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Finite-difference time-domain methods

The finite-difference time-domain (FDTD) method is a widespread numerical tool for full-wave analysis of electromagnetic fields in complex media and for detailed geometries. Applications of the FDTD method cover a range of time and spatial scales, extending from subatomic to galactic lengths and from classical to quantum physics. Technology areas that benefit from the FDTD method include biomedicine — bioimaging, biophotonics, bioelectronics and biosensors; geophysics — remote sensing, communications, space weather hazards and geolocation; metamaterials — sub-wavelength focusing lenses, electromagnetic cloaks and continuously scanning leaky-wave antennas; optics — diffractive optical elements, photonic bandgap structures, photonic crystal waveguides and ring-resonator devices; plasmonics — plasmonic waveguides and antennas; and quantum applications — quantum devices and quantum radar. This Primer summarizes the main features of the FDTD method, along with key extensions that enable accurate solutions to be obtained for different research questions. Additionally, hardware considerations are discussed, plus examples of how to extract magnitude and phase data, Brillouin diagrams and scattering parameters from the output of an FDTD model. Furthermore, the Primer ends with a discussion of ongoing challenges and opportunities to further enhance the FDTD method for current and future applications.

42 ENGINEERING↗

A Fast and Accurate Reduced-Order Model for High-Intensity Transferred Arc Discharges

Arc discharges are widely used in welding, plasma smelting, and other industrial processes, where variations in operating conditions strongly affect arc stability, temperature distribution, and energy transfer. Accurate modeling of these phenomena typically requires computationally expensive high-fidelity simulations. This study presents a hierarchy of three arc discharge models with progressively reduced physical fidelity. The high-fidelity model provides a fully physics-resolved reference, the reduced-order model reproduces the dominant thermal and flow characteristics of the arc with reasonable accuracy, and the Elenbaas-Heller model captures key trends in a simplified, rapid formulation. This hierarchy demonstrates that reduced-order model can effectively balance predictive fidelity and computational efficiency, providing practical tools for arc simulation and parametric studies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Shielding the Quantum Realm: Technical Considerations for Maintaining a Stable and Secure Radio Frequency Environment for Quantum Research

Advancements in quantum technology, which include quantum computing, quantum sensing, quantum communications, and associated research, continue to revolutionize various fields of study by solving challenging problems deemed too difficult or more efficient than those used for classical computers. However, as these systems become ever so complex, it is critical to secure their electromagnetic operational environments and the associated impact on quantum systems and infrastructure. The goal of this synopsis is to bring attention to the susceptibility of quantum technology facilities to potential issues related to the radio frequency (RF) environment within the broader electromagnetic context. A framework is proposed for identifying, mitigating, monitoring, and auditing these often complex operational environments. By establishing best practices in the consideration and evaluation of these criteria, one can enhance the operational integrity, resilience, and security of quantum technology systems and facilities, thereby supporting their continued development and application in research and industry.

42 ENGINEERING↗

Quantum calculations of the cavity shift in electron magnetic moment measurements

The measurement of the anomalous electron magnetic moment g – 2 through quantum transitions of a single trapped electron is the most stringent test of quantum field theory. These experiments are now so precise that they must account for the effects of the cavity containing the electron. Classical calculations of this “cavity shift” must subtract the electron’s divergent self-field, and thus require knowledge of the exact Green’s function for the cavity’s electromagnetic field. We perform the first fully quantum calculation of the cavity shift in a closed cavity, which instead involves subtracting linearly divergent cavity mode sums and integrals. Using contour integration methods, we find perfect agreement with existing classical results for both spherical and cylindrical cavities, justifying their current use. Moreover, our mode-based results can be naturally generalized to account for systematic effects, necessary to push future measurements to the next order of magnitude in precision.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Understanding the electromagnetic topology during the ohmic breakdown in tokamaks considering self-generated electric fields

We report that the physical mechanisms of the ohmic breakdown in a tokamak have been understood based on the classical Townsend avalanche theory. However, a new systematic theory (Yoo et al 2018 Nat. Commun.9 3523) recently demonstrated that electron avalanches during the ohmic breakdown are completely different from the Townsend avalanche due to strong self-generated electric fields. In this study, we elucidate the multi-dimensional effects of the self-generated electric field on plasma dynamics during the ohmic breakdown. We also propose a novel electromagnetic topology analysis method that can easily predict the overall plasma behavior and where the main plasma is generated. The topology analysis method is validated by a state-of-art particle simulation for various magnetic configurations. New physical insights into the complex electromagnetic topology would facilitate designing more reliable and optimized ohmic breakdown scenarios in future tokamaks, such as ITER and beyond.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Electromagnetic & Weak Probes: Experimental Overview

Electromagnetic and electroweak probes are the most versatile probes in the study of heavy-ion collisions. Produced at every stage in the evolution of QCD matter, its messengers are practically inert to the strongly interacting medium they travel through. In this contribution, I will discuss a selection of new results from experiments at the LHC, RHIC, and SIS facilities, spanning almost four orders of magnitude in beam energy. Finally, I will conclude with a brief overview of the experimental landscape in the near future.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Suppression of power losses during laser pulse propagation in underdense plasma slab

For current state-of-the-art terawatt lasers, the primary laser scattering mechanisms in plasma include Forward Raman Scattering (FRS), excitation of plasma waves, and the self-modulational instability (SMI). Using 2D PIC simulations, we demonstrate the dominance of the FRS in the regime with medium-to-low density plasma and non-relativistic laser fields. However, the use of multi-colored lasers with frequency detuning exceeding the plasma frequency, Δω > ω pe , suppresses the FRS. Finally, the laser power can then be transmitted efficiently.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Interaction effects in graphene in a weak magnetic field

A weak perpendicular magnetic field, B, breaks the chiral symmetry of each valley in the electron spectrum of graphene, preserving the overall chiral symmetry in the Brillouin zone. Here we explore the consequences of this symmetry breaking for the interaction effects in graphene. In particular, we demonstrate that the electron-electron interaction lifetime acquires an anomalous B dependence. Also, the ballistic zero-bias anomaly, δv(ω), where ω is the energy measured from the Fermi level, emerges at a weak B and has the form δv(B) ~ B 2 /ω 2 . Temperature dependence of the magnetic-field corrections to the thermodynamic characteristics of graphene is also anomalous. We discuss experimental manifestations of the effects predicted. The microscopic origin of the B-field sensitivity is an extra phase acquired by the electron wave function resulting from the chirality-induced pseudospin precession.

36 MATERIALS SCIENCE↗

Penrose process for a charged black hole in a uniform magnetic field

Spinning black holes create electromagnetic storms when immersed in ambient magnetic fields, illuminating the otherwise epically dark terrain. In an electromagnetic extension of the Penrose process, tremendous energy can be extracted, boosting the energy of radiating particles far more efficiently than the mechanical Penrose process. We locate the regions from which energy can be mined and demonstrate explicitly that they are no longer restricted to the ergosphere. Here we also show that there can be toroidal regions that trap negative energy particles in orbit around the black hole. We find that the effective charge coupling between the black hole and the superradiant particles decreases as energy is extracted, much like the spin of a black hole decreases in the mechanical analogue. While the effective coupling decreases, the actual charge of the black hole increases in magnitude reaching the energetically-favored Wald value, at which point energy extraction is impeded. We demonstrate the array of orbits for products from the electromagnetic Penrose process.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Enhanced tuneable rotatory power in a rotating plasma

We report that the gyrotropic properties of a rotating magnetized plasma are derived analytically. Mechanical rotation leads to a new cutoff for wave propagation along the magnetic field, and polarization rotation above this cutoff is the sum of the classical magneto-optical Faraday effect and the mechanico-optical polarization drag. Exploiting the very large effective group index near the cutoff, we expose here that polarization drag can be 10 4 larger than Faraday rotation at GHz frequency. The rotation leads to weak absorption while allowing direct frequency control, demonstrating the unique potential of rotating plasmas for nonreciprocal elements. The very large rotation frequency of a dense non-neutral plasma could enable unprecedented gyrotropy in the THz regime.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Experimental Limit on Nonlinear State-Dependent Terms in Quantum Theory

Linear time evolution is one of the fundamental postulates of quantum theory. Past theoretical attempts to introduce nonlinearity into quantum evolution have violated causality. However, a recent theory has introduced nonlinear state-dependent terms in quantum field theory, preserving causality [D. E. Kaplan and S. Rajendran, Phys. Rev. D 105, 055002 (2022)]. We report the results of an experiment that searches for such terms. Our approach, inspired by the Everett many-worlds interpretation of quantum theory, correlates a binary macroscopic classical voltage with the outcome of a projective measurement of a quantum bit, prepared in a coherent superposition state. Measurement results are recorded in a bit string, which is used to control a voltage switch. Presence of a nonzero voltage reading in cases of no applied voltage is the experimental signature of a nonlinear state-dependent shift of the electromagnetic field operator. We implement blinded measurement and data analysis with three control bit strings. Control of systematic effects is realized by producing one of the control bit strings with a classical random-bit generator. The other two bit strings are generated by measurements performed on a superconducting qubit in an IBM Quantum processor and on a N 15 nuclear spin in a nitrogen-vacancy center in diamond. Our measurements find no evidence for electromagnetic quantum state-dependent nonlinearity. We set a bound on the parameter that quantifies this nonlinearity | ε γ | < 4.7 × 10 - 11 , at 90% confidence level.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Multipole-based cable braid electromagnetic penetration model: magnetic penetration case

The goal of this paper is to present, for the first time, calculations of the magnetic penetration case of a first principles multipole-based cable braid electromagnetic penetration model. As a first test case, a one-dimensional array of perfect electrically conducting wires, for which an analytical solution is known, is investigated: we compare both the self-inductance and the transfer inductance results from our first principles cable braid electromagnetic penetration model to those obtained using the analytical solution. These results are found in good agreement up to a radius to half spacing ratio of about 0.78, demonstrating a robustness needed for many commercial and non-commercial cables. We then analyze a second set of test cases of a square array of wires whose solution is the same as the one-dimensional array result and of a rhomboidal array whose solution can be estimated from Kley's model. As a final test case, we consider two layers of one-dimensional arrays of wires to investigate porpoising effects analytically. We find good agreement with analytical and Kley's results for these geometries, verifying our proposed multipole model. Note that only our multipole model accounts for the full dependence on the actual cable geometry which enables us to model more complicated cable geometries.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The MOOSE electromagnetics module

The Multiphysics Object-Oriented Simulation Environment (MOOSE) electromagnetics module has been developed to increase MOOSE physics module capabilities, enabling standalone and coupled computational electromagnetics within the MOOSE multiphysics ecosystem. The module is actively being utilized in the areas of plasma physics and advanced manufacturing, and it currently provides initial demonstrated capability in multi-dimensional, complex-valued electromagnetic wave propagation, electrostatic contact, reflection and transmission, and electromagnetic eigenvalue problems. Two-dimensional wave propagation and one-dimensional wave reflection and transmission are showcased as examples in this work. The modularity, parallelism, and plug-in infrastructure for custom future development is inherited from MOOSE itself, and the module can be used with both MOOSE-based and external codes, giving great flexibility.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Scalable multiphoton quantum metrology with neither pre- nor post-selected measurements

The quantum statistical fluctuations of electromagnetic fields establish a limit, known as the shot-noise limit, on the sensitivity of optical measurements performed with classical technologies. However, quantum technologies are not constrained by this shot-noise limit. In this regard, the possibility of using every photon produced by quantum sources of light to estimate small physical parameters, beyond the shot-noise limit, constitutes one of the main goals of quantum optics. Here, we experimentally demonstrate a scalable protocol for quantum-enhanced optical phase estimation across a broad range of phases, with neither pre- nor post-selected measurements. This is achieved through the efficient design of a source of spontaneous parametric downconversion in combination with photon-number-resolving detection. The robustness of two-mode squeezed vacuum states against loss allows us to outperform schemes based on N00N states, in which the loss of a single photon is enough to remove all phase information from a quantum state. In contrast to other schemes that rely on N00N states or conditional measurements, the sensitivity of our technique could be improved through the generation and detection of high-order photon pairs. This unique feature of our protocol makes it scalable. Furthermore, our work is important for quantum technologies that rely on multiphoton interference such as quantum imaging, boson sampling, and quantum networks.

36 MATERIALS SCIENCE↗

A multi-dimensional Child–Langmuir law for any diode geometry

While prior theoretical studies of multi-dimensional space-charge limited current (SCLC) assumed emission from a small patch on infinite electrodes, none have considered emission from an entire finite electrode. In this paper, we apply variational calculus (VC) and conformal mapping, which have previously been used to derive analytic solutions for SCLC density (SCLCD) for nonplanar one-dimensional geometries, to obtain mathematical relationships for any multi-dimensional macroscopic diode with finite cathode and anode. We first derive a universal mathematical relationship between space-charge limited potential and vacuum potential for any diode and apply this technique to determine SCLCD for an eccentric spherical diode. We then apply VC and the Schwartz–Christoffel transformation to derive an exact equation for SCLCD in a general two-dimensional planar geometry with emission from a finite emitter. Particle-in-cell simulations using VSim agreed within 4%–13% for a range of ratios of emitter width to gap distance using the thinnest electrodes practical for the memory constraints of our hardware, with the difference partially attributed to the theory's assumption of infinitesimally thin electrodes. After generalizing this approach to determine SCLCD for any orthogonal diode as a function of only the vacuum capacitance and vacuum potential, we derive an analytical formulation of the three-dimensional Child–Langmuir law for finite parallel rectangular and disk geometries. These results demonstrate the utility for calculating SCLCD for any diode geometry using vacuum capacitance and vacuum potential, which are readily obtainable for many diode geometries, to guide experiment and simulation development.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Magnetic flux emergence in binary neutron star remnants

Using high-resolution AthenaK simulations of a twisted toroidal flux tube, we study the flux emergence of magnetic structures in the shear layer of a hot massive neutron star typical of a binary neutron star remnant. High-resolution simulations demonstrate that magnetic buoyant instabilities allow for emergence only for extremely large magnetic fields significantly exceeding 10 17 G, and more typical fields around 10 16 G are instead dominated by hydrodynamic effects. Because merger remnants tend to be stable against hydrodynamic convection, our work places strong limitations on the mechanisms by which massive binary neutron star remnants can produce the magnetically-driven outflows needed to power jets.

79 ASTRONOMY AND ASTROPHYSICS↗

Reduced-action-integral approach for photon-photon interactions in vacuum

Electromagnetic waves propagating through vacuum can polarize virtual electron–positron pairs; this polarization, in turn, nonlinearly modifies their propagation. A semi-classical nonlinear wave equation describing the propagation is derived from the Euler–Heisenberg Lagrangian density, which captures vacuum polarization effects up to the one-loop level. In this article, we present a reduced-actionintegral approach that enables rapid modeling of nonlinear phenomena arising from the Euler– Heisenberg Lagrangian. Application of the variational principle to the reduced action provides equations of motion for familiar light-pulse parameters, such as spot size, phase, polarization, and phase-front curvature, without requiring full-field simulations. Three examples demonstrate the utility of the approach: phase modulation, birefringence, and frequency mixing.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Reconfigurable plasma-dielectric hybrid photonic crystal as a platform for electromagnetic wave manipulation and computing

The introduction of 3D printing has enabled fabrication of photonic crystal devices with complex crystal structures that would be challenging to construct using other fabrication methods. In this paper, we construct and characterize a photonic crystal consisting of two 4 x 8 x 8 cubic lattices composed of spherical silicon nitride elements straddling a layer of 8 plasma discharge tubes, creating a 3D hybrid plasma photonic crystal device. Integrating under-dense gaseous plasma elements provides a unique coupling dynamic between the dielectric spheres and the cylindrical plasma discharges, creating a monolithic hybrid photonic crystal with solid state and reconfigurable elements. The device has resonant modes that have attenuation peaks that are either switchable, tunable in amplitude, or tunable in frequency with variations in plasma density. The response of these bands seen with varying plasma density is confirmed through simulations when effects due to the heating of the photonic crystal from the gaseous plasma elements are accounted for in the experiments. We discuss how this reconfigurable device may be used and expanded upon for applications in photonic artificial neural networks and optical computing systems.

3D printing↗