Simulation of transverse and longitudinal magnetic ripple structures induced by surface anisotropy

Micromagnetic ripple structures on the surfaces of thick specimens of ultra-soft magnetic material having strong surface anisotropy Ks favouring out-of-surface magnetization have been calculated. These ripples have wavelengths of the order of 0.1 μm and extend to a depth ∼ √A/Ms, where A is the exchange constant and Ms is the saturation magnetization. The wave-vectors of the ripple structures are either transverse or parallel to the bulk magnetization. Both structures have lower energy than the one-dimensional structure discussed by O'Handley and Woods, and they exhibit stronger normal magnetization. The transverse structure requires a surface anisotropy Ks ≥ 0.80K0, where is that required for the one-dimensional structure. The threshold for longitudinal ripples is 0.84K0. It is suggested that the transverse structure probably constitutes the ground state. The magnitudes of Ks and A should be obtainable from measurements of the ripple wavelength and amplitude, and Ms.

Micromagnetic simulation of domain walls in iron films

The micromagnetic structure and energy of 180° domain walls spanning laminar crystals of iron having (100) or (110) surfaces and ranging in thickness from 145 to 580 nm have been investigated by numerical integration of the Landau-Lifshitz-Gilbert equation. Stable equilibrium structures with two flux symmetries were obtained for both crystal orientations at all thicknesses studied.

Assessment of microInductors for DC-DC converters

There are increasing demands on the power density and efficiency of DC-DC power converters due to the soaring functionality and operational longevity required for today's electronic products. In addition, DC-DC converters are required to operate at new elevated frequencies in the MHz frequency regime. Typical ferrite cores, whose useable flux density falls drastically at these frequencies, have to be replaced and a method of producing compact component windings developed. In this study, two types of microinductors, pot-core and solenoid, for DC-DC converter applications have been analyzed for their performance in the MHz frequency range. The inductors were manufactured using an adapted UV-LIGA process and included electrodeposited nickel-iron and the commercial alloy Vitrovac 6025 as core materials. Using a vibrating sample magnetometer (VSM) and a Hewlett Packard 4192A LF- impedance analyzer, the inductor characteristics such as power density, efficiency, inductance and Q-factor were recorded. Experimental, finite element and analytical results were used to assess the suitability of the magnetic materials and component geometries for low MHz operation.

Modeling the dynamics of Magnetic Semilevitation Melting

In semilevitation melting, a cylindrical metal ingot is melted by a coaxial a.c. induction coil. A watercooled solid base supports the ingot, while the top and side free surface is confined by the magnetic forces as the melting front progresses. The dynamic interplay between gravity, hydrodynamic stress, and the Lorentz force in the fluid determines the instantaneous free surface shape. The coupled nonstationary equations for turbulent flow, heat with phase change, and high-frequency electromagnetic field are solved numerically for the axisymmetric time-dependent domain by a continuous mesh transformation, using a pseudospectral method. Results are obtained for the two actually existing coil configurations and several validation cases.

Rotating-frame nuclear magnetic relaxation of spins diffusing on a disordered lattice: a Monte Carlo model

The rotating-frame nuclear magnetic relaxation rate of spins diffusing on a disordered lattice has been calculated by Monte Carlo methods. The disorder includes not only variation in the distances between neighbouring spin sites but also variation in the hopping rate associated with each site. The presence of the disorder, particularly the hopping rate disorder, causes changes in the time-dependent spin correlation functions which translate into asymmetry in the characteristic peak in the temperature dependence of the dipolar relaxation rate. The results may be used to deduce the average hopping rate from the relaxation but the effect is not sufficiently marked to enable the distribution of the hopping rates to be evaluated. The distribution, which is a measure of the degree of disorder, is the more interesting feature and it has been possible to show from the calculation that measurements of the relaxation rate as a function of the strength of the radiofrequency spin-locking magnetic field can lead to an evaluation of its width. Some experimental data on an amorphous metal - hydrogen alloy are reported which demonstrate the feasibility of this novel approach to rotating-frame relaxation in disordered materials.

AC and DC magnetic levitation: melting, fluid flow and oscillations

The presented numerical modelling for the magnetic levitation involves coupling of the electromagnetic field, liquid shape change, fluid velocities and the temperature field at every time step during the simulation in time evolution. Combination of the AC and DC magnetic fields can be used to achieve high temperature, stable levitation conditions. The oscillation frequency spectra are analysed for droplets levitated in AC and DC magnetic fields at various combinations. An electrically poorly conducting, diamagnetic droplet (e.g. water) can be stably levitated using the dia- and para-magnetic properties of the sample material in a high intensity, gradient DC field.

Cold crucible melting of reactive metals using combined DC and AC magnetic fields

Cold crucible furnace is widely used for melting reactive metals for high quality castings. Although the water cooled copper crucible avoids contamination, it produces a low superheat of the melt. Experimental and theoretical investigations of the process showed that the increase of the supplied power to the furnace leads to a saturation in the temperature rise of the melt, and no significant increase of the melt superheat can be obtained. The computer model of theprocess has been developed to simulate the time dependent turbulent flow, heat transfer with phase change, and AC and DC magnetohydrodynamics in a time varying liquid metal envelope. The model predicts that the supermimposition of a strong DC field on top of the normal AC field reduces the level of turbulience and stirring in the liquid metal, thereby reducing the heat loss through the base of the crucible and increasing the superheat. The direct measurements of the temperature in the commercial size cold crucbile has confirmed the computer redictions and showed that the addition of a DC field increased the superheat in molten TiAl from ~45C (AC field only) to ~81C (DC+AC fields). The present paper reports further predictions of the effect of a dDC field on top of the AC field and compares these with experimental data.

Numerical modelling for electromagnetic processing of materials

Electromagnetic processing of materials (EPM) is one of the most widely practiced and fast growing applications of magnetic and electric forces to fluid flow. EPM is encountered in both industrial processes and laboratory investigations. Applications range in scale from nano-particle manipulation to tonnes of liquid metal treated in the presence of various configurations of magnetic fields. Some of these processes are specifically designed and made possible by the use of the electromagnetic force, like the magnetic levitation of liquid droplets, whilst others involve electric currents essential for electrothermal or electrochemical reasons, for instance, in electrolytic metal production and in induction melting. An insight for the range of established and novel EPM applications can be found in the review presented by Asai [1] in the EPM-2003 conference proceedings.

Droplet oscillations in high gradient magnetic field

In high intensity and high gradient magnetic fields the volumetric force on diamagnetic material, such as water, leads to conditions very similar to microgravity in a terrestrial laboratory. In principle, this opens the possibility to determine material properties of liquid samples without wall contact, even for electrically non-conducting materials. In contrast, AC field levitation is used for conductors, but then terrestrial conditions lead to turbulent flow driven by Lorentz forces. DC field damping of the flow is feasible and indeed practiced to allow property measurements. However, the AC/DC field combination acts preferentially on certain oscillation modes and leads to a shift in the droplet oscillation spectrum.What is the cause? A nonlinear spectral numerical model is presented, to address these problems

Droplet oscillations in high gradient static magnetic field

In high intensity and high gradient magnetic fields the volumetric force on diamagnetic material, such as water, leads to conditions very similar to microgravity in a terrestrial laboratory. In principle, this opens the possibility to determine material properties of liquid samples without wall contact, even for electrically non-conducting materials. In contrast, AC field levitation is used for conductors, but then terrestrial conditions lead to turbulent flow driven by Lorentz forces. DC field damping of the flow is feasible and indeed practiced to allow property measurements. However, the AC/DC field combination acts preferentially on certain oscillation modes and leads to a shift in the droplet oscillation spectrum.What is the cause? A nonlinear spectral numerical model is presented, to address these problems.

Levitated liquid droplets in AC and DC magnetic field

Electromagnetic levitation of liquid metal droplets can be used to measure the properties of highly reactive liquid materials. Two independent numerical models, the commercial COMSOL and the spectral-collocation based free surface code SPHINX, have been applied to solve the transient electromagnetic, fluid flow and thermodynamic equations, which describe the levitated liquid motion and heating processes. The SPHINX model incorporates free surface deformation to accurately model the oscillations that result from the interaction between the electromagnetic and gravity forces, temperature dependent surface tension, magnetically controlled turbulent momentum transport. The models are adapted to incorporate periodic laser heating at the top of the droplet, which is used to measure the thermal conductivity of the material. Novel effects in the levitated droplet of magnetically damped turbulence and nonlinear growth of velocities in high DC magnetic field are analysed.

Magnetic damping of levitated liquid droplets in AC and DC field

The intense AC magnetic field required to produce levitation in terrestrial conditions, along with the buoyancy and thermo-capillary forces, results in turbulent convective flow within the droplet. The use of a homogenous DC magnetic field allows the convective flow to be damped. However the turbulence properties are affected at the same time, leading to a possibility that the effective turbulent damping is considerably reduced. The MHD modified K-Omega turbulence model allows the investigation of the effect of magnetic field on the turbulence. The model incorporates free surface deformation, the temperature dependent surface tension, turbulent momentum transport, electromagnetic and gravity forces. The model is adapted to incorporate a periodic laser heating at the top of the droplet, which have been used to measure the thermal conductivity of the material by calculating the phase lag between the frequency of the laser heating and the temperature response at the bottom. The numerical simulations show that with the gradual increase of the DC field the fluid flow within the droplet is initially increasing in intensity. Only after a certain threshold magnitude of the field the flow intensity starts to decrease. In order to achieve the flow conditions close to the ‘laminar’ a D.C. magnetic field >4 Tesla is required to measure the thermal conductivity accurately. The reduction in the AC field driven flow in the main body of the drop leads to a noticeable thermo-capillary convection at the edge of the droplet. The uniform vertical DC magnetic field does not stop a translational oscillation of the droplet along the field, which is caused by the variation in total levitation force due to the time-dependent surface deformation.

Determining surface tension using DC magnetic levitation

The values of material physical properties are vital for the successful use of numerical simulations for electromagnetic processing of materials. The surface tension of materials can be determined from the experimental measurement of the surface oscillation frequency of liquid droplets. In order for this technique to be used, a positioning field is required that results in a modification to the oscillation frequency. A number of previous analytical models have been developed that mainly focus on electrically conducting droplets positioned using an A.C. electromagnetic field, but due to the turbulent flow resulting from the high electromagnetic fields required to balance gravity, reliable measurements have largely been limited to microgravity. In this work axisymmetric analytical and numerical models are developed, which allow the surface tension of a diamagnetic droplet positioned in a high DC magnetic field to be determined from the surface oscillations. In the case of D.C. levitation there is no internal electric currents with resulting Joule heating, Marangoni flow and other effects that introduce additional physics that complicates the measurement process. The analytical solution uses the linearised Navier-Stokes equations in the inviscid case. The body force from a DC field is potential, in contrast to the AC case, and it can be derived from Maxwell equations giving a solution for the magnetic field in the form of a series expansion of Legendre polynomials. The first few terms in this expansion represent a constant and gradient magnetic field valid close to the origin, which can be used to position the droplet. Initially the mathematical model is verified in microgravity conditions using a numerical model developed to solve the transient electromagnetics, fluid flow and thermodynamic equations. In the numerical model (as in experiment) the magnetic field is obtained using electrical current carrying coils, which provides the confinement force for a liquid droplet. The model incorporates free surface deformation to accurately model the oscillations that result from the interaction between the droplet and the non-uniform external magnetic field. A comparison is made between the analytical perturbation theory and the numerical pseudo spectral approximation solutions for small amplitude oscillations.

Effects of magnetic fields on crystal growth

The effects of a constant uniform magnetic field on thermoelectric currents during dendritic solidification were investigated using an enthalpy based numerical model. It was found that the resulting Lorentz force generates a complex flow influencing the solidification pattern. Experimental work of material processing under high magnetic field conditions has shown that the microstructure can be significantly altered. There is evidence that these effects can be atrtributed to the Lorentz force created through the thermoelectric magentohydrodynamic interactions.[1,2] However the mechanism of how this occurs is not very well understood. In this paper, our aim is to investigate the flow field created from the Lorentz force and how this influences the morphology of dendritic growth for both pure materials and binary alloys.