A theoretical analysis applied to electromagnetic instruments used in liquid sodium

The solution of Maxwell's equations to obtain the electric field distribution in a conductive, isotropic, inhomogeneous medium is performed using a finite difference approach. The initial application is devoted to the case of coils, carrying a low frequency sinusoidal driving current, which are surrounded by media having any desired combination of electrical conductivity and linear magnetic permeability. An estimate is made of the errors involved, particularly when using this technique to analyse electromagnetic sensors for use in liquid sodium. The results obtained when the developed program is used to solve a simple problem are compared with the corresponding analytical Bessel solution, proving the validity of the method. Expressions are derived to enable the calculation of flux density, induced voltage, coil impedance and the effect of flowing media from the computed values of electric field. Detailed analyses are made of an electromagnetic temperature sensor, constructed of stainless-steel-sheathed mineral-insulated cable, and of a flux distortion flow meter used in the Dounreay prototype fast reactor. Satisfactory agreement with the experimental performance of these sensors is obtained. (author)