Russian FederationModern accelerator systems and detectors contain magnetic systems of complex geometrical configuration. Design and optimization of the magnetic systems demands solving a nonlinear boundary-value problem of magnetostatic.The region in which the boundary-value problem is solved, consists of two sub-domains: a domain of vacuum and a domain of ferromagnetic. In view of the complex geometrical configuration of magnetic systems, the ferromagnetic/vacuum boundary can be nonsmooth, i.e. it contains a corner point near of which the boundary is formed by two smooth curves crossed in a corner point at some angle.Thereby, the solution of such a problem has to be found by numerical methods, a question arises about the behavior of the boundary value problem solution around the angular point of the ferromagnetic. This work shows that if the magnetic permeability function meets certain requirements, the corresponding solution of the boundary value problem will have a limited gradient. In this paper, an upper estimate of maximum possible growth of the magnetic field in the corner domain is given.In terms of this estimate, a method of condensing the differential mesh near the corner domain is proposed. This work represents an algorithm of constructing an adaptive mesh in the domain with a boundary corner point of ferromagnetic taking into account the character of behavior of the solution of the boundary value problem. An example of calculating a model problem in the domain containing a corner point is given.Key words and phrases: magnet systems, mathematical modeling, boundary value problem, elliptic equations, the behavior of solutions in the corner domain

No abstract

No abstract

Получено 9 апреля 2012 г., после доработки 15 октября 2014 г.В данной работе представлены результаты численного моделирования распределения магнитного поля некоторых модификаций спектрометрического магнита СП-40, используемого в экспериментальной установке НИС ОИЯИ. Основной особенностью такого магнита является прямоугольная апертура, следовательно, и область, в которой решается краевая задача, имеет всюду гладкую границу, за исключением угловой области ферромагнетика. В таких случаях решение задачи или производные решения могут иметь особенность. Изучено поведение магнитного поля в окрестности угловой области ферромагнетика и численным путем выбрана конфигурация магнита, для которой ширина области однородности (т. е. с / B B  < 1%) магнитного поля увеличилась с 0.5 м до 1.0 м, т. е. в два раза.Ключевые слова: магнитные системы, математическое моделирование, краевая задача, эллиптические уравнения, поведение решения в угловой области ферромагнетика Abstract. -In this work, we propose a method of the numerical solution of the magnetostatic problem for domains with boundaries containing corners. With the help of this numerical method, the magnetic systems of rectangular configuration were simulated with high accuracy. In particular, the calculations of some modifications of the magnetic system SP-40 used in the NIS JINR experimental installation, are presented. The basic feature of such a magnet is a rectangular aperture, hence, the area in which the boundary-value problem is solved, has a smooth border everywhere, except for a finite number of angular points in the vicinity of which the border is formed by crossing two smooth curves. In such cases the solution to the problem or derivatives of the solution can have a special feature. A behavior of the magnetic field in the vicinity of an angular point is investigated, and the configuration of the magnet was chosen numerically. The width of the area of homogeneity of the magnetic field increased from 0.5 m up to 1.0 m, i. e. twice.Keywords: magnet systems, mathematical modeling, boundary value problem, elliptic equations, the behavior of solutions in the corner domain

No abstract