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The energy production through thermo-nuclear fusion requires the confinement of the plasma into a bounded domain. In most of the cases, such configurations are obtained by using strong magnetic fields. Several models exist for describing…

Analysis of PDEs · Mathematics 2012-07-11 Mihai Bostan

The principle behind magnetic fusion is to confine high temperature plasma inside a device in such a way that the nuclei of deuterium and tritium joining together can release energy. The high temperatures generated needs the plasma to be…

Numerical Analysis · Mathematics 2024-03-26 Giacomo Albi , Giacomo Dimarco , Federica Ferrarese , Lorenzo Pareschi

We present a target field approach to analytically design magnetic fields using permanent magnets. We assume that their magnetisation is bound to a two-dimensional surface and is composed of a complete basis of surface modes. By posing the…

Applied Physics · Physics 2024-05-24 Peter J. Hobson , Chris Morley , Alister Davis , Thomas Smith , Mark Fromhold

The magnetic field from a uniformly magnetised, rectangular prism is known exactly, which is the basis for a large number of micromagnetic simulations. Here we derive an analytical solution for the field from a periodically repeating…

Materials Science · Physics 2026-04-15 Frederik Laust Durhuus , Andrea Roberto Insinga , Rasmus Bjørk

Topology optimization of permanent magnet systems consisting of permanent magnets, high permeability iron and air is presented. An implementation of topology optimization for magnetostatics is discussed and three examples are considered.…

Instrumentation and Detectors · Physics 2017-05-04 R. Bjørk , C. R. H. Bahl , A. R. Insinga

Access to the plasma chamber in a stellarator reactor is essential for maintenance and diagnostics. However, the complex geometry of stellarator coils, often characterized by their strong twisting, can severely limit the space available for…

Plasma Physics · Physics 2025-02-19 A. Baillod , E. J. Paul , T. Elder , J. M. Halpern

The fusion created by magnetically confined plasma is a promising clean and essentially unlimited future energy source. However, net energy generation has not been yet demonstrated in fusion experiments. Some of the main problems hindering…

Plasma Physics · Physics 2025-10-20 Natanael Bort-Soldevila , Jaume Cunill-Subiranas , Alvaro Sanchez

In this self-contained document, we aim to present the basic theoretical building blocks to understand modeling of stellarator magnetic fields, some of the challenges associated with modeling, and optimization for designing stellarators. As…

Plasma Physics · Physics 2020-08-11 Lise-Marie Imbert-Gerard , Elizabeth J. Paul , Adelle M. Wright

This work suggests to optimize the geometry of a quadrupole magnet by means of a genetic algorithm adapted to solve multi-objective optimization problems. To that end, a non-domination sorting genetic algorithm known as NSGA-III is used.…

This work deals with the numerical approximation of plasmas which are confined by the effect of a fast oscillating magnetic field (see \cite{Bostan2012}) in the Vlasov model. The presence of this magnetic field induces oscillations (in…

Numerical Analysis · Mathematics 2024-11-08 Megala Anandan , Benjamin Boutin , Nicolas Crouseilles

A novel design is presented for a permanent magnet array to address specific challenges with scalable trapped-ion quantum computing systems. Design and optimization of this magnet geometry is motivated by concepts for large-scale Quantum…

Quantum Physics · Physics 2026-04-06 Mitchell G. Peaks

In this paper, the design of the the plasma equilibrium and superconducting coils for the Electrons and Positrons in an Optimized Stellarator EPOS experiment is presented. With newly developed stellarator optimization tools, including…

Highly accurate simulation of plasma transport is needed for the successful design and operation of magnetically confined fusion reactors. Unfortunately, the extreme anisotropy present in magnetized plasmas results in thin boundary layers…

Numerical Analysis · Mathematics 2023-06-30 Christopher J. Vogl , Ilon Joseph , Milan Holec

In omnigeneous magnetic fields, charged particles are perfectly confined in the absence of collisions and turbulence. For this reason, the magnetic configuration is optimized to be close to omnigenity in any candidate for a stellarator…

Plasma Physics · Physics 2024-09-04 J. L. Velasco , I. Calvo , F. J. Escoto , E. Sánchez , H. Thienpondt , F. I. Parra

In this work, we utilize new coil objectives for stellarator optimization with autodifferentiation, including pointwise and net coil-coil forces and torques. We use these methods to perform the first large-scale optimization of planar…

We introduce a general method for designing tailored lattices of magnetic microtraps for ultracold atoms, on the basis of patterned permanently magnetized films. A fast numerical algorithm is used to automatically generate patterns which…

Quantum Physics · Physics 2010-10-19 Roman Schmied , Dietrich Leibfried , Robert J. C. Spreeuw , Shannon Whitlock

The magnetostatic field distribution in a nonlinear medium amounts to the unique minimizer of the magnetic coenergy over all fields that can be generated by the same current. This is a nonlinear saddlepoint problem whose numerical solution…

Numerical Analysis · Mathematics 2024-03-28 Herbert Egger , Felix Engertsberger , Klaus Roppert

We propose a new optimization method based on a demagnetization procedure well known in magnetism. We show how this procedure can be applied as a general tool to search for optimal solutions in any system where the configuration space is…

Disordered Systems and Neural Networks · Physics 2009-11-07 G. Zarand , F. Pazmandi , K. F. Pal , G. T. Zimanyi

Solving for charged particle motion in electromagnetic fields (i.e. the particle pushing problem) is a computationally intensive component of particle-in-cell (PIC) methods for plasma physics simulations. This task is especially challenging…

Computational Physics · Physics 2026-01-01 Tri P. Nguyen , Ilon Joseph , Mayya Tokman

Spherical plasma lens models are known to suffer from a severe over-pressure problem, with some observations requiring lenses with central pressures up to millions of times in excess of the ambient ISM. There are two ways that lens models…

Astrophysics of Galaxies · Physics 2020-02-19 Adam Rogers , Abdul Mohamed , Bailey Preston , Jason D. Fiege , Xinzhong Er