Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · physics/0606156

Boundary-integral method for poloidal axisymmetric AC magnetic fields

J. Priede·G. Gerbeth
View original source ↗Read source document ↗Export metadata ↓

Abstract

This paper presents a boundary-integral equation (BIE) method for the calculation of poloidal axisymmetric magnetic fields applicable in a wide range of ac frequencies. The method is based on the vector potential formulation and it uses the Green's functions of Laplace and Helmholtz equations for the exterior and interior of conductors, respectively. The work is particularly focused on a calculation of axisymmetric Green's function for the Helmholtz equation which is both simpler and more accurate compared to previous approaches. Three different approaches are used for calculation of the Green's function depending on the parameter range. For low and high dimensionless ac frequencies we use a power series expansion in terms of elliptical integrals and an asymptotic series in terms of modified Bessel functions of second kind, respectively. For the intermediate frequency range, Gauss-Chebyshev-Lobatto quadratures are used. The method is verified by comparing with the analytical solution for a sphere in a uniform external ac field. The application of the method is demonstrated for a composite model inductor containing an external secondary circuit.

Explore related subjects

physics.comp-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

J. Priede, G. Gerbeth. 2006-06-17. Boundary-integral method for poloidal axisymmetric AC magnetic fields. https://doi.org/10.1109/tmag.2005.861042

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Quantum-inspired space-time PDE solver and dynamic mode decomposition

The numerical solution of time-dependent PDEs posed over the combined space-time domain, instead of treating time sequentially, leads to space-time methods. Treating time as another spatial dimension allows parallelization across time and simultaneous adaptivity in spatial and temporal discretizations. However, space-time formulations suffer from the curse of dimensionality due to the (d+1)-dimensional domain. Time-series forecasting methods, such as dynamic mode decomposition (DMD), also suffer the same scaling for storing and processing measurement data. In this work, we investigate whether quantum-inspired tensor network methods can mitigate this curse for both solving PDEs and data-driven modeling. We formulate a space-time matrix product state (MPS) encoding to represent either the space-time solution or time-series data. Using this representation, we develop a unified framework that combines an MPS space-time PDE solver with an MPS-DMD algorithm. We benchmark our MPS space-time solver for linear and nonlinear PDEs in both (1+1) and (2+1) dimensions, including non-diffusive regimes such as shockwave formation and Allen-Cahn phase separation. We observe that the MPS ansatz efficiently captures the spatio-temporal correlations of the solutions, with a 99% reduction in parameters with respect to the grid size. We demonstrate the MPS-DMD algorithm in two cases. First, the MPS space-time solver generates the MPS encoding of the time-series data. We then apply MPS-DMD directly to predict the dynamics without solving PDEs. Second, for the general case where data is available as dense arrays, MPS-DMD needs an intermediate compression step. We implement a streaming-like compression algorithm and observe a 97% reduction in memory, with MPS-DMD predictions matching those of exact DMD.

physics.comp-ph↗
arXiv2026

CATAPULT: A CUDA-Accelerated Timestepper for Alpha Particles Using Local Tricubics

We introduce a CUDA-Accelerated Timestepper for Alpha Particles Using Local Tricubics (CATAPULT) for use in Monte Carlo calculations of alpha particle confinement in stellarators. Our GPU implementation is significantly faster than CPU-parallelized implementations of the same field representation such as SIMSOPT, and handles both equilibrium magnetic fields and Shear Alfven Waves. We test our implementation on several example stellarators to exhibit both the speed and correctness of our code. The source code is included in the firm3d Python package.

physics.comp-ph↗
arXiv2026

Signature of Short-Range Order in Static Response of the Three-Dimensional Electron Gas

The three-dimensional electron gas is a fundamental model in condensed matter physics and quantum chemistry, and the exchange-correlation energy derived from it serves as the starting point of \textit{ab initio} computations of materials. However, the wave-vector-dependent response, and hence the static local field factor $G(q)$, has remained without accurate ground-state benchmark in the strongly coupled regime for three decades. Using diffusion Monte Carlo, we calculate the static density-density response function and $G(q)$ across the liquid phase and find a pronounced structure in $G(q)$ at intermediate wave vectors, already visible at metallic densities and growing with increasing interaction strength. We identify it as a fingerprint of short-range order by showing that it is required to reproduce the static structure factor. Our parametrization, valid in the entire liquid phase, predicts a low-energy resonant mode inside the particle-hole continuum.

physics.comp-ph↗