Single point measurements of magnetic field gradient waveform

Pulsed magnetic field gradients are fundamental to spatial encoding and diffusion weighting in magnetic resonance. The ideal pulsed magnetic field gradient should have negligible rise and fall times, however, there are physical limits to how fast the magnetic field gradient may change with time. Finite gradient switching times, and transient, secondary, induced magnetic field gradients (eddy currents) alter the ideal gradient waveform and may introduce a variety of undesirable image artifacts. We have developed a new method to measure the complete magnetic field gradient waveform. The measurement employs a heavily doped test sample with short MR relaxation times (T(1), T(2), and T(2)(*)<100 micros) and a series of closely spaced broadband radiofrequency excitations, combined with single point data acquisition. This technique, a measure of evolving signal phase, directly determines the magnetic field gradient waveform experienced by the test sample. The measurement is sensitive to low level transient magnetic fields produced by eddy currents and other short and long time constant non-ideal gradient waveform behaviors. Data analysis is particularly facile permitting a very ready experimental check of gradient performance.     

Anisotropic water diffusion in macroscopically oriented lipid bilayers studied by pulsed magnetic field gradient NMR

The anisotropy, D(parallel)/D( perpendicular ), of water diffusion in fully hydrated bilayers of dimyristoylphosphatidylcholine at 29 degrees C has been measured by pulsed magnetic field gradient (pfg) NMR. By using NMR imaging hardware to produce magnetic field gradients in an arbitrary direction with respect to a stack of macroscopically aligned lipid bilayers, translational diffusion of water was measured as a function of the angle between the direction of the magnetic field gradient and the normal of the lipid membrane. The observed diffusion coefficient is found to depend strongly on this angle. The anisotropy cannot be accurately determined due to the very small value of D( perpendicular ), but a lower limit of about 70 can be estimated from the observed diffusion coefficients. The results are discussed in terms of the relatively low permeability of water across the lipid bilayer, instrumental limitations, and/or possible defects in the lamellae.     

Diffusion exchange NMR spectroscopy in inhomogeneous magnetic fields

Two-dimensional diffusion exchange experiments in the presence of a strong, static magnetic field gradient are presented. The experiments are performed in the stray field of a single sided NMR sensor with a proton Larmor frequency of 11.7 MHz. As a consequence of the strong and static magnetic field gradient the magnetization has contributions from different coherence pathways. In order to select the desired coherence pathways, a suitable phase cycling scheme is introduced. The pulse sequence is applied to study diffusion as well as the molecular exchange properties of organic solvents embedded in a mesoporous matrix consisting of a sieve of zeolites with a pore size of 0.8 nm and grain size of 2 μm. This pulse sequence extends the possibilities of the study of transport properties in porous media, with satisfying sensitivity in measurement times of a few hours, in a new generation of relatively inexpensive low-field NMR mobile devices.     

Radiofrequency magnetic field gradient echoes have reduced sensitivity to susceptibility gradients

The amplitudes of gradient-echoes produced using static field gradients are sensitive to diffusion of tissue water during the echo evolution time. Gradient-echoes have been used to produce MR images in which image intensity is proportional to the self-diffusion coefficient of water. However, such measurements are subject to error due to the presence of background magnetic field gradients caused by variations in local magnetic susceptibility. These local gradients add to the applied gradients. The use of radiofrequency (RF) gradients to produce gradient-echoes may avoid this problem. The RF magnetic field is orthogonal to the offset field produced by local magnetic susceptibility gradients. Thus, the effect of the local gradients on RF gradient-echo amplitude is small if the RF field is strong enough to minimize resonance offset effects. The effects of susceptibility gradients can be further reduced by storing magnetization longitudinally during the echo evolution period. A water phantom was used to evaluate the effects of background gradients on the amplitudes of RF gradient-echoes. A surface coil was used to produce an RF gradient of between 1.3 and 1.6 gauss/cm. Gradient-echoes were detected with and without a 0.16 gauss/cm static magnetic field gradient applied along the same direction as the RF gradient. The background static field gradient had no significant effect on the decay of RF gradient-echo amplitude as a function of echo evolution time. In contrast, the effect of the background gradient on echoes produced using a 1.6 gauss/cm static field gradient is calculated to be significant. This analysis suggests that RF gradient-echoes can produce MR images in which signal intensity is a function of the self-diffusion coefficient of water, but is not significantly affected by background gradients.     

An improved approach to calibrating high magnetic field gradients for pulsed field gradient experiments

Probes capable of generating short high intensity pulsed magnetic field gradients are commonly used in diffusion studies of systems with very short T(2). Traditional methods of calibrating magnetic field gradients present unique challenges at ultrahigh field strengths and are often inapplicable. Currently the most accurate method of determining magnetic gradient strength is to use the known diffusion coefficient of a standard sample and determine gradient strength from the echo attenuation plot of a diffusion experiment, however, there are problems with finding suitable standards for high intensity gradients. Here, we show that molecules containing at least two receptive nuclei (i.e. one with high and one with low gyromagnetic ratios) are excellent systems for calibrating high intensity gradients.     

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 1min. 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.     

An experiment to measure collisionless radial transport ofenergetic electrons confined by a dipole magnetic field

A new laboratory terrella has been constructed in order to study collisionless radial diffusion of particles trapped within a dipole magnetic field. Columbia's collisionless terrella experiment (CTX) aims to reproduce the process of wave-induced radial transport and does not try to simulate magnetospheric structure. The first experiment planned for CTX is the direct measurement of stochastic radial diffusion induced from wave-particle drift resonances. The motivation for the CTX experiment is described, and the procedures to be used to measure the intensity and spectrum of fluctuations generating chaos, the rate of radial transport, and the evolution of the density and pressure profiles are illustrated. Because of the success of similar experiments conducted earlier in a long thin magnetic mirror, these dipole experiments can be performed with a high degree of confidence. An example from these earlier experiments is presented     

带开口磁环的周期永磁聚焦系统的轴向磁场

 基于磁环的元电流模型,分析了永磁磁环的轴向磁场分布规律。理论计算和测试结果表明:轴向磁化磁环中心轴上的磁感应强度不存在径向分量,只有轴向分量;但磁环开口后,轴向磁场降低,而径向磁场增加,其中心轴上的合成磁感应强度体现出非轴对称性,不利于其在周期永磁（PPM）聚焦系统中的应用。根据磁场的轴向分量和径向分量的分布特点,设计和优化了带开口磁环的PPM系统,实现了轴向磁场的周期化。     

Diffusion interaction between Al and Mg controlled by a high magnetic field

The effects of an 11.5 T high magnetic field on the growth behavior of compounds layers during reactive diffusion in solid Al/solid Mg diffusion couples have been investigated. After annealing with and without a magnetic field, the interfacial zone was still composed of two layers of stable compounds β (Mg₂Al₃) and γ (Mg₁₇Al₁₂), but the thicknesses of the layers were increased by the magnetic field. Data analysis of the thicknesses of compound layers showed that the growth of the γ layer was controlled by grain boundary diffusion as well as volume diffusion at B=0 T, but only controlled by volume diffusion when an 11.5 T high magnetic field was applied. The interdiffusion coefficients for the samples annealed at 643–693 K were calculated from the parabolic relationship between the migration of the interface and the annealing time. The results show that the diffusion constant increased due to the high magnetic field, increasing the chemical potential gradient, and in turn it caused the interdiffusion coefficient to increase.     

Periodic structure of acicular magnetic clusters in a magnetic liquid

The behavior of magnetic clusters in a magnetic liquid placed in a circular capillary is considered. When a uniform magnetic field is applied to the system, acicular clusters grow from the sediment, being aligned with the field. The interaction of the clusters as magnetic dipoles with one another and with an external gradient magnetic field is considered theoretically. In a nonuniform symmetric magnetic field with a peak, the cluster distribution is uniform near the peak. Such a distribution is fairly stable when the magnetic field gradient is varied over certain limits. The ordered (periodic) cluster configuration is realized experimentally, and it is shown that its period can be controlled. As the magnetic field gradient exceeds a certain threshold, the clusters are redistributed, forming a multirow hexagonal array.     

Structure and magnetic field of periodic permanent magnetic focusing system with open magnetic rings

The magnetic field along the central axis for an axially magnetized permanent magnetic ring was investigated by analytical and finite element methods. For open magnetic rings, both calculated and measured results show that the existence of the radial magnetic field creates a remarkable cosine distribution field along the central axis. A new structure of periodic permanent magnet focusing system with open magnetic rings is proposed. The structure provides a satisfactory magnetic field with a stable peak value of 120 mT for a traveling wave tube system.     

磁屏蔽罩在梯度静磁场中的受力研究

在有梯度的静磁场中,对由软磁材料制作的磁屏蔽罩所受的静磁力的量级进行了评估。使用有限元分析和实验测试的方法研究了纯铁方形屏蔽罩在梯度静磁场中的受力情况,结果表明：把内腔尺寸100mm×100mm×150mm、罩体厚度为20mm的方形屏蔽罩放置在强度约为0.2T、梯度为0.03T?m?1的磁场中,其所受的静磁力约为184N,与其自身重力相当;静磁力随磁场强度的升高而增大;有限元分析与实验测试结果的偏差在0.2T背景磁场下约为21%。因此,在考虑一定余量的情况下,使用有限元计算评估屏蔽罩在静磁场中的受力情况是一种有效和比较可靠的方法。     

The internal magnetic field distribution, and single exponential magnetic resonance free induction decay, in rocks

When fluid saturated porous media are subjected to an applied uniform magnetic field, an internal magnetic field, inside the pore space, is induced due to magnetic susceptibility differences between the pore-filling fluid and the solid matrix. The microscopic distribution of the internal magnetic field, and its gradients, was simulated based on the thin-section pore structure of a sedimentary rock. The simulation results were verified experimentally. We show that the 'decay due to diffusion in internal field' magnetic resonance technique may be applied to measure the pore size distribution in partially saturated porous media. For the first time, we have observed that the internal magnetic field and its gradients in porous rocks have a Lorentzian distribution, with an average gradient value of zero. The Lorentzian distribution of internal magnetic field arises from the large susceptibility contrast and an intrinsic disordered pore structure in these porous media. We confirm that the single exponential magnetic resonance free induction decay commonly observed in fluid saturated porous media arises from a Lorentzian internal field distribution. A linear relationship between the magnetic resonance linewidth, and the product of the susceptibility difference in the porous media and the applied magnetic field, is observed through simulation and experiment.     

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在有梯度的静磁场中,对由软磁材料制作的磁屏蔽罩所受的静磁力的量级进行了评估.使用有限元分析和实验测试的方法研究了纯铁方形屏蔽罩在梯度静磁场中的受力情况,结果表明:把内腔尺寸100mm×100mm×150mm、罩体厚度为20mm的方形屏蔽罩放置在强度约为0.2T、梯度为0.03T?m-1的磁场中,其所受的静磁力约为184N,与其自身重力相当;静磁力随磁场强度的升高而增大;有限元分析与实验测试结果的偏差在0.2T背景磁场下约为21%.因此,在考虑一定余量的情况下,使用有限元计算评估屏蔽罩在静磁场中的受力情况是一种有效和比较可靠的方法.     

A modified PGSE for measuring diffusion in the presence of static magnetic field gradients

With a proper timing of pi pulses, it is possible to reduce the effect of the static internal magnetic field gradient on the measurement of diffusion with the pulsed gradient spin echo (PGSE). A pulse sequence that in the first order eliminates the effect of weak internal static gradients in a standard PGSE experiment is introduced. The method should be applied in the cases, where strong and short magnetic gradient pulses are used to investigate the motion of liquid in heterogeneous samples with large susceptibility differences such as porous media.     

Velocity autocorrelation spectra of fluid in porous media measured by the CPMG sequence and constant magnetic field gradient

Carr-Purcell-Meiboom-Gill (CPMG) train of radiofrequency pulses applied to spins in the constant magnetic field gradient is an efficient variant of the modulated magnetic field gradient spin echo method, which provides information about molecular diffusion in the frequency domain instead of in the time domain as with the two-pulse gradient spin echo. The frequency range of this novel technique is broad enough to sample the power spectrum of displacement fluctuation in water-saturated pulverized silica (SiO2) and provides comprehensive information about the molecular restricted motion as well as about the structure of the medium.     

Measurement of diffusion in the presence of shear flow

We demonstrate here a method whereby molecular diffusion coefficients may be measured in the presence of the deformational flow field of a rheo-NMR cell. The method, which uses a repetitive CPMG train of rf pulses interspersed with magnetic field gradient pulses, allows the anisotropic diffusion spectrum to be directly probed. We focus on the cylindrical Couette cell, for which the radial, tangential, and axial directions correspond to the hydrodynamic velocity gradient, velocity, and vorticity directions. While ideal Couette flow does not perturb the vorticity direction, it does perturb diffusion measurements for the velocity gradient direction, and to a lesser extent, the velocity direction. We show that with closely spaced gradient pulses operating in a flow-compensating mode, there exists a diffusion limit below which one cannot measure, that scales as T(2)gamma(4), where gamma is the shear rate and T the gradient pulse repetition period. For a typical rheo-NMR cell, and for the more challenging velocity gradient direction, diffusion rates above 10(-12) m(2) s(-1) can be accurately measured (to 1% error) at shear rates up to 3s(-1). We demonstrate the use of the method in measuring the diffusion spectrum of a lyotropic lamellar phase under shear.     

Two-dimensional model of the Penning discharge in a cylindrical chamber with the axial magnetic field

The drift–diffusion model of a Penning discharge in molecular hydrogen under pressures of about 1 Torr with regard to the external electric circuit has been proposed. A two-dimensional axially symmetric discharge geometry with a cylindrical anode and flat cathodes perpendicular to the symmetry axis has been investigated. An external magnetic field of about 0.1 T is applied in the axial direction. Using the developed drift–diffusion model, the electrodynamic structure of a Penning discharge in the pressure range of 0.5–5 Torr at a current source voltage of 200–500 V is numerically simulated. The evolution of the discharge electrodynamic structure upon pressure variations in zero magnetic field (the classical glow discharge mode) and in the axial magnetic field (Penning discharge) has been studied using numerical experiments. The theoretical predictions of the existence of an averaged electron and ion motion in a Penning discharge both in the axial and radial directions and in the azimuthal direction have been confirmed by the calculations.     

Efficient magnetic guiding and deflection of atomic beams with moderate velocities

We have studied guidance and deflection of a beam of cesium atoms by a strong toroidal magnetic quadrupole field. The beam guide is made from permanent magnets sustaining a radial field gradient of 2.8 T/cm. Atoms with moderate longitudinal velocities ranging from 30 m/s to 70 m/s were inserted across the 10-mm-diameter aperture of a 24.5° arc with radius 300 mm. We have measured transmission and beam divergence and find good agreement with ray-tracing calculations and analytical estimates. The magnetic beam guide allows for 100% transmission of heavy atoms over large angles. Received: 9 November 1998 / Revised version: 6 April 1999 / Published online: 30 July 1999     

DC column plasma kinetics in a longitudinal magnetic field

The cylindrical column plasma of a neon dc glow discharge under the influence of a weak longitudinal magnetic field is studied. An extended, fully self-consistent model of the column plasma has been used to determine the kinetic quantities of electrons, ions and excited atoms, the radial space charge field, and the axial electric field for given discharge conditions. The model includes a nonlocal kinetic treatment of the electrons by solving their spatially inhomogeneous kinetic equation, taking into account the radial space charge field and the axial magnetic field. The treatment is based on the two-term expansion of the velocity distribution and comprises the determination of its isotropic and anisotropic components in the axial, radial, and azimuthal direction. A transition from a distinctly nonlocal kinetic behavior of the electrons in the magnetic-field-free case to an almost local kinetic behavior has been found by increasing the magnetic field. The establishment of the electron cyclotron motion around the column axis increasingly restricts the radial electron energy transport and reduces the radial ambipolar current. The complex interaction of these transport phenomena with the alterations in the charge carrier production leads finally to a specific variation of the electric field components. The axial field increases by applying weak magnetic fields, however, decreases with increasingly higher magnetic fields. At higher magnetic fields, the radial space-charge field is considerably reduced