Linear and non-linear stability of melt flows in magnetic fields

This review considers the stability of melt motion in two simplified models of semiconductor crystal growth by either vertical gradient freeze (VGF) or Czochralski (Cz) processes under the influence of various magnetic fields. In VGF the crystal is grown at the bottom of the crucible, resulting in a stable thermal stratification of the melt. The presence of a stabilizing temperature gradient surprisingly decreases the stability of the flow driven by a rotating magnetic field (RMF). The instability of the travelling magnetic field (TMF)-driven flow, in contrast, is significantly delayed by thermal stratification in VGF. The TMF may, thus, be used in VGF to control the shape of the solidification interface or the radial dopant distribution without causing undesirable flow oscillations. The crystal is pulled out from the melt in the Cz process, producing an unstable temperature gradient below the crystal. The RMF is able to force the resulting unstable buoyant flow into a state of small-scale, high-frequency turbulence that may be regarded as stable for practical purposes. This effect is experimentally observed over a wide range of Grashof numbers, up to 10⁹, characteristic for a large Cz system.     

Electromagnetic melt flow control during solidification of metallic alloys

In this minireview, we summarize experimental and numerical studies particularly concerned with applications of rotating magnetic fields (RMF) or travelling magnetic fields (TMF) to directional solidification of metal alloys. After introducing some fundamentals of electromagnetic stirring, we review the insights gained into flow-induced modifications of microstructure and the formation of freckles and macrosegregations. We further discuss recent strategies, using time-modulated RMF and TMF, which aim to overcome the deficiencies of conventional stirring, in particular flow-induced macrosegregation, by effectively controlling the flow field. On the microscale, we show that time-varying flows are able to alter the sidebranch characteristics vital to the potential of fragmentation.     

Controlling mechanical and physical properties of Al-Si alloys by controlling grain size through grain refinement and electromagnetic stirring

The present study concerns the influence of a travelling magnetic field (TMF) on the hardness, tensile strength and electrical conductivity of directionally solidified grain-refined and non-refined Al-7 wt.% Si alloys. Upwards and downwards travelling fields have been applied to force convection within the solidifying melt. Modifications of the examined physical and mechanical properties depend on the formation of a fine equiaxed structure caused by both the addition of grain refining AlTi5B1-particles and by electromagnetic stirring as well. Electromagnetic stirring without grain refining particles leads to an increase in tensile strength. The addition of grain refiners into the melt leads to the highest reduction of the mean grain size and results in a decrease in electrical conductivity. A melt stirring by a sufficiently high magnetic field provides a homogeneous grain size distribution in the sample volume which impacts the distribution of hardness, tensile strength and electrical conductivity.     

Magnetic Resonance of Impurity Spin in Slow Fluctuating Local Field

A basic model of magnetic resonance is considered. The model takes into account external static and orthogonal to it rotating magnetic fields together with fluctuating (local) field directed along the static field. The local field is considered as smooth normal stochastic process. New solutions for longitudinal relaxation are obtained in the region of adiabatic slow fluctuations and nonadiabatic losses are estimated.     

Manipulation of cold atoms by an adaptable magnetic reflector

Adaptive optics for cold atoms has been experimentally realized by applying a bias magnetic field to a static magnetic mirror. The mirror consist of a 12-mm-diameter piece of commercial videotape, having a sine wave of wavelength 25.4 μm recorded in a single track across its width, curved to form a concave reflector with radius of curvature R=54 mm. We have studied the performance of the mirror by monitoring the evolution of a 24 μK cloud of ⁸⁵Rb atoms bouncing on it. A uniform static external magnetic field was added to the mirror field causing a corrugated potential from which the atoms bounce with increased angular spread. The characteristic angular distribution of the surface normal is mapped at the peak of the bounce for atoms dropped from a height of R/2 and at the peak of the second bounce for a drop height of R/4. In a second experiment a time-dependent magnetic field was applied and the angular distribution of the cloud was measured as a function of field frequency. In this scheme we demonstrate a corrugated potential whose time-dependent magnitude behaves like a diffraction grating of variable depth. Finally a rotating field was added to generate a corrugated potential that moves with a velocity given by the product of the external field rotation frequency and the videotape wavelength. This travelling grating provides a new method of manipulation as cold atoms are transported across the surface by surfing along the moving wave. Two theoretical methods have been developed to predict the behaviour of atoms reflecting from these stationary, variable magnitude and moving corrugated potentials. A simple analytic theory provides excellent agreement for reflection from a stationary corrugated potential and gives good agreement when extended to the case of a travelling grating. A Monte Carlo simulation was also performed by brute force numeric integration of the equations of motion for atoms reflecting from all three corrugated potential cases. Received: 1 December 1999 / Revised version: 3 February 2000 / Published online: 5 April 2000     

Hybrid helicity and magneto-vorticity flux conservation in superdense npe-plasma

In this paper, it is shown that the magnetic helicity dissipation per unit volume, coupled with the longitudinal conductivity, causes enhancement of the kinematic rotation of the electric (and magnetic) lines if the npe-plasma vorticity vector aligns with the electric (or the magnetic) field. In the case of a rigidly rotating npe-plasma under the influence of a strong magnetic field, the electric lines are rotating faster than the magnetic lines. It is deduced that the orthogonality of the electric and magnetic fields is an essential condition for the conduction current to remain finite in the limit of infinite electric conductivity of the npe-plasma. In this case, the magnetic field is not frozen into the npe-plasma, but the magnetic flux in the magnetic tube is conserved. The hybrid helicity is conserved if the “magneto-vorticity” vector is tangent to the level surfaces of constant entropy per baryon. The “magneto-vorticity” lines are rotating on the level surfaces of constant entropy per baryon due to the electromagnetic energy flow in the direction of the npe-plasma vorticity and the chemical potential variation locked with the kinematic rotation of the npe-plasma flow lines. In the case of an isentropic npe-plasma flow, there exists a family of timelike 2-surfaces spanned by the “magneto-vorticity” lines and the npe-plasma flow lines. In this case, the electric field is normal to such a family of timelike 2-surfaces. Maxwell like equations satisfied by “magneto-vorticity” bivector field are solved in axially symmetric stationary case. It is shown that the npe-plasma is in differential rotation in such a way that its each plasma shell (i.e., plasma surface spanned by “magneto-vorticity” lines) is rotating differentially without continually winding up “magneto-vorticity” lines frozen into the npe-plasma. It is also found that gravitational isorotation and Ferraro’s law of isorotation are intimately connected to each other because of coexistence of both the plasma vorticity and the magnetic field due to interaction between the electromagnetic field and npe-plasma flows.     

Liquid metal flows driven by rotating and traveling magnetic fields

Alternating magnetic fields provide a comfortable means for non-intrusive flow control in conductive fluids. However, despite a long history of applications in metallurgy and crystal growth, detailed investigation of the practically important transitional and turbulent flow regimes has become possible only in the last dozen years. The present review gives an overview of this topic with focus on recent experimental and numerical studies of the flow driven by rotating and traveling magnetic fields. We discuss the three-dimensional, instantaneous flow structure as well as the resulting average transport properties for a broad range of parameters, including the superposition of both field types. In addition to the ideal case, the effect of a misalignment of the field with respect to the container axis will be considered, too.     

A rotating phantom for the study of flow effects in MR imaging

A common type of phantom used for the study of flow effects in MR imaging is the tube phantom, where a liquid passes through a set of tubes placed in the main magnetic field of an MR scanner. Among the disadvantages with this type of phantom are that a distribution of velocities is present in each tube, and that quantifications of flow effects using tube phantoms may be very time-consuming. In this work, we describe the design and the properties of a rotating wheel flow phantom used for quantification of the effects of flow through the imaging plane as well as in the imaging plane. The proposed phantom is constructed as a rotating gel-filled wheel, surrounded by static volumes filled with the same gel, and the evaluation of the information from rotating and static parts is made with a specially designed computer program. The phantom can be used as a plug flow phantom covering simultaneously an interchangeable velocity interval, which at present has the range −52 mm/s, +52 mm/s. It is shown that the phantom gives adequate information on the dependence of pixel content on first-order motion in MR modulus and phase images. Among the fields of application are rapid calibration of MR imaging units for flow determination using phase information, as well as testing of pulse sequence characteristics and verification of theoretical predictions concerning the flow dependence in MR images.     

Influences of travelling magnetic field on the dendritic structures of Sn–1.8Cd peritectic alloy during directional solidification

The effects of melt flow driven by a travelling magnetic field (TMF) on solidification structures of Sn–1.8 wt.% Cd peritectic alloy have been investigated numerically and experimentally. Numerical results indicate that the flow velocity at the solid–liquid interface under a downward TMF is smaller than that under an upward TMF. The experimental results show that the growth directions of dendrites are chaotic, and several crotches among the dendrites are observed at the solid–liquid interface in the case of no field. It is concluded from TMF results that the ordered growth of dendrites at two different directions occurs, and only one crotch among the dendrites appears at the solid–liquid interface. The location of the crotch gradually approaches the interface center with increasing magnetic field intensity (B≤10.3 mT). Moreover, the growth of high-order branches occurs at the crotch under a downward TMF. A simple model is established for explanation and it well corresponds to the experimental results.     

Magnetic neutron-wave resonator

Expressions for the neutron density and reflection amplitude have been obtained in the case of a magnetic neutron-wave resonator placed in a static magnetic field or in static and rotating magnetic fields. It is shown that the enhancement of the spin-flip neutron reflection coefficient and that of spin-flip neutron density are proportional to the squared and cubic enhancements of nuclear neutron absorption or the non-spin-flip neutron density, respectively. The conditions for neutron measurements with a high sensitivity of the parameters of magnetic structures have been determined.     

旋转磁场对凝固组织形成的影响

研究了旋转磁场作用下Pb-45%Sn亚共晶合金的凝固组织.实验发现,旋转磁场的频率恒定时,凝固组织的晶粒尺寸随着磁场强度的增强而线性减小,同时,初生相的生长形态从枝晶转变为椭球状.X射线测试结果表明,初生相Pb发生了点阵膨胀,并且晶格常数随着磁场强度的增强先变大后减小,磁场强度在此存在一个临界值.能谱分析显示,随着磁场强度的增强,初生相Pb内Sn的含量逐渐降低.根据电磁场理论和扩散定律,对上述现象进行了理论分析,揭示出旋转磁场引起了液相强烈流动,加快了溶质原子的扩散以及对熔体的加热效应,导致了形核率的提高和长大速度的降低. 关键词： 旋转磁场 液相流动 晶格常数 溶质分配     

The Gyromagnetic Autoresonance

This paper concerns the analysis of a charged particles motion, for instance of an electron, in crossed magnetic (static or slowly varying in time) and fast rotating electric fields. Such a physical situation in the case of a static magnetic field is well known, and has been continuously discussed during many years and even decades.     

Magnetic fluid behavior in uniform DC,AC, and rotating magnetic fields

New flows and instabilities are demonstrated for magnetic fluids and by dual analogy to dielectric fluids. If a fluid drop is contained in a thin gap between two glass plates (Hele–Shaw cell) with a simultaneously applied in-plane rotating field and a DC axial field, smooth spirals or an abrupt transformation to many small droplets can occur. A preliminary minimum magnetization and surface energy analysis is presented to model the abrupt transformation in ferrofluids. An analysis of effective DC magnetoviscosity is also presented for planar Couette flow with an applied uniform DC field transverse to a duct axis with the effective magnetoviscosity and flow spin velocity calculated as a function of field strength. Related Couette viscometer measurements of ferrofluid viscosity show zero and negative magnetoviscosity values for rotating magnetic fields.     

Biological effects of magnetic fields: chronic exposure of the nematode Panagrellus redivivus

The Panagrellus redivivus bioassay, an established monitor of adverse toxic effects of different environments, has been used to study the biological effects of exposure to static and time-varying uniform and gradient magnetic fields, and to time-varying magnetic field gradients superimposed on a static uniform magnetic field of 2.35 Tesla. Temporally stationary magnetic fields have no effect on the fitness of the test animals. Time-varying magnetic fields cause some inhibition of growth and maturation in the test populations. The combination of pulsed magnetic field gradients in a static uniform magnetic field also has a small detrimental effect on the fitness of the test animals.     

On the effect of longitude-dependent fields on convection in stellar atmospheres

In rotating stellar convective zones, heat transfer is shown to be associated with unbalanced azimuth forces arising in the radially ascending (heated) or descending (cold) matter. The presence of a longitude-dependent magnetic field generates additional azimuth forces, hence, new ways of compensating for the unbalanced forces. Generally speaking, this magnetic field is variable but may be nearly static in layers where convective equilibrium is replaced by radiative equilibrium. The condition for the coexistence of the static and usual fields is derived. To this end, an axisymmetric azimuth magnetic field of energy comparable to the energy of rotation should be introduced into models under consideration. In such configurations, conditions for magnetic field generation, as in the Sun, may appear.     

Fatigue life of metal treated by magnetic field

This paper investigates theoretically the influence of magnetization on fatigue life by using non-equilibrium statistical theory of fatigue fracture for metals. The fatigue microcrack growth rate is obtained from the dynamic equation of microcrack growth, where the influence of magnetization is described by an additional term in the potential energy of microcrack. The statistical value of fatigue life of metal under magnetic field is derived, which is expressed in terms of magnetic field and macrophysical as well as microphysical quantities. The fatigue life of AISI 4140 steel in static magnetic field from this theory is basically consistent with the experimental data.     

Magnetized neutron-star mergers and gravitational-wave signals

We investigate the influence of magnetic fields upon the dynamics of, and resulting gravitational waves from, a binary neutron-star merger in full general relativity coupled to ideal magnetohydrodynamics. We consider two merger scenarios: one where the stars have aligned poloidal magnetic fields and one without. Both mergers result in a strongly differentially rotating object. In comparison to the nonmagnetized scenario, the aligned magnetic fields delay the full merger of the stars. During and after merger we observe phenomena driven by the magnetic field, including Kelvin-Helmholtz instabilities in shear layers, winding of the field lines, and transition from poloidal to toroidal magnetic fields. These effects not only mediate the production of electromagnetic radiation, but also can have a strong influence on the gravitational waves. Thus, there are promising prospects for studying such systems with both types of waves.     

Spin-flavor oscillations of neutrinos in rapidly varying external fields

Spin-flavor oscillations of neutrinos in rapidly varying external fields are studied. A method for describing neutrino oscillations in arbitrary rapidly varying external fields is developed. An effective Hamiltonian that describes the evolution of the averaged neutrino wave function is obtained. Neutrino oscillations in rapidly varying magnetic fields are considered on the basis of the general formalism developed in this study. Neutrino transitions in a superposition of a constant and a rotating (in space) magnetic field that are transverse with respect to the neutrino velocity are studied. The probabilities of transitions in spin-flavor oscillations of neutrinos in the magnetic fields of the Sun are estimated. Numerical solutions to the Schrödinger equation for the Hamiltonian that describes neutrino interaction with a constant and a rotating (in space) magnetic field are given. It is shown that the approximate analytic formula obtained in the present study for the probability of neutrino transitions is consistent with the respective numerical solution to the evolution equation at high frequencies of the rotating magnetic fields.     

Simulating magnetic nanoparticle behavior in low-field MRI under transverse rotating fields and imposed fluid flow

In the presence of alternating-sinusoidal or rotating magnetic fields, magnetic nanoparticles will act to realign their magnetic moment with the applied magnetic field. The realignment is characterized by the nanoparticle's time constant, τ. As the magnetic field frequency is increased, the nanoparticle's magnetic moment lags the applied magnetic field at a constant angle for a given frequency, Ω, in rad s⁻¹. Associated with this misalignment is a power dissipation that increases the bulk magnetic fluid's temperature which has been utilized as a method of magnetic nanoparticle hyperthermia, particularly suited for cancer in low-perfusion tissue (e.g., breast) where temperature increases of between 4 and 7 °C above the ambient in vivo temperature cause tumor hyperthermia. This work examines the rise in the magnetic fluid's temperature in the MRI environment which is characterized by a large DC field, B₀. Theoretical analysis and simulation is used to predict the effect of both alternating-sinusoidal and rotating magnetic fields transverse to B₀. Results are presented for the expected temperature increase in small tumors ( radius) over an appropriate range of magnetic fluid concentrations (0.002-0.01 solid volume fraction) and nanoparticle radii (1-10 nm). The results indicate that significant heating can take place, even in low-field MRI systems where magnetic fluid saturation is not significant, with careful the goal of this work is to examine, by means of analysis and simulation, the concept of interactive fluid magnetization using the dynamic behavior of superparamagnetic iron oxide nanoparticle suspensions in the MRI environment. In addition to the usual magnetic fields associated with MRI, a rotating magnetic field is applied transverse to the main B₀ field of the MRI. Additional or modified magnetic fields have been previously proposed for hyperthermia and targeted drug delivery within MRI. Analytical predictions and numerical simulations of the transverse rotating magnetic field in the presence of B₀ are investigated to demonstrate the effect of Ω, the rotating field frequency, and the magnetic field amplitude on the fluid suspension magnetization. The transverse magnetization due to the rotating transverse field shows strong dependence on the characteristic time constant of the fluid suspension, τ. The analysis shows that as the rotating field frequency increases so that Ωτ approaches unity, the transverse fluid magnetization vector is significantly non-aligned with the applied rotating field and the magnetization's magnitude is a strong function of the field frequency. In this frequency range, the fluid's transverse magnetization is controlled by the applied field which is determined by the operator. The phenomenon, which is due to the physical rotation of the magnetic nanoparticles in the suspension, is demonstrated analytically when the nanoparticles are present in high concentrations (1-3% solid volume fractions) more typical of hyperthermia rather than in clinical imaging applications, and in low MRI field strengths (such as open MRI systems), where the magnetic nanoparticles are not magnetically saturated. The effect of imposed Poiseuille flow in a planar channel geometry and changing nanoparticle concentration is examined. The work represents the first known attempt to analyze the dynamic behavior of magnetic nanoparticles in the MRI environment including the effects of the magnetic nanoparticle spin-velocity. It is shown that the magnitude of the transverse magnetization is a strong function of the rotating transverse field frequency. Interactive fluid magnetization effects are predicted due to non-uniform fluid magnetization in planar Poiseuille flow with high nanoparticle concentrations.     

Low frequency double electron muon resonance (Demur) in fused quartz

Double electron muon resonance was studied with comparable amplitudes of the static and rf magnetic fields. The experiments were carried out in fused quartz and employed a resonant linearly-polarized rf field and a small static field. For small amplitudes of the rf field a three-line frequency spectrum was obtained consisting of a central line at the rf frequency and two weaker lines of equal amplitude symmetrically positioned about the central line. A symmetrical three line spectrum is predicted for muonium using the rotating wave approximation (RWA). For large rf fields the amplitudes of the three lines were not symmetric and depended on whether positrons were observed parallel or perpendicular to the beam. For very large rf fields the total amplitude of all the lines was less than for lower rf fields. These results do not agree with the theory using the RWA and no satisfactory theory currently exists.