Magnetic Ripple Research Articles

Design of a Wedge-Shaped Toroidal Field Winding for KTX Device

The KTX device is a reversed field pinch (RFP) device currently under construction. Its maximum plasma current is designed as 1 MA with a discharge time longer than 100 ms. Its major radius is 1.4 m and its minor radius is 0.55 m. One of the most important problems in the magnet system design is how to reduce the TF magnetic field ripple and error field. A new wedge-shaped TF coil is put forward for the KTX device and its electromagnetic properties are compared with those of rectangular-shaped TF coils. The error field Bn/Bt of wedge-shaped TF coils with 6.4 degrees is about 6% as compared with 8% in the case of a rectangular-shaped TF coil. Besides, the wedge-shaped TF coils have a lower magnetic field ripple at the edge of the plasma region, which is smaller than 7.5% at R=1.83 m and 2% at R=1.07 m. This means that the tokamak operation mode may be feasible for this device when the plasma area becomes smaller, because the maximum ripple in the plasma area of the tokamak model is always required to be smaller than 0.4%. Detailed analysis of the results shows that the structure of the wedged-shape TF coil is reliable. It can serve as a reference for TF coil design of small aspect ratio RFPs or similar torus devices.

Coupling currents and hysteresis losses in MgB2 superconductors

MgB2 multi-filamentary superconductors are widely considered for use in dc applications. To expand the possible application range to ac apparatuses, the development of a low ac loss wire is needed. This development involves several steps, and a solid understanding of the loss mechanisms is important to optimize that process as well as for evaluating dc wires exposed to current or magnetic field ripple. In this study we discuss the coupling currents and their influence on hysteresis loss as well as on coupling current loss. We give a phenomenological explanation of the origin and behaviour of the coupling currents and describe the loss patterns for hysteresis loss and coupling current loss separately. Finally, we interpret measured ac losses in an MgB2 wire cut into different lengths representing different equivalent twist pitches. Under certain circumstances short sample lengths are shown to give inaccurate measurement results. On the other hand, short sample lengths of non-twisted wires can be used to estimate the twist pitch necessary to electromagnetically decouple the superconducting filaments. For the studied MgB2 wire, with a pure titanium matrix, the losses were mainly hysteretic, although the level of these losses was lowered when reducing the equivalent twist pitch, and thereby the coupling currents. At 35 K the reduction in loss started at an equivalent twist pitch of approximately 36 mm, where the filaments were assumed practically fully coupled. The decoupling then continued all down to the shortest equivalent twist pitch of 9 mm.

Proto-CIRCUS tilted-coil tokamak–torsatron hybrid: Design and construction

We present the field-line modeling, design, and construction of a prototype circular-coil tokamak–torsatron hybrid called Proto-CIRCUS. The device has a major radius R=16cm and minor radius a<5cm. The six “toroidal field” coils are planar as in a tokamak, but they are tilted. This, combined with induced or driven plasma current, is expected to generate rotational transform, as seen in field-line tracing and equilibrium calculations. The device is expected to operate at lower plasma current than a tokamak of comparable size and magnetic field, which might have interesting implications for disruptions and steady-state operation. Additionally, the toroidal magnetic ripple is less pronounced than in an equivalent tokamak in which the coils are not tilted. The tilted coils are interlocked, resulting in a relatively low aspect ratio, and can be moved, both radially and in tilt angle, between discharges. This capability will be exploited for detailed comparisons between calculations and field-line mapping measurements. Such comparisons will reveal whether this relatively simple concept can generate the expected rotational transform.

The manifestations of the two-dimensional magnetic correlations in the nanocrystalline ribbons Fe64Co21B15

Abstract We report and discuss the grain size dependence of the coercivity and approach magnetization to saturation in the FeCoB ribbons. Instead of expected three-dimensional magnetic correlations for 20 μm thick ribbon with grain size about 10 nm, the observed behavior could be attributed to the two-dimensional stochastic magnetic domains and two dimensional magnetization ripple.

Numerical study of fast ion behavior in the presence of magnetic islands and toroidal field ripple in the EAST tokamak

A peculiar first orbit loss type was found apart from the normal ones when we use ORBIT code to simulate fast ion orbits in the EAST tokamak. Fast ion orbits were studied in the presence of toroidal field (TF) ripple and magnetohydrodynamic (MHD) perturbations. We analyzed the properties of the drifted orbits in detail and compared their differences, finding that the combined effects of ripple and magnetic islands are much greater than the effects of either one of them alone. Then we investigated the orbit deviations as a function of pitch angle in different radial positions. The modeling results demonstrate that the loss of trapped particles is mainly caused by the ripple, while MHD perturbation mainly plays an important role in the passing particles. Furthermore we modeled the loss rate using different equilibriums. Results prove that a higher beta can indeed improve the confinement of fast ions, while a little change in the q profile can make the topologies of magnetic islands become quite different and results in quite different total particle losses.

Chaotic motion of charged particles in toroidal magnetic configurations.

We study the motion of a charged particle in a tokamak magnetic field and discuss its chaotic nature. Contrary to most of recent studies, we do not make any assumption on any constant of the motion and solve numerically the cyclotron gyration using Hamiltonian formalism. We take advantage of a symplectic integrator allowing us to make long-time simulations. First considering an idealized magnetic configuration, we add a nongeneric perturbation corresponding to a magnetic ripple, breaking one of the invariant of the motion. Chaotic motion is then observed and opens questions about the link between chaos of magnetic field lines and chaos of particle trajectories. Second, we return to an axisymmetric configuration and tune the safety factor (magnetic configuration) in order to recover chaotic motion. In this last setting with two constants of the motion, the presence of chaos implies that no third global constant exists, we highlight this fact by looking at variations of the first order of the magnetic moment in this chaotic setting. We are facing a mixed phase space with both regular and chaotic regions and point out the difficulties in performing a global reduction such as gyrokinetics.

Research on Direct Torque Control Adaptive Fuzzy Neural Network Controller of Permanent Magnet Synchronous Motor

Has the advantages of quick response of PMSM using the method of DTC, but will make the high torque and big magnetic flux linkage ripples. In order to solve this problem, using the fuzzy neural network hybrid system to replace the traditional hysteresis controller, Strong learning ability and fuzzy logic in handling uncertain information has the adaptive ability of neural network, the fuzzy neural network hybrid system to produce the expected voltage vector, the speed of a smooth transition of permanent magnet synchronous motor. The proposed method is validated by simulation under external disturbances in motor is very effective to reduce the ripple of torque and flux, the speed of the fast response and smooth transition.

Hysteresis losses in MgB2 superconductors exposed to combinations of low AC and high DC magnetic fields and transport currents

MgB2 superconductors are considered for generator field coils for direct drive wind turbine generators. In such coils, the losses generated by AC magnetic fields may generate excessive local heating and add to the thermal load, which must be removed by the cooling system. These losses must be evaluated in the design of the generator to ensure a sufficient overall efficiency. A major loss component is the hysteresis losses in the superconductor itself. In the high DC – low AC current and magnetic field region experimental results still lack for MgB2 conductors. In this article we reason towards a simplified theoretical treatment of the hysteresis losses based on available models in the literature with the aim of setting the basis for estimation of the allowable magnetic fields and current ripples in superconducting generator coils intended for large wind turbine direct drive generators. The resulting equations use the DC in-field critical current, the geometry of the superconductor and the magnitude of the AC magnetic field component as parameters. This simplified approach can be valuable in the design of MgB2 DC coils in the 1–4T range with low AC magnetic field and current ripples.

Features of the microwave radiation under the fan instability development and accelerated electron interaction with magnetic ripples in the FT-2 tokamak ohmically heated plasma

Results of observation of anomalously intense microwave radiation (MR) in the electron plasma frequency range of 10–20 GHz that is generated continuously during ohmic heating of moderately dense plasma in the FT-2 tokamak are presented. Its appearance is associated with development of the “fan” plasma instability, and the presence of a large number of the local ripples of the toroidal magnetic field. It was found that MR is accompanied by the short gigantic and less intense flashes in the range of magnetic broadening of the first harmonic of the electron gyrofrequency (57–75 GHz). As is known, the latter occurs upon maser amplification of the synchrotron radiation of accelerated electrons interacting with the harmonics of local magnetic ripples in an autoresonance cyclotron mode. In our conditions, due to the nonlinear transformation of plasma waves into electromagnetic ones under the buildup of the fan instability, collective radiation (CR) is generated. Therefore, an abnormally high MR-intensity is probably due to CR maser amplification, whereas gigantic flashes occur during the self-excitation of maser amplifier under suitable conditions.

Power Losses of 2G HTS Coils Measured in External Magnetic DC and Ripple Fields

Power losses are an important phenomenon in type-2 superconductors. Precise evaluation of power losses in superconducting coils is crucial for designing novel machines such as superconducting motors or generators. Although ac losses are relatively easy to measure with electrical methods, it is more difficult to measure power losses in the dc mode, which is induced by varying external magnetic fields, such as in a real operating environment. In particular, the problematic one could be the direct-drive wind generator, where several elements introduce nonsynchronous disturbances to the magnetic fields. Modeling had been carried out to estimate the power losses in second-generation high-temperature superconducting coils under various external dc or ripple fields; however, experimental work in the area is less common due to the difficulty of conducting experiments and special equipment requirements. In this paper, power losses under various magnetic fields are experimentally measured by the calorimetric method.

Intrinsic plasma rotation determined by neoclassical toroidal plasma viscosity in tokamaks

Intrinsic toroidal plasma rotation due to the neoclassical toroidal plasma viscosity (NTV) effect induced by a three-dimensional helical magnetic field ripple in tokamaks is investigated in this paper. The intrinsic rotation is determined self-consistently by searching for the roots of the ambipolarity constraint, after evaluation of the particle fluxes from the numerical modelling. In the low-collisionality case, there are three roots, in which two are stable roots. One corresponds to the ‘ion root’ in the counter-current direction, and the other stable one corresponds to the ‘electron root’ in the co-current direction, near which the electron flux is dominant. Both of the two stable roots scale like the diamagnetic frequency. In the high-collisionality case, there is only one ‘ion’ root. The application of this modelling for International Thermonuclear Experimental Reactor (ITER) cases is discussed. In a large range of plasma radii, there are three roots. The NTV torque drives plasma rotation in ITER towards one of the stable roots, depending on the initial condition. The amplitudes of the electron roots near the pedestal in both baseline and steady-state scenarios are much larger than that of the ion roots. The amplitudes of the NTV torque density and the electron roots near the pedestal increase with increasing height of the temperature pedestal in the ITER baseline scenario.

Vessel and In-Vessel Components Design Upgrade of the FAST machine

The Fusion Advanced Study Torus (FAST), with its compact Tokamak design, high toroidal field and plasma current, will face many of the problems that ITER will meet and will anticipate many DEMO relevant physics and technology issues. The Design Upgrade of the Vessel and In-Vessel Components is presented in this paper. Relevant modifications were performed to the Vacuum Vessel (VV) and to the Plasma Facing Components (PFCs), i.e. the First Wall (FW) and the Divertor.The VV was modified to insert active reduction coils (ARC), between VV and the toroidal field (TF) coils to keep toroidal field magnet ripple lower than 0.3% and to allow Remote Handling for the FW and the Divertor.The FW, was modified to house coils for ELMs control and other plasma instabilities. A 3D thermo-hydraulic analysis using ANSYS code was performed to check FW heat removal capability.A new Divertor was designed to withstand the largest thermal loads of the high performance, low density, H-mode and to be able to comply with a recent magnetic topology called as “Snow Flake”, increasing up a factor 4 the flux expansion. An exhaustive 3D thermo-hydraulic analysis using ANSYS code was carried out to show the capability of the Divertor to comply these high requirements. Design criteria were satisfied by present components of the upgraded machine.

Effect of an additional ferromagnetic material on the toroidal magnetic field ripple in the ITER

In the ITER tokamak, the toroidal magnetic field (TF) ripple is estimated with TF coils only, with the installation of ferromagnetic inserts (FIs), and with test blanket modules (TBMs) by using a 2-D code for easy and fast calculation. We assessed the effects of the thickness of the FIs on the TF ripple in order to optimize the FI. And we analyzed how the TBMs distort the TF, and calculated the TF ripple for various amounts of a ferromagnetic material and the positions of the TBMs. Even in the case of moving the TBMs outward up to 60-cm, and reducing the ferromagnetic material to 52%, the TF ripple is not decreased below 0.38%. So we had to adopt ripple correction coils. With a 52% reduced amount of the ferromagnetic material in a TBM, we could reduce the TF ripple to 0.28% at a coil current of 100kAturn per each coil. And with an outward recess of the TBM up to 60cm, we could reduce the TF ripple to 0.23% at a coil current of 250kAturn per each coil. As a combined approach, if we reduce the amount of a ferromagnetic material in a TBM to 30%, and recess the TBM to 15cm, we can efficiently obtain the TF ripple of 0.25% at a coil current of 150kAturn per each coil.

Effect of magnetic field configuration on parallel plasma flow during neutral beam injection in Heliotron J

The effect of magnetic field configurations on plasma flow velocity was investigated by measuring the parallel flow velocity (v∥) using a charge-exchange recombination spectroscopy during neutral beam injection in three different toroidal mirror configurations of Heliotron J: high, standard and reversed mirror configurations. The magnetic ripple strengths, γ, for these mirror configurations were γ = 0.073 m−1, 0.031 m−1 and 0.027 m−1, respectively, at the normalized averaged minor radius ρ = 0.07. The magnetic ripple strength is defined as γ = {〈(∂B/∂l)2/B2〉}1/2, where 〈…〉 is the flux surface averaged value and l is the length along the magnetic field line. At ρ = 0.07, the parallel flow velocity in the high mirror configuration (v∥ ∼ 4 km s−1) was 2–3 times smaller than those in the standard and reversed mirror configurations (v∥ ∼ 10–12 km s−1). An anticipated interpretation is that the difference in the neoclassical damping force contributes to the difference in v∥ among the three mirror configurations.

Nanoscale Dynamic Behavior of Surface Magnetic Domains on a La&lt;SUB&gt;0.7&lt;/SUB&gt;Sr&lt;SUB&gt;0.3&lt;/SUB&gt;MnO&lt;SUB&gt;3&lt;/SUB&gt; Thin Film

An oscillating magnetic tip can be used to induce the striped magnetic ripple pattern with alternating up-and-down striped magnetic domains on a ferromagnetic La0.7Sr0.3MnO3 (LSMO) thin film surface. Magnetic force microscopy (MFM) images show that the surface magnetic domains (SMDs) can be aligned in a well-ordered alternating up-and-down c(2 x 2) structure on the stripe magnetic domains, indicating that the oscillating magnetic tip turns the ferromagnetic LSMO surface into a canted antiferromagnetic state. The orientation of the SMDs is determined by their discrete phase distribution. A three-dimensional (3D) SMD orientation model is built to understand dynamic behavior of the SMDs.

Design and Analysis of Tubular Linear Machines with Dual Halbach Arrays

Linear machines are widely employed in robotics, transportation and manufacturing industries because complex rotation-to-translation conversion mechanism is no longer required. This paper proposed a novel tubular linear machine with dual permanent magnet (PM) Halbach arrays to achieve high force output performance. Based on Lorentz force law, the magnetic force output and force ripple for three-phase winding linear machine is formulated in analytical way. By taking advantage of the analytical models, the force output is simulated with respect to the motion of the mover. Numerical result is then obtained to validate the analytical force models. In addition, based on the technology of non-dimensionalization, the mathematical force models are employed to analyze the influence among the structure parameters on the force output and force ripple for design purpose of the tubular linear machines. The study in this paper could contribute to the design analysis and optimization of electromagnetic linear machines with similar poles patterns.

Design of Lost Fast-Ion Probe Based on Thin Faraday Films in Heliotron J

A lost fast-ion probe based on thin Faraday films (FLIP) is designed to measure fast-ion losses caused by fast-ion-driven MHD modes as well as magnetic field ripples in Heliotron J. The FLIP works as a magnetic spectrometer providing the energy and pitch angle of lost fast-ions. The installation location of FLIP is studied using Lorentz orbit code. Upper port of Heliotron J at the corner section is a primary target to install the FLIP, because not only co-going fast ions but also counter-going fast ions will be detected at this position. The FLIP will give the decisive information to study fast-ion losses in Heliotron J.

РАСЧЁТ ГОФРИРОВКИ ТОРОИДАЛЬНОГО ПОЛЯ В Т-10

Results of calculation of a toroidal magnetic field ripple in the T-10 tokamak are presented in the paper. Results of the ripple computations in the form of tabular data can be used for calculation of transport coefficients, at calculation of radial electric field at low collisionality. The values of formula parameters for the simplified calculation of a ripple in T-10 are determined. The calculation of magnetic field perturbation under the shift of one coil of the toroidal solenoid allows estimating the necessary accuracy of the ripple calculation.

Preliminary design of KTX magnet system

KTX is a reversed field pinch magnetic confinement device of which the magnet system is designed in ASIPP and USTC. The main parameter of KTX is between RFX and MST. Its magnet system includes the toroidal field (TF) winding and poloidal field (PF) winding (ohmic heating winding and equilibrium field winding), which are less complex than tokamak device due to the fact that a tokamak requires a superconducting system to perform quasi-steady state operation and achieve Q>10. However, the most important part of the magnet system design lies in how to keep the TF magnetic field ripple, as well as any kinds of stray field, to a minimum value. The main design activities of the KTX magnet system are presented as detailed as possible in this paper, and the main activities which have already been completed include magnet coils position and winding, insulation design, plasma modeling prediction, thermal analysis, magnetic field calculations were analyzed and so on. The magnet system design is one of the major activities for KTX device design, which is effective guarantee for the future R&D and manufacture. Besides, the detailed design activities should be continuously optimized and changed based on the results from future R&D and relevant tests.

Toroidal ripple transport of beam ions in the mega-ampère spherical tokamak

The transport of injected beam ions due to toroidal magnetic field ripple in the mega-ampère spherical tokamak (MAST) is quantified using a full orbit particle tracking code, with collisional slowing-down and pitch-angle scattering by electrons and bulk ions taken into account. It is shown that the level of ripple losses is generally rather low, although it depends sensitively on the major radius of the outer midplane plasma edge; for typical values of this parameter in MAST plasmas, the reduction in beam heating power due specifically to ripple transport is less than 1%, and the ripple contribution to beam ion diffusivity is of the order of 0.1 m2 s–1 or less. It is concluded that ripple effects make only a small contribution to anomalous transport rates that have been invoked to account for measured neutron rates and plasma stored energies in some MAST discharges. Delayed (non-prompt) losses are shown to occur close to the outer midplane, suggesting that banana-drift diffusion is the most likely cause of the ripple-induced losses.