Inductance Calculations for Noncoaxial Coils Using Bessel Functions

A relatively simple and general method for calculating the mutual inductance and self-inductance of both coaxial and noncoaxial cylindrical coils is given. For combinations of cylindrical coils, thin solenoids, pancake coils, and simple circular loops, the mutual inductance can be reduced to a one-dimensional integral of closed form expressions involving Bessel and related functions. Coaxial and noncoaxial cases differ only by the presence of an extra Bessel factor J ₀(sp) in the noncoaxial integral, where p is the perpendicular distance separating the coil axes and s is the variable of integration. The method is related to a recently given noncoaxial generalization of Ruby's formula for a nuclear radiation source and detector system, the analogy being close but not exact. In many cases, the Bessel function integral for the inductance can be easily evaluated directly using Maple or Mathematica. In other cases, it is better to transform the integral to a more numerically friendly form. A general analytical solution is presented for the inductance of two circular loops which lie in the same plane     

Mutual Inductance and Force Calculations Between Coaxial Bitter Coils and Superconducting Coils with Rectangular Cross Section

Mutual inductance and force calculations between coaxial Bitter coils and superconducting coils with rectangular cross section in a hybrid magnet system using derived semi-analytical expressions based on two integrations were performed. The mutual inductance and force calculations are based on the assumption of the uniform current density distribution in superconducting coils. The current density distribution of a Bitter coil in radial direction, however, is inversely proportional to the radius of the Bitter coil. The influence of the current density redistribution caused by a cooling hole and an inhomogeneous temperature distribution of Bitter coil of a water-cooled magnet was not considered. The obtained expressions can be implemented by Simpson’s integration with FORTRAN programming. We confirm the validity of mutual inductance calculation by comparing it with a filament method, and give the accuracy of two methods. The mutual inductance values computed by two methods are in excellent agreement. The derived semi-analytical expressions of mutual inductance allow a low computational time compared with filament method to a specific accuracy. The force is derived by multiplying the currents of the two coils by their mutual inductance gradient.     

Inductance Calculations for Circular Coils of Rectangular Cross Section and Parallel Axes Using Bessel and Struve Functions

A simple method for calculating the mutual and self inductances of circular coils of rectangular cross section and parallel axes is presented. The method applies to non-coaxial as well as coaxial coils, and self inductance can be calculated by considering two identical coils which coincide in space. It is assumed that current density is homogeneous in the coil windings. The inductances are given in terms of one-dimensional integrals involving Bessel and Struve functions, and an exact solution is given for one of these integrals. The remaining terms can be evaluated numerically to great accuracy using computer packages such as Mathematica. The method is compared with other exact methods for the coaxial case, and with a filamentary method for the non-coaxial case. Excellent agreement was found in all cases, and the exact method presented here agrees with another exact coaxial method to great numerical accuracy.     

Inductance Calculations of Permanent-Magnet Synchronous Machines Including Flux Change and Self- and Cross-Saturations

Accurate inductance calculation of permanent-magnet synchronous machines is a relevant topic, since the inductances determine a large part of the electrical machine behavior. However, the inductance calculation, as well as the inductance measurement, is never a completely straightforward task when saturation occurs. In this paper, the total flux in the $d$ and $q$ axes are obtained from finite-element method or measurements and therefore include saturation and cross-couplings. The inductances are obtained from analytical post-processing based on an equivalent magnetic circuit. The originality of this method is that it accommodates the changes in the magnet flux and the inductances with the level of saturation. The resulting inductance values are the ones seen by the converter or the grid, as found by a more accurate approach.      

基于伸缩矢量函数的平面参数曲线的插值变形

针对平面参数曲线的插值变形问题,构造了伸缩矢量函数,将插值数据点转化为变形主方向矢量,用此伸缩矢量函数去作用待变形曲线,使曲线发生形变且变形后能通过给定的插值点,此方法能够精确控制变形范围,在变形与未变形部分之间具有C2连续性。     

Mutual Impedance of Cylindrical Coils at an Arbitrary Position and Orientation Above a Planar Conductor

We derive a closed-form expression for the mutual impedance due to eddy-current induction for a pair of cylindrical air-core coils with arbitrary position and orientation above a planar conductor. By extending a recently devised model for individual coils with an arbitrary tilt with respect to the surface, we obtain a remarkably simple result. We validated our model with measurements on a conductive plate. The results should be useful for designing new probe configurations and for evaluating the signals in eddy-current inspections when driver-pickup coil configurations are utilized.     

Monte Carlo and Multicomponent Approximation Methods for Vector Radiative Transfer by use of Effective Mueller Matrix Calculations

For single scattering in a turbid medium, the Mueller matrix is the 4 x 4 matrix that multiplies the incident Stokes vector to yield the scattered Stokes vector. This matrix contains all the information that can be obtained from an elastic-scattering system. We have extended this concept to the multiple-scattering domain where we can define an effective Mueller matrix that, when operating on any incident state of light, will yield the output state. We have calculated this matrix using two completely different computational methods and compared the results for several simple two-layer turbid systems separated by a dielectric interface. We have shown that both methods give reliable results and therefore can be used to accurately predict the scattering properties of turbid media.     

一种精密互感测量的新方法

提出了一种精密互感测量的新方法,并且从理论上证明了利用这种方法对互感进行测量,互感的寄生电容、导线电阻、泄漏电导等寄生分布参数对最终的测量结果并不产生影响.初步的测量结果表明,利用这种新方法可以达到3.7×10-6量级的互感测量准确度.这一结果已经接近目前世界互感测量的最好水平2×10-6.     

Guiding of Vortices and Its Influence on the Hall Voltages in a Bianisotropic Planar Pinning Potential

The mediated by a small Hall effect odd resistive response of a superconductor in the mixed state is theoretically investigated within the framework of the two-dimensional stochastic model of bianisotropic pinning. It is shown that the odd magnetoresistivities ^– _, arise due to the interaction of the nonlinear guiding- and Hall-effects, and their resistive properties are analyzed by means of the diagram of the dynamic states of the vortex system on the (j _x, j _y) plane. Scaling relations for the Hall conductivity are found to be entirely different from the case of isotropic pinning.     

New Hall Resistivity Scaling Relations in the Presence of Competition between Point-like and Anisotropic Planar Pinning Potential

No Heading Explicit current- and temperature-dependent expressions for anisotropic longitudinal and transverse nonlinear magnetoresistivities are represented and analyzed on the basis of a Fokker-Planck approach for two-dimensional vortex dynamics in a washboard pinning potential in the presence of point-like disorder. It is shown that new scaling relations in discussed below longitudinal and transverse geometries of experiment can be presented in the form which is: a) similar formally to the well-known scaling relations for the point-like disorder, but contains instead of the bare Hall conductivity a renormalized one which depends on the pinning anisotropy b) just the same as for purely anisotropic scaling relations in the absence of point-like pins. Physical meaning of these results is discussed.PACS numbers: 74.60.Ge, 75.15.Gd, 74.25.Fy, 74.72.Bk.     

Influence of Point-Like Disorder on the Hall Resistivity Behavior in an Anisotropic Planar Pinning Potential

Explicit current- and temperature-dependent expressions for anisotropic longitudinal and transverse nonlinear magnetoresistivities are derived and analyzed on the basis of a Fokker–Planck approach for two-dimensional vortex dynamics in a washboard pinning potential in the presence of point-like disorder. Gradually increasing the strength of the point-like pinning (in an experiment this is simply done by irradiation of the sample with different doses of high-energy electrons) this theory predicts a gradual decrease of the anisotropy of the magnetoresistivities. The physics of the transition from the recently discussed new scaling relations for anisotropic Hall resistivities in the absence of point-like pins to the well-known scaling relations for isotropic pinning is elucidated. This is discussed in terms of a gradual isotropization of the guided vortex motion responsible for the existence in a washboard pinning potential of new anisotropic Hall voltages which are odd with respect to magnetic field reversal.     

Millimeter-Wave Polarimeters Using Kinetic Inductance Detectors for TolTEC and Beyond

We examine the dynamics of a one-dimensional harmonically trapped Bose–Einstein condensate (BEC), induced by the addition of a dimple trap whose depth oscillates with time. For this purpose, the Lagrangian variational method (LVM) is applied to provide the required analytical equations. The goal is to provide an analytical explanation for the quasiperiodic oscillations of the BEC size at resonance, that is additional to the one given by Adhikari (J Phys B At Mol Opt Phys 36:1109, 2003). It is shown that LVM is able to reproduce instabilities in the dynamics along the same lines outlined by Lellouch et al. (Phys Rev X 7:021015, 2017). Moreover, it is found that at resonance the energy dynamics display ordered oscillations, whereas at off-resonance they tend to be chaotic. Further, by using the Poincare–Lindstedt method to solve the LVM equation of motion, the resulting solution is able to reproduce the quasiperiodic oscillations of the BEC.     

Kinetic Inductance Phonon Sensors for the Cryogenic Dark Matter Search Experiment

An important challenge faced by phonon-mediated detectors for the next generation of dark matter detectors (>100 kg) is to instrument large target mass at low cost, while maintaining the large background suppression offered by the combination of phonons and ionization (or scintillation) measurement. Kinetic inductance phonon sensors, operating far below the superconducting transition temperature, offer an interesting solution to this scaling problem. They do not critically depend on the uniformity of T _c and their resonant-cavity readout is easy to multiplex. We are studying a microstrip (two parallel planes) transmission line architecture that may offer the additional advantage of a separation of functions: the main detector is just covered by an unpatterned aluminum film and the number of quasi-particles created in it by athermal phonons are sensed by a second film, which has been independently patterned and is mounted a few microns away from the detector. We present current results on the responsivity and noise of large area (∼33 mm²) microstrip kinetic inductance phonon sensors.      

Capacitance and Inductance Sensor Circuits for Detecting the Lengths of Open- and Short-Circuited Wires

The length of an open- or short-circuited wire is linearly proportional to the capacitance or inductance of the wire, respectively. Several types of simple and inexpensive circuits are introduced to measure these values. Open-circuited (capacitance) measurements are very effective. Short-circuited (inductance) measurements are more difficult, and not all of the circuits worked well. A 555 timer circuit was found to have the best overall performance to locate the ends of both open- and short-circuited wires. The capacitance and inductance values of various types of aircraft wires were measured and verified with analytical equations.      

轴对称非球面镜超精密加工新方法的几何模型

介绍了轴对称光学非球面镜超精密加工的新方法．超精密金刚石切削加工机床的刀具进给机构通常由直线导轨实现．由于旋转轴与同等精度的直线导轨相比,具有制造难度小、成本低及结构紧凑等优点,所以采用具有快速伺服机构的金刚石刀架摆臂代替直线导轨进给运动方式．根据非球面方程,快速伺服机构的微进给量根据车刀摆角实时计算．快速伺服机构、工件以及金刚石刀具的同时运动,可以实现轴对称非球面的超精密加工．构建了回转进给工具路径、快速伺服机构运动以及相关的几何模型．通过计算机模拟验证了该加工方法的简便与可靠性,可以降低非球面反射镜加工的设备投入,提高生产效率．     

Noise and Sensitivity of Aluminum Kinetic Inductance Detectors for Sub-mm Astronomy

Kinetic inductance detectors are based upon high Q superconducting resonators. We have measured the electrical Noise Equivalent Power (NEP) of 100 nm thick 1/4λ coplanar waveguide Aluminum resonators at 100 mK using phase readout and radius readout. We find that the phase NEP is independent of the Q factor of the resonator, limited by excess noise in the KID and given by NEP at 100 Hz. It increases with roughly f ^−0.5 at lower frequencies. The amplitude NEP is strongly Q factor dependent, limited by the setup noise, nearly frequency independent and as low as NEP for a high Q resonator (Q=454.000). For lower Q resonators the amplitude NEP increases to values equal to or even larger than the phase readout.      

Axisymmetric three- and four-node finite elements for large strain elastoplasticity

Within the framework of the finite element method an application of the logarithmic strain space formulation of large strain elastoplasticity is illustrated for the examples of axisymmetric three-node triangular and four-node quadrilateral finite elements. The formulation of the large strain elastoplasticity is based on a strain space formulation in conjunction with logarithmic (or Hencky) strain tensors with respect to the reference configuration. It is therefore—from a material point of view—a full Lagrangian formulation. The use of logarithmic strains enables an additive split of finite dilatation and distortion, which are given by the logarithmic strain trace and deviator. As a consequence of the strain space formulation no stress tensors are involved in order to describe the plasticity. The stress which is work-conjugate to the logarithmic strain follows from the stress-strain relations and may be transformed to Cauchy stress. The desired finite element matrices are derived via the principle of virtual work applied to the Cauchy stress distribution of the current configuration. It should be noted that our considerations are not restricted to axisymmetry and that they remain valid for isoparametric, position- (displacement-) based finite elements in general.     

电磁感应起爆系统电流互感原理的研究

通过试验和理论分析，得出ＱＢ－１型起爆器起爆系统的实质是电流互感，为起爆器的改进和线路联接方法的改变提供了理论依据；要想获得次线线圈足够大的电流，必须保证初次级线圈匝数比Ｗ１／Ｗ２〉１。