Assessment and optimization of field homogeneity in de-perm facilities
In this paper, the authors review various options for assessing homogeneity. One possibility is sampling at a set of discrete points to calculate mean value, standard deviation, maximum and minimum of the field. Options for choosing the sampling points are investigated. The other possibility is to express the field using coefficients of an orthogonal series, such as a Fourier series or Associated Legendre Polynomials. This option is viable because the solution to Laplace’s equation within an interior volume is completely defined by expressions using the harmonics evaluated at the exterior surface and the coordinates. Reducing the higher order harmonic coefficients (above the dipole) implies that the field is more homogeneous. Such methods are used regularly for assessment of field quality in other applications such as MRI and particle accelerator magnets.
To assess the effectiveness of the methods, each is subjected to a Pareto optimization to determine an optimum 9-coil longitudinal de-perm system design, which is then used in a de-perming simulation for a simple example model.
Authors: Ankita Modi, Faruk Kazi, VJTI, Mumbai; Christopher Riley, John Simkin, Opera Software, Oxford
Magnetic Signature Identification using Pareto optimization
In this paper, the same technique is applied to measured signatures (as would typically be obtained from a range). When the topology of the source is known (a hollow steel tube with hemispherical end caps, represented using a 2D thin-plate surface in the Opera software), two of the three optimization variables – length and outer radius – are predicted very accurately, while the third – thickness of steel – is less accurate. This example also shows the benefit of using objective functions that are based on integrations of the measured signature, rather than values of field at a set of discrete points.
In the second part of the presentation, unknown topologies are also examined. Several possible simple models which can be described using a small set of variables (including a hollow ellipsoid, a set of hollow spheres, and two hollow triangular prisms) are used to predict the major dimensions of both a measured submersible and surface vessel. The success (or otherwise) of each representation is reviewed.
Author: Christopher Riley, Opera Software, Oxford