Harmonic Coils Research Articles

Automated quadrupole magnet positioning for enhanced harmonic coil measurement

The precise measurements of the magnetic field are essential for particle accelerators, and the harmonic coil measurement system is especially suitable for the multipole field because of its unique advantages. The accurate placement of magnets is essential for accurate magnetic field measurements. The current positioning technique employed for harmonic coil measurement is inefficient due to its labor-intensive and time-consuming nature. The aim of this study is to automate the positioning of the quadrupole magnet. Therefore, a close-range photogrammetry system is utilized to monitor the position of the magnet due to its non-contact feature, and an electrically driven Stewart platform is utilized to manipulate the magnet. Meanwhile, a control system has been developed to regulate the automatic positioning. The system is capable of receiving measurements from the close-range photogrammetry system in order to ascertain the displacements of the magnet from its current position to the target. Subsequently, it can transmit commands to Stewart platform to regulate its movement. The experiments indicate that the efficiency of the quadrupole magnet positioning has increased significantly by at least 5 times, and the final positioning accuracy was verified by the laser tracker. The study also addresses the potential application of this technology in high radiation environments that are otherwise inaccessible.

Enhanced beam extraction system at the U-120M cyclotron

Since its commissioning in 1977, the U-120M cyclotron was initially equipped with a single pair of harmonic coils aimed at optimizing beam quality at lower accelerating radii. In 2022, a significant upgrade introduced a second pair of harmonic coils, positioned at a radius of approximately 50 cm, aligning with the outermost beam orbit. This addition is essential for the efficient extraction of positively accelerated ions and serves as the basis for the newly developed extraction system, which, unlike the original fully electrostatic system, consists of electrostatic deflectors and magnetic channels. This paper describes the design and installation of new harmonic coils in the accelerator vacuum chamber and presents a new extraction system using precession and linear integer resonance methods. Basic properties of these two extraction methods are given and finally, an evaluation of their advantages and limitations concerning their possible use in the cyclotron and an estimation of the efficiency of the new extraction system is made.

Research of Quadrupole Lenses for Ions Transport Channel

In Budker Institute of Nuclear Physics SB RAS the magnetic elements of transfer channel for charged particle beams from SIS18 to SIS100 (FAIR, Germany) [1] were developed. The article presents a description of the quadrupole magnet Q2 and serial magnetic measurements results. Magnetic measurements with application of rotating harmonic coil and moving carriage with linear array of Hall sensors were taken. Quadrupole lenses provide magnetic field integral gradient with high quality (<5·10-3) and satisfy the requirements. High order harmonics are present in the magnetic field due to manufacturing and assembly errors and can imperfect on beam dynamics. Main attention was considered to the third (sextupole) harmonic amplitude, determinate the chromatic properties of the lens. It allows select manufactured magnets to distortion value and minimize imperfection of beam dynamics by optimal theirs arrangement.

Beam dynamics and space charge studies for the InnovaTron cyclotron

At IBA a high-intensity compact self-extracting cyclotron is being studied. There is no dedicated extraction device but instead, a special shaping of the magnetic iron and the use of harmonic coils to create large turn-separation. Proton currents up to 5 mA are aimed for. This would open new ways for large-scale production of medical radioisotopes. The main features of the cyclotron are presented. A major variable of the beam simulations is the space charge effect in the cyclotron centre. Using the SCALA-solver of Opera3D, we attempt to find the ion source plasma meniscus and the beam phase space and current extracted from it. With these properties known, we study the bunch formation and acceleration under high space charge condition with our in-house tracking code AOC. We also discuss a new tool that automates optimization of cyclotron settings for maximizing beam properties such as extraction efficiency.

Research on automatic positioning technology for magnetic field measurement of multipole magnet harmonic coil in heavy ion accelerator

In the magnetic field measurement of accelerator magnets, efficient and accurate positioning of the magnetic field measurement system and the magnet is a critical process. By analyzing the mechanical structure and working principle of harmonic coil magnetic field measurement system, an automatic positioning technology is proposed in this research for the high-precision and fast positioning of multipole magnet and harmonic coil magnetic field measurement system. Through the special design and comprehensive application of multi-camera photogrammetry system, control system and six-degree-of-freedom (6DoF) attitude automatic adjustment system, fast non-contact measurement and automatic attitude adjustment of harmonic coil magnetic field measurement system and multipole magnet can be realized. The proposed automatic positioning system and operation scheme can not only save labor costs, but also improve the reliability of harmonic coils and the positioning efficiency of magnetic field measurement system. The proposed research can also monitor the position changes of the harmonic coil and the multipole magnet in the magnetic field measurement process in real time through the multi-camera photogrammetry system, and further control the accuracy of the magnetic field measurement of the harmonic coil.

Shim coils tailored for correcting B0 inhomogeneity in the human brain (SCOTCH): Design methodology and 48-channel prototype assessment in 7-Tesla MRI

Increased static field inhomogeneities are a burden for human brain MRI at Ultra-High-Field. In particular they cause enhanced Echo-Planar image distortions and signal losses due to magnetic susceptibility gradients at air-tissue interfaces in the subject’s head. In the past decade, Multi-Coil Arrays (MCA) have been proposed to shim the field in the brain better than the 2nd or 3rd order Spherical Harmonic (SH) coils usually offered by MRI manufacturers. Here we present a novel MCA, named SCOTCH, optimized for whole brain shimming. Based on a cylindrical structure, it features several layers of small coils whose shape, size and location are found from a principal component analysis of ideal stream functions computed from an internal 100-brain fieldmap database. From an Open-Access external database of 126 brains, our SCOTCH implementation is shown to be equivalent to a partial 7th-order SH system with unlimited power, outperforming all known existing MCA prototypes. This result is further confirmed by a low-cost 30-cm diameter SCOTCH prototype built with 48 coils on 3 layers, and tested on 7 volunteers at 7T with a parallel-transmit RF coil made to be inserted in SCOTCH. Echo-Planar images of the subject brains before and after SCOTCH shimming show large signal recoveries, especially in the prefrontal cortex.

Key technologies of 18 MeV self-extraction cyclotron

In this work, an 18 MeV self extraction high current cyclotron is designed, which provides a feasible design scheme for the self extraction system. For the main magnet, it is designed by restricting the parameter change of the main magnetic field through “three judgments”. For the self extraction system, the phase space suitable for particle extraction is scanned by injecting the phase space, and the gradient correction magnet is used to increase the acceptance of the extracted beam. For the harmonic coil, through the second harmonic change of the magnetic field, the beam characteristics are analyzed and the position of the harmonic coil is determined. Under the condition of scanning different harmonic coil surface currents, the extraction of the beam is obtained, and then the phase space of the beam is pushed to the acceptance. In order to match the radial dimension and the axial dimension of the target beam and obtain a stronger beam, the magnetic channel of the double structure is selected and the related design idea is given. The final beam size is 30.5 mm × 12.9 mm, the particles that can be extracted account for 82.62% of the successfully accelerated particles.

Cold Test of a Superconducting Quadrupole-Sextupole Nested CCT Prototype using matrix harmonic coil

IMP (Institute of Modern Physics) has been developing a Quadrupole-Sextupole nested CCT (Canted Cosine Theta Type) prototype for the HFRS (High Energy Fragment Separator) beamline of HIAF (High Intensity Heavy-ion Accelerator Facility) project. Hence a matrix harmonic coil method has been developed for magnetic field quality measurement of multi-pole nested magnets. Furthermore, a whole set of measurement system has been constructed and some special mechanical components, like cold bore, have been set up to cooperate with matrix harmonic coil measurement. After cold test at 4.2 K, the measurement results prove that the prototype property and field quality basically meets our requirement, and matrix harmonic coil also functioning well.

The Reduction of Force Component Produced by Short Sides by Analyzing the Corner of Coil in Planar Motor with Halbach Magnet Array

The planar motor with moving-magnet is purely levitated by the stator coils. The forces produced by coils are calculated with the analytical model of magnet array and coil surface model for applying to the real time control. Take the coil and the Halbach magnet array which is at 45 degree with the long side of coil for analysis. The force component produced by short sides can be eliminated for conveniently controlling when the length of coil takes certain dimension. In practice, the force component produced by short sides is small but not zero. There are two reasons, one is the higher harmonics and the other is the corner segments of coil. The force integral expressions of coil corner segments are given by the Lorenz force law. Then the forces numerically calculated with harmonic model and coil full model are verified by comparing with the magnetic surface charge model and finite element model. In order to reduce the force component produced by short sides, the different corners of coil are analyzed. Comparing the forces of different corners of coil, the force component produced by short sides can be significantly reduced with slightly change of the other force components.

Harmonic Coil Magnetic Measurement System for HESR Magnets − a Mathematical Model and Design

This paper presents the constructive design of the Sextupole, Horizontal Steerer and Vertical Steerer electromagnets manufactured by ICPE-CA for HESR storage ring from FAIR Project which will be set-up in Darmstadt Germany. Also, in this paper is presented the current method and system with Hall probe the one that we have performed the magnetic measurements so far by now. Regarding that this method takes a lot of time to perform the magnetic measurements, meanwhile we have developed a system with harmonic coils, which we intend to use in the further magnetic measurements. Also, in this paper is presented the method of magnetic measurements with harmonic coil also the development of mathematical model for this measurement method. To validate the mathematical model of magnetic measurements using harmonic coils we have made a simulation and we have compared with the measurements performed with Hall probe on the Sextupole electromagnet.

Design and Analysis of a Static Excitation Part of a Brushless Wound Rotor Excitation Synchronous Machine Without an Exciter

The static excitation part of a brushless wound rotor hybrid excitation generator without an exciter (brushless WRHEG) is analyzed in this paper. The DC stator excitation windings and rotor harmonic coils are placed in the iron core as the excitation part, so that the brushless excitation for a wound rotor hybrid excitation generator (WRHEG) can be realized. In this study, the selection of stator excitation windings and rotor harmonic coils, which are essential for achieving of the brushless excitation, is providing. The effect of the static magnetic field on the air-gap magnetic field is studied theoretically. The harmonic content of the air-gap magnetic field is analyzed by Fourier series form and the effect of harmonics on the output voltage is also investigated. The influence of the static excitation field on the iron loss is also considered. A 1.5 kVA prototype is fabricated to verify the validity of the theoretical and Finite Element (FE) analysis. The output voltage under the no-load and the rated load conditions are measured. The field regulation capacity and the efficiency of the brushless WRHEG are tested. It shows that the brushless excitation is achieved by remaining the operating performance of WRHEG unchanged.

Design of a shim coil array matched to the human brain anatomy.

The purpose of this study is to introduce a novel design method of a shim coil array specifically optimized for whole brain shimming and to compare the performance of the resulting coils to conventional spherical harmonic shimming. The proposed design approach is based on the stream function method and singular value decomposition. Eighty-four field maps from 12 volunteers measured in seven different head positions were used during the design process. The cross validation technique was applied to find an optimal number of coil elements in the array. Additional 42 field maps from 6 further volunteers were used for an independent validation. A bootstrapping technique was used to estimate the required population size to achieve a stable coil design. Shimming using 12 and 24 coil elements outperforms fourth- and fifth-order spherical harmonic shimming for all measured field maps, respectively. Coil elements show novel coil layouts compared to the conventional spherical harmonic coils and existing multi-coils. Both leave-one-out and independent validation demonstrate the generalization ability of the designed arrays. The bootstrapping analysis predicts that field maps from approximately 140 subjects need to be acquired to arrive at a stable design. The results demonstrate the validity of the proposed method to design a shim coil array matched to the human brain anatomy, which naturally satisfies the laws of electrodynamics. The design method may also be applied to develop new shim coil arrays matched to other human organs.

A new alignment method for HIMM magnetic field measurement system

Abstract The Heavy Ion Medical Machine (HIMM) is China’s first heavy ion accelerator specifically for cancer treatment. To minimize the uncontrollable beam orbit and beam loss, the HIMM accelerator magnets require the condition of stringent field uniformity. The best way to examine whether the actual field is consistent with the design or not is to perform an accurate and reliable measurement on the magnetic field, which requires the accurate alignment of the magnetic field measurement system as the prerequisite. This research adopts the alignment of a Hall probe mapping system, long coil integral system and harmonic coils system. Firstly, the preliminary test launched at the HIMM is described. Then, a new alignment method is developed to improve the positioning accuracy and performance of magnetic field measurement system. The experimental results show that the alignment accuracy (maximum deviations) of all components of each magnetic field measurement system is higher than 0.1 mm, which satisfies the requirements for the positioning accuracy of high-precision magnetic field measurement system.

Performance Investigation of a Brushless Synchronous Machine With Additional Harmonic Field Windings

This paper describes a brushless electrically excited synchronous machine with a distinctive rotor structure and additional harmonic field windings. Spatially distributed third harmonic magnetic fields will be created in the air gap by feeding the stator harmonic windings of a dc current. These harmonic MMFs will generate an induced voltage in the additional rotor harmonic coils, which can supply the field winding with a dc current after rectification. Based on this operation principle, distributions of harmonic windings and the stator harmonic magnetic fields are analyzed. The relationship between harmonic EMFs and rotor harmonic winding turns are studied. Mutual interference between the different magnetic fields and windings in the machine is discussed. The harmonic excitation fields and the air gap flux densities are then calculated by employing finite element methods, and the regulating characteristics of no-load EMF are analyzed and power losses of machine are discussed. Experimental results of one 1.0-kW prototype machine agree well with the theoretical analysis and finite element calculations, which helps to evaluate this type of synchronous machines having brushless electrical excitation.

The development of magnetic field measurement system for drift-tube linac quadrupole

In the China Spallation Neutron Source (CSNS) linac, a conventional 324MHz drift-tube linac (DTL) accelerating an H− ion beam from 3MeV to 80MeV has been designed and manufactured. The electromagnetic quadrupoles (EMQs) are widely used in a DTL accelerator. The main challenge of DTLQ׳s structure is to house a strong gradient EMQ in the much reduced space of the drift-tube (DT). To verify the DTLQ׳s design specifications and fabrication quality, a precision harmonic coil measurement system has been developed, which is based on the high precision movement platform, the harmonic coil with ceramic frame and the special method to make the harmonic coil and the quadrupoles coaxial. After more than one year׳s continuous running, the magnetic field measurement system still performs accurately and stably. The field measurement of more than one hundred DTLQ has been finished. The components and function of the measurement system, the key point of the technology and the repeatability of the measurement results are described in this paper.

Optimal Layout of the Multicoil for the B0 Shimming in Magnetic Resonance Imaging

The performance of the multicoil shimming is much better than that of the spherical harmonic coils in many aspects. The diameters and locations of the multicoil are optimized for the B0 shimming of the third order spherical harmonic field. And then every independent coil is decomposed into two series coils to take full advantage of a limited number of shim current supplies. The performance is improved by 16.7% when quantified by the surface root mean square.

First Results of the Magnetic Measurements of the Superconducting Magnets for the European XFEL

The European X-ray Free Electron Laser facility (XFEL) is currently under construction at DESY in the Hamburg area in Germany. A linear accelerator consisting of 102 accelerator modules is used to accelerate the electron beam. Each module contains eight superconducting RF cavities and one magnet package, all operating in a 2 K super-fluid helium bath. Each magnet package consists of three nested magnets. Two cos θ-type correction dipole magnets horizontal and vertical deflecting are glued onto the surface of the beam pipe being the inner wall of the cryostat vessel. They are inside of a superferric quadrupole magnet. Each magnet package together with a conduction cooled current lead assembly, based on a CERN design, will be tested at room temperature and at 2 K in a special cryostat XMTS at DESY. It allows access for the field measurement equipment into the magnet bore at room temperature by using an anti-cryostat. The cold magnet project is realized by three groups as in kind contributions to the XFEL project. CIEMAT designs and provides the magnets and DESY the current leads. Magnet testing at DESY is performed together with IFJ PAN. A description of the XMTS facility, the magnetic field measurement systems used (harmonic coils and stretched wire setups) are given. Finally a short discussion of the results obtained for the first third of the magnets is presented. All magnets tested so far perform very well up to the design current. The quality and strength of the magnetic field are as designed.

Magnetic Field Measurement of the Quadrupole and Sextupole Magnets for HLS-II Storage Ring

The Hefei Light Source upgrade project (HLS-II) contains 8 dipoles, 32 quadrupoles (2 spares), and 32 sextupoles (2 spares) for the storage ring. Magnets were manufactured and magnetic measurements were performed in collaboration with the Institute of High Energy Physics (IHEP), China. Magnet production and validation measurements were finished in December of 2012. Measurements for all quadrupole and sextupole magnets were performed using a harmonic coil magnetic measurements system. This paper describes the magnets and the measurement system and presents results for the integrated field strength, higher order multipole components, offsets between the mechanical and magnetic centers, and the effective length of the multipole magnets.

Analysis of the Performance of a Model Quadrupole Magnet for a Linear Accelerator

A model quadrupole magnet for a future linear accelerator has been designed, fabricated, and tested at KEK. The model quadrupole is a superferric superconducting magnet with a design field gradient of 57 T/m. The design field gradient is obtained by saturating the iron yoke. Superferric magnets are considered to have the advantage of simplicity, less sensitivity to the position of the superconductor coils, and are therefore thought to be easier to construct and less expensive than usual superconducting magnets. However, if the iron is heavily saturated, the magnetic field becomes more sensitive to the coil positions. The magnetic properties of the magnet were measured with a harmonic coil, and its field gradient, effective length, and multipole components were compared with a 3D simulation. The results are presented and discussed in this paper.

A polyvalent harmonic coil testing method for small-aperture magnets

A method to characterize permanent and fast-pulsed iron-dominated magnets with small apertures is presented. The harmonic coil measurement technique is enhanced specifically for small-aperture magnets by (1) in situ calibration, for facing search-coil production inaccuracy, (2) rotating the magnet around its axis, for correcting systematic effects, and (3) measuring magnetic fluxes by stationary coils at different angular positions for measuring fast pulsed magnets. This method allows a quadrupole magnet for particle accelerators to be characterized completely, by assessing multipole field components, magnetic axis position, and field direction. In this paper, initially the metrological problems arising from testing small-aperture magnets are highlighted. Then, the basic ideas of the proposed method and the architecture of the corresponding measurement system are illustrated. Finally, experimental validation results are shown for small-aperture permanent and fast-ramped quadrupole magnets for the new linear accelerator Linac4 at CERN (European Organization for Nuclear Research).