower electrical resistance of thicker films promotes charge transfer through the film body, leading to superior electrocatalytic properties.

charge-transfer↗

Spatial Mapping of Valence Excited-State Landscapes Using Time-Resolved Shake-Down Spectroscopy

Time-resolved X-ray photoelectron spectroscopy (XPS) is used to track the photodissociation dynamics of 2-iodothiophene following 262 nm excitation. The transient XPS features include both direct ionization of the initially populated excited states and pronounced satellite peaks arising from shake-down processes. While the direct ionization signals exhibit only minimal energy shifts during C−I bond cleavage, the shake-down transitions undergo a substantial, 5 eV, shift over the reaction coordinate. By correlating these shifts with simulated C−I bond lengths, a direct structural mapping is established that reveals the exceptional sensitivity of shake-down channels to molecular geometry. These results demonstrate that shake-down transitions provide a new and powerful probe of ultrafast structural dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Development of a Comprehensive Two-Phase Flow Database for the Validation of NEK-2P

Three-dimensional (3-D) two-phase Computational Fluid Dynamics (CFD) codes are emerging as a powerful and potentially practical tool for applications in which detailed local flow information is needed. However, two-phase flow models and associated closure relations are not well established for CFD applications, which is partly due to the lack of high-quality validation data. The main objective of this work is to develop a comprehensive database of two-phase flows that can be used to validate two-phase CFD codes such as NEK-2P. In this project, four advanced local measurement systems, including Particle Image Velocimetry and Planar Laser-Induced Fluorescence (PIV-PLIF), high-speed imaging, x-ray densitometry, and multi-sensor conductivity probe are employed to measure the local two-phase flow parameters of both gas and liquid phases. By combining these techniques, the local void fraction, bubble velocity, interfacial area concentration, bubble frequency, liquid velocity, turbulence intensity, etc., in various two-phase flow regimes can be obtained. These local measurement techniques are first used in a 25.4 mm circular pipe test section. Seven air-water two-phase flow conditions spanning the bubbly, slug, churn-turbulent, and annular flow regimes are measured in this facility. The obtained database contains the radial profiles of both gas- and liquid-phase parameters at three axial locations along the test section. The second facility used in this work contains a 30 mm × 10 mm rectangular test section, in which three two-phase flow and two single-phase flow conditions are measured. Two-dimensional distributions of local two-phase flow parameters in the cross-sectional plane are measured in this facility at three axial locations as well. A facility featuring a 3×3 electrically heated rod bundle is also designed and being constructed in this project. This facility is specially designed for optical measurements and is expected to provide high-quality boiling data in the future. Preliminary analyses have been performed for the data taken in the 25.4 mm circular pipe. Both center-peaked and wall-peaked void fraction profiles have been observed in the data depending on the two-phase flow conditions and/or developing lengths. The 1-D drift-flux model was evaluated with the newly obtained datasets, in which both gas- and liquid-phases data were directly measured. The distribution parameter model has been optimized based on a new void-profile classification method proposed in this study. The optimized drift-flux model shows a significant improvement in predicting both gas velocity and void fraction. The measured liquid-phase turbulence was used to benchmark Sato’s turbulence model considering the bubble-induced shear stress for the three tested bubbly flows. The benchmark results showed good agreement between the PIV measurements and model predictions. In the bubbly flows tested that have low void fractions less than 3%, the effect of the bubble-induced turbulence was found not significant. However, the bubble-induced shear stress becomes important with the increase of the void fraction. The Conjugate Heat Transfer (CHT) model was developed and implemented in NEK-2P. This model allows the coupled simulation of the solid domain and two-phase fluid domain, allowing the specification of realistic boundary conditions. The CHT implementation was verified first with non-boiling simulations. The predicted temperatures in the fluid domain were shown to be identical in simulations with or without the CHT model. The CHT model was then validated through simulations of three Becker benchmark CHF tests performed under both Dryout (DO) and Departure from Nucleate Boiling (DNB) conditions. Reasonably good agreement was obtained between calculated wall temperatures and corresponding experimental data.

42 ENGINEERING↗

Charge radii and electromagnetic moments of 214−218 Bi : Exploring the “southern” border of the 𝑍 > 82 octupole-deformation region

The changes in the mean-squared charge radii relative to 209 Bi 126 (𝛿⁢⟨𝑟 2 ⟩ 𝑁,126 ) and the magnetic dipole and electric quadrupole moments in 214−218 Bi have been measured using the in-source resonance-ionization spectroscopy technique at ISOLDE (CERN). Magnetic moments of odd-odd bismuth nuclei have been analyzed by the additivity relation. Previous tentative spin-parity and configuration assignments based on the 𝛽-decay feeding patterns have been supported. A normal odd-even staggering in charge radii of bismuth isotopes with 𝑁>126 has been observed. The new data for the 𝛿⁡⟨𝑟 2 ⟩ of bismuth isotopes allow a study of the isotonic dependencies in the charge radii, revealing jumps in 𝛿⁢⟨𝑟 2 ⟩ 132,126 and 𝛿⁢⟨𝑟 2 ⟩ 134,126 at 𝑍 = 84. This pattern could be explained by a sudden onset of octupole deformation at 𝑁 = 132 and 134 when going from polonium (𝑍 = 84) to astatine (𝑍 = 85).

fundamental symmetries↗