Analytical computation of magnetic field in coil-dominated superconducting quadrupole magnets based on racetrack coils

Currently,three types of superconducting quadrupole magnets are used in particle accelerators:cos 2θ,CCT,and serpentine.However,all three coil configurations have complex spatial geometries,which make magnet manufacturing and strain-sensitive superconductor applications difficult.Compared with the three existing quadrupole coils,the racetrack quadrupole coil has a simple shape and manufacturing process,but there have been few theoretical studies.In this paper,the two-dimensional and three-dimensional analytical expressions for the magnetic field in coil-dominated racetrack superconducting quadrupole magnets are presented.The analytical expressions of the field harmonics and gradient are fully resolved and depend only on the geometric parameters of the coil and current density.Then,a genetic algorithm is applied to obtain a solution for the coil geometry parameters with field harmonics on the order of 10^(-4).Finally,considering the practical engineering needs of the accelerator interaction region,electromagnetic design examples of racetrack quadrupole magnets with high gradients,large apertures,and small apertures are described,and the application prospects of racetrack quadrupole coils are analyzed.

Gradient coil design with enhanced shielding constraint for a cryogen-free superconducting MRI system

The relatively fragile low-temperature stability of cryogen-free superconducting magnetic resonance imaging(MRI)magnets requires the careful management of exogenous heat sources.A strongly shielded gradient magnetic field is important for the optimal operation of cryogen-free MRI systems.In this study,we present an enhanced shielding method incorporating a regionalized stray field constraining strategy.By optimizing the constraint parameters,we could develop engineering-feasible gradient coil schemes without increasing system complexity but with the stray field intensity reduced by half.In real measurement in an integrated MRI system,the developed gradient assembly demonstrated good performance and supported to output images of excellent quality.Our findings suggested that the proposed method could potentially form a useful design paradigm for cryogen-free MRI magnets.

Effect of coil and chamber structure on plasma radial uniformity in radio frequency inductively coupled plasma

Enhancing plasma uniformity can be achieved by modifying coil and chamber structures in radio frequency inductively coupled plasma(ICP)to meet the demand for large-area and uniformly distributed plasma in industrial manufacturing.This study utilized a two-dimensional self-consistent fluid model to investigate how different coil configurations and chamber aspect ratios affect the radial uniformity of plasma in radio frequency ICP.The findings indicate that optimizing the radial spacing of the coil enhances plasma uniformity but with a reduction in electron density.Furthermore,optimizing the coil within the ICP reactor,using the interior point method in the Interior Point Optimizer significantly enhances plasma uniformity,elevating it from 56%to 96%within the range of the model sizes.Additionally,when the chamber aspect ratio k changes from 2.8 to 4.7,the plasma distribution changes from a center-high to a saddleshaped distribution.Moreover,the plasma uniformity becomes worse.Finally,adjusting process parameters,such as increasing source power and gas pressure,can enhance plasma uniformity.These findings contribute to optimizing the etching process by improving plasma radial uniformity.

Fuzzy Proportional Integral Derivative control of a voice coil actuator system for adaptive deformable mirrors

Research on adaptive deformable mirror technology for voice coil actuators(VCAs)is an important trend in the development of large ground-based telescopes.A voice coil adaptive deformable mirror contains a large number of actuators,and there are problems with structural coupling and large temperature increases in their internal coils.Additionally,parameters of the traditional proportional integral derivative(PID)control cannot be adjusted in real-time to adapt to system changes.These problems can be addressed by introducing fuzzy control methods.A table lookup method is adopted to replace real-time calculations of the regular fuzzy controller during the control process,and a prototype platform has been established to verify the effectiveness and robustness of this process.Experimental tests compare the control performance of traditional and fuzzy proportional integral derivative(Fuzzy-PID)controllers,showing that,in system step response tests,the fuzzy control system reduces rise time by 20.25%,decreases overshoot by 78.24%,and shortens settling time by 67.59%.In disturbance rejection experiments,fuzzy control achieves a 46.09%reduction in the maximum deviation,indicating stronger robustness.The Fuzzy-PID controller,based on table lookup,outperforms the standard controller significantly,showing excellent potential for enhancing the dynamic performance and disturbance rejection capability of the voice coil motor actuator system.

Mathematical Modelling and Design of Helical Coil Heat Exchanger for Production of Hot Air for Fluidized Bed Dryer

In global industrialization, efforts have been made to increase the rate of heat transfer in heat exchanger, minimizing the size of heat exchanger to reduce cost as well as increasing the effectiveness. Helical coil heat exchanger (HCHE) has been proven to be effective in improving heat transfer due to its large surface area. In this study, HCHE was designed to provide hot air needed for fluidized bed drying processes. The HCHE design model was fabricated and evaluated to study the efficiency of the hot air output for a laboratory fluidized bed dryer. The mathematical model for estimation of the final (output) temperature of air, Taf, passing through the HCHE was developed and validated experimentally. The drying of bitter kola particulates was carried out with a drying temperature of 50C 3C and a bed height-to-bed diameter ratio (H/D) of 1.5. The time taken to dry bitter kola particulates to 0.4% moisture content was 1 hour 45 minutes. Hence, HCHE is recommended for use in the production of hot for laboratory-scale fluidized bed dryers.

Supersymmetry and Shape Invariance of Hartmann Potential and Ring-Shaped Oscillator Potential in the γ and θ Dimensions of Spherical Polar Coordinates

This article shows that in spherical polar coordinates, some noncentral separable potentials have super-symmetry and shape invariance in the r and θ dimensions, we choose Hartmann potential and ring-shaped oscillator astwo important examples, thus in principle the energy eigenvalues and energy eigenfunctions of such the potentials in ther and θ dimensions can be obtained by the method of supersymmetric quantum mechanics. Here we use an alternativemethod to get the required results.

Buckling-controlled two-way shape memory effect in a ring-shaped bilayer

Shape memory polymers(SMPs)usually have a one-way shape memory effect.In this paper,an easy-operating method to realize a two-way shape memory effect was demonstrated in a ring-shaped bilayer structure where the two layers are SMPs with different thermal transition temperatures.By designing specific thermomechanical processes,the mismatched deformation between the two layers leads to a morphology change of ring-shaped bilayer structures from a smooth ring to a gear-like buckling shape under cooling and a reversible recovery to the smooth shape under heating.Such a morphology change is ascribed to occurrence and recovery of thermoelastic buckling.This method was validated by finite element simulation.We experimentally investigated the influence of pre-strain on buckling,and it was found that both the buckling occurrence and recovery temperature vary with pre-strain.Furthermore,considering a ring-shaped SMP-SMP bilayer structure,finite element analysis was conducted to study the influence of film thickness and modulus ratio of two layers on buckling behavior.The results showed that the critical buckling wavelength was greatly influenced by film thickness and modulus ratio.W e made a theoretical analysis that accorded well with the numerical results.

Central corneal epithelium self-healing after ring-shaped glycerin-cryopreserved lamellar keratoplasty in Terrien marginal degeneration

Dear Sir, I am Dr Yan-Long Bi, from the Department of Ophthalmology, Tongji University Affiliated to Tongji University School of Medicine, Shanghai, China. I write to present a case report of total limbal stem cells deficiency after treatment with ring-shaped lamellar keratoplasty secondary to Terrien marginal degeneration. During 3 years

A Longitudinal Zeeman Slower Based on Ring-Shaped Permanent Magnets for a Strontium Optical Lattice Clock

We report a longitudinal Zeeman slower based on ring-shaped permanent magnetic dipoles used for the strontium optical lattice clock. The Zeeman slower is composed of 40 permanent magnets with the same outer diameter but different inner diameters. The maximum variation of the axial field from its target values is less than 2%. In most parts of the Zeeman slower, the intensity variations of the field in radial spatial distribution are less than 0.1 roT. With this Zeeman slower, the strontium atoms are slowed down to 95m/s, and approximately 2% of the total atoms are slowed down to less than 50m/s.

Generation of ring-shaped human iPSC-derived functional heart microtissues in a M?bius strip configuration

Although human-induced pluripotent stem cell-derived cardiomyocytes(hi PSC-CMs) have been used for disease modeling and drug discovery, clinically relevant three-dimensional(3D) functional myocardial microtissues are lacking. Here, we developed a novel ring-shaped cardiac microtissue comprised of chamber-specific tissues to achieve a geometrically non-orientable ventricular myocardial band, similar to a M?bius loop. The ring-shaped cardiac tissue was constructed of hi PSC-CMs and human cardiac fibroblasts(h CFs) through a facile cellular self-assembly approach. It exhibited basic anatomical structure,positive cardiac troponin T(c Tn T) immunostaining, regular calcium transients, and cardiac-like mechanical strength. The cardiac rings can be self-assembled and scaled up into various sizes with outstanding stability, suggesting their potential for precise therapy, pathophysiological investigation, and large-scale drug screening.

Deformation Analysis on Shear-Bending of Ring-Shaped Piezoelectric Actuator

Deformation of a simple single piezoelectric actuator is usually quite small.A ring-shaped piezoelectric actuator with large piezoelectrically generated displacement was proposed.The thickness of the actuator was1 mm,and the inner and outer diameters were 4 mm and 40 mm,respectively.The ring-shaped actuator was made of BiScO_3-PbTiO_3(BS-PT)ceramic and polarized in radial direction.An electric field was applied to thickness direction and a large shear-bending deformation emerged.Then Rayleigh-Ritz method and Bessel functions were adopted to analyze the shear-bending deformation.Results show that under an electric field of 7.5kV/cm,the maximum displacement at the inner edge of the actuator reached 5.07μm,which agreed well with the corresponding experimental results.

Exact solutions of the Klein-Gordon equation with ring-shaped oscillator potential by using the Laplace integral transform

We present exact solutions for the Klein Gordon equation with a ring-shaped oscillator potential. The energy eigenvalues and the normalized wave functions are obtained for a particle in the presence of non-central oscillator potential. The angulm＂ functions are expressed in terms of the hypergeometric functions. The radial eigenfunetions have been obtained by using the Laplace integral transform. By means of the Laplace transform method, which is efficient and simple, the radial Klein-Gordon equation is reduced to a first-order differential equation.

The relativistic bound states for a new ring-shaped harmonic oscillator

In this paper a new ring-shaped harmonic oscillator for spin 1/2 particles is studied, and the corresponding eigenfunctions and eigenenergies are obtained by solving the Dirac equation with equal mixture of vector and scalar potentials. Several particular cases such as the ring-shaped non-spherical harmonic oscillator, the ring-shaped harmonic oscillator, non-spherical harmonic oscillator, and spherical harmonic oscillator are also discussed.

The spin-one Duffin Kemmer Petiau equation in the presence of pseudo-harmonic oscillatory ring-shaped potential

The Duffin-Kemmer-Petiau equation （DKP） is studied in the presence of a pseudo-harmonic oscillatory ring-shaped potential in （1 ＋ 3）-dimensional space-time for spin-one particles. The exact energy eigenvalues and the eigenfunctions are obtained using the Nikiforov-Uvarov method.

Quantum transport signatures of non-trivial topological edge states in a ring-shaped Su–Schrieffer–Heeger double-chain system

In the ring-shaped Su–Schrieffer–Heeger(SSH)double-chain,the quantum interference between the two different electron tunneling paths of the upper and lower chains has an important influence on the electron transport properties of non-trivial topological edge states.Here,we have studied the electron transport signatures of non-trivial topological edge states in a ring-shaped SSH double-chain system based on the wave-guide theory and transfer-matrix method.In the ringshaped SSH double-chain with the upper chain being different from the lower one,it is demonstrated that the electron transmission probability displays the four and two resonance peaks associated with the non-trivial topological edge states in the weak and strong coupling regimes,respectively.Whereas in the case of the upper chain being the same as the lower one,the two transmission resonance peaks associated with the non-trivial topological edge states in the weak coupling regime are only found,and that in the strong coupling regime disappear that originated from the destructive interference between the two different electron tunneling paths of the upper and lower chains.Consequently,the variation of the number of transmission resonance peaks associated with the non-trivial topological edge states in the weak and strong coupling regimes suggests that an alternative scheme for detecting non-trivial topological edge states in the ring-shaped SSH doublechain system.

Analytic solutions of the double ring-shaped Coulomb potential in quantum mechanics

The exact solutions of the Schr6dinger equation with the double ring-shaped Coulomb potential are presented, including the bound states, continuous states on the ＂k/2π scale＂, and the calculation formula of the phase shifts. The polar angular wave functions are expressed by constructing the so-called super-universal associated Legendre polynomials. Some special cases are discussed in detail.

AERODYNAMIC ANALYSIS OF CIRCULAR PLATE-SHAPED AND CIRCULAR RING-SHAPED SQUEEZE FILM BEARINGS

Aerodynamics of circular plate- and circular ring-shaped squeeze film hearings is analyzed in detail, yielding analytic expressions for the pressure distribution of these hearings. Several formulae for these hearings are modified using the developed method. The paper also gives numerical results oj pressure distribution and load-hearing capacities of these hearings.

Transient multi-physics behavior of an insert high temperature superconducting no-insulation coil in hybrid superconducting magnets with inductive coupling

A transient multi-physics model incorporated with an electromagneto-thermomechanical coupling is developed to capture the multi-field behavior of a single-pancake(SP)insert no-insulation(NI)coil in a hybrid magnet during the charging and discharging processes.The coupled problem is resolved by means of the finite element method(FEM)for the magneto-thermo-elastic behaviors and the Runge-Kutta method for the transient responses of the electrical circuits of the hybrid superconducting magnet system.The results reveal that the transient multi-physics responses of the insert NI coil primarily depend on the charging/discharging procedure of the hybrid magnet.Moreover,a reverse azimuthal current and a compressive hoop stress are induced in the insert NI coil during the charging process,while a forward azimuthal current and a tensile hoop stress are observed during the discharging process.The induced voltages in the insert NI coil can drive the currents flowing across the radial turns where the contact resistance exists.Therefore,it brings forth significant Joule heat,causing a temperature rise and a uniform distribution of this heat in the coil turns.Accordingly,a thermally/mechanically unstable or quenching event may be encountered when a high operating current is flowing in the insert NI coil.It is numerically predicted that a quick charging will induce a compressive hoop stress which may bring a risk of buckling instability in the coil,while a discharging will not.The simulations provide an insight of hybrid superconducting magnets under transient start-up or shutdown phases which are inevitably encountered in practical applications.

The Calibration and Use of a New Ring-Shaped Ionization Chamber for Monitoring and Dosimetry of X-Ray Beams

Today, dosimeters are used generally for dosimetry of the diagnostic X-ray beam. Ionization chambers are appropriate instruments for monitoring and also the dosimetry of X-ray beam in medical diagnostic equipment. The present work introduces design and investigation of a new ring-shaped monitor chamber with a PMMA body, graphite-coated PMMA windows (0.5 mm thick), a special graphite-foil central electrode (0.1 mm thick, 0.7 g/cm3 dense) that creating two sensitive volumes and a central hole for crossing the radiation beam with less attenuation. The results of performance tests conducted at the Nuclear Science and Technology Research Institute, AEOI in Karaj- Iran proved the high short and long-term stability, the very low leakage current, the low directional dependence and very high ion collection efficiency through the special design of the collecting electrode. Moreover, the FLUKA Monte Carlo simulations certified the negligible effect of central electrode on this new ring-shaped monitor chamber. According to the results of the performance tests, the new monitor chamber can be used as a standard dosimeter in order to monitor X-ray beam in primary standard dosimetry laboratories.

Construction of Exactly Solvable Ring-Shaped Potentials

We propose a method for construction of exactly solvable ring-shaped potentials where the linear homogeneous second-order differential equation satisfied by special function is subjected to the extended transformation comprising a coordinate transformation and a functional transformation to retrieve the standard Schr?dinger polar angle equation form in non-relativistic quantum mechanics. By invoking plausible ansatze, exactly solvable ring-shaped potentials and corresponding angular wave functions are constructed. The method is illustrated using Jacobi and hypergeometric polynomials and the wave functions for the constructed ring-shaped potentials are normalized.