基于积分方程法和奇异值分解的磁性目标磁场延拓技术研究

对磁性目标磁场延拓技术进行了研究,提出了一种基于积分方程法和奇异值分解的新方法.应用该方法只需要采用积分方程法对磁性目标的结构进行较为粗略的单元划分,利用目标下方大平面上的磁场测量值,得到相应的线性方程组.采用基于奇异值分解的截断奇异值方法和修正奇异值方法对该线性方程组进行正则化求解,可实现磁性目标磁场的三维磁场重建、向上或向下延拓.该方法较以前的方法,提高了磁性目标磁场延拓的精度和可靠性,并且解决了磁性目标磁场在一定范围内向上延拓的技术难题. 关键词： 磁性目标磁场 延拓 积分方程法 奇异值分解     

基于磁荷面分布的舰船磁场预测方法

利用等效源观点, 把钢铁建造的舰船船体视为等效磁荷面分布, 建立了该分布与磁场传感器测量值之间应满足的第一类Fredholm积分方程, 然后利用广义逆矩阵对积分方程离散化后得到的线性方程组进行求解, 并以矩阵条件数来衡量方程组的病态程度, 最后利用求解得到的磁荷分布来预测舰船在空间中任意点上产生的磁场. 数值模拟表明该方法可以准确地识别磁性从而得到精确的磁场预测值. 最后利用一个船模实验验证了本方法. 关键词： 舰船 磁场 磁荷 积分方程     

翻转线圈系统在波荡器积分场测量中的应用

 为了更有效地测量用于上海同步辐射光源波荡器的积分场误差,在已有的伸展线磁测系统的基础上研制了一套翻转线圈磁测系统,该系统的运动控制、数据采集和数据分析处理均可自动完成。在利用这套磁测系统测量3.4×10^-6 T·m磁场积分时获得高于1×10^-6 T·m的测量精度,初步的实验结果表明这套波荡器积分磁场测量系统具有测量精度好、速度快的特点,与已有的伸展线磁测系统、平移线圈磁测系统和霍尔点测系统相比,它更适合于测量波荡器的一、二次场积分和多极场分量。     

Surface currents of a superconducting axisymmetric body that screen an external coaxial magnetic field

A time-saving method to find currents on the surface of a superconducting axisymmetric body is suggested for the case when the axis of the body and the symmetry axis of an external magnetic field coincide. The method is based on solving a one-dimensional integral equation. Analytical solutions are derived for the superconductor in the form of an ellipsoid of revolution that is placed in a uniform magnetic field and in the form of a sphere placed in a magnetic field varying as a polynominal at the symmetry axis. To find the current density on the surface of an arbitrarily shaped axisymmetric body placed in an arbitrarily varying magnetic field, a method of numerically solving the integral equation is proposed. It is a combination of the iterative regularization method and the projective method with a projector in the form of B splines. The results of numerical reconstruction of the sought functions by the latter method for a number of particular cases are presented.     

Kinetic theory of the generation of magnetic fields in the radiation-dominated stage of expansion of the universe

The system of linearized Einstein and Maxwell equations and a kinetic equation with model collision integral for the cosmological plasma are used to calculate the magnetic field generated by solenoidal perturbations in the radiation-dominated stage of expansion of the universe. The magnetic field is generated by two effects — the Harrison effect and a new effect due to kinetic processes. The second effect contributes to the magnetic field if solenoidal gravitational perturbations exist from the very beginning of the radiation-dominated stage.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 122–126, January, 1992.     

考虑磁透镜边缘场的质子成像系统优化设计

高能质子照相系统由四极磁透镜和准直器组成,实际透镜的边缘场将影响成像系统的性能.本文将含边缘场的磁场梯度用贝尔函数近似,提出了一种含边缘场的成像系统优化方法.通过Geant 4程序模拟了能量为1.6 GeV的质子成像系统,并通过优化方法给出了考虑边缘场的优化后的系统参数.研究了考虑边缘场时的成像系统参数对准直器孔径的影...     

An electron in a quantized plane wave and in a constant magnetic field

The Dirac equation is considered for an electron in a constant homogeneous magnetic field and in a quantized electromagnetic plane wave propagating along the direction of the former. This problem is shown to be reduced to the Schrödinger equation for a system of many interacting oscillators. The corresponding Hamiltonian is diagonalized. An equation is established relating the total energy with the moment of a system along the magnetic field. Approximate solutions of this equation are given. A behaviour of a system close to cyclotron resonance is discussed.     

Electron energy levels in a QW within a tilted magnetic field

The analytical solutions of the Schrödinger equation for a square well system subjected to an externally applied tilted magnetic field are obtained and the results are discussed. The dependency of energy spectrum of the system on the externally applied magnetic field direction is discussed.     

Complex magnetic susceptibility of uniaxial superparamagnetic particles in a strong static magnetic field

The magnetic relaxation of a system of single-domain ferromagnetic particles in the presence of a strong static magnetic field directed at an arbitrary angle relative to the particle anisotropy axis is investigated. A system of linear difference-differential equations for the moments (averaged spherical harmonics) is derived without recourse to the Fokker-Planck equation by averaging Gilbert’s equations with a fluctuating field. An exact solution (in terms of matrix continuous fractions) is found for this system. The relaxation times and spectra of the complex magnetic susceptibility are calculated. Fiz. Tverd. Tela (St. Petersburg) 40, 1642–1649 (September 1998)     

Double quantum well electronic energy spectrum within a tilted magnetic field

The analytical solutions of the Schrödinger equation for a double quantum well structure (DQWS) subjected to an externally applied tilted magnetic field are obtained and the results are discussed. The dependency of the energy spectrum of the system on the applied magnetic field direction is also given.     

On Suhl's dispersion equations for dilute magnetic alloys in a finite magnetic field

A one dimensional, nonlinear, singular integral equation was recently shown to be equivalent to Suhl's dispersion equations for the Kondo-problem of a half-spin magnetic impurity in a finite magnetic field. We investigate this integral equation further analytically and numerically and obtain numerical solutions which we use for a calculation of transport coefficients. The normal part of the scattering potential of the magnetic impurity is included via ans-wave phase shift. The transport coefficients are universal functions of the ratiosT/T _K andB/B _K of the temperatureT and the zero magnetic field Kondo-temperatureT _K and of the magnetic inductionB and the Kondo magnetic inductionB _K. We find maxima in the electrical and thermal resistivities as functions ofT/T _K forBB _K. These are typical Kondo phenomena, and can be influenced by. Interference of and the phases of Kondo-scattering amplitudes leads to dramatic effects in the thermopower and the Hall coefficient.SFB 125The numerical part of this work was performed at the Institut für Festkörperforschung, Kernforschungsanlage Jülich, F.R. Germany     

On quark matter in a strong magnetic field

The effect of strong magnetic field on the bulk properties of quark matter is reinvestigated takingu, d ands-quarks as well as electrons in the presence of magnetic field. Here the bag pressure is chosen such that in the absence of magnetic field and at zero temperature the binding energy of theuds-system is <930 MeV while that ofud-system is greater than 940 MeV. It is observed that the equation of state changes significantly in a strong magnetic field. At finite temperature the electron chemical potential varies between 6 and 50 MeV. Thus the expansion of thermodynamical quantities in powers ofT/(Μ _i ² -M _v ⁽ⁱ⁾² )^1/2 is valid only up to few MeV. For high temperatures ∼40 MeV the exact integral expressions are to be taken.     

Method of the magnetic field synthesis on the axis of cylinder solenoid

The paper presents the magnetic field synthesis on a solenoid axis for the case the problem is described a Fredholm integral equation of the first kind. Solution of the problem, which is ill-posed according to Hadamard, was obtained by means of the regularization method.     

A microscopic derivation of the critical magnetic field in a superconductor

The propagator for a noninteracting many electron system in a constant magnetic field in three space time dimensions is computed. This formula and the results of [FT1,2] are used to give a microscopic derivation of a BCS-equation with magnetic field. It is shown that this equation has no solution if the magnetic field is sufficiently large. Perturbation theory in the interaction around the magnetic field propagator is discussed.     

Spin connection resonance in magnetic motors

A mechanism is proposed for rotation of magnetic assemblies by a torque consisting of the magnetic dipole moment of the assembly and a magnetic field generated from space–time in Einstein–Cartan–Evans (ECE) field theory. It is shown that when the magnetic assembly is stationary, the space–time is described by a Helmholtz wave equation in the tetrad as eigenfunction. This is a balance condition in which the Cartan torsion of the space–time is zero, but in which the tetrad and spin connection are non-zero. This balance may be broken by a driving current density produced by the magnetic assembly. The Helmholtz equation becomes an undamped oscillator equation. At resonance the torque on the magnetic assembly may be amplified sufficiently to cause the whole assembly to rotate, as observed experimentally in a repeatable and reproducible manner.     

XY spin fluid in an external magnetic field

A method of integral equations is developed to study anisotropic fluids with planar spins in an external field. As a result, the calculations for these systems appear to be no more difficult than those for ordinary homogeneous liquids. The approach proposed is applied to the ferromagnetic XY spin fluid in a magnetic field using a soft mean spherical closure and the Born-Green-Yvon equation. This provides an accurate reproduction of the complicated phase diagram behavior obtained by cumbersome Gibbs ensemble simulation and multiple histogram reweighting techniques.     

Designing shielded radio-frequency phased-array coils for magnetic resonance imaging

In this paper, an approach to the design of shielded radio-frequency (RF) phased-array coils for magnetic resonance imaging (MRI) is proposed. The target field method is used to find current densities distributed on primary and shield coils. The stream function technique is used to discretize current densities and to obtain the winding patterns of the coils. The corresponding highly ill-conditioned integral equation is solved by the Tikhonov regularization with a penalty function related to the minimum curvature. To balance the simplicity and smoothness with the homogeneity of the magnetic field of the coil’s winding pattern, the selection of a penalty factor is discussed in detail.     

The structure of chaotic magnetic field lines in a tokamak withexternal nonsymmetric magnetic perturbations

We consider the effects of external nonsymmetric magnetostatic perturbations caused by resonant helical windings and a chaotic magnetic limiter on the plasma confined in a tokamak. The main purpose of both types of perturbation is to create a region in which field lines are chaotic in the Lagrangian sense: two initially nearby field lines diverge exponentially through many turns around the tokamak. The equilibrium field is obtained from the equations of magneto-hydrodynamic equilibrium written down in a polar toroidal coordinate system. The magnetic fields generated by the resonant helical windings and the chaotic magnetic limiter are obtained through an analytical solution of Laplace equation. The magnetic field line equations are integrated to give a Hamiltonian mapping of field lines that we use to characterize the structure of chaotic field lines. In the case of resonant windings, we obtained the map by both numerical integration and a Hamiltonian formulation. For a chaotic limiter, we analytically derived a symplectic map by using a Hamiltonian formulation     

Electron-ion collision integral in a strong magnetic field

Boltzmann’s collision integral is extended to the case of helical (Larmor) particle trajectories in a magnetic field of arbitrary strength. The main characteristics of collisions of electrons with positively charged ions in strong magnetic fields, where the Larmor radius of electrons becomes less than the characteristic impact parameter of close collisions in the absence of a magnetic field (Landau’s parameter), are investigated. The differential scattering cross section and the corresponding electron-ion collision integral in strong fields are found. The transport collision frequencies are calculated, and the results are compared with the similar quantities for weaker magnetic fields.     

Hofstadter spectrum in electric and magnetic fields

The problem of Bloch electrons in two dimensions subjected to magnetic and intense electric fields is investigated. Magnetic translations, electric evolution, and energy translation operators are used to specify the solutions of the Schrödinger equation. For rational values of the magnetic flux quanta per unit cell and commensurate orientations of the electric field relative to the original lattice, an extended superlattice can be defined and a complete set of mutually commuting space-time symmetry operators is obtained. Dynamics of the system is governed by a finite difference equation that exactly includes the effects of: an arbitrary periodic potential, an electric field orientated in a commensurable direction of the lattice, and coupling between Landau levels. A weak periodic potential broadens each Landau level in a series of minibands, separated by the corresponding minigaps. The addition of the electric field induces a series of avoided and exact crossing of the quasienergies, for sufficiently strong electric field the spectrum evolves into equally spaced discreet levels, in this “magnetic Stark ladder” the energy separation is an integer multiple of hE/aB, with a the lattice parameter.