Modular Coils Research Articles

Dimensional accuracy of additively manufactured structures for modular coil windings of stellarators

The paper studies the dimensional accuracy of additively manufactured (AM) coil winding structures for small experimental stellarators fabricated under industrial non-laboratory conditions. Insufficient accuracy is one of the main issues hindering the use of additive manufacturing (AM) for coil windings structures (coil casings and coil forms or frames) for stellarators.The dimensional accuracy of one complex modular coil frame and four planar coil casings is studied for different AM techniques and materials, in particular Selective Laser Sintering (SLS) in polyamide, Stereolithography (SLA) in resin, Fused Deposition Modelling (FDM) in ABS and PolyJet in resin. The measurements are performed by a Mitutoyo Coordinate Measuring Machine. The AM parts are hollow for subsequent internal casting with (fibre-reinforced) resin for strength and performance enhancement, method named 3Dformwork. The paper reports the features of the sample parts, the metrology methodology utilised, the performed measurements and the resulting dimensional deviations for each AM technique.Professional AM in FDM showed deviation between nominal dimensions and measurements of ±0.1% (one sigma, 68% of measurements) and PolyJet ±0.15%. Personal web-based AM in SLA exhibited deviation ±0.3% and SLS in polyamide ±0.4% (one sigma). The PolyJet part showed dimensional instability under harsh environment and would require immediate 3Dformwork. The FDM part presented the lower cost for the particular case study among the professional AM. Thus, high quality PolyJet and FDM additive manufacturing in plastics are at the verge of achieving the requirement of 0.1% minimum accuracy for stellarator coil windings. Therefore, AM may contribute to the fabrication of accurate winding structures for stellarators and other accurate components in fusion.

Modular Coils with Low Hydrogen Content Especially for MRI of Dry Solids.

IntroductionRecent advances have enabled fast magnetic resonance imaging (MRI) of solid materials. This development has opened up new applications for MRI, but, at the same time, uncovered new challenges. Previously, MRI-invisible materials like the housing of MRI detection coils are now readily depicted and either cause artifacts or lead to a decreased image resolution. In this contribution, we present versatile, multi-nuclear single and dual-tune MRI coils that stand out by (1) a low hydrogen content for high-resolution MRI of dry solids without artifacts; (2) a modular approach with exchangeable inductors of variable volumes to optimally enclose the given object; (3) low cost and low manufacturing effort that is associated with the modular approach; (4) accurate sample placement in the coil outside of the bore, and (5) a wide, single- or dual-tune frequency range that covers several nuclei and enables multinuclear MRI without moving the sample.Materials and MethodsThe inductors of the coils were constructed from self-supporting copper sheets to avoid all plastic materials within or around the resonator. The components that were mounted at a distance from the inductor, including the circuit board, coaxial cable and holder were manufactured from polytetrafluoroethylene.Results and ConclusionResidual hydrogen signal was sufficiently well suppressed to allow 1H-MRI of dry solids with a minimum field of view that was smaller than the sensitive volume of the coil. The SNR was found to be comparable but somewhat lower with respect to commercial, proton-rich quadrature coils, and higher with respect to a linearly-polarized commercial coil. The potential of the setup presented was exemplified by 1H / 23Na high-resolution zero echo time (ZTE) MRI of a model solution and a dried human molar at 9.4 T. A full 3D image dataset of the tooth was obtained, rich in contrast and similar to the resolution of standard cone-beam computed tomography.

Tracking of the magnet system geometry during Wendelstein 7-X construction to achieve the designed magnetic field

Wendelstein 7-X, currently under commissioning at the Max-Planck-Institut für Plasmaphysik in Greifswald, Germany, is a modular advanced stellarator, combining the modular coil concept with optimized properties of the plasma. Most of the envisaged magnetic configurations of the machine are rather sensitive to symmetry breaking perturbations which are the consequence of unavoidable manufacturing and assembly tolerances. This overview describes the successive tracking of the Wendelstein 7-X magnet system geometry starting from the manufacturing of the winding packs up to the modelling of the influence of operation loads. The deviations found were used to calculate the resulting error fields and to compare them with the compensation capacity of the trim coils.

Construction concepts and validation of the 3D printed UST_2 modular stellarator

High accuracy, geometric complexity and thus high cost of stellarators tend to hinder the advance of stellarator research. Nowadays, new manufacturing methods might be developed for the production of small and middle-size stellarators. The methods should demonstrate advantages with respect common fabrication methods, like casting, cutting, forging and welding, for the construction of advanced highly convoluted modular stellarators. UST_2 is a small modular three period quasi-isodynamic stellarator of major radius 0.26 m and plasma volume 10 litres being currently built to validate additive manufacturing (3D printing) for stellarator construction. The modular coils are wound in grooves defined on six 3D printed half period frames designed as light truss structures filled by a strong filler. A geometrically simple assembling configuration has been concocted for UST_2 so as to try to lower the cost of the device while keeping the positioning accuracy of the different elements. The paper summarizes the construction and assembling concepts developed, the devised positioning methodology, the design of the coil frames and positioning elements and, an initial validation of the assembling of the components.

Constructing a small modular stellarator in Latin America

This paper aims at briefly describing the design and construction issues of the stellarator of Costa Rica 1 (SCR-1). The SCR-1 is a small modular stellarator for magnetic confinement of plasma developed by the Plasma Laboratory for Fusion Energy and Applications of the Instituto Tecnológico de Costa Rica (ITCR). SCR-1 will be a 2-field period small modular stellarator with an aspect ratio > 4.4; low shear configuration with core and edge rotational transform equal to 0.32 and 0.28; it will hold plasma in a 6061-T6 aluminum torus shaped vacuum vessel with an minor plasma radius 54.11 mm, a volume of 13.76 liters (0.01 m3), and major radius R = 238 mm. Plasma will be confined in the volume by on axis magnetic field 43.8 mT generated by 12 modular coils with 6 turns each, carrying a current of 767.8 A per turn providing a total toroidal field (TF) current of 4.6 kA-turn per coil. The coils will be supplied by a bank of cell batteries of 120 V. Typical length of the plasma pulse will be between 4 s to 10 s. The SCR-1 plasmas will be heated by ECH second harmonic at 2.45 GHz with a plasma density cut-off value of 7.45M016 m-3. Two magnetrons with a maximum output power of 2 kW and 3 kW will be used.

SCR-1: Design and Construction of a Small Modular Stellarator for Magnetic Confinement of Plasma

This paper describes briefly the design and construction of a small modular stellarator for magnetic confinement of plasma, called Stellarator of Costa Rica 1, or SCR-1; developed by the Plasma Physics Group of the Instituto Tecnológico de Costa Rica, PlasmaTEC. The SCR-1 is based on the small Spanish stellarator UST_1, created by the engineer Vicente Queral.The SCR-1 will employ stainless steel torus-shaped vacuum vessel with a major radius of 460.33 mm and a cross section radius of 110.25mm. A typical SCR-1 plasma will have an average radius 42.2 mm and a volume of 8 liters (0.01 m3), and an aspect ratio of 5.7.The magnetic resonant field will be 0.0878 T, and a period of 2 (m=2) with a rotational transform of 0.3. The magnetic field will be provided by 12 modular coils, with 8 turns each, with an electrical current of 8704 A per coil (1088 A per turn of each coil). This current will be fed by a bank of cell batteries. The plasma will be heated by ECRH with magnetrons of a total power of 5kW, in the first harmonic at 2.45GHz. The expected electron temperature and density are 15 eV and 1017 m−3 respectively with an estimated confinement time of 7.30 x 10−4 ms. The initial diagnostics on the SCR-1 will consist of a Langmuir probe, a heterodyne microwave interferometer, and a field mapping system.The first plasma of the SCR-1 is expected at the end of 2011.

A Systematic study of modular coil characteristics for 2-field periods quasi-axisymmetric stellarator QAS-LA

Modular coil characteristics of a 2-field periods quasi-axisymmetric stellarator QAS-LA configuration with an aspect ratio Ap=3, magnetic pressure ∼4% and rotational transform ι∼0.15 per field period supplied by its own shaping have been detailed studied. In addition, the characteristics of modular coils for QAS-LA were compared with those of an intermediate QA configuration QAS-LAx and a tokamak based on the same center magnet field B0, aspect ratio and number of coils. As expected, the Bmax/B0, force F and overturning moment M, increase with the increased complexity of the coil shape. The relationships between the modular coils’ parameters (such as radius curvature ρ, distance from coil to coil Δc–c and the cross-section of coils) and the electromagnetic characteristics have been systematically summarized. The approximate formula for the maximum magnetic field in the coil body as functions of modular coil parameters (Δc–c, ρ) was derived for a simple two wire system which will be useful when optimizations of coil properties are called for.

Thermo-mechanical behavior of retro-reflector and resulting parallelism error of laser beams for Wendelstein 7-X interferometer

A 10 channels interferometer will be used in the Wendelstein 7-X (W7-X) for plasma density control and density profile tracking with laser beams passing through the plasma. Due to complex shape of non-planar modular coils and divertor structure, there are no large poloidally opposite ports on the plasma vessel (PV). Therefore 10 in-vessel Corner Cube Retro-reflectors (CCRs) will be used. The CCRs are integrated in the water cooled heat shield and exposed directly to thermal loads from plasma radiation. Thermo-mechanical issues are very important for the design of the CCR because deformation and flatness as well as mutual angles of the three reflecting surfaces would affect the parallelism of the laser beams and the functionality of the interferometer. Intensive work has been done to explore a suitable design for the CCR concerning thermo-mechanical behavior. Previous studies Ye et al. (2008, 2009) and Köppen et al. (2011) focused on structural optimization to decrease thermal stress in the reflecting plates under the thermal loads, and on computation and check of curvature radii of the deformed reflecting surfaces with the design criterion that the curvature radius must be bigger than 200m. The paper presents detailed thermo-mechanical analysis of the current improved CCR under thermal loads and bolt preloads. The results of the thermo-mechanical analysis were used for the study of the resulting parallelism error of the laser beams with newly developed and more reasonable design criterion.

Design study of 4.5 MJ sector-toroidal SMES coil

In continuation of SMES technology development in our centre, design study of a 4. 5 MJ (1.25 kW h) sector-toroidal SMES coil using custom make Rutherford type NbTi cable is reported. The sector- toroid is optimized with six modular type solenoid coils connected in series. The basic module is considered to be solenoid type because of its easier winding technique though it is not the best choice from stress considerations. The coil operating current as well as maximum magnetic field at the inner layer has been determined in order to limit voltage across the coil during discharging mode of its operation and also to minimize the overall dynamic and static load in the cryostat. Due to asymmetric field distribution around the coil, each coil experiences a huge centered force that needs to be arrested with proper support structures. Therefore, extensive magneto-structural stress analysis has been carried out using commercial finite element code ANSYS. The paper describes the magnetic design, three dimensional stress analyses in coil and its support structure during cool-down and energisation, design scheme of sector- toroidal SMES cryostat, etc.

Measurement of 3D plasma response to external magnetic perturbations in the presence of a rotating external kink

The detailed measurements of the 3D plasma response to applied external magnetic perturbations in the presence of a rotating external kink are presented, and compared with the predictions of a single-helicity linear model of kink mode dynamics. The modular control coils of the High Beta Tokamak-Extended Pulse (HBT-EP) device are used to apply resonant m/n = 3/1 magnetic perturbations to wall-stabilized tokamak plasmas with a pre-existing rotating 3/1 kink mode. The plasma response is measured in high-resolution with the extensive magnetic diagnostic set of the HBT-EP device. The spatial structures of both the naturally rotating kink mode and the externally driven response are independently measured and observed to be identical, while the temporal dynamics are consistent with the independent evolution and superposition of the two modes. This leads to the observation of a characteristic change in 3D field dynamics as a function of the applied field amplitude. This amplitude dependence is found to be different for poloidal and radial fields. The measured 3D response is compared to and shown to be consistent with the predictions of the linear single-helicity model in the “high-dissipation” regime, as reported previously [M. E. Mauel et al., Nucl. Fusion 45, 285 (2005)].

Modular 32-channel transceiver coil array for cardiac MRI at 7.0T

To design and evaluate a modular transceiver coil array with 32 independent channels for cardiac MRI at 7.0T. The modular coil array comprises eight independent building blocks, each containing four transceiver loop elements. Numerical simulations were used for B1 (+) field homogenization and radiofrequency (RF) safety validation. RF characteristics were examined in a phantom study. The array's suitability for accelerated high spatial resolution two-dimensional (2D) FLASH CINE imaging of the heart was examined in a volunteer study. Transmission field adjustments and RF characteristics were found to be suitable for the volunteer study. The signal-to-noise intrinsic to 7.0T together with the coil performance afforded a spatial resolution of 1.1 × 1.1 × 2.5 mm(3) for 2D CINE FLASH MRI, which is by a factor of 6 superior to standardized CINE protocols used in clinical practice at 1.5T. The 32-channel transceiver array supports one-dimensional acceleration factors of up to R = 4 without impairing image quality significantly. The modular 32-channel transceiver cardiac array supports accelerated and high spatial resolution cardiac MRI. The array is compatible with multichannel transmission and provides a technological basis for future clinical assessment of parallel transmission techniques at 7.0T.

Coil fabrication of the UST_1 modular stellarator and potential enhancements

Physics of stellarators has been optimized up to excellence levels. In contrast, optimization and innovation in the engineering and construction of stellarators is still comparatively modest. Particularly for stellarators but also for tokamaks, geometric complexity, small dimensional tolerances and large size currently imply relatively high fabrication costs, delaying the evolution of the stellarator research line and also hindering tokamaks. In this framework, the small low-cost modular stellarator UST_1, built and operated in a private laboratory, may contribute to the background of cost-reasonable construction methods for small fusion devices, particularly stellarators. The paper summarizes the engineering development and fabrication of UST_1 coils and outlines possible engineering R&D lines for the enhancement of the UST_1 construction methods. UST_1 consists of 12 resistive modular coils wound in grooves mechanised on a single monolithic toroidal frame surrounding the vacuum vessel. A special milling machine working on toroidal coordinates was developed, tested and built in order to accurately mechanise the grooves in the monolithic frame.

High resolution detection and excitation of resonant magnetic perturbations in a wall-stabilized tokamak

We report high-resolution detection of the 3D plasma magnetic response of wall-stabilized tokamak discharges in the High Beta Tokamak-Extended Pulse [T. H. Ivers et al., Phys. Plasmas 3, 1926 (1996)] device. A new adjustable conducting wall has been installed on HBT-EP made up of 20 independent, movable, wall segments instrumented with three distinct sets of 40 modular coils that can be independently driven to generate a wide variety of magnetic perturbations. High-resolution detection of the plasma response is made with 216 poloidal and radial magnetic sensors that have been located and calibrated with high-accuracy. Static and dynamic plasma responses to resonant and non-resonant magnetic perturbations are observed through measurement of the step-response following a rapid change in the toroidal phase of the applied perturbations. Biorthogonal decomposition of the full set of magnetic sensors clearly defines the structures of naturally occurring external kinks as being composed of independent m/n = 3/1 and 6/2 modes. Resonant magnetic perturbations were applied to discharges with pre-existing, saturated m/n = 3/1 external kink mode activity. This m/n = 3/1 kink mode was observed to lock to the applied perturbation field. During this kink mode locked period, the plasma resonant response is characterized by a linear, a saturated, and a disruptive plasma regime dependent on the magnitude of the applied field and value of the edge safety factor and plasma rotation.

Stellarator Configuration Improvement Using High Temperature Superconducting Monoliths

Substantial advances have been made in the design of stellarator configurations to satisfy physics properties and fabrication feasibility requirements for experimental devices. However, reactors will require further advances in configuration design, in particular with regard to maintenance and operational characteristics, in order to have high availability. The diamagnetic properties of bulk high temperature superconductor (HTS) material can be used to provide simple mechanisms for magnetic field-shaping by arranging them appropriately in an ambient field produced by relatively simple coils.A stellarator configuration has been developed based on this concept. A small number of toroidal field coils carrying appropriate current would be sufficient to create a background toroidal field. Discrete HTS monoliths (“pucks” or “tiles”) are placed on a shaped structure that can be split in the poloidal direction at arbitrary locations. This allows modular stellarators to be designed with large openings that provide access to remove interior plasma facing components, no longer restricted by highly shaped back legs of the modular coil winding. Unlike a coil, the structure can be assembled and disassembled in pieces of convenient size, facilitating maintenance.Calculations of the effect of the use of monoliths for field modification in stellarators and tokamaks will be described.

High temporal and spatial resolution 3D time-resolved contrast-enhanced magnetic resonance angiography of the hands and feet

Methods are described for generating 3D time-resolved contrast-enhanced magnetic resonance (MR) angiograms of the hands and feet. Given targeted spatial resolution and frame times, it is shown that acceleration of about one order of magnitude or more is necessary. This is obtained by a combination of 2D sensitivity encoding (SENSE) and homodyne (HD) acceleration methods. Image update times from 3.4-6.8 seconds are provided in conjunction with view sharing. Modular receiver coil arrays are described which can be designed to the targeted vascular region. Images representative of the technique are generated in the vasculature of the hands and feet in volunteers and in patient studies.

The high beta tokamak-extended pulse magnetohydrodynamic mode control research program

The high beta tokamak-extended pulse (HBT-EP) magnetohydrodynamic (MHD) mode control research program is studying ITER relevant internal modular feedback control coil configurations and their impact on kink mode rigidity, advanced digital control algorithms and the effects of plasma rotation and three-dimensional magnetic fields on MHD mode stability. A new segmented adjustable conducting wall has been installed on the HBT-EP and is made up of 20 independent, movable, wall shell segments instrumented with three distinct sets of 40 saddle coils, totaling 120 in-vessel modular feedback control coils. Each internal coil set has been designed with varying toroidal angular coil coverage of 5, 10 and 15°, spanning the toroidal angle range of an ITER port plug based internal coil to test resistive wall mode (RWM) interaction and multimode MHD plasma response to such highly localized control fields. In addition, we have implemented 336 new poloidal and radial magnetic sensors to quantify the applied three-dimensional fields of our control coils along with the observed plasma response. This paper describes the design and implementation of the new control shell incorporating these control and sensor coils on the HBT-EP, and the research program plan on the upgraded HBT-EP to understand how best to optimize the use of modular feedback coils to control instability growth near the ideal wall stabilization limit, answer critical questions about the role of plasma rotation in active control of the RWM and the ferritic resistive wall mode, and to improve the performance of MHD control systems used in fusion experiments and future burning plasma systems.

Collisionless fast-particle confinement in high-β W7-X equilibria

Fast-particle collisionless confinement in Wendelstein 7-X is revisited exploring the configurational space given by the currents in the modular and auxiliary coils and a two-parameter pressure profile. Preliminary results indicate that at 〈β〉 ∼ 0.04 the core-plasma loss cone usually present in stellarators can be approximately eliminated.

ICONE19-43983 An Engineering Approach to the Design and Construction of a Small Modular Stellarator for Magnetic Confinement of Plasma : SCR-1

This paper briefly describes the design and construction of Stellarator of Costa Rica 1 (SCR-1) from an engineering perspective. SCR-1 is a small modular Stellarator for magnetic confinement of plasma developed by the Plasma Physics Group of the Instituto Tecnologico de Costa Rica (ITCR). The SCR-1 is based on the small Spanish Stellarator UST_1 (Ultra Small Torus 1), created by engineer Vicente Queral [1]. Some of the characteristics of the SCR-1 are the following: it will be a 2-field period modular stellarator with an aspect ratio &ap; 6; low shear configuration with core and edge rotational transform equal to 0.32 and 0.28; it will employ stainless steel torus-shaped vacuum vessel which will hold a plasma with an average radius a &ap; 42.2 mm, a volume of 8 liters (0.008 m^3), and major radius R=238 mm. This plasma will be confined by a magnetic field (B &ap; 90 mT) given by 12 modular coils with 12 turns each, carrying a current of 725 A per turn providing a total toroidal field (TF) current of 8.7 kA-turn per coil. The coils will be supplied by a bank of cell batteries of 120 V. Typical length of the plasma pulse will be between 4 s to 10 s. The plasma heating will be achieved by electron cyclotron radio-frequency (ECH) from two magnetrons providing a total power of 5kW, at a frequency of 2.45GHz corresponding to the first harmonic (B_0=87.8 mT). The expected electron temperature and density are 15 eV and 7×10^<16> m^<-3> respectively. The initial diagnostics on the SCR-1 will consist of a Langmuir probe with a displacement system, a heterodyne microwave interferometer (frequency of 28 GHz, corresponding to a wavelength of λ=10.71 mm). The first plasma of the SCR-1 is expected at the beginning of 2012.

New classes of quasi-helically symmetric stellarators

New classes of quasi-helically symmetric stellarators with aspect ratios ⩽10 have been found which are stable to the perturbation of magnetohydrodynamic modes at plasma pressures of practical interest. These configurations have large rotational transform and good quality of flux surfaces. Characteristics of some selected examples are discussed in detail. The feasibility of using modular coils for these stellarators has been investigated. It is shown that practical designs for modular coils can be achieved.

Stellarator coil design and plasma sensitivity

The rich information contained in the plasma response to external magnetic perturbations can be used to help design stellarator coils more effectively. We demonstrate the feasibility by first developing a simple direct method to study perturbations in stellarators that do not break stellarator symmetry and periodicity. The method applies a small perturbation to the plasma boundary and evaluates the resulting perturbed free-boundary equilibrium to build up a sensitivity matrix for the important physics attributes of the underlying configuration. Using this sensitivity information, design methods for better stellarator coils are then developed. The procedure and a proof-of-principle application are given that (1) determine the spatial distributions of external normal magnetic field at the location of the unperturbed plasma boundary to which the plasma properties are most sensitive, (2) determine the distributions of external normal magnetic field that can be produced most efficiently by distant coils, and (3) choose the ratios of the magnitudes of the efficiently produced magnetic distributions so the sensitive plasma properties can be controlled. Using these methods, sets of modular coils are found for the National Compact Stellarator Experiment (NCSX) which are either smoother or can be located much farther from the plasma boundary than those of the present design.