The Effect of Non-homogeneous Parts into Materials

Abstract

This article deals with the verification of experimental results obtained by numerical simulation. We solved the effect of changes in the homogeneity of magnetic fields evoked by different samples from conductive and/or magnetic materials and the different types of inhomogeneity in the MR tomograph. Moreover, the paper will describe the suitable magnetic resonance techniques. 1. ANALYSIS OF THE TASK The numerical modelling was realized using the finite element method together with the Ansys system. As the boundary condition, there was set the scalar magnetic potential φm by solving Laplace’s equation ∆φm = divμ (−gradφm) = 0 (1) together with the Dirichlet boundary condition φm = konst. on the areas Γ1 a Γ2 (2) and the Neumann boundary condition un · gradφm = 0 on the areas Γ3 a Γ4. (3) The continuity of tangential elements of the magnetic field intensity on the interface of the sample region is formulated by the expression un × gradφm = 0 (4) The description of the quasi-stationary model MKP is based on the reduced Maxwell’s equations rotH = J (5) divB = 0 (6) where H is the magnetic field intensity vector, B is the magnetic field induction vector, J is the current density vector. For the case of the static magnetic irrotational field, the Equation (5) is reduced to the Expression (7). rotH = 0 (7) Material relations are represented by the equation B = μ0μrH (8) where μ0 is the permeability of vacuum, μr(B) is the relative permeability of ferromagnetic material. The closed area Ω, which will be applied for solving the Equations (6) and (7), is divided into the region of the sample Ω1 and the region of the medium Ω2. For these, there holds Ω = Ω1 ∪Ω2. For the magnetic field intensity H in area there holds the relation (7). The magnetic field distribution from the winding is expressed with the help of the Biot-Savart law, which is formulated as