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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Excitation and tunneling spectra of a fractional quantum Hall system in the thin-cylinder limit

Here, the excitations of fractional quantum Hall effect (FQHE) states have been largely inaccessible to experimental probes until recently. New electron scanning tunneling microscopy (STM) results from Hu et al. [Nat. Phys. 21, 716 (2025)] show promise in detecting and identifying these excited states via the local density of states (LDOS) spectrum. On a torus, there exists a mapping from the lowest Landau level states to a 1D lattice with a Hamiltonian that features dipole moment conservation. In this work, we apply perturbation theory starting from the thin-cylinder limit (𝐿 𝑥 → ∞, 𝐿 𝑦 < 𝑙 𝐵 for torus dimensions 𝐿 𝑥 and 𝐿 𝑦 and magnetic length 𝑙 𝐵 ) to obtain an analytical approach to the low-lying neutral and charged excitations of the 𝜈 = 1/3 FQHE state. Notably, in the thin cylinder, we can systematically enumerate all the low-lying excitations by the patterns of “dipoles” formed by the electron occupation pattern on the 1D lattice. We find that the thin-cylinder limit predicts a significant dispersion of the low-lying neutral excitations but sharpness of the LDOS spectra, which measure charged excitations. We also discuss connections between our work and several different approaches to the FQHE STM spectra, including those using the composite fermion theory. Numerical exact diagonalization beyond the thin-cylinder limit suggests that the energies of charged excitations remain largely confined to a narrow range of energies, which in experiments might appear as a single peak.

Adhidewata, Jyesta M. [University of California, B↗
DOE OSTI2021

Spin-induced linear polarization of photoluminescence in antiferromagnetic van der Waals crystals

Antiferromagnets are promising components for spintronics due to their terahertz resonance, multilevel states and absence of stray fields. However, the zero net magnetic moment of antiferromagnets makes the detection of the antiferromagnetic order and the investigation of fundamental spin properties notoriously difficult. Here, we report an optical detection of Néel vector orientation through an ultra-sharp photoluminescence in the van der Waals antiferromagnet NiPS 3 from bulk to atomically thin flakes. The strong correlation between spin flipping and electric dipole oscillator results in a linear polarization of the sharp emission, which aligns perpendicular to the spin orientation in the crystal. By applying an in-plane magnetic field, we achieve manipulation of the photoluminescence polarization. Furthermore, this correlation between emitted photons and spins in layered magnets provides routes for investigating magneto-optics in two-dimensional materials, and hence opens a path for developing opto-spintronic devices and antiferromagnet-based quantum information technologies.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

The Muon g-2 Experiment overview and status as of June 2016

The Muon g-2 Experiment at Fermilab will measure the anomalous magnetic moment of the muon to a precision of 140 parts per billion, which is a factor of four improvement over the previous E821 measurement at Brookhaven. The experiment will also extend the search for the electric dipole moment (EDM) of the muon by approximately two orders of magnitude, with a sensitivity down to 10 -21 e.cm. Both of these measurements are made by combining a precise measurement of the 1.45T storage ring magnetic field with an analysis of the modulation of the decay rate of higher-energy positrons (from anti-muons), recorded by 24 calorimeters and 3 straw tracking detectors. Furthermore, the recent progress in the alignment of the electrostatic quadrapole plates and the trolley rails inside the vacuum chambers, and in establishing the uniform storage ring magnetic field will be described.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2017

Investigation of Microbunching Instabilities in Modern Recirculating Accelerators

Particle accelerators are machines to accelerate and store charged particles, such as electrons or protons, to the energy levels for various scientific applications. A collection of charged particles usually forms a particle beam. There are three basic types of particle accelerators: linear accelerators (linac), storage-ring (or circular) accelerators, and recirculating accelerators. In a linac, particles are accelerated and pass through once along a linear or straight beamline. Storage-ring accelerators propel particles around a circular track and repetitively append the energy to the stored beam. The third type, also the most recent one in chronology, the recirculating accelerator, is designed to accelerate the particle beam in a short section of linac, circulate the beam, and then either continue to accelerate for energy boost or decelerate it for energy recovery. The beam properties of a linac machine are set at best by the initial particle sources. For storage rings, the beam equilibria are instead determined by the overall machine design. The modern recirculating machines share with linacs the advantages to both accelerate and preserve the beam with high beam quality, as well as efficiently reuse the accelerating components. The beamline design in such a machine configuration can however be much more complicated than that of linacs. As modern accelerators push toward the high-brightness or high-intensity frontier by demanding particles in a highly charged bunch (about nano-Coulomb per bunch) to concentrate in an ever-decreasing beam phase space (transverse normalized emittance about 1 μm and relative energy spread of the order of 10^-5 in GeV beam energy), the interaction amongst particles via their self-generated electromagnetic fields can potentially lead to coherent instabilities of the beam and thus pose significant challenges to the machine design and operation. In the past decade and a half, microbunching instability (MBI) has been one of the most challenging issues for such high-brightness or high-intensity beam transport, as it would degrade lasing performance in the fourth-generation light sources, reduce cooling efficiency in electron cooling facilities, and compromise the luminosity of colliding beams in lepton or lepton-hadron colliders. The dissertation work will focus on the MBI in modern recirculating electron accelerators. It has been known that the collective interactions, the coherent synchrotron radiation (CSR) and the longitudinal space charge (LSC) forces, can drive MBI. The CSR effect is a collective phenomenon in which the electrons in a curved motion, e.g. a bending dipole, emit radiation at a scale comparable to the micro-bunched structure of the bunch distribution. The LSC effect stems from non-uniformity of the charge distribution, acts as plasma oscillation, and can eventually accumulate an amount of energy modulation when the beam traverses a long section of a beamline. MBI can be seeded by non-uniformity or shot noise of the beam, which originates from granularity of the elementary charge. Through the aforementioned collective effects, the modulation of the bunch sub-structure can be amplified and, once the beam-wave interaction formed a positive feedback, can result in MBI. The problem of MBI has been intensively studied for linac-based facilities and for storage-ring accelerators. However, systematic studies for recirculation machines are still very limited and form a knowledge gap. Because of the much more complicated machine configuration of the recirculating accelerators than that of linacs, the existing MBI analysis needs to be extended to accommodate the high-brightness particle beam transport in modern recirculating accelerators. This dissertation is focused on theoretical investigation of MBI in such machine configuration in the following seven themes: (1) Development and generalization of MBI theory The theoretical formulation has been extended so as to be applicable to a general linear beamline lattice including horizontal and vertical transport bending elements, and beam acceleration or deceleration. These featured generalizations are required for MBI analysis in recirculation accelerators. (2) Construction of CSR impedance models In addition to the steady-state CSR interaction, it has been found that the exit transient effect (or CSR drift) can even result in more serious MBI in high-brightness recirculation arcs. The onedimensional free-space CSR impedances, especially the exit transients, are derived. The steady-state CSR impedance is also extended to non-ultrarelativistic beam energy for MBI analysis of low-energy merger sections in recirculating accelerators. (3) Numerical implementation of the derived semi-analytical formulation This includes the development of a semi-analytical Vlasov solver for MBI analysis, and also benchmarking of the solver against massive particle tracking simulations. (4) Exploration of multistage amplification behavior of CSR microbunching development The CSR-induced MBI acts as an amplifier, which amplifies the sub-bunch modulation of a beam. The amplification is commonly quantified by the amplification gain. A beam transport system can be considered as a cascaded amplifier. Unlike the two-stage amplification of four-dipole bunch compressor chicanes employed in linacs, the recirculation arcs, which are usually constituted by several tens of bending magnets, show a distinguishing feature of up to six-stage microbunching amplification for our example arc lattices. That is, the maximal CSR amplification gain can be proportional to the peak bunch current up to sixth power. A method to compare lattice performance has been developed in terms of gain coefficients, which nearly depend on the lattice properties only. This method has also proven to be an effective way to quantify the current dependence of the maximal (5) Control of CSR MBI in multibend transport or recirculation arcs The existing mitigation schemes of MBI mostly aim to linac-based accelerators and may not be practical to the recirculating accelerator facilities. Thus a set of conditions for suppression of CSR MBI was proposed and examined for example lattices from low (~100 MeV) to high (~1 GeV) energies. (6) Study of more aspects of microbunched structures in beam phase spaces For a cascaded amplifier in circuit electronics, the total amplification gain can be estimated as the product of individual gains. In a beam transport line of an accelerator, the (scalar) gain multiplication was examined and found to under-estimate the overall microbunching amplification. The concept of gain matrix was developed, which includes the density, energy and transverse-longitudinal modulations in a beam phase space, and used to analyze MBI for a proposed recirculating machine. Throughout the gain matrix approach, it reasonably gives the upper limit of spectral MBI gain curves. This extended analysis can be employed to study multi-pass recirculation. (7) Study of MBI for magnetized beams Driven by a recent energy-recovery-linac based cooler design for electron cooling at Jefferson Lab Electron-Ion Collider Project, the generalized theoretical formulation for MBI to a transversely coupled beam has been developed and applied to this study. A magnetized beam in general features non-zero canonical angular momentum, thus considered to be a transversely coupled beam. A novel idea of utilizing magnetized beam transport was proposed for improvement of cooling efficiency and possible mitigation of collective effects. A concern of MBI regarding this design was studied and excluded. The large transverse beam size associated with the beam magnetization is found to help suppress MBI via the transverse-longitudinal correlation.

43 PARTICLE ACCELERATORS↗
DOE OSTI2018

NSLS-II upgrade proposal with splitting dipole scheme

In this note, a preliminary study of the NSLS-II upgrade lattice with splitting-dipole scheme is presented. The constraints from maintaining the layout of the ring and re-using the existing magnets have been illustrated. The linear and nonlinear beam dynamics are discussed as well.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Out-of-plane polarization and topological magnetic vortices in multiferroic CrPSe 3

Two-dimensional multiferroic materials are ideal systems for exploring new coupling mechanisms between different ferroic orders and producing novel quantum phenomena with potential applications. Here we employ first-principles density functional theory calculations to discover intrinsic ferroelectric and antiferroelectric phases of Cr⁢P⁢Se 3 , which show ferromagnetic order and compete with the centrosymmetric phase with an antiferromagnetic order. Our analysis shows that the electrical dipoles of such type-I multiferroic phases come from the out-of-plane displacements of phosphorus ions due to the stereochemically active lone pairs. The coupling between polar and magnetic orders creates the opportunity for tuning the magnetic ground state by switching from the centrosymmetric to the ferroelectric phase using an out-of-plane electric field. In ferroelectric and antiferroelectric phases, the combination of easy-plane anisotropy and Dzyaloshinskii-Moriya interactions indicates that they can host topological magnetic vortices such as meron pairs.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Quantifying Species Populations in Multivalent Borohydride Electrolytes

Multivalent batteries represent an important beyond Li-ion energy storage concept. The prospect of calcium batteries, in particular, has emerged recently due to novel electrolyte demonstrations, especially that of a ground-breaking combination of the borohydride salt Ca(BH 4 ) 2 dissolved in tetrahydrofuran. Recent analysis of magnesium and calcium versions of this electrolyte led to the identification of divergent speciation pathways for Mg 2+ and Ca 2+ despite identical anions and solvents, owing to differences in cation size and attendant flexibility of coordination. To test these proposed speciation equilibria and develop a more quantitative understanding thereof, we have applied pulsed-field-gradient nuclear magnetic resonance and dielectric relaxation spectroscopy to study these electrolytes. Additionally, concentration-dependent variation in anion diffusivities and solution dipole relaxations, interpreted with the aid of molecular dynamics simulations, confirms these divergent Mg 2+ and Ca 2+ speciation pathways. These results provide a more quantitative description of the electroactive species populations. We find that these species are present in relatively small quantities, even in the highly active Ca(BH 4 ) 2 /tetrahydrofuran electrolyte. This finding helps interpret previous characterizations of metal deposition efficiency and morphology control and thus provides important fundamental insight into the dynamic properties of multivalent electrolytes for next-generation batteries.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Electromagnon with Sensitive Terahertz Magnetochromism in a Room-Temperature Magnetoelectric Hexaferrite

An electromagnon in the magnetoelectric (ME) hexaferrite Ba 0.5 Sr 2.5 Co 2 Fe 24 O 41 (Co 2 Z-type) single cystal is identified by time-domain terahertz (THz) spectroscopy. The associated THz resonance is active on the electric field (E ω ) of the THz light parallel to the c axis (∥ [001]), whose spectral weight develops at a markedly high temperature, coinciding with a transverse conical magnetic order below 410 K. The resonance frequency of 1.03 THz at 20 K changes -8.7% and +5.8% under external magnetic field (H) of 2 kOe along [001] and [120], respectively. A model Hamiltonian describing the conical magnetic order elucidates that the dynamical ME effect arises from antiphase motion of spins which are coupled with modulating electric dipoles through the exchange striction mechanism. Moreover, the calculated frequency shift points to the key role of the Dzyaloshinskii-Moriya interaction that is altered by static electric polarization change under different H.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Mixed Delay/Nondelay Embeddings Based Neuromorphic Computing with Patterned Nanomagnet Arrays

Patterned nanomagnet arrays (PNAs) have been shown to exhibit a strong geometrically frustrated dipole interaction. Some PNAs have also shown emergent domain wall dynamics. Previous works have demonstrated methods to physically probe these magnetization dynamics of PNAs to realize neuromorphic reservoir systems that exhibit chaotic dynamical behavior and high-dimensional nonlinearity. These PNA reservoir systems from prior works leverage echo state properties and linear/nonlinear short-term memory of component reservoir nodes to map and preserve the dynamical information of the input time-series data into nondelay spatial embeddings. Such mappings enable these PNA reservoir systems to imitate and predict/forecast the input time series data. However, these prior PNA reservoir systems are based solely on the nondelay spatial embeddings obtained at component reservoir nodes. As a result, they require a massive number of component reservoir nodes, or a very large spatial embedding (i.e., high-dimensional spatial embedding) per reservoir node, or both, to achieve acceptable imitation and prediction accuracy. These requirements reduce the practical feasibility of such PNA reservoir systems. To address this shortcoming, we present a mixed delay/nondelay embeddings-based PNA reservoir system. Our system uses a single PNA reservoir node with the ability to obtain a mixture of delay/nondelay embeddings of the dynamical information of the time-series data applied at the input of a single PNA reservoir node. Our analysis shows that when these mixed delay/nondelay embeddings are used to train a perceptron at the output layer, our reservoir system outperforms existing PNA-based reservoir systems for the imitation of NARMA 2, NARMA 5, NARMA 7, and NARMA 10 time series data, and for the short-term and long-term prediction of the Mackey Glass time series data.

Ti, Changpeng↗
DOE OSTI2020

Observation of weakly damped modes using high resolution measurement of turbulence in a dipole confined plasma

When plasma is confined by a levitated superconducting current ring, the turbulent radial particle flux changes the direction depending upon the gradient of the particle number within tubes of equal magnetic flux [Garnier et al., Phys. Plasmas 24, 012506 (2017)]. When the density profile is highly peaked, the particle flux is outward. When the density profile is less peaked, turbulence drives an inward “particle pinch.” This change in the direction of particle flux coincides with a reversal of the mean toroidal propagation direction of turbulent fluctuations. Previously, only the mean wavenumber of the fluctuations was reported. The mean wavenumber was computed from the ensemble correlation between two probes. Here, the full frequency-wavenumber power spectrum of the saturated turbulence is calculated by applying Capon’s “maximum likelihood method” to floating potential measurements from an array of probes. The power spectrum shows that the highest intensity modes are due to unstable entropy modes, and the less intense modes coincide with weakly damped convective cells, which rotate toroidally in the direction opposite to the unstable modes. Because the weakly damped modes make up a significant fraction of the fluctuating power, these measurements imply that saturated turbulence in a dipole-confined plasma involves the excitation of weakly damped rotating convective cells.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Probe Mössbauer Spectroscopy of BiNi{sub 0.96}{sup 57}Fe{sub 0.04}O{sub 3}

This paper presents results of a {sup 57}Fe probe Mössbauer spectroscopy study of the BiNi{sub 0.96}{sup 57}Fe{sub 0.04}O{sub 3} nickelate. The spectra measured above its TN demonstrate that Fe{sup 3+} cations heterovalently substitute for Ni{sup 2+} nickel (←Fe{sup 3+}), being stabilized on four sites of the nickel sublattice in the structure of BiNiO{sub 3}. Calculations in an ionic model with allowance for monopole and dipole contributions to the electric field gradient indicate that the parameters of electric hyperfine interactions between {sup 57}Fe probe atom nuclei reflect the specifics of the local environment of the nickel in the structure of the unsubstituted BiNiO{sub 3} nickelate. Below T{sup N}, Mössbauer spectra transform into a complex Zeeman structure, which is analyzed in terms of first-order perturbation theory with allowance for electric quadrupole interactions as a small perturbation of the Zeeman levels of the {sup 57}Fe hyperfine structure, as well as for specific features of the magnetic ordering of the Ni{sup 2+} cations in the nickelate studied.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Permanent magnets for the return loop of the Cornell-Brookhaven energy recovery linac test accelerator

214 neodymium permanent magnets have been manufactured for the return loop of the CBETA multi-turn ERL at Cornell University. There are 5 types of quadrupole and combined-function gradient magnets using a variant of the circular Halbach design. These are made out of NdFeB material and glued into an aluminium housing with water channels for temperature stabilisation. The NdFeB wedges and magnet construction were done by outside companies, while the final “tuning” using inserts containing 64 iron rods per magnet was done at BNL over a period of about 6 months. Average relative field errors of 2.2×10 -4 were achieved on the beam region. The magnet strengths vary by type but are of order 10 T/m for quadrupole component and up to 0.3 T for the dipole. This paper reports on the field quality and timeline achieved in this production process

43 PARTICLE ACCELERATORS↗
DOE OSTI2021

Zero-field spin resonance in graphene with proximity-induced spin-orbit coupling

In this work we investigate collective spin excitations in graphene with proximity-induced spin-orbit coupling (SOC) of the Rashba and valley-Zeeman types, as it is the case, e.g., for graphene on transition-metal-dichalcogenide substrates. It is shown that, even in the absence of an external magnetic field, such a system supports collective spin modes, which correspond to coupled oscillations of the uniform and valley-staggered magnetizations. These modes can be detected via both zero-field electron spin resonance (ESR) and zero-field electric-dipole spin resonance (EDSR), with EDSR response arising solely due to Rashba SOC. We analyze the effect of electron-electron interaction within the Fermi-liquid kinetic equation and show that the interaction splits both the ESR and EDSR peaks into two. The magnitude of splitting and the relative weights of the resonances can be used to extract the spin-orbit coupling constants and many-body interaction parameters that may not be accessible by other methods.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Lattice Design of the Beam Transfer Line (BTL) from PIP-II LINAC to the Booster at Fermilab

PIP-II beam transfer line (BTL) to transport the beam from PIP-II Linac to the Booster ring at Fermilab. The latest design eliminates rolling the dipoles in the beam line to cross over the Tevatron tunnel. Also re-designed is the lattice in the region of the Booster Injection to meet the request of the civil construction needs and accommodate the constrains of the Booster injection request. A beam line to the beam absorber (BAL) is designed based on the request from the results of Mars simulations and ANASYS calculation of the absorber. Simulations with dipole and quadrupole field errors for the Beam Transport Line (BTL) to the Booster, which provides the specifications for all the magnets and Power supplies, will be presented too.

43 PARTICLE ACCELERATORS↗
DOE OSTI2020

Radial Shift Lattice Design using BMAD toolkit

The electron-ion collider (EIC) conceptual design [1] requires that the hadron storage ring (HSR) be able to demonstrate radial shifts using a dual rigidity system. The dual rigidity system is a system in which the dipoles in the utility straight sections(USS) of the EIC lattice have a different rigidity than the arc dipoles thus affecting the beam orbit in the lattice arcs. This difference in rigidity allows the orbital offset in the arc magnets to reach approximately 18.7 mm offset, with a circumference lengthening of 73.2 mm.

43 PARTICLE ACCELERATORS↗
DOE OSTI2019

Impact of Pulsar and Fallback Sources on Multifrequency Kilonova Models

We explore the impact of pulsar electromagnetic dipole and fallback accretion emission on the luminosity of a suite of kilonova models. The pulsar models are varied over pulsar magnetic field strength, pulsar lifetime, ejecta mass, and elemental abundances; the fallback models are varied over fallback accretion rate and ejecta mass. For the abundances, we use Fe and Nd as representatives of the wind and dynamical ejecta, respectively. We simulate radiative transfer in the ejecta in either 1D spherical or 2D cylindrical spatial geometry. For the grid of 1D simulations, the mass fraction of Nd is 0, 10 –4 , or 10 –3 , and the rest is Fe. Our models that fit the bolometric luminosity of AT 2017gfo (the kilonova associated with the first neutron star merger discovered in gravitational waves, GW170817) do not simultaneously fit the B , V , and I time evolution. Here, we find that the trends of the evolution in B and V magnitudes are better matched by the fallback model relative to the pulsar model, implying the time-dependence of the remnant source influences the color evolution. Further exploration of the parameter space and model deficiencies is needed before we can describe AT 2017gfo with a remnant source.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Design and fabrication of a 30 T superconducting solenoid using overpressure processed Bi2212 round wire

High field magnets are needed for frontier accelerator facilities and have many applications beyond high-energy physics. Of particular interest are 30-40T class (LTS/HTS hybrid) solenoids required for the final beam cooling stages of a muon collider facility. The successful design of such magnets using Bi2212 conductor depends critically on the conductor processing, stress management in the coil, and quench protection. These are the challenges addressed in the proposal and the overall objectives of the combined Phase I and Phase II projects. Bi2212 round wire conductor will be evaluated for accelerator use by concentrating on the design of a solenoid magnet that will be the enabling technology for realizing the final stages of muon beam cooling and thus a high luminosity muon collider. A full mechanical characterization of a test coil made from overpressure-processed conductor with engineering current density JE in the range of & gt;600 A/mm2 at 20-30 T will be performed. The data from the test coil will serve as input to a 30+ T magnet that will be designed, built, and tested to demonstrate the suitability of overpressure-processed Bi2212 for solenoids for final muon cooling and 6D cooling channels. Short lengths and coils wound from up to 100 m length conductor will be overpressure processed. Characterization of an overpressure processed Bi2212 round-wire based solenoid will be performed at 4.2 K in a background field of up to 14 T. The characterization will include mechanical, thermal, and quench properties. The data will be used as input to a 30+ T coil design that has suitable stress management and quench protection, to be built and tested in Phase II. Commercial applications and other benefits: The technology developed by this work will benefit high-energy physics applications. The knowledge and expertise gained from this project will enable the development of very high-field solenoids, dipoles, and quadrupoles using Bi2212 cable at low temperature for applications in future particle accelerators. The technology will also extend the range available to Nuclear Magnetic Resonance Spectroscopy, an important technique used to understand molecular structures of proteins and other materials.

43 PARTICLE ACCELERATORS↗
DOE OSTI2023

Status and Challenges of the Interaction Region Magnets for HL-LHC

About one hundred magnets of six different types shall be installed in the High Luminosity LHC (HL-LHC) in the years 2026-2028 at CERN. The magnets design, construction and test are based on CERN collaborations with institutes and industrial partners in USA, Spain, Italy, Japan and China. Three types of correctors are based on Nb-Ti technology and feature conductor peak fields in the 2 to 4 T range: for all of them the prototype phase has been successfully completed. The production is well advanced for the superferric correctors, and is starting for the canted cosine theta correctors and for the nested correctors. The separation and recombination Nb-Ti dipoles D1 and D2, with a 4.5-6 T bore field range, are both in the prototype phase after the completion of the short model program. The most challenging magnet, the Nb 3 Sn quadrupole with conductor peak field above 11 T, is in the prototype phase at CERN and halfway through the production phase in the USA. In this paper we will give, for each type of magnet, an overview of the main achievements obtained so far and we will outline the technical points still needing validation from the prototype program.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗