A semi-implicit dispersive thin-wire finite-difference time-domain (FDTD) scheme is proposed for fast analysis of waveguide metamaterials. The proposed scheme is based on combining the Newmark-beta ...method with Mäkinen's improved thin-wire FDTD model based on the contour-path integral of Maxwell's equations around a wire corrected with scaling factors and Wait's surface-impedance boundary condition for thin wires of finite conductivity. Its stability condition is determined by only the two meshes in the transverse plane to the wire axis. This feature allows using larger mesh steps than a wire radius without time step reducing. In order to verify the scheme, we demonstrate four device applications: plasmonic parallel-plate waveguide filled with only positive dielectrics, edge Fabry-Pérot resonator, waveguide metatronic high-pass filter, and coaxial-to-waveguide matching with an epsilon-near-zero narrow channel. Its stability, accuracy, and computational efficiency are assessed in comparison with the standard FDTD explicit scheme, analytical solutions, and existing experimental data.
The hybrid implicit-explicit single-field finite-difference time-domain (HIE-SF-FDTD) method based on the wave equation of electric field is reformulated in a concise matrix-vector form. The global ...approximation error of the scheme is discussed theoretically. The second-order convergence of the HIE-SF-FDTD is numerically verified.
The electromagnetic coupling of a charged particle beam with vacuum chambers is of great interest for beam dynamics studies in the design of a particle accelerator. A deep learning-based method is ...proposed as a mesh-free numerical approach for solving the field of space charges of a particle beam in a vacuum chamber. Deep neural networks based on the physical model of a relativistic particle beam with transversally nonuniform charge density moving in a vacuum chamber are constructed using this method. A partial differential equation with the Lorentz factor, transverse charge density, and boundary condition is embedded in its loss function. The proposed physics-informed neural network method is applied to round, rectangular, and elliptical vacuum chambers. This is verified in comparison with analytical solutions for coupling impedances of a round Gaussian beam and an elliptical bi-Gaussian beam. The effects of chamber geometries, charge density, beam offset, and energy on the beam coupling impedance are demonstrated.
The electromagnetic interaction of a charged particle beam with multilayer vacuum chambers is of particular interest in accelerator physics. This paper presents a deep learning-based approach for ...calculating electromagnetic fields generated by the beam in infinitely long multilayer vacuum chambers with arbitrary cross section. The presented approach is based on physics-informed neural networks and the surface impedance boundary condition of a multilayer structure derived from the transmission line theory. Deep neural networks (DNNs) are utilized to approximate the solution of partial differential equations (PDEs) describing the physics of electromagnetic fields self-generated by a charged particle beam traveling in a particle accelerator. A residual network is constructed from the output of DNNs, the PDEs and boundary conditions are embedded into the loss function and differential operators are calculated using the automatic differentiation. As a result, the presented approach is regarded to be mesh-free. The approach is applied to circular and elliptical vacuum chambers with a three-layer structure. It is verified in comparison with the recently proposed boundary element method. The effects of chamber geometries and multilayer structure on the beam coupling impedance are demonstrated.
This letter presents a complex-frequency shifted perfectly matched layer (CFS-PML) formulation for the partially implicit Magnetically-mixed Newmark-Leapfrog finite-difference time-domain (MNL-FDTD) ...method. Its formulation is based on time-dependent Maxwell's equations in CFS-PML media and the auxiliary differential equation (ADE) of PML auxiliary variables. In the PML region, the efficiency of auxiliary variable terms of the formulated scheme is same as that of Roden's convolutional PML for Yee's FDTD. It is demonstrated that reflection error of MNL-FDTD with CFS-PML is comparable to those of the conventional explicit and implicit FDTDs with CFS-PML.
A two-dimensional boundary element method for calculating the impedance of infinitely long cryogenic vacuum chambers of general cross section is presented. The formulation is based on combining ...Kirchhoff’s boundary integral representation of an electromagnetic field with the surface impedance boundary condition for the anomalous skin effect, which can occur in metals at cryogenic temperature. As a result, the electromagnetic field in the chamber is expressed as a superposition of the direct and indirect space charge fields and resistive-wall wakefield. This feature allows us to compute the corresponding three impedance contributions separately. This method does not assume a specific transverse charge density such as uniform and Gaussian distributions as well as the ultrarelativistic approximation. A technique for computing the impedances and the form factors in the method is also described. The presented method is applied to circular, rectangular, elliptical, and racetrack-type vacuum chambers. The geometric effect of the cryogenic vacuum chamber cross section on the resistive-wall impedance is shown. The effect of beam velocity is demonstrated for the racetrack-type cryogenic vacuum chamber.
In this letter, the implicit Newmark-Beta formulation is partially and magnetically introduced into the explicit leapfrog scheme of Yee's finite-difference time-domain (Yee-FDTD) method in general ...orthogonal grids. We describe a partially implicit three-dimensional (3-D) FDTD formulation with directionally implicit time updating only for magnetic field and the conventional explicit time updating for electric field. The time discrete electric and magnetic field quantities are updated in a slightly modified leapfrog manner. Interestingly, the resulting 3-D scheme can be reduced to the conventional Yee-FDTD scheme when the Newmark parameter is chosen as zero. Its stability condition is more relaxed than the Courant-Friedrichs-Lewy stability condition of the Yee-FDTD, and the spatial mesh size in a specific direction on general orthogonal grids can be eliminated. This feature allows us to efficiently analyze electromagnetic field problems with fine structures in one spatial direction on general orthogonal grids. In order to validate the presented formulation, its applications to 3-D simulations of canonical cavity resonator problems with cylindrical and spherical grids are demonstrated.
The defining characteristic
of Cooper pairs with finite centre-of-mass momentum is a spatially modulating superconducting energy gap Δ(r), where r is a position. Recently, this concept has been ...generalized to the pair-density-wave (PDW) state predicted to exist in copper oxides (cuprates)
. Although the signature of a cuprate PDW has been detected in Cooper-pair tunnelling
, the distinctive signature in single-electron tunnelling of a periodic Δ(r) modulation has not been observed. Here, using a spectroscopic technique based on scanning tunnelling microscopy, we find strong Δ(r) modulations in the canonical cuprate Bi
Sr
CaCu
O
that have eight-unit-cell periodicity or wavevectors Q ≈ (2π/a
)(1/8, 0) and Q ≈ (2π/a
)(0, 1/8) (where a
is the distance between neighbouring Cu atoms). Simultaneous imaging of the local density of states N(r, E) (where E is the energy) reveals electronic modulations with wavevectors Q and 2Q, as anticipated when the PDW coexists with superconductivity. Finally, by visualizing the topological defects in these N(r, E) density waves at 2Q, we find them to be concentrated in areas where the PDW spatial phase changes by π, as predicted by the theory of half-vortices in a PDW state
. Overall, this is a compelling demonstration, from multiple single-electron signatures, of a PDW state coexisting with superconductivity in Bi
Sr
CaCu
O
.
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