On one selected problem in mathematical modeling of superconducting cylindrical coils in case of using the I-c(B) characteristic linearized in parts

摘要

The task to design the dimensions of cylindrical superconducting coil, which generates the maximum central field within a constant overall conductor length, represents mathematically the problem to find for a solution of the constrained extremum of a function. This problem can be transformed into the task of solving a non-linear equation because the value of gradient in the position of extremum (maximum) must be zero. The optimization procedure requires inter alia to evaluate the derivative of the I-c(B) characteristic of the conductor concerned. We show that a certain problem may arise if the I-c(B) characteristic is expressed by the function linear in parts. In this particular case, the derivative of the I-c(B) is a discontinuous function consisting of constants. As a consequence, the results of optimization needn't be correct. The aim of this study is to analyze the nature of the above problem and to propose a way to minimize it. We show that the computational error in determining the dimensions of optimum coil reduces with decreasing a distance between the I-c(B) nodal points. Moreover, the error is completely eliminated if the I-c(B) is expressed in analytical form. This effect is typical for superconducting conductors with a strong non-linearity in I-c(B), such as e.g. MgB2. On the other hand, the effect is not applied in case of e.g. NbTi superconducting conductors, the I-c(B) of which is linear in a broad field range. In this work we only study the case of isotropic I-c(B) characteristic. (C) 2016 Elsevier Ltd. All rights reserved.