Purpose -The paper presents an application of the scaling theory in a description of energy losses in soft magnetic materials in order to improve an agreement between measurements and theoretical models. Design/methodology/approach -The scaling theory allows the description of energy losses by a generalized homogenous function, which depends on scaling exponents a, b and amplitudes G (n) . The values of the scaling exponents and amplitudes were estimated on the basis of measurement data of total energy losses. Findings -The main findings of the paper are: the linear relationships between the scaling exponents a and b, the data collapse of energy losses and the scaling laws for asymptotic exponents of energy losses derivatives.Research limitations/implications -The origin of the data collapse and the relationship between the scaling exponents will be the subject of further research with the aid of renormalization group method Practical implications -The paper could be useful both for device designers and researchers involve in computational electromagnetism. Particularly, the data collapse allows a comparison of energy loss values measured in laboratories on different samples and by different methods. Originality/value -The application of the scaling theory in a description of energy losses in soft magnetic materials improves an agreement between measurement and theoretical models.

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Basing on scale invariance of considered system an improvement of the Bertotti formula for energy loss in soft magnetic materials has been achieved. Assumptions of the Bertotti theory were discussed and criticized. As an alternative to this theory a new approach basing on the scale invariance of complex systems has been presented. The generalized description of energy loss has been recently postulated by us in the form of the homogeneous function in a general sense which leads to a series expansion for the energy loss. On the basis of measurement data it has been proved that only two first terms of the series are relevant. New measurements of the energy loss in soft magnetic materials have been performed which confirms the scaling theory. The obtained formula enables very simple description of the energy loss in soft magnetic materials, taking into considerations wide ranges of frequency and magnetic induction. The revealed data collapse of energy loss enables comparison of energy losses data taken by different methods. This phenomenon also supplies new criterion for correctness of empirical data.

New algoritm for optimizing technological parameters of soft magnetic compozites has been derived on the base of topological structure of the power loss characteristics. In optimization processes of magnitudes obeying scaling it happen binary relations of magnitudes having different dimensions. From mathematical point of view in general case such a procedure is not permissible. However, in a case of the system obeying the scaling law it is so. It has been shown that in such systems binary relations of magnitudes of different dimensions is correct and has mathematical meaning which is important for practical use of scaling in optimization processes. Derived here structure of the set of all power loss characteristics in soft magnetic composite enables us to derive a formal pseudo-state equation of SMC. This equation constitutes a realation of the hardening temperature, the compaction pressure and a parameter characterizing the power loss characteristic. Finally, the pseudo-state equation improves the algoritm for designing the best values of technological parameters.

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