Mathematical modelling of the magnetic system by A. N. Tikhonov regularization method

In this paper the problem of searching for the design of the magnetic system for creation a magnetic field with the required characteristics in the given area is solved. 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 is written by the Fredgolm equation $H(z) = \int_{S_I}J(s)G (z,s)ds, z\in S_H, s\in S_I$. It was necessary to define the I 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.