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Magnetic Materials for Accelerator Electromagnets

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Magnetic Materials for Accelerator Electromagnets Bulletin of the Transilvania University of Braşov Series I: Engineering Sciences • Vol. 6 (55) No. 2 - 2013 MAGNETIC MATERIALS FOR ACCELERATOR ELECTROMAGNETS V. PRICOP1 Gh. SCUTARU1 E. HELEREA1 Abstract: Accelerator electromagnets are used in synchrotrons for the guidance of particles. For the successful operation of such synchrotrons, high field homogeneity is required to be provided by the electromagnets. Furthermore, the magnetic field characteristics of all electromagnets of one type installed have to be identical. A high field homogeneity and equal performance from electromagnet to electromagnet can only be achieved if great care is taken when the selection of magnetic materials is done, and if a rigorous quality assurance plan is implemented during manufacturing. In this paper a procedure is presented for selecting the magnetic material and mandatory steps during manufacturing are outlined. Key words: magnetic materials, high-energy particles, electromagnet, accelerator. 1. Introduction electromagnet has to decide on the magnetic material based on the field Particle accelerators are used to generate requirements. The first decision considers high-energy particles which are for example the dynamic requirements of the magnetic brought to collision to perform fundamental field. In case of static operation a solid particle research, to generate light with magnetic core can be used. high-brightness, or to produce ions for If the electromagnet will be ramped, the medical treatment. Modern research fields core will have to be laminated to minimize would not be possible without controlled the effects of the magnetic field due to access to these high-energy particles. eddy currents. If the electromagnet will not For the successful operation of such be ramped the magnetic saturation and synchrotrons, electromagnets with high field permeability of the material in the working homogeneity and equal magnetic properties range will be the driving factors. from electromagnet to electromagnet within If the electromagnet will be ramped, one type are required. To achieve these saturation, coercivity, remanence, requirements the choice of the material to be permeability, resistivity and lamination used for the core of an electromagnet and the thickness is usually taken into account quality assurance during manufacturing is of during the selection process of the material. paramount concern. Typically synchrotrons contain a small The required steps of the selection number of different electromagnet types procedure for the core material are which are partially powered in series. presented in Figure 1. The designer of the Therefore, it is extremely important that all 1 Centre “Advanced Electric Systems”, Transilvania University of Braşov. 82 Bulletin of the Transilvania University of Braşov • Series I • Vol. 6 (55) No. 2 - 2013 Is the electromagnet YES ramped? NO Laminated core Laminated core Preferred solution: Solid core Parameters of interest: Parameters of Permeability interest: Saturation Section 2 Permeability Coercivity Saturation Resistivity Thickness Section 4 FeNi: FeCo: Low coercivity, Decision based on Highest High permebility, requirements of saturation, Low saturation, material parameters High price. High price. Section 3 Carbon steel: High purity Fe: Medium FeSi: High saturation, saturation, High Si content – high resistivity, Low coercivity, Low remanence, high permeability, increasing High permeability, Low permeability, price. High price. Low coercivity, Low Si content – decreasing Low price. resistivity permeability, decreasing price. Fig. 1. Flowchart of selection process of magnetic materials for the core of an electromagnet electromagnets of one type show the same one type show the same performance if performance. The most common reason their mechanical construction is the same. why electromagnets within one family are First, we present the influence of the core different is because of mechanical material to the operation of the manufacturing errors and differences of the electromagnet. Second, we present the magnetic performance of the selected core most important classes of materials. material from electromagnet to Finally, we present a procedure for electromagnet. Laminating the yoke opens selecting the most suitable class of the possibility to shuffle the laminations material, depending on the boundary used for the manufacturing of one type of conditions of the project. electromagnet. The shuffling ensures that Following we will limit our discussion to inequalities in the magnetic material are dipole electromagnets. The results may be averaged out and that all electromagnets of easily extended to other types of Pricop, V., et al.: Magnetic Materials for Accelerator Electromagnets 83 electromagnets such as quadrupoles and following equation: sextupoles. Additional information regarding electromagnets with multiple 1 d B . (2) pairs of poles can be found in [6]. r μ d H 0 2. Relevant Magnetic Properties of the Magnetic hysteresis cycle Materials 2 B S 1.5 B In this section the relevant magnetic R properties of typical materials employed in 1 electromagnets for accelerators, and the 0.5 effect on the operation of an electromagnet 0 -H H C C are analysed. B[T] Following, we limit our discussion to -0.5 properties of soft ferromagnetic materials, -1 -B because these are the materials most often -1.5 R employed for the construction of -B -2 S electromagnet cores. -200 -150 -100 -50 0 50 100 150 200 H [A/m] 2.1. Magnetic Characterization of a Fig. 2. Magnetic hysteresis cycle and Material relevant quantities The state of magnetization of a material Remanence represents the level of is determined by the magnetic field magnetization characterizing a material strength H and is characterized by the when the excitation field is switched off, B in Figure 2. magnetic flux density B and magnetic R Coercivity represents the value of the polarization J . The relation between these magnetic field strength required to bring quantities is: the magnetization of the material from the remanence level to zero, HC in Figure 2. B 0 H J . (1) Saturation represents the state of the material when an increase of the excitation Ferromagnetic materials behave field strength no longer leads to an nonlinearly due to hysteresis effects and increase of the magnetization of the eddy-currents. Magnetic hysteresis material, BS in Figure 2. phenomenon represents the offset in The magnetic characterization of a response of the magnetic polarization to the material is related to the shape of the excitation field. When the magnetization of a hysteresis cycle. The shape of the cycle is ferromagnetic material is changed by some determined by the properties of the amount, energy is dissipated. substance and is strongly influenced by A full hysteresis cycle is presented in eddy-currents and temperature. Figure 2. In this figure, relevant quantities When magnetic materials are exposed to like saturation, remanence and coercivity a time-varying magnetic field, eddy- are presented as well. currents will be induced in the material: The slope of the hysteresis curve the penetration of the magnetic field in the represents the relative permeability of the material will be limited in depth and its material. It is determined with the phase will be shifted to the excitation field. 84 Bulletin of the Transilvania University of Braşov • Series I • Vol. 6 (55) No. 2 - 2013 The harmonic skin depth is defined as magnetic permeability of the magnetic the depth in the material where the circuit material. magnetic field reaches 1/e (36.8%) of its The influence of the relative magnetic value at the surface, and it is defined as: permeability on the transfer function of an electromagnet is presented in Figure 3. The 1 material has to have a high permeability in s , (3) 0 r f the working range in order to achieve linear operation of the electromagnet (the where: δS is the skin depth [m]; σ is the term l/µr has to be much smaller than h). electrical conductivity of the material -5 x 10 Electromagnet transfer function [S/m]; f is the frequency of the excitation 2.5 field [Hz]. The response of the magnetic field in the 2 material, to a linearly ramped excitation h=50 mm; l=1000 mm field, will be delayed with a time constant 1.5 h=100 mm; l=1000 mm h=150 mm; l=1000 mm τd [3]: /NI [T/A] p a g 1 x2 B d , (4) 2 0.5 where x is the depth in the material [m]. 0 The choice of lamination thickness will 0 50 100 150 /l [m-1] be determined by the ramp rate of the r electromagnet, requirements for damping Fig. 3. The influence of the relative the ripples of the power converter, and by magnetic permeability on the transfer economic considerations (thicker laminations function of an electromagnet are often cheaper to manufacture). To achieve a linear operation of the 2.2. Transfer Function electromagnet (saturation of the curves in Figure 3) the core material has to operate in The value of the magnetic flux density the high, and preferably linear, permeability generated by an electromagnet in its air region. The closer to saturation a material gap depends on its geometry and on the is, the lower its permeability, and the field material parameters of the core: of the electromagnet decreases. The higher the saturation of the material is, the wider μ NI 0 the range in which it can operate linearly. Bgap , (5) l h Saturation does not occur homogenously μr through the yoke and therefore will also change the field distribution within the pole where: Bgap is the value of the magnetic tips, resulting in reduced field homogeneity. flux density in the gap of the electromagnet [T]; µ0 is the magnetic 2.3. Residual Field permeability of free space [H/m]; NI is the magnetomotive force of the electromagnet The residual field represents the [A]; h is the height of the electromagnet’s electromagnetic field generated by the air gap [m]; l is the length of the magnetic electromagnet when the coils are no longer circuit of the core [m]; µr is the relative powered.
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