On models for magnetic field line diffusion

In this contribution, certain aspects of the nonlinear dynamics of magnetic field lines are reviewed. First, the basic facts (known from literature) concerning the Hamiltonian structure are briefly summarized. The paper then concentrates on the following subjects: (i) Transition from the continuous description to discrete maps; (ii) Characteristics of incomplete chaos; (iii) Control of chaos. The presentation is concluded by some remarks on the motion of particles in stochastic magnetic fields.

A theoretical and experimental analysis of the no-load air gap magnetic field in squirrel cage induction machines

In induction machines the tooth frequency losses due to permeance variation constitute a signif'icant, portion of the total loss. In order to predict and estimate these losses it, is essential to obtain a clear understanding of the no-load distribution of the air gap magnetic field and the magnitude of flux pulsation in both stator and rotor teeth. The existing theories and methods by which the air gap permeance variation in a doubly slotted structure is calculated are either empirical or restricted. The main objective of this thesis is to obtain a detailed analysis of the no-load air gap magnetic field distribution and the effect of air gap geometry on the magnitude and waveform of the tooth flux pulsation. In this thesis a detaiiled theoretical and experimental analysis of flux distribution not only leads to a better understanding of the distribution of no-load losses but also provides theoretical analysis for calculating the losses with greater accuracy

Asymptotic theory of wall-attached convection in a horizontal fluid layer with a vertical magnetic field

A horizontal fluid layer heated from below in the presence of a vertical magnetic field is considered. A simple asymptotic analysis is presented which demonstrates that a convection mode attached to the side walls of the layer sets in at Rayleigh numbers much below those required for the onset of convection in the bulk of the layer. The analysis complements an earlier analysis by Houchens [J. Fluid Mech. 469, 189 (2002)] which derived expressions for the critical Rayleigh number for the onset of convection in a vertical cylinder with an axial magnetic field in the cases of two aspect ratios. © 2008 American Institute of Physics.

Magnetic resonance imaging of the manipulation of a chemical wave using an inhomogeneous magnetic field

The effects of applied magnetic fields on the traveling wave formed by the reaction of (ethylenediaminetetraacetato)cobalt(II) (Co(II)EDTA2-) and hydrogen peroxide have been studied using magnetic resonance imaging (MRI). It was found that the wave could be manipulated by applying pulsed magnetic field gradients to a sample contained in a vertical cylindrical tube in the 7.0 T magnetic field of the spectrometer. Transverse field gradients decelerated the propagation of the wave down the high-field side of the tube and accelerated it down the low-field side. This control of the wave propagation eventually promoted the formation of a finger on the low-field side of the tube and allowed the wave to be maneuvered within the sample tube. The origin of these effects is rationalized by considering the Maxwell stress arising from the combined homogeneous and inhomogeneous magnetic fields and the magnetic susceptibility gradient across the wave front.

Magnetic resonance imaging of a magnetic field-dependent chemical wave

The magnetic field dependence of the travelling wave formed during the reaction of (ethylenediaminetetraacetato)cobalt (II) (Co(II)EDTA2- ) and hydrogen peroxide was studied using magnetic resonance imaging (MRI). The reaction was investigated in a vertical tube, in which the wave was initiated from above. The wave propagated downwards, initially with a flat wavefront before forming a finger. Magnetic field effects were observed only once the finger had formed. The wave propagation was accelerated by a magnetic field with a negative gradient (i.e., when the field was stronger at the top of the tube than at the bottom) and slightly decelerated by positive field gradients.

Dynamics of cholesteric liquid crystals in the presence of a random magnetic field:stochastic dynamics of cholesteric liquid crystal

Based on dynamic renormalization group techniques, this letter analyzes the effects of external stochastic perturbations on the dynamical properties of cholesteric liquid crystals, studied in presence of a random magnetic field. Our analysis quantifies the nature of the temperature dependence of the dynamics; the results also highlight a hitherto unexplored regime in cholesteric liquid crystal dynamics. We show that stochastic fluctuations drive the system to a second-ordered Kosterlitz-Thouless phase transition point, eventually leading to a Kardar-Parisi-Zhang (KPZ) universality class. The results go beyond quasi-first order mean-field theories, and provides the first theoretical understanding of a KPZ phase in distorted nematic liquid crystal dynamics.

Magneto-vibratory separation of glass and bronze granular mixtures immersed in a paramagnetic liquid

A fluid-immersed granular mixture may spontaneously separate when subjected to vertical vibration, separation occurring when the ratio of particle inertia to fluid drag is sufficiently different between the component species of the mixture. Here, we describe how fluid-driven separation is influenced by magneto-Archimedes buoyancy, the additional buoyancy force experienced by a body immersed in a paramagnetic fluid when a strong inhomogeneous magnetic field is applied. In our experiments glass and bronze mixtures immersed in paramagnetic aqueous solutions of MnCl2 have been subjected to sinusoidal vertical vibration. In the absence of a magnetic field the separation is similar to that observed when the interstitial fluid is water. However, at modest applied magnetic fields, magneto-Archimedes buoyancy may balance the inertia/fluid-drag separation mechanism, or it may dominate the separation process. We identify the vibratory and magnetic conditions for four granular configurations, each having distinctive granular convection. Abrupt transitions between these states occur at well-defined values of the magnetic and vibrational parameters. In order to gain insight into the dynamics of the separation process we use computer simulations based on solutions of the Navier-Stokes' equations. The simulations reproduce the experimental results revealing the important role of convection and gap formation in the stability of the different states.

Cross-correlation-aided transport in stochastically driven accretion flows

The origin of linear instability resulting in rotating sheared accretion flows has remained a controversial subject for a long time. While some explanations of such non-normal transient growth of disturbances in the Rayleigh stable limit were available for magnetized accretion flows, similar instabilities in the absence of magnetic perturbations remained unexplained. This dichotomy was resolved in two recent publications by Chattopadhyay and co-workers [Mukhopadhyay and Chattopadhyay, J. Phys. A 46, 035501 (2013)1751-811310.1088/1751-8113/46/3/035501; Nath, Phys. Rev. E 88, 013010 (2013)PLEEE81539-375510.1103/PhysRevE.88.013010] where it was shown that such instabilities, especially for nonmagnetized accretion flows, were introduced through interaction of the inherent stochastic noise in the system (even a "cold" accretion flow at 3000 K is too "hot" in the statistical parlance and is capable of inducing strong thermal modes) with the underlying Taylor-Couette flow profiles. Both studies, however, excluded the additional energy influx (or efflux) that could result from nonzero cross correlation of a noise perturbing the velocity flow, say, with the noise that is driving the vorticity flow (or equivalently the magnetic field and magnetic vorticity flow dynamics). Through the introduction of such a time symmetry violating effect, in this article we show that nonzero noise cross correlations essentially renormalize the strength of temporal correlations. Apart from an overall boost in the energy rate (both for spatial and temporal correlations, and hence in the ensemble averaged energy spectra), this results in mutual competition in growth rates of affected variables often resulting in suppression of oscillating Alfven waves at small times while leading to faster saturations at relatively longer time scales. The effects are seen to be more pronounced with magnetic field fluxes where the noise cross correlation magnifies the strength of the field concerned. Another remarkable feature noted specifically for the autocorrelation functions is the removal of energy degeneracy in the temporal profiles of fast growing non-normal modes leading to faster saturation with minimum oscillations. These results, including those presented in the previous two publications, now convincingly explain subcritical transition to turbulence in the linear limit for all possible situations that could now serve as the benchmark for nonlinear stability studies in Keplerian accretion disks.

Visual evoked electrical and magnetic response to half-field stimulation using pattern reversal stimulation

The visual evoked magnetic response to half-field stimulation using pattern reversal was studied using a d.c. SQUID coupled to a second order gradiometer. The main component of the magnetic response consisted of a positive wave at around 100 ms (P100M). At the time this component was present the response to half-field stimulation consisted of an outgoing magnetic field contralateral and extending to the midline. When the left half field was stimulated the outgoing field was over the posterior right visual cortex and when the right half field was stimulated it was over the left anterior visual cortex. These findings would correctly identify a source located in the contralateral visual cortex. The orientation of the dipoles was not that previously assumed to explain the paradoxical lateralization of the visual evoked potential. The results are discussed in terms of both electrical and magnetic models of the calcarine fissure. © 1992.

Radial-field magnetic electron lenses

This investigation looks critically at conventional magnetic lenses in the light of present-day technology with the aim of advancing electron microscopy in its broadest sense. By optimising the cooling arrangements and heat transfer characteristics of lens windings it was possible to increase substantially the current density in the winding, and achieve a large reduction in the size of conventional magnetic electron lenses. Following investigations into the properties of solenoidal lenses, a new type of lens with only one pole-piece was developed. The focal properties of such lenses, which differ considerably from those.of conventional lenses, have been derived from a combination of mathematical models and experimentally measured axial flux density distributions. These properties can be profitably discussed with reference to "half-lenses". Miniature conventional twin pole-piece lenses and the proposed radial field single pole-piece lenses have been designed and constructed and both types of lenses have been evaluated by constructing miniature electron optical columns. A miniature experimental transmission electron microscope (TEM), a miniature scanning electron microscope (SEM) and a scanning transmission microscope (STEM) have been built. A single pole-piece miniature one million volt projector lens of only lOcm diameter and weighing 2.lkg was designed, built and tested at 1 million volts in a commercial electron microscope. iii. Preliminary experiments indicate that in single pole lenses it is possible to extract secondary electrons from the specimen in spite of the presence of the magnetic field of the probe-forming lens. This may well be relevant for the SEM in which it is desirable to examine a large specimen at a moderately good resolution.

Femtosecond laser inscribed Bragg sensor in Terfenol-D coated optical fibre with ablated microslot for the detection of static magnetic fields

A novel device for the detection and characterisation of static magnetic fields is presented. It consists of a femtosecond laser inscribed fibre Bragg grating (FBG) that is incorporated into an optical fibre with a femtosecond laser micromachined slot. The symmetry of the fibre is broken by the micro-slot, producing non-uniform strain across the fibre cross section. The sensing region is coated with Terfenol-D making the device sensitive to static magnetic fields, whereas the symmetry breaking results in a vectorial sensor for the detection of magnetic fields as low as 0.046 mT with a resolution of ±0.3mT in transmission and ±0.7mT in reflection. The sensor output is directly wavelength encoded from the FBG filtering, leading to simple demodulation through the monitoring of wavelength shifts that result as the fibre structure changes shape in response to the external magnetic field. The use of a femtosecond laser to both inscribe the FBG and micro-machine the slot in a single stage, prior to coating the device, significantly simplifies the sensor fabrication.

Femtosecond laser inscribed Bragg sensor in Terfenol-D coated optical fibre with ablated microslot for the detection of static magnetic fields

A novel device for the detection and characterisation of static magnetic fields is presented. It consists of a femtosecond laser inscribed fibre Bragg grating (FBG) that is incorporated into an optical fibre with a femtosecond laser micromachined slot. The symmetry of the fibre is broken by the micro-slot, producing non-uniform strain across the fibre cross section. The sensing region is coated with Terfenol-D making the device sensitive to static magnetic fields, whereas the symmetry breaking results in a vectorial sensor for the detection of magnetic fields as low as 0.046 mT with a resolution of ±0.3mT in transmission and ±0.7mT in reflection. The sensor output is directly wavelength encoded from the FBG filtering, leading to simple demodulation through the monitoring of wavelength shifts that result as the fibre structure changes shape in response to the external magnetic field. The use of a femtosecond laser to both inscribe the FBG and micro-machine the slot in a single stage, prior to coating the device, significantly simplifies the sensor fabrication.

Real-time control of a Tokamak plasma using neural networks

This paper presents results from the first use of neural networks for the real-time feedback control of high temperature plasmas in a Tokamak fusion experiment. The Tokamak is currently the principal experimental device for research into the magnetic confinement approach to controlled fusion. In the Tokamak, hydrogen plasmas, at temperatures of up to 100 Million K, are confined by strong magnetic fields. Accurate control of the position and shape of the plasma boundary requires real-time feedback control of the magnetic field structure on a time-scale of a few tens of microseconds. Software simulations have demonstrated that a neural network approach can give significantly better performance than the linear technique currently used on most Tokamak experiments. The practical application of the neural network approach requires high-speed hardware, for which a fully parallel implementation of the multi-layer perceptron, using a hybrid of digital and analogue technology, has been developed.

The missing link:Analogous human and primate cortical gamma oscillations

Recent animal studies highlighting the relationship between functional imaging signals and the underlying neuronal activity have revealed the potential capabilities of non-invasive methods. However, the valuable exchange of information between animal and human studies remains restricted by the limited evidence of direct physiological links between species. In this study we used magnetoencephalography (MEG) to investigate the occurrence of 30-70 Hz (gamma) oscillations in human visual cortex, induced by the presentation of visual stimuli of varying contrast. These oscillations, well described in the animal literature, were observed in retinotopically concordant locations of visual cortex and show striking similarity to those found in primate visual cortex using surgically implanted electrodes. The amplitude of the gamma oscillations increases linearly with stimulus contrast in strong correlation with the gamma oscillations found in the local field potential (LFP) of the macaque. We demonstrate that non-invasive magnetic field measurements of gamma oscillations in human visual cortex concur with invasive measures of activation in primate visual cortex, suggesting both a direct representation of underlying neuronal activity and a concurrence between human and primate cortical activity. © 2005 Elsevier Inc. All rights reserved.

A study of magnetic non-linearity and finite length effects in solid iron subjected to a travelling MMF wave

This thesis describes an experimental and analytic study of the effects of magnetic non-linearity and finite length on the loss and field distribution in solid iron due to a travelling mmf wave. In the first half of the thesis, a two-dimensional solution is developed which accounts for the effects of both magnetic non-linearity and eddy-current reaction; this solution is extended, in the second half, to a three-dimensional model. In the two-dimensional solution, new equations for loss and flux/pole are given; these equations contain the primary excitation, the machine parameters and factors describing the shape of the normal B-H curve. The solution applies to machines of any air-gap length. The conditions for maximum loss are defined, and generalised torque/frequency curves are obtained. A relationship between the peripheral component of magnetic field on the surface of the iron and the primary excitation is given. The effects of magnetic non-linearity and finite length are combined analytically by introducing an equivalent constant permeability into a linear three-dimensional analysis. The equivalent constant permeability is defined from the non-linear solution for the two-dimensional magnetic field at the axial centre of the machine to avoid iterative solutions. In the linear three-dimensional analysis, the primary excitation in the passive end-regions of the machine is set equal to zero and the secondary end faces are developed onto the air-gap surface. The analyses, and the assumptions on which they are based, were verified on an experimental machine which consists of a three-phase rotor and alternative solid iron stators, one with copper end rings, and one without copper end rings j the main dimensions of the two stators are identical. Measurements of torque, flux /pole, surface current density and radial power flow were obtained for both stators over a range of frequencies and excitations. Comparison of the measurements on the two stators enabled the individual effects of finite length and saturation to be identified, and the definition of constant equivalent permeability to be verified. The penetration of the peripheral flux into the stator with copper end rings was measured and compared with theoretical penetration curves. Agreement between measured and theoretical results was generally good.