Toroidal System Research Articles

A Functional 3D-Printable Magnet Model of the ATLAS Toroid

The ATLAS detector is the largest particle detector at the LHC and one of the most complex machines ever built. It allows precise measurements of particles emanating from proton collisions. Due to its complexity, introducing the ATLAS detector in the high-school physics classroom can be challenging. Nonetheless, we show how to use 3D printing to provide a hands-on classroom activity by constructing a functional 3D model of the toroidal ATLAS magnet system. This model can be used to discover, visualize and explain the shape of a toroidal magnetic field and to start a discussion about the role of magnetic fields in particle detectors in general.

Topological Symmetry Transition between Toroidal and Klein Bottle Graphenic Systems

In the current study, distance-based topological invariants, namely the Wiener number and the topological roundness index, were computed for graphenic tori and Klein bottles (named toroidal and Klein bottle fullerenes or polyhexes in the pre-graphene literature) described as closed graphs with N vertices and 3N/2 edges, with N depending on the variable length of the cylindrical edge LC of these nano-structures, which have a constant length LM of the Möbius zigzag edge. The presented results show that Klein bottle cubic graphs are topologically indistinguishable from toroidal lattices with the same size (N, LC, LM) over a certain threshold size LC. Both nano-structures share the same values of the topological indices that measure graph compactness and roundness, two key topological properties that largely influence lattice stability. Moreover, this newly conjectured topological similarity between the two kinds of graphs transfers the translation invariance typical of the graphenic tori to the Klein bottle polyhexes with size LC ≥ LC, making these graphs vertex transitive. This means that a traveler jumping on the nodes of these Klein bottle fullerenes is no longer able to distinguish among them by only measuring the chemical distances. This size-induced symmetry transition for Klein bottle cubic graphs represents a relevant topological effect influencing the electronic properties and the theoretical chemical stability of these two families of graphenic nano-systems. The present finding, nonetheless, provides an original argument, with potential future applications, that physical unification theory is possible, starting surprisingly from the nano-chemical topological graphenic space; thus, speculative hypotheses may be drawn, particularly relating to the computational topological unification (that is, complexification) of the quantum many-worlds picture (according to Everett’s theory) with the space-curvature sphericity/roundness of general relativity, as is also currently advocated by Wolfram’s language unification of matter-physical phenomenology.

A Ioffe Trap Magnet for the Project 8 Atom Trapping Demonstrator

The goal of the Project 8 experiment (B. Monreal and J. Formaggio, 2009) is to measure the absolute neutrino mass using tritium, which involves precisely measuring the energies of the beta-decay electrons in the high-energy tail of the spectrum (A. A. Esfahani et al. , 2017). The experimental installation of Project 8 Atom Trapping Demonstrator requires a magnet with rather unusual field properties. The magnet has to contain within the cold mass a large volume enclosed by a continuous, uninterrupted boundary higher than 2 T, whereas the field in a substantial volume inside this boundary has to be of the order of 10−4 T or less. A 1-T solenoid field provides the background field necessary for the detection of the beta-decay electrons (A. A. Esfahani et al. , 2019). A proposed toroidal magnet system [a Ioffe-Pritchard trap (T. Bergeman et al. , 1987)] comprised of specially shaped multiple racetrack windings with opposing polarities satisfies these unusual requirements. The magnet is made of NbTi wire and expected to be conduction cooled. Manufacturability issues are addressed as well as the effect of tolerances on the field quality. The design includes additional topological features providing a low-field duct for interfacing with the peripheral coils of the velocity and state selector.

Upgraded KSTAR Toroidal Field Coil Quench Protection System

The upgradation of the Korea superconducting tokamak advanced research (KSTAR) toroidal field (TF) superconducting coil quench protection (QP) system has been performed since the failure of the 40-kA dc interruption switch of it in 2016. The complicated design and protection logic led to the accident of the QP switch during the malfunction of the interlock power-line carrier (PLC). To improve the reliability of the TF coil QP system, the KSTAR decided to apply the pyrobreaker (PB) from the Efremov Institute as a backup for the slow discharge (SD) and QP switches. In addition, the upgraded design segregates the QP circuit from the SD circuit. The simulation was performed to analyze the TF coil QP system with the consideration of the switching behavior of the PB and the stray parameters of the circuit. The upgraded KSTAR TF coil QP system has been designed, manufactured, installed, and tested successfully. This article will present the issues of the previous design of the KSTAR TF coil QP system and the results of the upgraded system.

Design updates and analysis of the Korean fusion demonstration reactor superconducting toroidal field magnet system

Abstract After a conceptual design study for a steady-state Korean fusion demonstration reactor (K-DEMO) was initiated in 2012, the preliminary design of superconducting magnet system which is one of the key components of the K-DEMO has been done in 2015. The superconducting magnet system of K-DEMO has 16 Toroidal Field (TF) coils, 8 Central Solenoids (CS) modules and 12 Poloidal Field (PF) coils which use Cable-In-Conduit Conductors (CICC). For a high 7.4 T magnetic field generation at plasma center, high performance Nb3Sn based superconductor will be developed and used for TF magnet. Starting from the preliminary conceptual design, design updates of K-DEMO TF magnet is being conducted for checking engineering issues. For a validation of the magnet design, thermo-hydraulic stability and mechanical stability are being considered. In this work, the conceptual design studies for updates of K-DEMO TF magnet system is described.

Conceptual design of a high temperature superconducting magnet for a particle physics experiment in space

In the frame of a collaboration between CERN, ASI, University of Trento, and TIFPA, the HTS demonstrator magnet for space project has started to define methods and procedures for manufacturing high temperature superconducting magnets for space applications. To this purpose, we developed a conceptual design of a superconducting magnetic spectrometer for a physics experiment in space. The configuration is a toroid with twelve superconducting coils based on ReBCO tape. By using ReBCO tape with an engineering critical current density, Je, exceeding 1000 A mm−2 at and , as reached in the H2020-ARIES program, the magnet system provides an average bending strength of . This is sufficient to measure charged particles with rigidities up to , more than two orders of magnitude higher than the present state-of-the-art space spectrometer. The magnet system requires about of ReBCO tape and produces a peak magnetic field of at an operating temperature of . A small scale single coil, which is about one third in size of a coil from the toroidal magnet system, will be manufactured and tested as demonstrator of the magnet technology. The mechanical structure and performance of the toroidal magnet system and demonstrator coil are described.

The development of charge exchange recombination spectroscopy diagnostics for the T-15MD tokamak

In 2020 a modernized tokamak T-15MD (R=1.5 m, a=0.67 m, κ=1.8, Ipl≤2 MA, Bt≤2 T, discharge duration ≤10 s, Paux≤24 MW) will be launched in the National Research Center “Kurchatov Institute”. For this installation, a modern Charge eXchange Recombination Spectroscopy (CXRS-diagnostics) has been developed. It can function both on a diagnostic injector (EDNB=60 keV) and heating injector (ENBI=80 keV) . CXRS-diagnostics of T-15MD can be used to measure local values of the following plasma parameters with high spatial (≈1 cm) and temporal (≈1 ms) resolutions: ion temperature (Ti), density of main gas and light impurities nuclei (nz), toroidal and poloidal rotation velocity (Vpol, Vtor) and the fast-ion spectrum. The composition of the CXRS-diagnostic complex and its schematic is presented. Its main components are the DNB (H, 60 keV, 150 kW), four spectrometers (two of them based on Echelle gratings, one based on holographic grating and another utilizes both types of gratings), and EMCCD-cameras. The attenuation of the diagnostic beam in the plasma is calculated considering its ionization and charge exchange by the main gas and impurities (C, O), as well as electron impact ionization. The intensities of active and passive components of λ=5291 Åline of C5+ ion are calculated considering the line fine structure, Doppler, and Zeeman effects. The active and passive signals emitted by C5+ ion are estimated for toroidal and poloidal registration systems. It is established that the acquisition time of 1 – 3 ms is enough to achieve the valid signal level to measure Ti with a statistical error ≈ 3 %. The calculated ratio between the active and passive CXRS-signal in the plasma center is 2.2 – 3.7. Measurement error is estimated for λ=5291 ÅCX-line and calculations show low measurement errors for Ti and nz (around 2 – 5 %), Vpol and Vtor (around 2 km/s). This indicates that CXRS-diagnostics have potential to provide reliable and accurate measurements of the named plasma parameters on T-15MD.

Lanthanoid pyridyl-β-diketonate 'triangles'. New examples of single molecule toroics.

Trinuclear lanthanoid clusters have been synthesised and investigated as toroidal spin systems. A pyridyl functionalised β-diketonate, 1,3-bis(pyridin-2-yl)propane-1,3-dione (o-dppdH) has been used to synthesise a family of clusters of the form [Dy3(OH)2(o-dppd)3Cl2(H2O)4]Cl2·7H2O (1), [Tb3(o-dppd)3(μ3-OH)2(CH3CH2OH)3Cl3][Tb3(o-dppd)3(μ3-OH)2(H2O)(CH3CH2OH)2Cl3]Cl2·H2O (2), [Ho3(OH)2(o-dppd)3Cl(H2O)5]Cl3·3H2O (3) and [Er3(OH)2(o-dppd)3Cl2(H2O)3(CH3OH)]Cl2·3H2O·CH3OH (4). Despite the previous occurrence of this structural motif in the literature, these systems have not been widely investigated in terms of torodic behaviour. Magnetic studies were used to further characterise the complexes. DC susceptibility studies support weak antiferromagnetic exchange in the complexes. Slow magnetic relaxation behaviour is observed in the dynamic AC magnetic studies for complex 1. Theoretical studies predict that complex 1 and 3 have a non-magnetic ground state based on a toroidal arrangement of spins. Changes to the coordination environment in 2 do not support a toroic spin state. The prolate nature of the ErIII centres in complex 4 and large transverse anisotropy do not support the toroidal arrangement of lanthanoid spins in the complex.

Asymptotic solutions and convergence studies of the resistive inner region equations

A recent publication presents a detailed prescription for constructing global eigenfunctions and complex growth rates for resistive instabilities in axisymmetric toroidal systems, using the method of matched asymptotic expansions. At each singular surface in the plasma, the small-x asymptotic solutions of the ideal MHD outer-region equations are matched to the large-x asymptotic solutions of the resistive inner-region equations, with x being the distance from the singular surface. The success of this method depends upon accurate asymptotic solutions of the resistive inner region equations. Extensive studies have shown that there are not only regimes of excellent agreement with straight-through methods, without asymptotic matching, but also regimes of strong disagreement. In an effort to find the cause of this discrepancy, we present here a different method of constructing asymptotic solutions of the inner region equations and we study the convergence properties of the new and old solutions.

Instantons for particles joined by strings in three dimensional gravity

We study the instantons describing the production of particles at the ends of codimension-one objects (strings and struts) in (2 + 1)-dimensional Minkowski and de Sitter spaces. A Minkowskian background allows only for systems with vanishing total mass, so that either negative mass particles or negative tension struts are required. On a de Sitter background, on the other hand, we find processes describing the production of string/particle systems with no negative energies involved. We also compute the probabilities of creating and of breaking an infinite cosmic string in de Sitter space. We perform our analysis of the system in de Sitter space employing a generalization of the toroidal coordinate system to the three-sphere.

Nonlinear Free Vibration Analysis of a Toroidal Pressure Vessel under Constrained Volume Condition

This paper focussed on the large displacement nonlinear free vibration of a toroidal pressure vessel in free space under constrained volume condition. Three states of the toroidal pressure vessel surface comprising the initial unstrained surface, reference surface, and vibrating surface were considered in the energy functional of the toroidal pressure vessel system based on the principle of virtual work. For the reference surface, it was assumed that the toroidal pressure vessel has a circular cross-section and is subjected to uniform internal pressure. Nonlinear numerical solutions were obtained utilizing the FEM and a modified direct iteration technique, and compared with those generated by ABAQUS. More importantly, this study showed that the fundamental nonlinear natural frequency of a toroidal pressure vessel under the constrained volume condition was lower than that of the published results for an inflated toroidal membrane and shell.

Analysis of Ag/blood-mediated transport in curved annulus with exclusive nature of convective boundary

This model is concerned with the shape impact of Ag nanoparticles on peristaltic flow through a curved annulus having convective heated walls. An endoscope is a medical device for surgical use, which is inserted into the body to treat diseases. The silver nanoparticles are incorporated with unusual shapes such as platelets, cylinders and bricks. In the curved tube, the nature of Ag/blood-mediated transport is formulated in a toroidal coordinate system. The ratio of the half-tube-width to the wavelength is tiny enough to maintain a uniform pressure over the cross-section. A perturbation technique is used to solve the formulated equations for axial velocity and energy. The plots for explicit values of the embedded parameters such as the Biot number, endoscope radius, amplitude ratio and volume fraction are presented. One important finding of the present study is that the velocity increases near the inner wall of the endoscope whereas it declines close to the outer tube wall. A notable difference is observed between the flows through a non-curved and curved annulus in the obtained results. The curvature parameter enhances the velocity for the curved tube more significantly.

Tore Supra/WEST Toroidal Field Coil Quench Following a Plasma Disruption With Runaway Electrons

Tore Supra/WEST is a Tokamak operating at CEA/IRFM since 1988. Its toroidal field system is composed of 18 NbTi toroidal field coils (TFC) cooled by superfluid helium bath at 1.8 K. The system is used to operate at full current during every day of a plasma campaign, and is protected by a quench detection system (QDS) which can trigger a fast safety discharge (FSD). In December 2017, an FSD was triggered. After analysis, we could show that it was caused by the quench of TFC9, and that the quench had been triggered by a high flux of runaway electrons at the end of a plasma shot. The detection and protection systems were effective to protect the TF magnet, which is presently back in operation at nominal current without any fault. This paper presents the analyses conducted to determine the origin of the quench, the details of the QDS operation, and the impact of the quench on our cryomagnetic system.

Spectral structure of the Neumann–Poincaré operator on tori

We address the question whether there is a three-dimensional bounded domain such that the Neumann–Poincaré operator defined on its boundary has infinitely many negative eigenvalues. It is proved in this paper that tori have such a property. It is done by decomposing the Neumann–Poincaré operator on tori into infinitely many self-adjoint compact operators on a Hilbert space defined on the circle using the toroidal coordinate system and the Fourier basis, and then by proving that the numerical range of infinitely many operators in the decomposition has both positive and negative values.

Methods of multidimensional signal processing under toroidal coordinate systems

Methods of multidimensional signal processing under spatial toroidal coordinate systems configured on a set of combining sums over vector "Glory to Ukraine Star" combinatorial configurations. Base vectors are discussed, and the two theoretically grounded approaches to formation such coordinate systems in order for optimum encoding and conversion of vector signals using its unique properties, both optimum monolithic and group vector codes, and non-redundant codes are proposed. On the particular examples described the benefits of each method of coding of multidimensional signals pointing to corresponding theorems, calculations and illustrative material. Extension of the “star” combinatorial configurations opens new possibilities for the application of methods of optimized coding and processing of multidimensional signals under toroidal coordinate systems for designing modern systems of communication and development of optimized vector information technologies. The remarkable technical merits of the vector configurations, which properties hold for the same set of an optimum encoded design in varieties permutations of its terms is demonstrated, and methods for processing of two- or multidimensional vector signals based on both the optimum binary monolithic and non-redundant codes are presented. Proposed methods of multidimensional signal processing under toroidal coordinate systems provide, essentially, a new approach to generalize them to great class of optimized problems in radio-telecommunications, navigation and information technology. Moreover, the optimization embedded in the underlying combinatorial configurations. The favorable qualities of the "stars" provide breakthrough opportunities to apply them to numerous branches of science and advanced technology, with direct applications to vector data telecommunications, vector encoded design, and optimal vector information technology.

PARAMETRIC ANALYSIS AND STRAY FIELDS OF TOROIDAL SUPERCONDUCTING MAGNETIC ENERGY STORAGE

Purpose. To carry out a parametric analysis of superconducting toroidal magnetic systems with a discrete winding, establishing the possibility of using an idealized model in the form of a toroidal current surface and an approximate method for determining the level of fields of scattering of a real magnetic system. Methodology. The calculation of the distribution of the magnetic flux density in the winding, the field of scattering and energy of the storage’s field was carried out using asymptotic methods for solution of the problems of electrodynamics in systems with massive curvilinear conductors with current. An iterative calculation procedure was used to determine the dimensionless characteristics. Results. The dimensionless characteristics of a toroidal magnetic system with a winding in the form of individual superconducting coils of circular shape are calculated. The results are obtained depending on the value of the storage's energy capacity for various values of the relative radial size of the torus. For a toroidal superconducting storage device with energy capacity of 450 MJ, enough to perform the function of damping irregular oscillations of power transmitted over the transmission line, magnetic fields of scattering are calculated for different numbers of coils and torus section sizes. Originality. Based on a comparison of the values of dimensionless characteristics calculated for a system with individual coils, and for an idealized mathematical model of a continuous current surface, it was established that the relative deviation of the dimensionless characteristics does not exceed 10 %. In contrast to the idealized model, the magnetic field of a toroidal system composed of individual coils spreads beyond the toroidal surface and decreases the faster, the smaller the relative radial sectional size of the torus, the greater the number of coils used and the closer they are to each other. Practical value. The results obtained for dimensionless characteristics allow to conclude that the idealized model can be used at the first stage of the development of a superconducting inductive storage. The estimation of the field of scattering can be made on the basis of a simple model of unidirectional current filaments.

RFP based Fusion-Fission Hybrid reactor model for nuclear applications

The Reversed Field Pinch (RFP) configuration looks to be an attractive option for fusion-fission hybrid reactors: the toroidal magnetic systems would be made of copper coils instead of more expensive superconductive magnets; fusion conditions could be reached by ohmic heating only, therefore additional heating systems would not be required; the fission blanket could be located in the most external part of the torus thus facilitating maintenance operations. The paper aims at assessing the potentialities, such as fuel fertilization and/or nuclear waste transmutation and electricity production of a hybrid reactor with a RFP fusion core (R = 6 m, a = 1) whose conceptual design and plasma performances are based on RFX-mod, the largest RFP experiment currently in operation. Fusion conditions can be reached by heating a D-T plasma up to 9.6 keV by ohmic heating, generated by a 20 MA plasma current induced and sustained by flux swing only. The neutron flux (2.1 × 1013 fast neutron/cm2/s) is used to breed tritium in both the inner and outer blanket sections and induce fission reactions in dedicated areas in the external blanket section where Pu + MA (60%)-Zr (40%) rods are located. Both neutronic and safety analyses corroborate the viability of a FFH reactor with a RFP core.

Control and Protection Strategy Design of ITER Toroidal Field Coil Power Supply System

Eighteen Toroidal Field (TF) coils are operated on steady-state mode at highest current of 68 kA in comparison with the other pulse operation coils such as Poloidal Field and Central Solenoid coils in ITER superconductive magnet system, which are fed by Coil Power Supply Systema (CPSS). The reliability of TF circuit is significant to investment and nuclear safety of ITER machine. Hence, the comprehensive protection functions as Slow Discharge, Accelerated Discharge and Fast Discharge are required by ITER TF CPSS and the detailed realizations have been illustrated according to the different levels of faults to guarantee the safety of components including TF coils. In addition, the simulation model has been built by MATLAB/SIMULINK according to the real configuration of circuit and control system to verify the protection strategies and the satisfied simulation results have been obtained.

MHD equilibria with magnetic islands in the TJ-II heliac

ABSTRACTMagnetic islands normally form at the low-order magnetic rational surfaces in toroidal confinement systems when a symmetry-breaking perturbation arises. In stellarators, the equilibrium state for the plasma once the perturbation has created the islands is not easy to describe due to its complexity. Numerical computation of equilibria can be done following a variational principle that minimizes the energy under given boundary constraints when no islands are allowed, as the VMEC code does. Islands can be included by adding helical perturbations and allowing magnetic field line slipping, which was incorporated in the SIESTA code. Here we use these two codes for the TJ-II heliac in order to compute the MHD equilibrium state that provides the environment for the occurrence of all other plasma processes. The computation was done in two parts, first, obtain an equilibrium with VMEC for the whole toroidal cycle and second, superimpose the magnetic islands to obtain a final equilibrium with SIESTA by adjusting the appropriate parameters.

3D ultrasound file reading and coordinate transformations.

SummaryThe Kretzfile format is used to store 3D ultrasound data, from GE Voluson ultrasound scanners. The geometry used in these hies is a toroidal coordinate system. Cartesian coordinates are required to allow application of advanced image libraries like ITK and scikit-image.We present ITK transformation and utilities to convert Kretzfiles to cartesian coordinates. Previous work (SlicerHeart, 2017) has enabled the reading of kretz files and approximate coordinate transformations. This work will enable medical imaging researchers to investigate clinically 3D ultrasound.