Uniform Static Magnetic Field Research Articles

Self-diffusion measurements by a mobile single-sided NMR sensor with improved magnetic field gradient

A simple and fast method of measuring self-diffusion coefficients of protonated systems with a mobile single-sided NMR sensor is discussed. The NMR sensor uses a magnet geometry that generates a highly flat sensitive volume where a strong and highly uniform static magnetic field gradient is defined. Self-diffusion coefficients were measured by Hahn- and stimulated echoes detected in the presence of the uniform magnetic field gradient of the static field. To improve the sensitivity of these experiments, a Carr–Purcell–Meiboom–Gill pulse sequence was applied after the main diffusion-encoding period. By adding the echo train the experimental time was strongly shortened, allowing the measurement of complete diffusion curves in less than 1 min. This method has been tested by measuring the self-diffusion coefficients D of various organic solvents and poly(dimethylsiloxane) samples with different molar masses. Diffusion coefficients were also measured for n-hexane absorbed at saturation in natural rubber with different cross-link densities. The results show a dependence on the concentration that is in good agreement with the theoretical prediction. Moreover, the stimulated-echo sequence was successfully used to measure the diffusion coefficient as a function of the evolution time in systems with restricted diffusion. This type of experiment proves the pore geometry and gives access to the surface-to-volume ratio. It was applied to measure the diffusion of water in sandstones and sheep Achilles tendon. Thanks to the strong static gradient G 0, all diffusion coefficients could be measured without having to account for relaxation during the pulse sequence.

Saddle coils for uniform static magnetic field generation in NMR experiments

The magnetic flux density field (called, henceforth, “magnetic field,” for the sake of simplicity) generated by a saddle coil system is numerically calculated in the whole space and experimentally tested in two different spatial planes. The uniformity of the magnetic field is studied using Taylor series expansions of the three components separately. The optimum geometry is revised and obtained from the second-order Taylor expansions. The most favorable relationship between saddle coil geometric parameters is determined in case the optimum geometry cannot be achieved (because of experimental restrictions). Approximated manipulable analytical expressions are obtained via fourth-order Taylor expansions of the three components of the magnetic field and compared with exact expressions. They were found to differ in less than 10−3% within a sample region, when typical sample and coil dimensions are considered. Deviations of the magnetic field produced by an optimum-compensating saddle coil system were contrasted with typical NMR field-cycling magnetic field inhomogeneities. Possible influences of such deviations in NMR experiments are discussed. © 2006 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 29B: 9–19, 2006

Velocity imaging by ex situ NMR

A pulsed field gradient stimulated spin-echo NMR sequence is combined with imaging methods to spatially resolve velocity distributions and to measure 2D velocity maps ex situ. The implementation of these techniques in open sensors provides a powerful non-invasive tool to measure molecular displacement in a large number of applications inaccessible to conventional closed magnets. The method is implemented on an open tomograph that provides 3D spatial localization by combining slice selection in the presence of a uniform static magnetic field gradient along the depth direction with pulsed field gradients along the two lateral directions. Different pipe geometries are used to demonstrate that the sequence performs well even in the extremely inhomogeneous B 0 and B 1 fields of these sensors.

Nonlinear response formula for an interacting two-dimensional electron gas under a magnetic field and microwave radiation

Introducing a canonical transformation of the second quantized field operators for two-dimensional interacting electrons under a uniform static magnetic field and a microwave radiation field, an exact formula that transforms the retarded density response function of the electrons to that of the electrons without the radiation field is derived. The formula provides a new way to treat the effects of the microwave radiation field on the electron density response when the conventional linear response approximation is not applicable.

Effect of High Magnetic Fields on the Conductivity of a Quantum Cylinder under Stark Ladder Conditions

The conductivity of a quantum cylinder with a parabolic lateral confinement potential and a superstructure is studied under conditions where uniform static quantizing electric and magnetic fields are applied along the cylinder axis. The charge carriers are assumed to be scattered by optical phonons. The dependence of the current density along the superlattice axis on the dc magnetic field is obtained. It is shown that, under certain conditions, the so-called Stark-hybrid-phonon resonance appears due to the hybridization of the electronic energy spectrum. In turn, this gives rise to a sharply nonmonotonic magnetic-field dependence of the current density.

Effects of strong magnetic fields on the electron distribution and magnetisability of rare gas atoms

Strong uniform static magnetic fields compress the electronic distribution of rare gas atoms and cause a ‘spindle effect’, which can be illustrated by plotting charge–density functions which depend quadratically on the flux density of the applied field. The fourth rank hypermagnetisabilities of He, Ne, Ar and Kr are predicted to have small positive values. Accordingly, the diamagnetism of rare gas atoms diminishes by a very little amount in the presence of intense magnetic field.

Electric-field induced exponential enhancement of electromagnetic absorption in semiconductors at a strong magnetic field

The influence is investigated of a dc (electric) field F perpendicular to a strong uniform static magnetic field H on the absorption coefficient of a semiconductor for high-frequency electromagnetic waves polarized along the electric field. The absorption coefficient for some (e.g., phonon-assisted) cyclotron resonances is predicted to exhibit a strong, almost exponential increase by orders of magnitude with increasing F up to a relatively weak F c , the upper limit of the range in which the considered absorption mechanism holds true. The predicted effect is suggested to be observable in typical semiconductors at realistic electric and strong magnetic fields and low temperatures.

Long-range transport of magnetic microbeads using simple planar coils placed in a uniform magnetostatic field

We propose an approach for magnetic microbead transport in microfluidic channels over long-range distances using an array of simple planar coils. The latter are placed in a uniform static magnetic field, the role of which is to impose a permanent magnetic moment to the microbeads. The very small magnetic field gradient of a simple planar coil is then sufficient to displace the microbeads. The long-range displacement is assured by arranging adjacent coils in the array with spatial overlap in a three-phase actuation scheme.

Rayleigh–Lamb waves in magneto-thermoelastic homogeneous isotropic plate

The propagation of magnetic-thermoelastic plane wave in an initially unstressed, homogeneous isotropic, conducting plate under uniform static magnetic field has been investigated. The generalized theory of thermoelasticity is employed, by assuming electrical behaviour as quasi-static and the mechanical behaviour as dynamic, to study the problem. The secular equations for both symmetric and skew-symmetric waves have been obtained. The magneto-elastic shear horizontal (SH) mode of wave propagation gets decoupled from rest of the motion and it is not influenced by thermal variations and thermal relaxation times. At short wavelength limits, the secular equations for symmetric and skew-symmetric modes reduce to Rayleigh surface wave frequency equation, because a finite thickness plate in such a situation behaves like a semi-infinite medium. Thin plate results are also deduced at the end. Dispersion curves are represented graphically for various modes of wave propagation in different theories of thermoelasticity. The amplitudes of displacement, perturbed magnetic field and temperature change are also obtained analytically and computed numerically. The result in case of elastokinetics, magneto-elasticity and coupled magneto-elasticity has also been deduced as special cases at appropriate stages of this work.

Equations for the order parameter and effective magnetic field for nonunitary phases of superfluid Fermi liquids with spin-triplet p-wave pairing

On the basis of generalized Fermi-liquid approach we have derived the systems of coupled equations for the components of the order parameter and effective magnetic field for nonunitary phases of neutral paramagnetic superfluid Fermi liquids with spin-triplet pairing in strong static uniform magnetic field at arbitrary temperatures from the interval 0⩽ T⩽ T c ( T c is the normal–superfluid transition temperature). These equations are presented here for dense superfluid neutron matter (existing inside fluid core of neutron stars) with triplet p-wave pairing of 3 He –A 2 type and using the effective Skyrme interaction between neutrons.

Induced resonance processes accompanying interaction of the field of a tem trap with oscillating charges

We theoretically analyze resonance processes in an electromagnetic trap (TEM trap) formed by a circularly polarized high-frequency standing field of homogeneous plane waves and a uniform static magnetic field aligned with the direction of wave propagation. The regime of resonance amplification of the trap field by an ensemble of initially nonphased oscillators in the absence of a static magnetic field is described. The regime of resonance acceleration of charges from thermal to relativistic velocities for a bounded particle motion in the presence of a static magnetic field is considered. It is shown that charge oscillations in the trap are similar to flutter in mechanical systems. The efficient energy exchange is stipulated by an M-type interaction mechanism.

Calculations of Xe line shapes in model nanochannels: Grand canonical Monte Carlo averaging of the Xe129 nuclear magnetic resonance chemical shift tensor

The nuclear shielding of the Xe atom is a tensor molecular electronic property that is a very sensitive indicator of the local environment. Xe atoms in nanochannels of a crystal exhibit anisotropic NMR line shapes that are characteristic of the average shielding tensor; the line shape is a manifestation of the systematic variation of the observed component of the tensor with the orientation of the nanochannel axis in the static uniform external magnetic field. In this paper, a method of calculating the Xe line shapes in nanochannels is presented. The averaging of the shielding tensor is carried out with a grand canonical ensemble at constant (μ, V, T). The line shapes are obtained by assuming a random distribution of orientations of the crystallites within a sample. The equivalent procedure is carried out by finding the component of the Xe shielding tensor along the magnetic field directions selected uniformly on the surface of a sphere. The approach developed here is used to predict the general behavior of Xe line shapes for Xe in elliptical channels of nanoscale dimensions. The channel architecture of crystalline aluminum phosphate ALPO-11 with dimensions 6.7×4.4 Å is used here as a model channel architecture. ALPO-11 is known to impose on Xe atoms an intermolecular NMR shielding response that is highly deshielded compared to a free Xe atom and with a line shape systematically changing with Xe occupancy [J. A. Ripmeester and C. I. Ratcliffe, J. Phys. Chem. 99, 619 (1995)]. In the present work, model channels are constructed with Ne or Ar atoms in the ALPO-11 architecture, and grand canonical Monte Carlo simulations of Xe in these model channels are carried out. The difficulty lies in the construction of the Xe chemical shift tensor for each Xe in the channel at each configuration. We propose a new approach to calculations of the Xe chemical shift tensor in a nanochannel: the additive dimer tensor model. For a model nanochannel constituted entirely of rare gas atoms (Ne, for example) that are located at the crystallographic positions of the atoms constituting the channel walls, the Xe shielding tensor is determined as follows: For a given configuration of Xe atoms within the channel, the Xe shielding tensor of the Jth Xe atom at position (xJ,yJ,zJ) is calculated by a summation over all i of the contribution of XeJ–Nei dimer, the Ne atom located at the ith position, using the ab initio Xe–Ne rare gas dimer shielding tensor. To this is added the Xe–Xe contributions that are calculated by a summation over all L of the contribution of the XeJ–XeL dimer, using the ab initio Xe–Xe dimer shielding tensor. The systematic variations with Xe occupancy of the line shapes obtained from GCMC simulations using the additive dimer tensor model in the model Ne and Ar channels are used to provide general insight into the average Xe shielding tensor in nanochannels. The invariant qualitative aspects of the behavior of Xe line shapes in the model channels provide general predictions independent of the atoms constituting the channel. The chemical shift response of the Xe to the specific atoms constituting the channel walls provides the quantitative details. The specific application to Xe in ALPO-11 crystals compares favorably with experiment.

Local density of states and scattering matrix in quasi-one-dimensional systems

Mathematical relations between the local density of states (LDOS) and the scattering matrix (i.e., transmission and reflection amplitudes) for quasi-one-dimensional systems are derived in the presence of static uniform magnetic fields. Starting from the definition of the LDOS expressed by the Green's function, we derive the formulas for the LDOS in terms of the functional derivative of the scattering matrix or the Friedel phase with respect to a scattering potential.

Gain in a free-electron laser with planar wiggler and ion-channel guiding

A theory of ion-channel guiding in a planar wiggler is presented. For the sake of generality, a uniform static axial magnetic field is included in addition to the ion electrostatic field and wiggler magnetic field. The pendulum equation that describes the interaction between an electron and the radiation field is derived. A formula for the gain is then derived in the low-gain-per-pass limit. The results of a numerical study of gain enhancement due to the ion channel are presented and discussed.

Effect of magnetic field on the confinement of ions in a three-dimensional radio frequency quadrupole trap

The confining field of a three-dimensional radio frequency ion trap has been modified by the addition of a static uniform one-dimensional magnetic field. The physical properties of the confined ions under this combined field are not identical in z and r directions. Numerical calculations show that for a weak magnetic field the changes in the ion secular frequency are negligible for certain applications.

About nonunitary phases of superfluid helium-3 in a magnetic field

We have derived a system of coupled equations for the order parameter, effective magnetic field and unified expression for the magnetic susceptibility for nonunitary superfluid phases 3 He — A 2, 3 He — A 1 and nonunitary 2D-phase of 3 He with spin-triplet p-wave pairing in sufficiently strong static uniform magnetic field at temperatures 0 ≤ T ≤ T c ( T c is the temperature of phase transition from the normal to the superfluid state). These results are obtained within the Fermi-liquid theory generalized to superfluid systems and the Landau spin-exchange Fermi-liquid interaction is taken into account.

Some questions in the theory of a superfluid Fermi liquid with triplet pairing in a magnetic field

General expressions are obtained in explicit form for the anomalous and normal distribution functions of quasiparticles in nonunitary phases of a superfluid paramagnetic Fermi liquid consisting of electrically neutral fermions with triplet pairing (the pairs have spin s=1 and an arbitrary odd value of the orbital angular momentum l) in a uniform static magnetic field. A generalized Fermi-liquid approach is used which takes into account the exchange Fermi-liquid interaction but does not specify the form of the energy functional of the superfluid Fermi liquid. The results are valid at any temperature in the interval 0⩽T⩽Tc, where Tc is the temperature of the phase transition from the normal to the superfluid state. When an explicit form of the energy functional is specified, the general formulas for the distribution function can be used to describe the various nonunitary phases of a superfluid Fermi liquid of the He3 type in a high magnetic field. In particular, for He3-A1, He3-A2, and the nonunitary two-dimensional phase of He3 in a high magnetic field at 0⩽T⩽Tc, an energy functional quadratic in the distribution function is used to find a system of coupled equations for the order parameter and the effective magnetic field and to obtain an expression is obtained for the nonlinear magnetic susceptibility.

NMR 1 J(HD) coupling in HD as a function of interatomic distance in the presence of an external magnetic field

A theoretical study has been made of the dependence of the 1 J(HD) coupling in HD on the interatomic distance R in the presence of a static uniform magnetic field B 0. The behaviour of all coupling terms arising from Ramsey's magnetic electron-nucleus interactions, Fermicontact (FC), spin-dipolar (SD) and paramagnetic (PSO) and diamagnetic (DSO) spin-orbital interactions is analysed qualitatively for large R. It is concluded that the PSO, DSO and SD terms become negligibly small as R increases. Detailed calculations were carried out for the FC term following two different approaches: detailed full CI calculations within a non-perturbative approach; and explicit diagonalization of the Hamiltonian operator restricted to the subspace spanned by the 1Σ+;g and the 3Σ+;u states. Within the approximations considered, the FC term of 1 J(HD) is found to be independent of B 0 and to increase by several orders of magnitude, in agreement with previous results by Bacskay, G. B., 1995, Chem. Phys. Lett., 242, 507, until a critical distance R(B 0) is reached, beyond which it almost vanishes. The quenching of the coupling at R(B 0) is due to the splitting of the 3Σ+;u state in the presence of the field B 0. The stronger the field the shorter is R(B 0).

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.

Absolute measurements of ultrasonic pressure by using high magnetic fields

A hydrophone is introduced that exploits the emf signal generated in a conductor when sonicated in the presence of a uniform static magnetic field. The method uses a small metal coil or metal membrane as a hydrophone receiver. Acoustic signals at 748 kHz are introduced in 1.5 T and 4.7 T fields and recorded both through direct electrical contact with the hydrophone and via RF pick-up coils, allowing wireless placement of the hydrophone. Linear response Is confirmed over four orders of magnitude in the pressure amplitude. Waveforms determined from the detected voltage are shown to be in excellent agreement with those obtained using a calibrated polyvinylidene difluoride film, and absolute values correlate within 20%. The methods are conceptually suitable for use in the presence of the high and uniform field of commercial MR scanners. The hydrophone may appear particularly useful as a quality assurance device in therapeutic and diagnostic acoustic techniques that use MRI.