Trigonometric Integrals for the magnetic field of the coil of rectangular cross section

Formulas are derived giving the vector potential and the magnetic field components of a general coil of rectangular cross section and constant winding density. The solution is given in a cylindrical coordinate system in terms of trigonometric integrals. The formulas presented have been cross-checked and validated against alternative expressions giving the various field components as integrals of expressions containing Bessel and Struve functions. The trigonometric integrals for the fields can be evaluated easily to several hundred significant figures using mathematical packages such as Maple or Mathematica. Alternatively, they can be evaluated with a small FORTRAN program. Sample results and field line plots obtained with the method are given, and the field of a coil of rectangular cross section is examined in some detail. A comparison with the results of a finite-element method is also given.     

Integral analysis of a magnetic field for an arbitrary geometry coil with rectangular cross section

The integral method can effectively analyze magnetic fields, but the traditional integral method can analyze only coils with regular geometries. Therefore, a new integral method was developed to calculate the three-dimensional (3-D) magnetic field created by an arbitrary geometry coil with a rectangular cross section using the local coordinate method and a 3-D coordinate transformation. However, when the field points are on the surface of the coil or the basic segment is the right angle trapezoidal prism, singularities occur that make the numerical analysis of the magnetic field more difficult. Thus, we present here some mathematical methods to eliminate the singularities to allow accurate numerical analysis of the magnetic field. We validate the integral method by comparing it with the analytical solutions for regular geometry coils.     

Vector potential and magnetic field of current-carrying circularfinite arc segment in analytical form. V. Polygon cross section

For pt.IV see ibid., vol.MAG-20, p.2145-50 (1984). Analytical expressions for the components of the vector potential and magnetic field of a circular-arc segment of a current-carrying conductor of polygonal cross section and arbitrary azimuthal length are derived. The expressions developed consists of known analytical functions such as Jacobian elliptic functions and complete and incomplete elliptic integrals of the first, second, and third kind, which permit the formulation of a time-saving efficient computation algorithm. An example of application is given. The case of a beam with polygonal cross-section carrying a longitudinal current is also examined     

电磁流量计椭圆截面管道流场仿真研究

通过ICEM CFD软件将局部截面变为椭圆形的异径导流筒进行了三维建模,使用Fluent对不同入口速度下的流线场与速度分布进行仿真计算,建立了不同结构的导流筒所适用的速度范围.结果表明,速度的大小和椭圆截面离心率对流场产生的影响较大.当速度减小或离心率变大时,导流筒尾部渐扩管容易发生回流,致使流场紊乱.本研究能为椭圆形管道电磁流量计的结构设计提供参考方案,为设计合理的导流筒提供理论依据.     

The hall cross in a perpendicular inhomogeneous magnetic field

Equations are derived which give the voltage that is generated in a Hall conductor when an inhomogeneous magnetic field is applied normal to the plane of the Hall conductor. These equations are used to solve a specific example of a Hall cross in such a field, using finite difference techniques. The results are shown to be in excellent agreement with measured data.     

Wavelength dependence of the Raman cross section for liquid water

We report measurements of the wavelength dependence of the 3400-cm(-1) Raman scattering cross section of liquid water for excitation wavelengths between 215 and 550 nm. Using previous measurements of the absolute Raman scattering cross section, we have determined an expression for the wavelength dependence of the absolute Raman cross section for water.     

Shape effect of the matrix on the capture cross section of particles in high gradient magnetic separation

A high gradient magnetic separator consists of a region of a high and approximately uniform magnetic field and a ferromagnetic matrix of fine wires which distort the field and produce large local gradients. As a particle is carried through the separator by a carrying fluid, both magnetic forces and drag forces are exerted on it. In order to gain insight into the capture mechanism, the drag and magnetic forces on a spherical paramagnetic particle were examined. The equilibrium of these forces defines the path of the particle as it passes by a matrix element. It is shown that for any geometry the particle motion is a function of two dimensionless variables. A computer with a plotter was used to compute the particle paths. In order to provide for most flexibility the magnetic field is that of a magnetized elliptical cylinder with any orientation with respect to the background field and flow stream, while the flow velocities are those corresponding to another elliptical cylinder of different configuration and orientation which allows computation of the change of capture cross section as the matrix element collects material. Examples of particle orbits and changes of capture cross section are given inthe paper for various aspect ratios of the original matrix element.     

The experimental determination of the neutron cross section for selected solvents

An experiment was conducted in order to determine the macroscopic neutron cross section of various solvents useful in neutron radiographic inspection. These solvents are used to dissolve the salts of high cross-section elements in order to formulate a fluid of maximal neutron cross section. The resulting fluid could then be used as a contrast enhancing agent in neutron radiographic inspection. This experiment was planned using statistical experimental design techniques. The results of this experiment provided a quantitative measure of the mean and standard deviation of the macroscopic neutron cross section for the nine fluids investigated. A control fluid was found to be in close agreement with published values.     

Novel transmission detector used for total cross section measurements

A new apparatus for total cross section measurements was developed and tested at Saturne II, Sacalay. The transmission ratios are determined using a ring-counter system coded in the Gray code, involving an exclusive four-fold coincidence between 4 counters among 8. Beam rate effects are suppressed by an electronic device which permits reaching an accuracy of better than 10^?4 in any transmission ratio. The apparatus was first used at SIN for the measurements of the total polarized proton-proton cross section difference Δσ_L and of the spin correlation parameter A_00kk in pp → pp and pp → dπ⁺ reactions, and then at Saturne II for Δσ_γ and Δσ_L measurements in p-p scattering.     

Simulation to improve the magnetic field in the straight section of the rectangular planar DC magnetron

For the rectangular planar DC magnetron, Gaussian type erosion profile may occur in the straight section of target and lead to lower target utilization. Considering the influence of magnetic field on the trajectories of energetic electrons, the target erosion profile and deepest eroded position are analyzed, and then the approaches of magnetic field improvement are proposed. Based on this, two magnet structures with AlNiCo and SmCo are discussed, which could be improved by fitting a shunt bar. According to 2D non-self-consistent particle simulation and Yamamura/Tawara formula, the target erosion profile could be predicted. Via the simulation, the approaches of magnetic field improvement are verified. In the same order of magnetic field intensity, the horizontal component of the magnetic field with wider distribution and larger concavity is proved to make the target utilization much increased.     

On the identification of an effective cross section for a cruciform specimen

Biaxial tensile testing of sheet metals is becoming increasingly popular for sheet metal forming. Determining equivalent stresses in biaxial tensile specimens is more complicated than in conventional uniaxial tensile specimens. In the present study, we compare four different approaches to calculate effective stresses during biaxial tensile loading of a cruciform specimen: (a) partial unloading method, where stresses are determined based on force–strain curves; (b) identification with uniaxial tensile testing; (c) an analysis of equivalent biaxial tests; and (d) numerical simulations. Considering experimental results for an AA1050 aluminium alloy and for a low‐carbon steel DC06, we show that, for the cruciform sample studied here, two methods do not yield physically reasonable results: The uniaxial approach does not properly take into account the effect of transverse loading, and the equivalent biaxial approach exhibits uncertainties in strain measurement data. The most comprehensible approach is the numerical method, because it also yields detailed information about the local stress and strain states. The numerical results are in excellent agreement with the partial unloading method in terms of the initial flow stress and of effective stress–strain curves for strains up to 0.02, with both methods predicting a similar effective cross section of 18.0 mm² for the considered specimen.     

Methods for measuring the magnetic field

This paper introduces the following group of four papers, which review recent advances in selected areas of magnetometry: superconducting, thin film, resonance, and fluxgate. In addition, it refers to several other methods for measuring the magnetic field, pointing out their special utilities and any recent developments. A comparison of some of the performance characteristics of most types of magnetometers in use today is also presented.     

Hydrodynamics of tubes of varying cross section

A method is suggested of reducing the hydrodynamic resistance by replacing circular cylindrical tubes (CT) by socalled asymmetrical wavy tubes of varying cross section with long exist cone and short nozzle portions. Mathematical simulation of laminar motion of an incompressible fluid (the Navier-Stokes equations) has shown that a change in geometric parameters can change the resistance substantially, making it larger or smaller than the resistance of an ordinary cylindrical tube. The velocity and pressure fields, friction resistances, pressure profiles, and total resistances of such tubes are given. An experiment has been carried out. A numerical experiment provides a resistance reduced by up to 80%, while the physical experiment provides a reduction by 50%.Donetsk State University. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 62, No. 4, pp. 525–533, April, 1992.     

Scaling of the L-vacancy-production cross section at kiloelectronvolt-ion collisions

A method is proposed for determining the vacancy-production probability from the dependence of the emission cross section of Auger-electrons or characteristic radiation on the collision energy. Based on the generalization of the existing experimental data on the collisions of atomic particles in gas and solid phases, a universal character of the dependence of the vacancy production probability on the closest approach distance is established for the first time. Scaling is proposed that makes it possible to calculate an L-vacancyproduction cross section from the universal dependence.     

Acoustic intensity for a long vessel with noncircular cross section

The acoustic intensity distribution around and within long vessels of noncircular cross section was investigated for parameters typical of biomedical ultrasound and blood vessels. We have developed a collocation method for finding the acoustic field when a uniform plane wave is obliquely incident on a long, not necessarily cylindrical, impedance interface. Results are presented for vessels of noncircular cross section and for vessels with thick walls of nonuniform thickness. The intensity in the vicinity of the vessel, throughout the lumen, and in the wall, is calculated for intermediate length scales, i.e., vessel radius and wall thickness in the range 1 to 10 wavelengths. The intensity distribution is an interference pattern, with complicated regions of increased and decreased intensity. These results are compared with approximate intensity obtained using ray theory. Effects not predicted by ray theory and intensity variations that will be significant in any close ultrasonic investigation of these vessels are revealed.