The deformation of the moving magnet plate of a commutated magnetically levitated planar actuator

This paper presents a method to calculate the deformation of the magnet plate of a commutated magnetically levitated planar actuator using a linked electromagnetic–mechanical model. The force and torque distribution on the moving magnet array is obtained from an electromagnetic model based on the surface charge method and the Lorentz force and torque integral. The mechanical model is a state-space model derived from FEM. This mechanical model uses the force and torque distribution to determine the deformation of the magnet plate during movement due to the commutated coil set.     

On the design of NMR sensor for well-logging applications

The magnetic fields of antenna and magnet used in inside-out nuclear magnetic resonance (NMR) well-logging tool are computed using a finite-element method (FEM). A typical operating frequency of such tools is 2 MHz, at which the skin depth is about 47 μm for copper conductor. A direct application of FEM to evaluate power loss at such frequency, therefore, requires very fine discretization of the conductors, which, in turn, makes the problem numerically ill-conditioned. A perturbation technique along with FEM is used to evaluate the power loss in conductors that avoids the need for small discretization steps along the conductor thickness. The design of the magnet, on the other hand, is complicated by the fact that the model is nonlinear in nature because of the presence of ferrites and steel materials surrounding the magnet and because the size of the problem is usually quite large; quarter of a million unknowns is fairly common. A typical nonlinear FEM model requires about 35 h of central processing unit (CPU) time on a Sun Ultra 60 296 MHz workstation with one gigabyte of RAM. The magnet is built by stacking several magnet segments along the axial direction and the objective of the design is to magnetize these segments in such a way so as to produce a desired field profile in front of the magnet. It generally requires many executions of the nonlinear FEM model. An optimal control technique is used in conjunction with the FEM to speed up the design process. Very good agreement between the measured and computed antenna efficiency and magnetic field is obtained thus validating the numerical model     

Random errors induced by the superconducting windings in the LHCdipoles

The problem of estimating the random errors in the LHC dipole is considered. The main contributions to random errors are due to random displacements of the coil position with respect to nominal design and to the variation of the magnetization of the superconducting cable. Coil displacement can be induced either by mechanical tolerances or by the manufacturing process. Analytical and numerical scaling laws that provide the dependence of the random errors due to random displacements on the multipolar order are worked out. Both simplified and more realistic models of the coil structure are analysed. The obtained scaling laws are used to extract from experimental field shape data the amplitude of the coil displacements in the magnet prototypes. Finally, random errors due to interstrand resistance variation during the ramp are estimated     

R&D for a single-layer Nb/sub 3/Sn common coil dipole using the react-and-wind fabrication technique

A dipole magnet based on the common coil design, using prereacted Nb/sub 3/Sn superconductor, is under development at Fermilab, for a future Very Large Hadron Collider. This magnet has some innovative design and technological features such as single layer coils, a 22 mm wide 60-strand Rutherford type cable and stainless steel collars reinforced by horizontal bridges inserted between coil blocks. Both left and right coils are wound simultaneously into the collar structure and then impregnated with epoxy. In order to optimize the design and fabrication techniques an R&D program is underway. The production of cables with the required characteristics was shown possible. Collar laminations were produced, assembled and tested in order to check the effectiveness of the bridges and the validity of the mechanical design. A mechanical model consisting in a 165 mm long section of the magnet straight section was assembled and tested. This paper summarizes the status of the program, and reports the results of fabrication and test of cable, collars and the mechanical model.     

Study of Kapton insulated superconducting coils manufactured forthe LHC inner triplet model magnets at Fermilab

Fermilab has constructed a number of 2 m model quadrupoles as part of an ongoing program to develop and optimize the design of quadrupoles for the LHC Interaction Region inner triplets. The quadrupole design is based upon a two layer shell type coil of multi-filament NbTi strands in Rutherford cable, insulated with Kapton film. As such, the coil size and mechanical properties are critical in achieving the desired prestress and field quality targets for the agent. Throughout the model magnet program, different design and manufacturing techniques have been studied to obtain coils with the required mechanical properties. This paper summarizes the structural material and coil mechanical properties, coil design optimization results and production experience accumulated in the model R&D program     

Production follow-up of the LHC main dipoles through magnetic measurements at room temperature

In this paper, we review the tools used for controlling the production of the LHC main dipoles through warm magnetic measurements. For the collared coil measurements, control limits are based on the statistics relative to the pre-series production. For the cold mass, the difference between collared coil and cold mass is considered, allowing a very stringent test. In both cases, measurements are split in straight part average, variations and coil ends contributions. Two different alarm levels exist in case the measured field is out of limits. The analysis can be carried out at the manufacturer and allows detection of anomalies in the measured magnetic field. These can be either due to wrong measurements or caused by assembly defects. Techniques used to work out information on the magnet assembly from the field harmonics are outlined. We summarize the experience gathered on about 180 collared coils and 120 cold masses, pointing out the bad cases and investigating the reliability of the measurements.     

Modeling of Quench Limit for Steady State Heat Deposits in LHC Magnets

A quench, the transition of a conductor from the superconducting to the normal conducting state, occurs irreversibly in the accelerator magnets if one of the three parameters: temperature, magnetic field or current density exceeds a critical value. Energy deposited in the superconductor by the particle beams provokes quenches detrimental for the accelerator operation. In particular if particles impacting on the vacuum chamber and their secondary showers depose energy in the magnet coils. The large hadron collider (LHC) nominal beam intensity is 3.2 ldr 10¹⁴ protons. A quench occurs if a fraction of the order of 10⁷ protons per second is lost locally. A network model is used to simulate the thermodynamic behavior of the magnets. The heat flow in the network model was validated with measurements performed in the CERN magnet test facility. A steady state heat flow was introduced in the coil by using the quench heaters implemented in the LHC magnets. The value of the heat source current is determined by the network model and the magnet coil current which is required to quench the coil is predicted accordantly. The measured and predicted value comparison is regarded as a sensitive test of the method.     

基于SH0导波的电磁超声换能器设计与实验研究

传统基于周期性永磁体的电磁超声换能器结构较复杂,为此该文提出了一种由单一永磁体和导线阵列线圈构成的电磁超声换能器(EMAT)用于激发板中的SH0导波.首先叙述了设计的原理,并采用有限元软件进行三维数值仿真分析,利用水平极化永磁体垂直于板面的磁场在铝板中成功激发出SH0导波.为使EMAT换能效率达到最优,研究长和宽为10...     

On the interior resonance problem when applying a hybrid FEM/MoMapproach to model printed circuit boards

A hybrid finite element method/method of moments (FEM/MoM) technique is used to analyze a printed circuit board power bus structure where the source and observation points are in the near field. The FEM is used to model the lossy region between the planes of the board including the source. The MoM is used to model the region outside the planes and provide a radiation boundary condition to terminate the FEM mesh. Numerical results for a bridged power bus structure are compared with measurements. A nonphysical interior resonance of the electric field integral equation is observed. The problem can be avoided by using a hybrid technique based on a combined field integral equation     

Construction and measurement of the pre-series twin aperture resistive quadrupole magnet for the LHC beam cleaning insertions

CERN's Large Hadron Collider (LHC) requires 48 twin aperture resistive quadrupoles in the beam cleaning insertions. Canada is contributing these magnets to CERN in the framework of the TRIUMF-LHC collaboration contracts. A pre-series magnet was produced by Canadian industry and delivered in March 2001. This magnet incorporates important design changes that resulted from experience with a prototype magnet. The construction of this pre-series magnet and the measurements made at ALSTOM and at CERN are reported. A comparison is made between high precision pole distance measurements and the magnetic measurements performed with a rotating coil mole. Conclusions for series production and possibilities for multipole corrections are outlined.     

Magnetic Performance of the Main Superconducting Magnets for the LHC

The field strength and homogeneity of all the LHC superconducting magnets were measured as a part of the production control and qualification process that has taken place during the past four years. In addition to field measurements at room temperature performed on the integral of the production, a significant part of the magnets has been subjected to extensive magnetic measurements at cold. The measurements at cryogenic temperatures, generally performed up to excitation currents of 12 kA corresponding to the ultimate LHC energy of 7.6 TeV, were mainly based on static and dynamic field integral and harmonic measurements. This allowed us to study in detail the DC effects from persistent current magnetization and long-term decay during constant current excitation. These effects are all expected to be of relevance for the field setting and error compensation in the LHC. This paper reports the main results obtained during these tests executed at operating conditions. The integrated field quality is discussed in terms of distribution (average and spread) of the field strength and low-order harmonics as obtained for all the main ring magnet families (dipoles, main and matching quadrupoles). The dependence of field quality on coil geometry, magnet and cable manufacturer is analyzed. A projection of the field quality expected for the critical components in the machine is presented.     

Design and Manufacturing Main Linac Superconducting Quadrupole for ILC at Fermilab

The design and manufacturing of the first model of an International Linear Collider (ILC) Main Linac superconducting quadrupole is in progress at Fermilab. The quadrupole has a 78 mm aperture, a 36 T integrated gradient, and a cold mass length of 700 mm. A superferric magnet configuration with iron poles and four racetrack coils was chosen based on magnet performance, cost, and reliability considerations. Each coil is wound using enamel insulated, 0.5 mm diameter, NbTi superconductor. The quadrupole package also includes shell type dipole steering coils. The results of the quadrupole design, including magnetic and mechanical analyses, are presented. Specific issues related to the quadrupole magnetic center stability, superconductor magnetization and mechanical stability are discussed and analyzed. The magnet quench protection system, current leads, and mounting the quadrupole inside ILC Main Linac cryomodule will also be briefly discussed.     

The bending magnets for the LHC injection transfer lines

Two injection transfer lines, each about 2.8 km long, with 51 and 107 degree horizontal deflection, are being built to transfer protons at 450 GeV from the Super Proton Synchrotron (SPS) to the Large Hadron Collider (LHC). A total of 360 dipole magnets are required; they have been produced in the framework of the contribution of the Russian Federation to the construction of the LHC. The classical dipoles, built from laminated steel cores and copper coils, have a core length of 6.3 m, 25 mm gap height and a nominal field of 1.81 T at a current of 5270 A. The magnet design was made in collaboration between CERN and BINP. An unusual design has been chosen for the coils to cope with the limited voltage from the available power supplies. All magnets in each of the two lines will be powered in series. The coil is composed of overlapping, but electrically insulated, half coils of 3 1/2 turns each. Thus, the power connections for IN and OUT are placed on opposite magnet ends. Short copper braids are used to connect all upper or lower half coils in series and the whole string can be powered without power consuming cable links running alongside the magnets. Precautions are taken to avoid transmission line effects and hazards from differences in voltage between upper and lower half coil. Advantages and drawbacks of this concept are discussed as well as results of the acceptance test including mechanical, electrical and magnetic field measurements. Fabrication and measurement of the magnets at BINP, with the half core production subcontracted to EFREMOV, have been finished in June 2001.     

Micromechanical modeling of stress evolution induced during cure in a particle-filled electronic packaging polymer

Particle-filled polymers are widely used in electronic industries. From microscale view, cure-induced residual stress can be generated not only by the external constraints but also by the constraint effect among the particles. In this paper, a three-dimensional micromechanical finite element method (FEM) model has been setup for a silica particle filled epoxy. In the micromechanical model, the epoxy matrix is modeled with a previously developed cure-dependent viscoelastic constitutive model, whereas the silica particles are modeled as elastic with high stiffness. Cure shrinkage is applied to the matrix as an initial strain for each time increment. The cure-dependent viscoelastic properties were obtained from shear and tension-compression dynamical mechanical analysis measurements. Cure shrinkage and reaction kinetics were characterized with online density measurement and differential scanning calorimeter measurements, respectively. In order to simulate a partly constrained object, the micromechanical model is coupled with a macromodel FEM analysis. The displacements from the macromodel are used as boundary conditions for the micromodel. The effect of external constraints on the generation of the micro stresses is studied by using the boundary conditions related to different external constrained states.     

Recent results from the LHC inner triplet quadrupole developmentprogram at Fermilab

Fermilab, in collaboration With LBNL and BNL, is in the process of developing a focusing quadrupole for installation in the interaction region inner triplets of the LHC. This magnet is required to have an operating gradient of 215 T/m across a 70 mm coil bore, and operates in superfluid helium at 1.9 K. The design is based on a two layer cos (20) coil, mechanically supported by standalone steel collars. The collared coil assembly is surrounded by a iron yoke for flux return, and the assembly enclosed by a stainless steel shell. The development program has addressed mechanical, magnetic, quench protection, and thermal issues, through a series of model magnets constructed at Fermilab. This paper summarizes results from the recent model tests, and the status of the program     

Correlations between field quality and geometry of components in the collared coils of the LHC main dipoles

The Large Hadron Collider (LHC) (1995), a proton-proton superconducting accelerator, will consist of about 8400 superconducting magnet units, all operating in superfluid helium at a temperature of 1.9 K. The design of the superconducting main dipole magnets for the LHC is guided by the requirement of an extremely high field quality in the magnet aperture which is mainly defined by the layout of the superconducting coil and the position of the conductors. In order to avoid conductor movements within the magnet cross-section, the superconducting coils are held in place by surrounding stainless steel collars. In this paper, we review the dependence of field harmonics in the LHC main dipoles on dimensions of the hardware components of the collared coils. An analysis of the dimensional measurements of these components which are used in the collared coils produced so far is given. Sensitivity tables which are worked out through a coupled magneto-static model give the variation of the multipoles on collars, copper wedge dimensions and cable geometry. A Monte Carlo method is used to simulate the effects of possible errors on the multipoles.     

Qualification of the LHC Corrector Magnet Production With the CERN-Built Measurement Benches

The LHC will incorporate about 7600 superconducting single aperture corrector magnets mounted in the main magnet cold masses. In order to follow up their production, we have designed and built 12 different benches for warm magnetic measurements based on rotating coils. Each bench was manufactured in two copies, one installed at the industry sites and the other kept at CERN for cross checks and monitoring of the measurement quality. These systems measure the main field, the field quality and the position and orientation of the field relative to the mechanical construction, all properties that are required for an effective use of the magnets. After calibration, the benches automatically refer the measured quantities to the mechanical interfaces used to align the correctors in the cold masses (pin holes or keys). In this paper we evaluate the global uncertainty achieved with the benches and compare the field measurements performed at room temperature in industry with measurements at 1.9 K performed at CERN on samples of each corrector type.     

Influence of mechanical tolerances on field quality in the LHC maindipoles

We evaluate the influence of mechanical tolerances in the field quality in the LHC dipoles. We show that the most relevant effect is due to tolerances on the coil and on the internal part of the collars. The sensitivities of the field error multipoles on the mechanical tolerances are worked out using a finite element model of the dipole cross section. A Monte Carlo method is used to simulate the overall effect of both collar and coil tolerances on field quality. Correlation between random multipoles is worked out, and a comparison with the target table of the LHC field errors is given     

Model of electrostatic actuated deformable mirror using strongly coupled electro-mechanical finite element

The aim of this paper is to deal with multi-physics simulation of micro-electro-mechanical systems (MEMS) based on an advanced numerical methodology. MEMS are very small devices in which electric as well as mechanical and fluid phenomena appear and interact. Because of their microscopic scale, strong coupling effects arise between the different physical fields, and some forces, which were negligible at macroscopic scale, have to be taken into account. In order to accurately design such micro-electro-mechanical systems, it is of primary importance to be able to handle the strong coupling between the electric and the mechanical fields. In this paper, the finite element method (FEM) is used to model the strong coupled electro-mechanical interactions and to perform static and transient analyses taking into account large mesh displacements. These analyses will be used to study the behaviour of electrostatically actuated micro-mirrors.