Fractional operators for the magnetic dynamic behavior of ferromagnetic specimens: An overview

B Ducharne,B Zhang,P Tsafack,G Sebald,Y A Tene Deffo

doi:10.1063/9.0000044

B Ducharne, B Zhang + Show 3 more

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https://doi.org/10.1063/9.0000044

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Abstract

This paper reviews the use of the fractional derivative operators for the dynamic magnetization of ferromagnetic specimens. Magnetic behaviors in ferromagnetic specimens are strongly nonlinear and frequency dependent. Magnetism has an atomic origin but the magnetic behavior as observed at the human scale is highly affected by phenomena occurring at larger scales. Under the influence of an external magnetic field, the homogeneity of a ferromagnetic sample magnetization is linked to the excitation dynamics. Models and simulations in this domain are strongly needed, as they provide theoretical explanations and allow us to anticipate complex phenomena, difficult to observe in a practical way. On the one hand, such multi-scale dynamical behaviors can hardly be taken into account with the usual mathematical operators. On the other hand, correct simulation results on large frequency bandwidths can be obtained using fractional derivative operators. The use of fractional derivatives can be envisaged through different approaches: Lump models based on time fractional differential equations is one option, and fractional anomalous diffusion equations is another. In this manuscript, these two methods are detailed and compared. Theoretical results are compared to experimental ones, and conclusions and perspectives are drawn such as possible improvements.

Highlights

Ferromagnetic behaviors and properties have been studied for more than a century but ferromagnetism is extremely complex.1–5 The majority of electromagnetic devices rely on magnetic conversions, in this domain progresses are continuous
The influence of magnetic excitation dynamics on the magnetization behaviors manifests itself through the frequency dependence of the hysteresis cycle
It is worth mentioning here that in a recent article,30 Liu et al obtained improved results with the lump method by adding a second term, the fractional contribution is restricted to the classic losses and the excess losses are taken into account according to the Bertotti separation losses theory. This manuscript reviewed the use of fractional derivative operators for taking into account the frequency dependent magnetization in ferromagnetic specimens

Summary

INTRODUCTION

Ferromagnetic behaviors and properties have been studied for more than a century but ferromagnetism is extremely complex. The majority of electromagnetic devices rely on magnetic conversions, in this domain progresses are continuous. Beyond the quasi-static threshold, the varying magnetic excitation induces a ripple effect on the domain wall motions which become larger and faster, generating a surplus of microscopic eddy currents and their corresponding Joules losses. By adjusting the fractional order, this alternative simulation method allows to match precisely the experimental observations This is not the only way to simulate hysteresis precisely on a large frequency bandwidth, another solution consists on a phenomenological approach, based a lump model: a quasi-static hysteresis model extended to the frequency dependence through the adjunction of a fractional viscous-type dynamic effect. 17 and 18, this method have been tested with success for the well-known Preisach and Jiles-Atherton (J-A) quasi-static hysteresis models In both methods fractional derivative operators bring flexibility in the simulation process.

Fractional anomalous diffusion equation

Lump model combined to a fractional viscous-type dynamic effect

EXPERIMENTAL VALIDATION

CONCLUSIONS