Discrete Coils Research Articles

Retraction Note: Comparison between Discrete Magnetic Coils and Multipole Coils for Measurement of Plasma Displacement in IR-T1 Tokamak

Retraction Note: Comparison between Discrete Magnetic Coils and Multipole Coils for Measurement of Plasma Displacement in IR-T1 Tokamak

Designing gradient coils with the shape derivative and the closed B-spline curves

This study proposes a versatile and efficient optimisation method for discrete coils that induce a magnetic field by their steady currents. The prime target is gradient coils for MRI (Magnetic Resonance Imaging). The derivative (gradient) of the z-component the magnetic field, which is calculated by the Biot–Savart's law, with respect to the z-coordinate in the Cartesian xyz coordinate system is considered as the objective function. Then, the derivative of the objective function with respect to a change of coils in shape is formulated according to the concept of shape optimisation. The resulting shape derivative (as well as the Biot–Savart's law) is smoothly discretised with the closed B-spline curves. In this case, the control points (CPs) of the curves are naturally selected as the design variables. As a consequence, the shape derivative is discretised to the sensitivities of the objective function with respect to the CPs. Those sensitivities are available to solve the present shape-optimisation problem with a certain gradient-based nonlinear-programming solver. The numerical examples exhibit the mathematical reliability, computational efficiency, and engineering applicability of the proposed methodology based on the shape derivative/sensitivities and the closed B-spline curves.

Distributed Poloidal Magnetic Field Measurement in Tokamaks Using Polarization-Sensitive Reflectometric Fiber Optic Sensor.

Determination of the poloidal magnetic field distribution in tokamaks is of prime importance for the successful operation of tokamaks. In this paper, we propose a polarization-sensitive reflectometry-based optical fiber sensor for measuring the spatial distribution of the poloidal magnetic field in tokamaks. The measurement method exploits the Rayleigh backscattering and Faraday magneto-optic effect in optical fibers. The former is an intrinsic property of optical fibers and enables distributed polarization measurements, while the latter arises in the presence of a magnetic field parallel to the optical fiber axis and rotates the polarization state of the light. When an optical fiber is looped around a toroidal section of the vacuum vessel, the local polarization rotation of the light is proportional to the local poloidal magnetic field in the tokamak. The proposed method is discussed theoretically and experimentally using the results from JET. The obtained magnetic field measurement shows a good agreement with that of the internal discrete coils. A potential solution to recover the magnetic field data from the noise-affected region of the optical measurement is proposed and is demonstrated through simulations using the JET magnetic field configuration.

Magnetic field design in a cylindrical high-permeability shield: The combination of simple building blocks and a genetic algorithm

Magnetically sensitive experiments and newly developed quantum technologies with integrated high-permeability magnetic shields require increasing control of their magnetic field environment and reductions in size, weight, power, and cost. However, magnetic fields generated by active components are distorted by high-permeability magnetic shielding, particularly when they are close to the shield’s surface. Here, we present an efficient design methodology for creating desired static magnetic field profiles by using discrete coils electromagnetically coupled to a cylindrical passive magnetic shield. We utilize a modified Green’s function solution that accounts for the interior boundary conditions on a closed finite-length high-permeability cylindrical magnetic shield and determine simplified expressions when a cylindrical coil approaches the interior surface of the shield. We use an analytic formulation of simple discrete building blocks to provide a complete discrete coil basis to generate any physically attainable magnetic field inside the shield. We then use a genetic algorithm to find optimized discrete coil structures composed of this basis. We use our methodology to generate an improved linear axial gradient field, dBz/dz, and a transverse bias field, Bx. These optimized structures generate the desired fields with less than 1% error in volumes seven and three times greater in spatial extent than equivalent unoptimized standard configurations. This coil design method can be used to optimize active–passive magnetic field shaping systems that are compact and simple to manufacture, enabling accurate control of magnetic field changes in spatially confined experiments at low cost.

Performance Analysis of a New HTS-Excitation Claw-Pole Doubly-Salient Machine

This paper proposes a new 12-slot/10-pole high-temperature superconducting excitation claw-pole doubly-salient (HTS-CPDS) machine with a single HTS-excitation unit using stationary seal cooling. The key advantage of adopting claw-pole structure is that a ring-shaped HTS-excitation coil can be easily wound and artfully placed in the claw-pole cavity to realize the design of single excitation unit, and thus the cooling Dewar design for stationary seal is easily implemented. Also, due to using HTS-excitation, the air-gap flux can be flexibly regulated by changing the HTS current, thus keeping a constant amplitude of phase back-EMF under different rotor speeds. The cooling Dewar construction and the key parameter optimization are illustrated in detail. And compared to a counterpart employing the discrete racetrack HTS coils, the proposed machine can significantly reduce the HTS wire consumption and electromagnetic stress to a certain extent, thus cutting the cost and improving the anti-quench ability. By using the finite element analysis (FEA), the machine electromagnetic performances are evaluated, and its validity is verified.

Advancing the physics basis for quasi-helically symmetric stellarators

A new optimized quasi-helically symmetric configuration is described that has the desirable properties of improved energetic particle confinement, reduced turbulent transport by three-dimensional shaping and non-resonant divertor capabilities. The configuration presented in this paper is explicitly optimized for quasi-helical symmetry, energetic particle confinement, neoclassical confinement and stability near the axis. Post optimization, the configuration was evaluated for its performance with regard to energetic particle transport, ideal magnetohydrodynamic stability at various values of plasma pressure and ion temperature gradient instability induced turbulent transport. The effects of discrete coils on various confinement figures of merit, including energetic particle confinement, are determined by generating single-filament coils for the configuration. Preliminary divertor analysis shows that coils can be created that do not interfere with expansion of the vessel volume near the regions of outgoing heat flux, thus demonstrating the possibility of operating a non-resonant divertor.

Fusion α loss due to toroidal field ripple perturbation in CFETR

The key issue of burning plasma in tokamak is the loss and confinement of the energetic particles, and one of the loss channels is the perturbation due to discrete toroidal field coils. The work investigated the α ripple loss of CFETR hybrid scenario with plasma transportation code TRANSP/NUBEAM and guiding center code ORBIT, which have considered the initial α distribution, classical steady state slowing down distribution and other models. The results of the work can give the information of the lost particles, including the lost position, fraction and localized heat load on the wall. The study reveals the heat load on CFETR is about 0.13 MW/m2, which is below the safety threshold of ITER, 0.5 MW/m2, and the paper also gives the direction to reduce the α ripple loss.

Оценка роли взаимоиндукции между путевыми катушками в системе электродинамического подвеса высокоскоростного поезда

A high-speed train with an electrodynamic suspension with discrete track coils, a superconducting excitation winding and a null-flux connection scheme of the suspension coils is considered. The influence of the individual coefficients of mutual inductance in the system of track coils on the average lift forces, lateral stabilization, electrodynamic resistance to motion and the amplitude of their pulsations as a function of speed is estimated. The change in the levitation quality parameter is analyzed depending on the mutual inductance of the suspension coils at all speeds of motion. For a given car mass m = 20 tons, the balance vertical offset (when the lift force compensates the car’s weight) is obtained from the speed of movement.The dependence of the lateral and vertical stiffness of the system on speed is demonstrated. The dependence of the required lateral deviation of the train on the radius of the curve to be overcome is obtained.

Design of the Toroidal Field Coil System for the TPM-1U Tokamak

Using infrastructure from the old TPM-1 tokamak in Mexico, there is an ongoing project to bring it back into operation, but with important upgrades. One of the main planned improvements will be the substitution of the continuous winding used to generate the toroidal field (TF) with a set of discrete circular coils. The new toroidal magnetic field configuration should also allow stable operation of the machine at plasma currents of up to 50 kA for 30 ms. At this design stage, decisions regarding number and characteristics of the coils and power delivery strategy to them need to be addressed. In the present paper, a study regarding the parameters required for the generation of the adequate TF are presented, including the process for determining number of TF coils, their size and position, the required current pulse for operation, and a potential strategy for generating such pulse based on passive pulse-forming networks.

Equilibrium evaluation for Wendelstein 7-X experiment programs in the first divertor phase

Wendelstein 7-X (W7-X) is a modular advanced stellarator, which successfully went into operation in December 2015 at the Max-Planck-Institut für Plasmaphysik in Greifswald, Germany, and continued to thrive at the experimental campaign with the first divertor phase in August-December 2017. The nested magnetic surfaces in W7-X are created by a system of 3-D toroidally discrete coils, providing both toroidal and poloidal field components, and designed with the aim to create optimum equilibrium properties. The optimization criteria included the high quality of vacuum magnetic surfaces, good finite beta equilibrium and MHD-stability properties as well as a substantial reduction of the neoclassical transport and bootstrap current in comparison to classical stellarators.Equilibrium calculations, devoted to the analysis of the experiment programs dedicated to measure the bootstrap current, were performed with help of the Variational Moments Equilibrium Code, available as Wendelstein 7-X web service. Pressure profiles based on experimental data served as an input for calculations. The mapping of measurements using pre-calculated equilibria for different beta values has been analyzed. A comparison with reconstruction results obtained by means of the Minerva Framework, considering only experimental data of magnetics measurements, and the V3FIT code is presented.

2-D quasi-static Fourier series solution for a linear induction motor

PurposeThis paper aims to present a method for calculating electromagnetic fields, eddy currents and forces for a quasi-static two-dimensional (2-D) model of linear induction motors (LIMs) where the primary side is modeled as a collection of individual coils.Design/methodology/approachAn analytical solution using Fourier series is derived for a general source with current excitations residing in an airgap and moving relative to a conducting plate and back iron. Ideal magnetic material with infinite permeability is used to model the primary iron above the primary source and the back iron below the conducting plate.FindingsThe analytical solution is compared to a commercial 2-D finite element analysis (FEA) simulation for validation and then compared to a 2-D FEA model with a more detailed geometry of the LIM. The analytical model accurately predicts LIM thrust even though the geometry of the primary core is simplified as an infinitely long flat slab. 2-D frequency FEA can be used successfully to predict in motion LIM performance.Originality/valueThe analytical solution presented here models the primary excitations as individual discrete coils instead of current sheets, which all existing models are based on. The discrete coils approach provides a more intuitive and realistic model of the LIM.

A Continuous Toroidal Winding SRM With 6- or 12-Switch DC Converter

A new toroidally wound switched reluctance machine (TSRM) with a single continuous multitapped winding is presented. This machine may be driven by a 6-switch asymmetric converter that supplies unipolar coil currents or by a 12-switch voltage source converter that supplies bipolar coil currents. The TSRM magnetic design and power electronic control is described, and its performance is compared with a conventional switched reluctance motor (CSRM) and with a previously reported toroidal format switched reluctance machine that utilizes six discrete winding coils in a three-phase wye connection (WSRM) driven by a voltage source inverter. A fixed 6–4 CSRM magnetic circuit design is selected for the comparative analysis of the three machine topologies by static and dynamic finite-element simulations.

3D toroidal physics: Testing the boundaries of symmetry breakinga)

Toroidal symmetry is an important concept for plasma confinement; it allows the existence of nested flux surface MHD equilibria and conserved invariants for particle motion. However, perfect symmetry is unachievable in realistic toroidal plasma devices. For example, tokamaks have toroidal ripple due to discrete field coils, optimized stellarators do not achieve exact quasi-symmetry, the plasma itself continually seeks lower energy states through helical 3D deformations, and reactors will likely have non-uniform distributions of ferritic steel near the plasma. Also, some level of designed-in 3D magnetic field structure is now anticipated for most concepts in order to provide the plasma control needed for a stable, steady-state fusion reactor. Such planned 3D field structures can take many forms, ranging from tokamaks with weak 3D edge localized mode suppression fields to stellarators with more dominant 3D field structures. This motivates the development of physics models that are applicable across the full range of 3D devices. Ultimately, the questions of how much symmetry breaking can be tolerated and how to optimize its design must be addressed for all fusion concepts. A closely coupled program of simulation, experimental validation, and design optimization is required to determine what forms and amplitudes of 3D shaping and symmetry breaking will be compatible with the requirements of future fusion reactors.

Calculation of 3-D Magnetic Fields Produced by MHD Active Control Systems in Fusion Devices

An accurate control of the magnetic boundary of a thermonuclear plasma is an important issue in magnetic confinement research. The development of methods for the active control of magnetohydrodynamic instabilities and correction of error fields is mandatory in view of fusion reactors or experimental test reactors under design. Recently, a very effective control scheme, named clean mode control (CMC), has been proposed in a reversed field pinch experiment (RFX-mod). The CMC is based on the real-time correction (cleaning), under simplifying hypothesis, of the sideband harmonics in the magnetic field produced by the discrete local active coils. In this paper, we focus on the problem of carefully computing the penetration of sidebands through a realistic load assembly, but still with a simplified cylindrical geometry, to allow for a detailed comparison with the crude CMC algorithm without the additional complication of the coupling between the poloidal harmonics due to the toroidal geometry.

Half of internal inductance plus poloidal beta and plasma position in a circular cross-section tokamak

A special analytical solution of the Grad–Shafranov equation (GSE) is presented with source functions, where the plasma pressure is linear in ψ and the squared poloidal current has both a quadratic and a linear ψ term. Half of internal inductance plus poloidal beta and plasma position have been calculated for a typical discharge of IR-T1 tokamak with circular cross-section. In the presented solution, six parameters are measured by the magnetic measurements. The calculated parameters approach the values measured by discrete magnetic coils in the middle of IR-T1 discharge.

Plasma Position Determination by Using Fixed Boundary Conditions in GSE Solution Versus Experimental Technique in IR-T1 Tokamak

Plasma position displacement is presented by considering linear source functions in the Grad-Shafranov equation (GSE) solution and by assuming circular fixed boundary conditions and a constant plasma minor radius in the IR-T1 Tokamak. A new method for the GSE analytical solution is demonstrated by imposing constraints on the plasma current measured by the Rogowski coil and βp + li/2 measured by four discrete magnetic coils. Plasma position displacement is also measured by four discrete magnetic coils as an experimental technique, and the result is compared with our analytical technique. The result comparison shows good agreement around the steady-state equilibrium.

Stability analysis for axially-symmetric magnetic field levitation of a superconducting sphere

For a magnetically levitated superconducting sphere, the stability analysis in both axial and radial directions is analyzed theoretically using a direct boundary-value problem approach. The external magnetic field is produced by a system of current-carrying coils with axial symmetry. We also assume complete exclusion of magnetic fields from the interior of the superconductor. Use of the P l 1 associated Legendre functions as a basis set allows for a simple series solution for the magnetic stiffness coefficients as tridiagonal quadratic forms in terms of the expansion coefficients. Analysis shows that stability for this problem is not guaranteed in general. Stability is guaranteed though, if coil windings are designed in such away that all but one of the expansion coefficients are zero. Further cases with two and three non-zero coefficients are also solved. In particular the important 1, 3 and 2, 4 cases are treated in detail, and stability maps have been produced. Finally, the case where levitation is attempted by one pair of discrete current coils has been solved and stability mapping has been thoroughly explored.

Comparison Between Discrete Magnetic Coils and Multipole Coils for Measurement of Plasma Displacement in IR-T1 Tokamak

We have expressed two different methods to determine the plasma positions in the IR-T1 tokamak. An array of magnetic probes are placed polidally outside the chamber surface and their signals are plugged in the displacement equation and horizontal displacement of plasma column is obtained. The results of this measurement are compared with the experimental data obtained from sensors of multipole moment. It was detected a fluctuation in plasma displacement obtained with discrete magnetic coils, so the method of multiple moments is better than the discrete magnetic coils for the determination plasma displacement that used for feed back control.

Lorenz Forces Exerted by the Magnetic Mirror and Magnetic Influence of the Cryostat on the ATLAS BT Coils During the Test

The air-core Barrel Toroid of the ATLAS Detector at the CERN Large Hadron Collider, is the largest superconducting magnet ever built. This muon-spectrometer magnet consists of 8 discrete coils, arranged symmetrically around the beam axis. The average field is 0.5 T, and the stored energy 1.1 GJ. The windings are 25 m long, 5 m wide and 0.4 m thick. Each coil cold mass consists of 2 double pancakes of aluminum-stabilized NbTi conductor securely fixed in an aluminum alloy casing. Before assembly, each coil is tested individually in the presence of a magnetic mirror to simulate the magnetic forces exerted on the tie rods. This mirror is composed of several iron plates made of magnetically non-linear material. Each coil is enclosed in a separate, stainless-steel cryostat with relative magnetic permeability slightly larger than 1. In this paper the magnetic field distribution and Lorenz forces between the magnetic mirror and the coil in centered and shifted positions are presented. The magnetic influence of the cryostat on the field distribution is also discussed.

Magnetic self organization, MHD active control and confinement in RFX-mod

RFX-mod is a reversed field pinch (RFP) experiment equipped with a system that actively controls the magnetic boundary. In this paper we describe the results of a new control algorithm, the clean mode control (CMC), in which the aliasing of the sideband harmonics generated by the discrete saddle coils is corrected in real time. CMC operation leads to a smoother (i.e. more axisymmetric) boundary. Tearing modes rotate (up to 100 Hz) and partially unlock. Plasma–wall interaction diminishes due to a decrease of the non-axisymmetric shift of the plasma column. With the ameliorated boundary control, plasma current has been successfully increased to 1.5 MA, the highest for an RFP. In such regimes, the magnetic dynamics is dominated by the innermost resonant mode, the internal magnetic field gets close to a pure helix and confinement improves.