Background due to stored electrons following nuclear decays in the KATRIN spectrometers and its impact on the neutrino mass sensitivity

In this paper, a new method for the calculation of leakage inductances between short-circuited windings is proposed. The main objective is to find an analytical alternative to the finite-element method (FEM) for the computation of short-circuit inductances in electromagnetic transients-type (EMT-type) programs. Typical EMT-type tools do not provide complex FEM-based computation engines for this sole purpose. The new approach is derived from the method of images and uses analytical formulations for magnetic vector potential and energy developed in this work. It is shown that the difference between the inductance calculated with the FEM in 2-D and that computed with the method of images decreases as the number of layers of images increases. Also, it is demonstrated that the classical approach, based on an axial flux distribution, can lead to considerable error if the windings have unequal heights and if they are located far from the core yokes.

Analytical Calculation of Leakage Inductance for Low-Frequency Transformer Modeling

The electric potential and fleld of an axially symmetric electric system can be computed by expansion of the central and remote zonal harmonics, using the Legendre polynomials. Garrett showed the usefulness of the zonal harmonic expansion for magnetic fleld calculations, and the similar radial series expansion has been widely used in electron optics. In this paper, we summarize our experience of using the zonal harmonic expansion for practically interesting axisymmetric electric fleld computations. This method provides very accurate potential and fleld values, and it is much faster than calculations with elliptic integrals. We present formulas for the central and remote expansions and for the coe-cients of the zonal harmonics (source constants) in the case of general axisymmetric electrodes and dielectrics. We also discuss the general convergence properties of the zonal harmonic series (proof, rate of convergence, and connection with complex series). Practical considerations about the computation method are given at the end. In our appendix, one can flnd many useful formulas about properties of the Legendre polynomials, various derivatives of the zonal harmonic functions, and a simple numerical integration algorithm.

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Axisymmetric electric field calculation with zonal harmonic expansion

A comparative analysis of the zeroth, first, and (pseudo) second-order optimization methods for n-parametric optimization of magnet systems is reported. The following families of optimization methods are compared: Monte-Carlo iteration, steepest descent, conjugate gradient, and quasi-Newton (DFP, BFGS). These methods were tested for a large class of magnetostatic optimization problems (global, nonlinear, nonconvex, constrained, discontinuous), associated, e.g. with the coil magnet design for NMR imaging and NMR spectroscopy. >

Comparative analysis of optimization methods for magnetostatics

In this paper, a new method for the calculation of leakage inductances between short-circuited windings is proposed. The main objective is to find an analytical alternative to the finite element method (FEM) for the computation of short-circuit inductances in electromagnetic transients type (EMT-type) programs. Typical EMT-type tools do not provide complex FEM based computation engines for this sole purpose. The new approach is derived from the method of images and uses analytical formulations for magnetic vector potential and energy developed in this work. It is shown that the difference between the inductance calculated with the FEM in 2-D and that computed with the method of images decreases as the number of layers of images increases. Also, it is demonstrated that the classical approach, based on an axial flux distribution, can lead to considerable error if the windings have unequal heights and if they are located far from the core yokes.

Analytical calculation of leakage inductance for low-frequency transformer modeling

The analytic solutions are given for three simple axisymmetric systems involving toroidal conductors and iron. The solutions can be used for testing and gauging the accuracy of three-dimensional numerical schemes. In each case it is demonstrated how the fields can be calculated from a spherical harmonic expansion. This provides a unified and efficient method for calculating the fields.

Analytic solutions for axisymmetric magnetostatic systems involving iron

The scalar potential of any system of axisymmetric conductors can be expressed in terms of Legendre polynomials. This paper describes a method for including into the expansion coefficients the effects of iron on coil systems. Although the basis of the method is taken from the Rutherford Laboratory program GFUN the approach is specifically orientated towards cylindrical symmetry. The iron is divided into small cylindrical elements for which the magnetisation and permeability are determined. These elements are then used to calculate the coefficients of the Legendre polynomial expansion of the potential due to the iron. The accuracy of the method is gauged by comparing the results with an analytical solution.

A GFUN approach to include the effects of iron on coil systems with cylindrical symmetry

The scalar potential of any system of axisymmetric conductors can be expressed as a Legendre polynomial expansion, and this provides an efficient and convenient method for computing the field variables. A method is presented for augmenting the expansion coefficients to include the effects of iron of constant permeability on the system. The approach is based on the boundary element method (BEM). As well as giving physical insight into the effects of the iron, the use of the coefficients circumvents the problem of expensive field retrieval. Numerical accuracy is assessed by considering two geometries for which an exact solution is known.

A legendre polynomial BEM for axisymmetric coil systems including Iron

The effects of iron of constant permeability on the fields of axisymmetric conductors are considered by expanding the fields in a series of spherical harmonics. The coefficients of the expansion are a natural and compact description of the system. In particular the relative size of the first few coefficients provides a very convenient measure of the field uniformity. The effects of different iron geometries and varying the permeability are discussed.

The effects of iron on the fields of axisymmetric conductors using a Legendre polynomial approach

The scalar potential of any system of axisymmetric conductors can be expanded in terms of Legendre polynomials. This paper describes a method for including the effects of a spherical iron shell into the Legendre polynomial expansion. The scalar potential is found using a surface integral approach by dividing the iron surface into elements over which the potential is constant and then using point collocation. Numerical results are obtained for a range of values of permeability by varying the number of elements and are found to agree well with the analytical results.

R. Saunders

Papers

Analytic solutions for axisymmetric magnetostatic systems involving iron

A GFUN approach to include the effects of iron on coil systems with cylindrical symmetry

A legendre polynomial BEM for axisymmetric coil systems including Iron

The effects of iron on the fields of axisymmetric conductors using a Legendre polynomial approach

A surface integral approach to determine the effects of iron on axisymmetric coil systems