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At least 127 records · Page 7

A Fast Algorithm for Scanning Transmission Electron Microscopy Imaging and 4D-STEM Diffraction Simulations

Scanning transmission electron microscopy (STEM) is an extremely versatile method for studying materials on the atomic scale. Many STEM experiments are supported or validated with electron scattering simulations. However, using the conventional multislice algorithm to perform these simulations can require extremely large calculation times, particularly for experiments with millions of probe positions as each probe position must be simulated independently. Recently, the plane-wave reciprocal-space interpolated scattering matrix (PRISM) algorithm was developed to reduce calculation times for large STEM simulations. Here, we introduce a new method for STEM simulation: partitioning of the STEM probe into “beamlets,” given by a natural neighbor interpolation of the parent beams. This idea is compatible with PRISM simulations and can lead to even larger improvements in simulation time, as well requiring significantly less computer random access memory (RAM). We have performed various simulations to demonstrate the advantages and disadvantages of partitioned PRISM STEM simulations. We find that this new algorithm is particularly useful for 4D-STEM simulations of large fields of view. We also provide a reference implementation of the multislice, PRISM, and partitioned PRISM algorithms.

97 MATHEMATICS AND COMPUTING↗

Low-spin cobalt(ii) redox shuttle by isocyanide coordination

Coordination of the strong-field ligand 2,6-dimethylphenyl isocyanide (DMP-CN) to the Co(PY5Me 2 ) framework, where PY5Me 2 represents the pentadentate ligand 2,6-bis(1,1-bis(2-pyridyl)ethyl)pyridine, has resulted in a new low-spin Co(II) complex with a relatively low reorganization energy and fast electron-transfer kinetics compared to the prototypical cobalt tris-bipyridine redox shuttle, [Co(bpy) 3 ] 3+/2+ , where bpy represents 2,2'-bipyridine. Despite nearly 160 mV reduced regeneration driving force, the [Co(PY5Me 2 )(DMP-CN)]3+/2+ redox shuttle displayed an increased regeneration efficiency relative to [Co(bpy)3] 3+/2+ , however recombination losses hinder the performance as evidenced by a reduced recombination resistance. Finally, future directions point to low-spin Co(II) redox shuttles with more negative redox potentials to be paired with a dye or dye mixture that absorbs into the near infrared region.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A fast, dense Chebyshev solver for electronic structure on GPUs

Matrix diagonalization is almost always involved in computing the density matrix needed in quantum chemistry calculations. In the case of modest matrix sizes (≲4000), performance of traditional dense diagonalization algorithms on modern GPUs is underwhelming compared to the peak performance of these devices. This motivates the exploration of alternative algorithms better suited to these types of architectures. We newly derive, and present in detail, an existing Chebyshev expansion algorithm whose number of required matrix multiplications scales with the square root of the number of terms in the expansion. Focusing on dense matrices of modest size, our implementation on GPUs results in large speed ups when compared to diagonalization. Additionally, we improve upon this existing method by capitalizing on the inherent task parallelism and concurrency in the algorithm. Furthermore, this improvement is implemented on GPUs by using CUDA and HIP streams via the MAGMA library and leads to a significant speed up over the serial-only approach for smaller (≲1000) matrix sizes. Finally, we apply our technique to a model system with a high density of states around the Fermi level, which typically presents significant challenges.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Development, construction and tests of the Mu2e electromagnetic calorimeter mechanical structures

The “muon-to-electron conversion” (Mu2e) experiment at Fermilab will search for the charged lepton flavour violating neutrino-less coherent conversion of a muon into an electron in the field of an aluminum nucleus. The observation of this process would be the unambiguous evidence of the existence of physics beyond the standard model. Mu2e detectors comprise a straw-tracker, an electromagnetic calorimeter and an external veto for cosmic rays. In particular, the calorimeter provides excellent electron identification, a fast calorimetric online trigger, and complementary information to aid pattern recognition and track reconstruction. The detector has been designed as a state-of-the-art crystal calorimeter and employs 1348 pure Cesium Iodide (CsI) crystals readout by UV-extended silicon photosensors and fast front-end and digitization electronics. A design consisting of two identical annular matrices (named “disks”) positioned at the relative distance of 70 cm downstream the aluminum target along the muon beamline satisfies the Mu2e physics requirements. The hostile Mu2e operational conditions, in terms of radiation levels (total expected ionizing dose of 12 krad and a neutron fluence of 5 × 10$^{10}$ n/cm$^{2}$ @ 1 MeV$_{eq}$ (Si)/y), magnetic field intensity (1 T) and vacuum level (10$^{-4}$ Torr) have posed tight constraints on scintillating materials, sensors, electronics and on the design of the detector mechanical structures and material choice. The support structure of each 674 crystal matrix is composed of an aluminum hollow ring and parts made of open-cell vacuum-compatible carbon fiber. The photosensors and front-end electronics for the readout of each crystal are inserted in a machined copper holder and make a unique mechanical unit. The resulting 674 mechanical units are supported by a machined plate of vacuum-compatible plastic material. The plate also integrates the cooling system made of a network of copper lines flowing a low temperature radiation-hard fluid and placed in thermal contact with the copper holders to constitute a low resistance thermal bridge. The data acquisition electronics are hosted in aluminum custom crates positioned on the external lateral surface of the disks. The crates also integrate the electronics cooling system as lines running in parallel to the front-end system. In this paper we report on the calorimeter mechanical structure design, the mechanical and thermal simulations that have determined the design technological choices, and the status of component production, quality assurance tests and plans for assembly at Fermilab.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Fast and robust all-electron density functional theory calculations in solids using orthogonalized enriched finite elements

Here, we present a computationally efficient approach to perform systematically convergent real-space all-electron Kohn-Sham density functional theory calculations for solids using an enriched finite element (FE) basis. The enriched FE basis is constructed by augmenting the classical FE basis with atom-centered numerical basis functions, comprising of atomic solutions to the Kohn-Sham problem. Notably, to improve the conditioning, we orthogonalize the enrichment functions with respect to the classical FE basis, without sacrificing the locality of the resultant basis. In addition to improved conditioning, this orthogonalization procedure also renders the overlap matrix block diagonal, greatly simplifying its inversion. Subsequently, we use a Chebyshev polynomial based filtering technique to efficiently compute the occupied eigenspace in each self-consistent field iteration. We demonstrate the accuracy and efficiency of the proposed approach on periodic unit cells and supercells. The benchmark studies show a staggering 130× speedup of the orthogonalized enriched FE basis over the classical FE basis. We also present a comparison of the orthogonalized enriched FE basis with the linearized augmented plane-wave + local orbitals basis, both in terms of accuracy and efficiency. Notably, we demonstrate that the orthogonalized enriched FE basis can handle large system sizes of ~10 000 electrons. Finally, we observe good parallel scalability of our implementation with 92% efficiency at 22× speedup for a system with 620 electrons

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Accounting for electron-beam-induced warping of molecular nanocrystals in MicroED structure determination

High-energy electrons induce sample damage and motion at the nanoscale to fundamentally limit the determination of molecular structures by electron diffraction. Using a fast event-based electron counting (EBEC) detector, we characterize beam-induced, dynamic, molecular crystal lattice reorientations (BIRs). These changes are sufficiently large to bring reciprocal lattice points entirely in or out of intersection with the sphere of reflection, occur as early events in the decay of diffracted signal due to radiolytic damage, and coincide with beam-induced migrations of crystal bend contours within the same fluence regime and at the same illuminated location on a crystal. These effects are observed in crystals of biotin, a series of amino acid metal chelates, and a six-residue peptide, suggesting that incident electrons inevitably warp molecular lattices. The precise orientation changes experienced by a given microcrystal are unpredictable but are measurable by indexing individual diffraction patterns during beam-induced decay. Reorientations can often tilt a crystal lattice several degrees away from its initial position before irradiation, and for an especially beam-sensitive Zn(II)-methionine chelate, are associated with dramatic crystal quakes prior to 1 e − Å −2 electron beam fluence accumulates. Since BIR coincides with the early stages of beam-induced damage, it echoes the beam-induced motion observed in single-particle cryoEM. As with motion correction for cryoEM imaging experiments, accounting for BIR-induced errors during data processing could improve the accuracy of MicroED data.

Vlahakis, Niko (ORCID:0000000250920265)↗

Machine Learning Training for HOM reduction and Emittance Preservation in a TESLA-type Cryomodule at FAST

Low emittance electron beams are of high importance at facilities like the LCLS-II at SLAC. Emittance dilution effects due to off-axis beam transport for a TESLA-type cryomodule (CM) have been shown at the Fermilab Accelerator Science and Technology facility. The results showed the correlation between the electron beam-induced cavity high-order modes (HOMs) and submacropulse centroid slewing and oscillation downstream of the CM. Mitigation of emittance dilution can be achieved by reducing the HOM signals and the variances in the submacropulse beam positions downstream of the CM. Here we present a Machine Learning based optimization and model construction for HOM signal level reduction using Neural Networks and Gaussian Processes. To gather training data we performed experiments using single bunch and 50 bunch electron beams with charges up to 125 pC/b. We measured HOM signals of all cavities and beam position with a set of BPMs downstream of the CM. The beam trajectory was changed using V/H125 corrector set located upstream of the CM. The results presented here will inform the LCLS-II injector commissioning and will serve as a prototype for HOM reduction and emittance preservation.

43 PARTICLE ACCELERATORS↗

An integrated approach to examine fuel-cladding chemical interaction in HT9/U-10Zr metallic fast reactor fuels: Coupling machine learning with electron microscopy and local mechanical properties analysis

The metallic U-Zr nuclear fuel alloy has garnered renewed interest as a promising candidate for next-generation sodium-cooled fast reactors. Recent studies and technology assessments have identified several areas requiring improvements, enhanced knowledge, and reliable data to strengthen the U-Zr fuel design basis for qualification and commercial applications. One of the most challenging phenomena impacting this fuel system’s performance is fuel-cladding chemical interaction (FCCI). This work aimed to harvest FCCI data by examining selected HT9/U-10Zr (wt. %) fuel samples of prototypic full-length fuel pins through an integrated approach. This approach integrated scanning electron microscopy (SEM) microstructure characterization with localized mechanical properties examination to deepen understanding of FCCI phenomenon in HT9/U-10Zr fuel system. Particularly, this study focused on MFF fuel pins irradiated at Fast Flux Test Facility (FFTF), which aimed to qualify metallic fuel as a driver fuel for FFTF and to assess its viability for larger-scale fast reactors. Electron microscopy provided high confidence in detecting and distinguishing the different FCCI layers, while small-scale mechanical testing (SSMT) probed the mechanical properties of these layers. SEM examination of a MFF-2 pin 192167, with a time averaged inner cladding temperature (TICT) slightly over 500°C, revealed minimal cladding-side FCCI (cladding wastage). In contrast, significantly thicker cladding wastage comprising two distinct sublayers was observed in samples from the thermally hot MFF-3 pin 193045 and MFF-5 pin 195011 where the TICT ranged from 610-635°C. SSMT indicated complete embrittlement in the sublayer adjacent to the fuel and a tendency toward embrittlement in the other sublayer. Additionally, a new machine learning method was developed, validated, and used to quantify cladding wastage thickness. The machine learning method reliably predicted the wastage thickness across various fuel pins and sample cross-sections. Furthermore, the available cladding wastage data from HT9/U-10Zr fuel system demonstrated a strong temperature dependency. However, the dataset remains small, and ongoing research activities are essential to further understand the FCCI phenomenon and develop a reliable FCCI model for enhanced fuel performance simulation under various conditions.

36 - MATERIALS SCIENCE↗

Fast correlation heating in moderately coupled electron–ion plasmas

If the electrons in a plasma are suddenly heated, the resulting change in Debye shielding causes the ion kinetic energy to quickly increase. For the first time, this correlation heating , which is much faster than collisional energy exchange, is rigorously derived for a moderately coupled, electron–ion plasma. The electron–ion mass ratio is taken to be the smallest parameter in the Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy, smaller even than the reciprocal of the plasma parameter. This ordering differs from conventional kinetic theory by making the electron collision rates faster than the ion plasma frequency, which allows stronger coupling and makes the ion heating a function only of the total energy supplied to the electrons. The calculation uses known formulae for correlations in a two-temperature plasma, for which a new, elementary derivation is presented. Suprathermal ions may be created more rapidly by this mechanism than by ion–electron Coulomb collisions. This means that the use of a femtosecond laser pulse could potentially help to achieve ignition in certain fast ignition approaches to inertial confinement fusion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Suppression of the vacuum space-charge effect in fs-photoemission by a retarding electrostatic front lens

The performance of time-resolved photoemission experiments at fs-pulsed photon sources is ultimately limited by the e–e Coulomb interaction, downgrading energy and momentum resolution. Here, we present an approach to effectively suppress space-charge artifacts in momentum microscopes and photoemission microscopes. A retarding electrostatic field generated by a special objective lens repels slow electrons, retaining the k-image of the fast photoelectrons. The suppression of space-charge effects scales with the ratio of the photoelectron velocities of fast and slow electrons. Fields in the range from -20 to 01100 V/mm for E kin = 100 eV to 4 keV direct secondaries and pump-induced slow electrons back to the sample surface. Ray tracing simulations reveal that this happens within the first 40 to 3 μm above the sample surface for E kin = 100 eV to 4 keV. An optimized front-lens design allows switching between the conventional accelerating and the new retarding mode. Time-resolved experiments at E kin = 107 eV using fs extreme ultraviolet probe pulses from the free-electron laser FLASH reveal that the width of the Fermi edge increases by just 30 meV at an incident pump fluence of 22 mJ/cm2 (retarding field -21 V/mm). For an accelerating field of +2 kV/mm and a pump fluence of only 5 mJ/cm 2 , it increases by 0.5 eV (pump wavelength 1030 nm). At the given conditions, the suppression mode permits increasing the slow-electron yield by three to four orders of magnitude. The feasibility of the method at high energies is demonstrated without a pump beam at E kin = 3830 eV using hard x rays from the storage ring PETRA III. The approach opens up a previously inaccessible regime of pump fluences for photoemission experiments.

47 OTHER INSTRUMENTATION↗

Quantitative time-resolved diagnostics of electric field dynamics during individual plasma breakdown events using burst laser pulse electric field induced second harmonic generation

In plasma discharges, the acceleration of electrons by a fast varying electric field and the subsequent collisional electron energy transfer determines the plasma dynamics, chemical reactivity, and breakdown. Current in situ electric field measurements require reconstruction of the temporal profile over many observations. However, such methods are unsuitable for non-repetitive and unstable plasmas. Here, in this paper, we present a method for creating “movies” of dynamic electric fields in a single acquisition at sample rates of 500 × 10 6 fps. This ultrafast diagnostic was demonstrated in radio frequency electric fields between two parallel plates in air, as well as in Ar nanosecond-pulsed single-sided dielectric barrier discharges.

42 ENGINEERING↗

A Compton transmission polarimeter for DC and SRF electron photo-injectors

The production of high-current and intense spin polarized electron beams is of great importance in electron-based facilities. Tests are planned to produce such beams in 2023 using GaAs-based photocathodes installed in the Brookhaven National Lab RHIC Coherent electron Cooling superconducting radiofrequency (SRF) photogun [1]. A fast and efficient electron polarimeter operating in the MeV energy range is required to measure the beam spin polarization. While Mott polarimeters provide larger measured asymmetries, a Compton Transmission polarimeter is well suited in the few MeV energy range. In this work, we report on a relatively compact and cost-effective Compton transmission polarimeter which has been built and calibrated at Jefferson Lab (JLab). First, we present the design of the polarimeter radiator, polarized target analyzing magnet, BGO detector assembly and data acquisition system. Next, results of a two-week commissioning study performed at the JLab Upgraded Injector Test Facility will be described. Here, a well-known polarized electron beam produced from a bulk GaAs photocathode in a dc high-voltage photogun was first measured in a 180 keV Mott scattering polarimeter, then used to characterize and calibrate the Compton transmission polarimeter as a function of the polarized target magnetization and beam properties. Finally, we report an effective analyzing power of the Compton polarimeter and compare experimental results with those produced via Geant4 simulations.

Blume, G.↗

A Compton transmission polarimeter for DC and SRF electron photo-injectors

The production of high-current and intense spin polarized electron beams is of great importance in electron-based facilities. Tests are planned to produce such beams in 2023 using GaAs-based photocathodes installed in the Brookhaven National Lab RHIC Coherent electron Cooling superconducting radiofrequency (SRF) photogun [1]. A fast and efficient electron polarimeter operating in the MeV energy range is required to measure the beam spin polarization. While Mott polarimeters provide larger measured asymmetries, a Compton Transmission polarimeter is well suited in the few MeV energy range. In this work, we report on a relatively compact and cost-effective Compton transmission polarimeter which has been built and calibrated at Jefferson Lab (JLab). First, we present the design of the polarimeter radiator, polarized target analyzing magnet, BGO detector assembly and data acquisition system. Next, results of a two-week commissioning study performed at the JLab Upgraded Injector Test Facility will be described. Here, a well-known polarized electron beam produced from a bulk GaAs photocathode in a dc high-voltage photogun was first measured in a 180 keV Mott scattering polarimeter, then used to characterize and calibrate the Compton transmission polarimeter as a function of the polarized target magnetization and beam properties. Finally, we report an effective analyzing power of the Compton polarimeter and compare experimental results with those produced via Geant4 simulations.

Blume, G.↗

Achieving stable all-solid-state lithium-metal batteries by tuning the cathode-electrolyte interface and ionic/electronic transport within the cathode

All-solid-state batteries with sulfide electrolytes and high-nickel layered oxide cathodes attract much interest due to their high specific energy. However, their cycling performance is primarily influenced by the interface between the sulfide electrolyte and the high-Ni layered oxide particles, which requires the use of composite cathodes with high ionic and electronic conductivities to achieve a kinetically stable interface inside the cathode. Here, we apply Ti 2 O 3 particles to the high-Ni cathode LiNi 0.8 Co 0.1 Mn 0.1 O 2 (NCM811), where Ti 2 O 3 not only acts as an electronic conductor to provide a fast diffusion path for electrons in the composite cathode, but also absorbs the lattice oxygen released from NCM811 cathode during cycling, stabilizing the Li 6 PS 5 Cl/NCM811 interface and suppressing electrolyte oxidation. The as-modified cathode exhibits an initial specific capacity of 192 mAh g -1 and retains 166 mAh g -1 after 140 cycles at 0.1C rate with a good capacity retention of 86.5%. Furthermore, the composite cathode displays high rate capability even at 1C rate. By contrast, the unmodified Li 6 PS 5 Cl/NCM811 cathode shows poor cycling performance with only 130 mAh g -1 remaining after 130 cycles. This work provides a new direction for the design of cathodes for all-solid-state batteries that can deliver high specific energy with long cycle life.

25 ENERGY STORAGE↗

Observation of high-pressure polymorphs in bulk silicon formed at relativistic laser intensities

Silicon polymorphs with exotic electronic and optical properties have recently attracted significant attention due to their wide range of useful band gap characteristics. They are typically formed by static high-pressure techniques, which limits the crystal structures that can be made. This constitutes a major obstacle to study these polymorphs and their incorporation into existing technology. Approaches have attempted to address this shortcoming through using dynamic conditions and chemical precursor materials. Here, we report on an approach to create unusual crystal structures deep in the bulk of a silicon crystal by irradiating it with a laser pulse at ultrarelativistic intensity of up to 7.5 × 10 19 W/ c m 2 . Laser-generated electrons with MeV energy swiftly penetrate the target with speed close to the speed of light and deposit their energy into a large volume across the whole thickness of the sample. The relativistic electron current creates, via branching propagation and ionization, high-energy-density conditions for thermodynamically nonequilibrium phase transformation paths into new crystal polymorphs. X-ray microdiffraction and synchrotron x-ray diffraction analyses indicate, along with conventional dc-Si, the presence of exotic silicon structures in the bulk of the laser intact target volume. These structures are identified as body-centered bc8-Si, rhombohedral r8-Si, hexagonal-diamond hd-Si, and the tetragonal Si-VIII, all phases of Si that have previously been made through static techniques. Additionally, simple-tetragonal st12-Si and body-centered tetragonal bt8-Si were observed along with signatures of not yet identified diffraction spots. Both st12-Si and bt8-Si have only been observed in ultrafast laser microexplosion conditions at much lower laser intensity ∼ 10 14 W/ c m 2 and within a micron-thin surface layer. The findings here are supported by direct observation of nanoparticles with high-resolution transmission electron microscopy and corresponding fast Fourier transform analysis of their interatomic distances. The presented analyses of absorbed laser energy, generation of the MeV electron current, and deposition of energy across the whole target thickness provide a solid basis for drawing the conclusion that the observed silicon polymorphs were produced because of laser-generated high-energy electrons fast-penetrating deeply into the bulk of silicon. In contrast to solid-solid transformations, the plasma-solid transitions offer a paradigm for the creation of exotic, high-energy density materials inside the bulk of the sample by using laser pulses at relativistic intensities. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Methods to Calculate Electronic Excited-State Dynamics for Molecules on Large Metal Clusters with Many States: Ensuring Fast Overlap Calculations and a Robust Choice of Phase

Here, we present an efficient set of methods for propagating excited-state dynamics involving a large number of configuration interaction singles (CIS) or Tamm-Dancoff approximation (TDA) single-reference excited states. Specifically, (i) following Head-Gordon et al., we implement an exact evaluation of the overlap of singly-excited CIS/TDA electronic states at different nuclear geometries using a biorthogonal basis and (ii) we employ a unified protocol for choosing the correct phase for each adiabat at each geometry. For many-electron systems, the combination of these techniques significantly reduces the computational cost of integrating the electronic Schrodinger equation and imposes minimal overhead on top of the underlying electronic structure calculation. As a demonstration, we calculate the electronic excited-state dynamics for a hydrogen molecule scattering off a silver metal cluster, focusing on high-lying excited states, where many electrons can be excited collectively and crossings are plentiful. Interestingly, we find that the high-lying, plasmon-like collective excitation spectrum changes with nuclear dynamics, highlighting the need to simulate non-adiabatic nuclear dynamics and plasmonic excitations simultaneously. In the future, the combination of methods presented here should help theorists build a mechanistic understanding of plasmon-assisted charge transfer and excitation energy relaxation processes near a nanoparticle or metal surface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Asynchronous Grid Connections Providing Fast-Frequency Response: System Integration Study

This paper presents an integration study for the recent power electronic-based fast-frequency response technology, "asynchronous grid connection" which operates as an aggregator for behind-the-meter resources and distributed generators. Both technical feasibility and techno-economic viability studies are presented. The fast-frequency response characteristics, validated against Power Hardware-in-the-Loop experiments, are integrated into an IEEE 9- bus system in DigSilent PowerFactory for system-level dynamic analysis. It demonstrates that droop-based control enhancements to local distributed generators allow their aggregation to provide grid-supporting functionalities and participate in the ancillary service markets. To this end, a long-term simulation embedding the system within the ancillary service market framework of PJM has been performed. The fast-frequency response regulation is subsequently used to calculate the potential revenue and project the results on a 15-year investment horizon. Finally, the techno-economic analysis provides recommendations for enhancements to access the full potential of distributed generators on a technical and regulatory level.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Interface-induced fast Li+ transport in mixed ionic–electronic conductors

Interfacial instability between lithium metal and solid-state electrolytes limits the performance of all-solid-state lithium metal batteries (ASSLBs), leading to parasitic reactions, non-uniform Li+ flux, and dendrite growth. Here, we develop a composite interlayer composed of the anti-perovskite Li2OHCl0.75Br0.25 (AP) and carbon nanotubes (CNTs) to enhance both interfacial stability and ionic transport. The AP–CNT interlayer exhibits enhanced Li+ conductivity arising from interfacial electron transfer from AP to CNTs, which generates a built-in electric field that facilitates Li+ migration. Lithium symmetric cells incorporating this interlayer achieve a high critical current density of 2.4 mA cm−2 at 55 °C. This design integrates chemical robustness with coupled ion–electron transport, offering a generalizable strategy for safe, dendrite-free, and high-performance ASSLBs.

He, Chenche↗