A bending magnet with nonsaturating shimming /

"AEC Contract AT(04-3)-400."

Experimental tests of quantum nonlinear dynamics in atom optics

Cold atoms in optical potentials provide an ideal test bed to explore quantum nonlinear dynamics. Atoms are prepared in a magneto-optic trap or as a dilute Bose-Einstein condensate and subjected to a far detuned optical standing wave that is modulated. They exhibit a wide range of dynamics, some of which can be explained by classical theory while other aspects show the underlying quantum nature of the system. The atoms have a mixed phase space containing regions of regular motion which appear as distinct peaks in the atomic momentum distribution embedded in a sea of chaos. The action of the atoms is of the order of Planck's constant, making quantum effects significant. This tutorial presents a detailed description of experiments measuring the evolution of atoms in time-dependent optical potentials. Experimental methods are developed providing means for the observation and selective loading of regions of regular motion. The dependence of the atomic dynamics on the system parameters is explored and distinct changes in the atomic momentum distribution are observed which are explained by the applicable quantum and classical theory. The observation of a bifurcation sequence is reported and explained using classical perturbation theory. Experimental methods for the accurate control of the momentum of an ensemble of atoms are developed. They use phase space resonances and chaotic transients providing novel ensemble atomic beamsplitters. The divergence between quantum and classical nonlinear dynamics is manifest in the experimental observation of dynamical tunnelling. It involves no potential barrier. However a constant of motion other than energy still forbids classically this quantum allowed motion. Atoms coherently tunnel back and forth between their initial state of oscillatory motion and the state 180 out of phase with the initial state.

Winding patterns for biplanar MRI shim coils with rectangular and circular target-field regions

A method is presented for calculating the winding patterns required to design independent zonal and tesseral biplanar shim coils for magnetic resonance imaging. Streamline, target-field, Fourier integral and Fourier series methods are utilized. For both Fourier-based methods, the desired target field is specified on the surface of the conducting plates. For the Fourier series method it is possible to specify the target field at additional depths interior to the two conducting plates. The conducting plates are confined symmetrically in the xy plane with dimensions 2a x 2b, and are separated by 2d in the z direction. The specification of the target field is symmetric for the Fourier integral method, but can be over some asymmetric portion pa < x < qa and sb < y < tb of the coil dimensions (-1 < p < q < 1 and -1 < s < t < 1) for the Fourier series method. Arbitrary functions are used in the outer sections to ensure continuity of the magnetic field across the entire coil face. For the Fourier series case, the entire field is periodically extended as double half-range sine or cosine series. The resultant Fourier coefficients are substituted into the Fourier series and integral expressions for the internal and external magnetic fields, and stream functions on both the conducting surfaces. A contour plot of the stream function directly gives the required coil winding patterns. Spherical harmonic analysis of field calculations from a ZX shim coil indicates that example designs and theory are well matched.

A time-harmonic target-field method for designing unshielded RF coils in MRI

Time-harmonic methods are required in the accurate design of RF coils as operating frequency increases. This paper presents such a method to find a current density solution on the coil that will induce some desired magnetic field upon an asymmetrically located target region within. This inverse method appropriately considers the geometry of the coil via a Fourier series expansion, and incorporates some new regularization penalty functions in the solution process. A new technique is introduced by which the complex, time-dependent current density solution is approximated by a static coil winding pattern. Several winding pattern solutions are given, with more complex winding patterns corresponding to more desirable induced magnetic fields.

A wave equation technique for designing compact gradient coils

A primary purpose of this research is to design a gradient coil that is planar in construction and can be inserted within existing infrastructure. The proposed wave equation method for the design of gradient coils is novel within the field. it is comprehensively shown how this method can be used to design the planar x-, y-, and z-gradient wire windings to produce the required magnetic fields within a certain domain. The solution for the cylindrical gradient coil set is also elucidated. The wave equation technique is compared with the well-known target held method to gauge the quality of resultant design. In the case of the planar gradient coil design, it is shown that using the new method, a set of compact gradient coils with large field of view can be produced. The final design is considerably smaller in dimension when compared with the design obtained using the target field method, and therefore the manufacturing costs and materials required are somewhat reduced.

An inverse method for designing loaded RF coils in MRI

Radio-frequency ( RF) coils are designed such that they induce homogeneous magnetic fields within some region of interest within a magnetic resonance imaging ( MRI) scanner. Loading the scanner with a patient disrupts the homogeneity of these fields and can lead to a considerable degradation of the quality of the acquired image. In this paper, an inverse method is presented for designing RF coils, in which the presence of a load ( patient) within the MRI scanner is accounted for in the model. To approximate the finite length of the coil, a Fourier series expansion is considered for the coil current density and for the induced fields. Regularization is used to solve this ill-conditioned inverse problem for the unknown Fourier coefficients. That is, the error between the induced and homogeneous target fields is minimized along with an additional constraint, chosen in this paper to represent the curvature of the coil windings. Smooth winding patterns are obtained for both unloaded and loaded coils. RF fields with a high level of homogeneity are obtained in the unloaded case and a limit to the level of homogeneity attainable is observed in the loaded case.

Dual-symmetric Lagrangians in quantum electrodynamics: I. Conservation laws and multi-polar coupling

By using a complex field with a symmetric combination of electric and magnetic fields, a first-order covariant Lagrangian for Maxwell's equations is obtained, similar to the Lagrangian for the Dirac equation. This leads to a dual-symmetric quantum electrodynamic theory with an infinite set of local conservation laws. The dual symmetry is shown to correspond to a helical phase, conjugate to the conserved helicity. There is also a scaling symmetry, conjugate to the conserved entanglement. The results include a novel form of the photonic wavefunction, with a well-defined helicity number operator conjugate to the chiral phase, related to the fundamental dual symmetry. Interactions with charged particles can also be included. Transformations from minimal coupling to multi-polar or more general forms of coupling are particularly straightforward using this technique. The dual-symmetric version of quantum electrodynamics derived here has potential applications to nonlinear quantum optics and cavity quantum electrodynamics.

Strong electronic correlations in superconducting organic charge transfer salts

We review the role of strong electronic correlations in quasi-two-dimensional organic charge transfer salts such as (BEDT-TTF)(2)X, (BETS)(2)Y, and beta'-[Pd(dmit)(2)](2)Z. We begin by defining minimal models for these materials. It is necessary to identify two classes of material: the first class is strongly dimerized and is described by a half-filled Hubbard model; the second class is not strongly dimerized and is described by a quarter-filled extended Hubbard model. We argue that these models capture the essential physics of these materials. We explore the phase diagram of the half-filled quasi-two-dimensional organic charge transfer salts, focusing on the metallic and superconducting phases. We review work showing that the metallic phase, which has both Fermi liquid and 'bad metal' regimes, is described both quantitatively and qualitatively by dynamical mean field theory (DMFT). The phenomenology of the superconducting state is still a matter of contention. We critically review the experimental situation, focusing on the key experimental results that may distinguish between rival theories of superconductivity, particularly probes of the pairing symmetry and measurements of the superfluid stiffness. We then discuss some strongly correlated theories of superconductivity, in particular the resonating valence bond (RVB) theory of superconductivity. We conclude by discussing some of the major challenges currently facing the field. These include parameterizing minimal models, the evidence for a pseudogap from nuclear magnetic resonance (NMR) experiments, superconductors with low critical temperatures and extremely small superfluid stiffnesses, the possible spin- liquid states in kappa-(ET)(2)Cu-2(CN)(3) and beta'-[Pd(dmit)(2)](2)Z, and the need for high quality large single crystals.

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.

Quantification of the relationship between, magnetoencephalographic (MEG) and blood oxygenation dependent (BOLD) images of brain function

Magnetoencephalography (MEG) is the measurement of the magnetic fields generated outside the head by the brain’s electrical activity. The technique offers the promise of high temporal and spatial resolution. There is however an ambiguity in the inversion process of estimating what goes on inside the head from what is measured outside. Other techniques, such as functional Magnetic Resonance Imaging (fMRI) have no such inversion problems yet suffer from poorer temporal resolution. In this study we examined metrics of mutual information and linear correlation between volumetric images from the two modalities. Measures of mutual information reveal a significant, non-linear, relationship between MEG and fMRI datasets across a number of frequency bands.

Biology of sensory systems

A comprehensive and highly illustrated text providing a broad and invaluable overview of sensory systems at the molecular, cellular and neurophysiological level of vertebrates, invertebrates and prokaryotes. It retains a strong focus on human systems, and takes an evolutionary and comparative approach to review the mechanosenses, chemosenses, photosenses, and other sensory systems including those for detecting pain, temperature electric and magnetic fields etc. It incorporates exciting and significant new insights provided by molecular biology which demonstrate how similar the molecular architecture and physiology of sensory cells are across species and across sensory modality, often indicationg a common ancestry dating back over half a billion years. Written by a renowned author, with extensive teaching experience in the biology of sensory systems, this book includes: - Over 400 illustrations - Self–assessment questions - Full bibliography preceded by short bibliographical essays - Boxes containing useful supplementary material. It will be invaluable for undergraduates and postgraduates studying biology, zoology, animal physiology, neuroscience, anatomy, molecular biology, physiological psychology and related courses.

Normative MEG data to flash and pattern reversal stimuli

We have attempted to establish normative values of components of the magnetic evoked field to flash and pattern reversal stimuli prior to clinical use of the MEG. Full visual field, binocular evoked magnetic fields were recorded from 100 subjects 16 to 86 years of age with a single channel dc Squid (BTI) second-order gradiometer at a point 5-6cm above the inion. The majority of subjects showed a large positive component (out going magnetic field) of mean latency 115 ms (SD range 2.5 -11.8 in different decades of life) to the pattern reversal stimulus. In many subjects, this P100M was preceeded and succeeded by negative deflections (in going field). About 6% of subjects showed an inverted response i.e. a PNP wave. Waveforms to flash were more variable in shape with several positive components; the most consistent having a mean latency of 110ms (SD range 6.4-23.2). Responses to both stimuli were consistent when measured on the same subject on six different occasions (SD range 4.8 to 7.3). The data suggest that norms can be established for evoked magnetic field components, in particular for the pattern reversal P100M, which could be used in the diagnosis of neuro-opthalmological disease.

Functional localisation of human sensory-motor cortex using magnetoencephalography

The 19 channel Neuromagnetometer system in the Clinical Neurophysiology Unit at Aston University is a multi-channel system, unique in the United Kingdom. A bite bar head localisation and MRI co-registration strategy which enabled accurate and reproducible localisation of MEG data into cortical space was developed. This afforded the opportunity to study magnetic fields of the human cortex generated by stimulation of peripheral nerve, by stimulation of visceral sensory receptors and by those evoked through voluntary finger movement. Initially, a study of sensory-motor evoked data was performed in a healthy control population. The techniques developed were then applied to patients who were to undergo neurosurgical intervention for the treatment of epilepsy and I or space occupying lesions. This enabled both validation of the effective accuracy of source localisation using MEG as well as to determine the clinical value of MEG in presurgical assessment of functional localisation in human cortex. The studies in this thesis have demonstrated that MEG can repeatedly and reliably locate sources contained within a single gyrus and thus potentially differentiate between disparate gyral activation. This ability is critical in the clinical application of any functional imaging technique; which is yet to be fully validated by any other 'non-invasive' functional imaging methodology. The technique was also applied to the study of visceral sensory representation in the cortex which yielded important data about the multiple cortical representation of visceral sensory function.

Neuro-electromagnetic imaging of the human visual cortex

Methods of solving the neuro-electromagnetic inverse problem are examined and developed, with specific reference to the human visual cortex. The anatomy, physiology and function of the human visual system are first reviewed. Mechanisms by which the visual cortex gives rise to external electric and magnetic fields are then discussed, and the forward problem is described mathematically for the case of an isotropic, piecewise homogeneous volume conductor, and then for an anisotropic, concentric, spherical volume conductor. Methods of solving the inverse problem are reviewed, before a new technique is presented. This technique combines prior anatomical information gained from stereotaxic studies, with a probabilistic distributed-source algorithm to yield accurate, realistic inverse solutions. The solution accuracy is enhanced by using both visual evoked electric and magnetic responses simultaneously. The numerical algorithm is then modified to perform equivalent current dipole fitting and minimum norm estimation, and these three techniques are implemented on a transputer array for fast computation. Due to the linear nature of the techniques, they can be executed on up to 22 transputers with close to linear speedup. The latter part of the thesis describes the application of the inverse methods to the analysis of visual evoked electric and magnetic responses. The CIIm peak of the pattern onset evoked magnetic response is deduced to be a product of current flowing away from the surface areas 17, 18 and 19, while the pattern reversal P100m response originates in the same areas, but from oppositely directed current. Cortical retinotopy is examined using sectorial stimuli, the CI and CIm ;peaks of the pattern onset electric and magnetic responses are found to originate from areas V1 and V2 simultaneously, and they therefore do not conform to a simple cruciform model of primary visual cortex.

Effective electromagnetic noise cancellation with beamformers and synthetic gradiometry in shielded and partly shielded environments

The major challenge of MEG, the inverse problem, is to estimate the very weak primary neuronal currents from the measurements of extracranial magnetic fields. The non-uniqueness of this inverse solution is compounded by the fact that MEG signals contain large environmental and physiological noise that further complicates the problem. In this paper, we evaluate the effectiveness of magnetic noise cancellation by synthetic gradiometers and the beamformer analysis method of synthetic aperture magnetometry (SAM) for source localisation in the presence of large stimulus-generated noise. We demonstrate that activation of primary somatosensory cortex can be accurately identified using SAM despite the presence of significant stimulus-related magnetic interference. This interference was generated by a contact heat evoked potential stimulator (CHEPS), recently developed for thermal pain research, but which to date has not been used in a MEG environment. We also show that in a reduced shielding environment the use of higher order synthetic gradiometry is sufficient to obtain signal-to-noise ratios (SNRs) that allow for accurate localisation of cortical sensory function.