Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia8774Calculation of the Magnetic System by the Solution of Inverse ProblemPolyakovaR V; Institute for Nuclear Research Joliot-Curiepolyakova@jinr.ruYudinI P; Joint Institute for Nuclear Researchyudin@jinr.ruInstitute for Nuclear Research Joliot-CurieJoint Institute for Nuclear Research150120121616908092016Copyright © 2012,2012In this paper we study the problem of searching for the design of the magnetic system for creation of a magnetic field with the required characteristics in the given area. On the basis of analysis of the mathematical model of the magnetic system rather a general approach is proposed to the solving of the inverse problem, which was written by the Fredholm equation: H(z) = ? SJ(s)G(z,s)ds, z ? U, s ? S.
It was necessary to define the current density distribution function J(s) and the existing winding geometry for creation of a required magnetic field H(z). In the paper a method of solving those by means of regularized iterative processes is proposed. On the base of the concrete magnetic system we perform the numerical study of influence of different factors on the character of the magnetic field being designed.magnet systemsinverse problemFredholm equationregularized iterative processesмагнитные системыуравнение Фредгольмаметод регуляризации[Arsenin V.Y., Tikhonov A.N. Method of the Solution of Non-Correct Problem. - Moscow: Nauka, 1979.][Morozov V. A. // Numerical Methods and Programming. - Publication MSU, 1967. - Issue 8. - P. 63.][Polyak B.T. Iterationing Methods of Solution of Any Non-Correct Variation Problems // Numerical Methods and Programming. - Publication MSU, 1969. - Issue 12. - Pp. 38-52.][Zhidkov E.P., Polyakova R.V., Yudin I.P., Tikhonov A.N. Regularization in a Magnitostatic Problem // 13th conference of MCE. - Dubna, 2006. - Pp. 171- 177.]