Three-dimensional Field Mapping Research Articles

Field Measurements of Magnets for Modern SR Sources and FEL

Magnets for modern accelerators and storage rings may have a rather complex field distribution and strict quality requirements. The Budker Institute of Nuclear Physics (Novosibirsk, Russia) is a well-known producer of magnets for various accelerator projects worldwide. This paper describes our magnet measurement facility with examples of NSLS-II booster magnets, small-aperture X-FEL quadrupoles, and PETRA-III dipoles. NSLS-II booster dipoles have quadrupole and sextupole components with a rather high field quality of $1\cdot 10^{-3}$ in the good field region of ±2 cm, providing booster operation at energy from 170 MeV to 3.15 GeV with a 2-Hz repetition rate. We designed a special bench with a ceramic rotation coil to measure X-FEL quadrupoles. The equipment provided measurements of the magnetic axis with accuracy better than 5 $\mu\text{m}$ . We used the system of three temperature-stabilized Hall sensor arrays distributed vertically to obtain a three-dimensional field map from a single measurement of PETRA-III dipole magnets.

High-precision three-dimensional field mapping of a high resolution magnetic spectrometer for hypernuclear spectroscopy at JLab

The High Resolution Kaon Spectrometer (HKS), which consists of two quadrupole magnets and one dipole magnet, was designed and constructed for high-resolution spectroscopy of hypernuclei using the (e,e′K+) reaction in Hall C, Jefferson Lab (JLab). It was used to analyze momenta of around 1.2GeV/cK+ s with a resolution of 2 ×10−4 (FWHM). To achieve the target resolution, a full three-dimensional magnetic field measurement of each magnet was successfully performed, and a full three-dimensional magnetic field map of the HKS magnets was reconstructed. Using the measured field map, the initial reconstruction function was generated. The target resolution would be achieved via careful tuning of the reconstruction function of HKS with the p(e,e′K+)Λ,Σ0 and 12C (e,e′K+)12Λ Bg.s. reactions. After tuning of the initial reconstruction function generated from the measured map, the estimated HKS momentum resolution was 2.2×10−4 (FWHM).

Interferometric methods for mapping static electric and magnetic fields

The mapping of static electric and magnetic fields using electron probes with a resolution and sensitivity that are sufficient to reveal nanoscale features in materials requires the use of phase-sensitive methods such as the shadow technique, coherent Foucault imaging and the Transport of Intensity Equation. Among these approaches, image-plane off-axis electron holography in the transmission electron microscope has acquired a prominent role thanks to its quantitative capabilities and broad range of applicability. After a brief overview of the main ideas and methods behind field mapping, we focus on theoretical models that form the basis of the quantitative interpretation of electron holographic data. We review the application of electron holography to a variety of samples (including electric fields associated with p–n junctions in semiconductors, quantized magnetic flux in superconductors and magnetization topographies in nanoparticles and other magnetic materials) and electron-optical geometries (including multiple biprism, amplitude and mixed-type set-ups). We conclude by highlighting the emerging perspectives of (i) three-dimensional field mapping using electron holographic tomography and (ii) the model-independent determination of the locations and magnitudes of field sources (electric charges and magnetic dipoles) directly from electron holographic data. La cartographie de champs électriques et magnétiques statiques avec une sonde d'électrons à un niveau de résolution et de sensibilité suffisant pour révéler des variations à l'échelle nanométrique requiert l'utilisation de méthodes sensibles à la phase, telles que la technique de l'ombrage, l'imagerie cohérente en mode de Foucault ou l'équation de transport de l'intensité (TIE). Parmi ces différentes approches, l'holographie électronique « hors axe » en microscopie électronique à transmission joue un rôle prépondérant, en raison de son caractère quantitatif et de son vaste domaine d'utilisation. Après une brève revue des principales idées et méthodes sous-jacentes, nous nous attacherons à décrire les modèles théoriques qui constituent le fondement de l'interprétation quantitative des données holographiques. Nous passerons rapidement en revue l'utilisation de l'holographie électronique pour étudier un grand nombre d'échantillons avec leurs champs électriques et magnétiques associés : jonctions p–n dans les semi-conducteurs, lignes de flux magnétique quantifié dans les supraconducteurs, topographies du champ magnétique dans et autour de nanoparticules et autres… Les aspects relatifs aux géométries utilisées en optique électronique (doubles biprismes et dispositifs mixtes pour jouer sur la phase et l'amplitude) sont aussi mentionnés. Enfin, nous identifions plusieurs perspectives émergentes de grand intérêt : (i) la cartographie tridimensionnelle de champs en associant tomographie et holographie, (ii) la détermination de la position et de l'intensité de sources de champ (charges électriques et dipôles magnétiques) directement à partir des données holographiques.

Growth and demise of a Burdigalian coral bioconstruction on a granite rocky substrate (Bonifacio Basin, southeastern Corsica)

During the Early Miocene, coincident with the Sardinia–Corsica block rotation, mixed carbonate–siliciclastic sediments of the Cala di Labra Formation were deposited on the southern margin of the Bonifacio Basin (southeastern Corsica, France). The Burdigalian marine transgression is spectacularly represented by a peculiar coral bioconstruction, unconformably lying on the eroded Variscan granitic basement. Superb exposures allowed detailed, three-dimensional field mapping, lithofacies analysis, and characterization of the Cala di Labra coral bioconstruction. As a result of the extremely irregular and articulated substrate, the coral buildup appears as an organized lens-shaped structure, and its core is constituted by a relatively dense coral domestone with a moderate increase of platy corals in the upper part. A coral rubble associated with granitic cobbles and pebbles is locally present at the base. The inter-coral sediment consists of poorly sorted bioclastic wackestone to packstone. Results from this study clearly show evidence for the occurrence of a former submerged granitic substrate that, as very rarely documented in the geological record, is here interpreted as the subtidal substrate for growth of a small bioconstruction under relatively high energy and clear water conditions. The Cala di Labra bioconstruction is overlain by a fining-upward quartzose conglomerate and sandstone succession interpreted as deposited in a coastal setting near fluvial point sources. The demise of coral growth was caused by a regressive event and by the consequent quite-sudden burial and related changes of trophic conditions.

Application of a new procedure for design of 325 MHz RFQ

A new procedure for designing Radio Frequency Quadrupole (RFQ) accelerators has been developed. We present an integrated RFQ design procedure, which is based on modern three-dimensional field map calculations and beam dynamics simulations. The design procedure was integrated with the beam dynamics design and simulation codes DESRFQ & TRACK and applied to the development of a 325 MHz RFQ capable of delivering a 2.5 MeV H− beam with 40 mA peak current for the proton driver (PD) at Fermi National Accelerator Laboratory (FNAL).

Quantification of B0 homogeneity variation with head pitch by registered three-dimensional field mapping

In this study, we quantify the extent to which B 0 homogeneity in adult humans is dependent on head pitch relative to the B 0 vector. Three-dimensional, whole-brain B 0 field maps were acquired in five normal subjects for three generalized head pitch angles. Optimal first- and second-order shimming of the experimental B 0 maps were simulated numerically. The spatial B 0 distribution within the brain was analyzed following automated volumetric co-registration of all data. Increasing head pitch improves both the resonance offset and local homogeneity in the inferior frontal lobes, but introduces inhomogeneities in other regions of the brain which cannot be compensated by first-order shimming but are further improved by second-order shimming.

An electrically transparent barrier for conducting fluids

An electrically transparent fluid barrier (ETFB) is proposed as a means of separating fluids of different conductivity for use in two- or three-dimensional field mapping experiments. The concept is demonstrated in the context of a conducting analog to the problem of the microstrip transmission line.