Jeno Takacs

A phenomenological mathematical model of hysteresis

This paper starts with the description of a purely mathematical model of the saturation curve and the hysteresis loop based on the fundamental similarities between the Langevin function the specified T(x) function and the sigmoid shape. The T(x) function which is composed of tangent hyperbolic and linear functions with its free parameters can describe the regular anhysteretic magnetisation curve. Developed from this function the model describes not only the regular hysteresis loop but also the biased and other minor loops like the ones produced by the interrupted and reversed magnetisation process and the open “loops” created by a piecewise monotonic magnetising field input of diminishing amplitude. The remanent magnetism as the function of the interrupted field co‐ordinates is predicted by the model in this mathematical form for the first time. The model presented here is based on the principle that all processes follow the shape of the T(x) function describing the shape of the major hysteresis loop of the ferromagnetic specimen under investigation. The model is also applicable to hysteretic processes in other fields.

Spatial subharmonic instabilities

Abstract A simple theory based on Kukhtarevs materials equations and linear stability analysis is developed providing the threshold conditions for the spontaneous emergence of spatial subharmonics. Experimental results obtained with a photorefractive Bi 12 SiO 20 crystal in the presence of an applied dc voltage and frequency detuning show good agreement with the theoretical predictions.

Spatial subharmonics in photorefractive Bi12SiO20 crystal with a square wave applied field

The instability leading to the appearance of subharmonics in the presence of a square wave applied field is investigated both theoretically and experimentally. The threshold conditions are found for a range of parameters and the temporal variation of the subharmonic amplitude is measured. It is shown that a relatively simple theory, based on a set of material equations, gives good agreement with some of the experimental results but other experiments indicate that the materials equations alone cannot describe all the observations.

Subharmonic domains in a bismuth germanate crystal.

It is shown that a subharmonic grating may have two different phase relationships relative to the fundamental grating, leading to the appearance of domains. The subharmonic beam is generated in a Bi12GiO20 crystal illuminated by two beams in the presence of an applied ac square-wave voltage. The domain structure and the relative phases of the gratings contained in them have been observed with the aid of an interferometric technique.

Barkhausen instability and its implication in T(x) modelling of hysteresis

Purpose – The paper sets out to formulate the intermolecular forces leading to Barkhausen instability. In the approach the known concept of effective field is used within the framework of the T(x) model. The aim is to provide a mathematical tool to theoreticians and applied scientists in magnetism that is easier to use than those of other models. At the same time to demonstrate the easy applicability of the T(x) model to hysteretic phenomena.Design/methodology/approach – With the combination of the effective and the external field the model is applied to hysteresis loops as well as to the anhysteretic state showing in both cases the local development of unstable conditions at beyond a critical point, leading to local hysteresis loops.Findings – The paper formulates the critical conditions for the hysteretic and the anhysteretic process and calculates the susceptibility as the functions of magnetisation and the applied field.Research limitations/implications – Experimental verification will be required to ...

Energy consideration of the T(x) model of hysteresis

Purpose – The paper sets out to develop the T(x) model, based on well known principles and using the free energy of the ferromagnetic binary system as a starting point.Design/methodology/approach – With the inclusion of the coercive and the intermolecular forces the model fully describes the hysteretic process for both major and minor loops, with exchange field between adjacent magnetic moments.Findings – The paper formulates the dependence of the hysteretic systems normalised free energy on parameters such as the temperature, coercivity, other magnetic and materials properties of the ferromagnetic medium.Research limitations/implications – Experimental verification will still be needed as to the accuracy of the model and the applicability to the various magnetic materials.Practical implications – The paper provides an easy mathematical and visual method to present the energy state and its variation of the magnetic materials during magnetisation, including non‐saturation conditions. It has a great value ...

Scatter rings in bismuth silicate illuminated by a single beam

We have observed cones of diffracted light by illuminating a crystal of bismuth silicate with a single beam of light while applying an electric field across the crystal. The scatter rings are a result of the preferential amplification of noise, which we explain here using the Ewald sphere construction.

Multiple forward phase conjugation in a photorefractive bismuth silicate crystal

Abstract The geometrical configuration in which two pump beams and one non coplanar signal beam are incident upon the same side of a bismuth silicate crystal is investigated. It is shown that a strong interaction giving rise to a multiplicity of output beams (three of them phase conjugate) may be obtained when the pump beams are detuned in the opposite directions by the same amount. The phase conjugate images obtained are analysed.

Hysteresis loop reversing by applying Langevin approximation

Purpose The purpose of this paper is to model one of the unsolved problems of magnetism, the reversal of hysteresis loops, in an analytical way. The mathematical models, describing the multiphase steel used in engineering practice, without any exception, are unsuited to provide a way to reverse the hysteretic process. In this paper, a proposal is put forward to model it by using analytical expressions, applying the reversal of the Langevin function. This model works with a high accuracy, giving useful answers to a long unsolved magnetic problem, the lack of reversibility of the hysteresis loop. The use of the proposal is shown by applying the reversal of Langevin function to a sinusoidal and a triangular waveform, the two most frequently used waveforms in research, test and industrial applications. Schematic representations are given for the wave reconstruction by using the proposed method. Design/methodology/approach The unsolved reversibility of the hysteresis loop is approached by a simple analytical formula, providing close approximation for most applications. Findings The proposed solution, applying the reversal of Langevin function, to the problem provides a good practical solution. Research limitations/implications The simple analytical formula has been applied to a number of loops of widely different shapes and sizes with excellent results. Practical implications The proposed solution provides a missing mathematical tool to an unsolved problem for practical applications. Social implications The solution proposed will reduce the work required and provide replacement for expensive complex test instrumentation. Originality/value To the best of the authors’ knowledge, this approach used in this study is the first successful approach in this field, irrespective of the required waveform, and is completely independent of the model used by the user.

The effect of molecular mean‐field interaction on remanent magnetism: The Henkel plots

Purpose – The paper aims to take a critical view of the Wholfarths assumption and the Henkel plots as the measure of molecular mean‐field interaction in magnetic materials. At the same time it seeks to formulate the effect of the molecular field interaction on the anhysteretic remanence.Design/methodology/approach – Based on the recently verified Bosorths original definition of anhysteretic state, the paper verifies Wohlfarths conjecture. By including the molecular field interaction into the effective field expression it formulates the hysteretic and anhysteretic remanent behavior of the magnetic material.Findings – The hysteretic and anhysteretic character of the material can be formulated up to and beyond the Barkhausen jump. The paper also points out that, the now verified, Wholfarths conjecture is applicable to not only major hysteresis loops but also to symmetrical minor loops as well, within the same set. By doing so it removes the uncertainty surrounding its mathematical formulation.Research li...