Theory of eddy current losses in finite width sheet exhibiting simple bar-like domain structures

Abstract

In the present paper we outline the analysis and present the analytical expressions for the eddy current losses for the case of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">'N'</tex> domains where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">'N'</tex> may be any integer. The only assumptions made in this analysis are: (1) constant conductivity; (2) infinite length in the direction of magnetization; and (3) sinusoidal motion of domain walls for sinusoidal application of field. For various values of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">'N'</tex> the losses computed from these expressions are compared to those predicted by the Pry and Bean model. When <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N \rightarrow \infin, W</tex> (width of crystal) <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\rightarrow \infin</tex> and for a constant finite domain size our model reduces to that of Pry and Bean, and for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N = 2</tex> we obtain Agarwal and Rabins results. However, these limits are never realized in real materials, and it is shown that for realistic domain width to sheet thickness ratios, the losses per unit volume computed from the model presented here are significantly lower than those predicted from the Pry and Bean model.