Simple mobile single-sided NMR apparatus with a relatively homogeneous B0 distribution

This work presents a simple design for a mobile single-sided nuclear magnetic resonance (NMR) apparatus with a relatively homogeneous static magnetic field (B₀) distribution. In the proposed design, the B₀ magnetic field of the apparatus is synthesized using only two permanent magnet blocks, i.e., a cube (main) magnet and a small shim magnet placed above the main magnet. The magnetic flux of the shim magnet partially cancels out that of the main magnet, subsequently creating a smooth B₀ profile above the shim magnet where low-resolution NMR experiments are performed. Compared with many previously published designs, this straightforward design simplifies the construction of the apparatus and simultaneously generates a B₀ field parallel to the apparatus surface, allowing the use of a simple loop-type radiofrequency (RF) coil. Additionally, an apparatus prototype is constructed according to the proposed design. Weighing only 1.8 kg, the constructed apparatus has a compact structure and can be held in the palm of a hand. The apparatus generates a B₀ strength of about 0.0746 T. Within a B₀ field deviation of 3 mT, the region with a relatively homogeneous B₀ distribution extends to about 11 mm above the shim magnet. The proposed apparatus can detect a clear Hahn echo or Carr-Purcell-Meiboom-Gill (CPMG) echoes of a pencil eraser block or a bottle of oil placed on the apparatus in 5 s with signal averaging using an RF transmitter power of only 19 W; the detection range of the apparatus exceeds 6 mm. The strength of the residual static magnetic field gradient of the apparatus is roughly estimated at 0.58 T/m. Applying different CPMG echo spacings in this residual static gradient leads to various transverse relaxation time (T₂) contrasts for liquids with distinct viscosities such as water and oil. Two nondestructive inspection applications of the apparatus, including correlating the concentrations of magnetic nanoparticle solutions with their measured transverse relaxation rates (R₂) and monitoring the outgassing from an opened bottle of oxygen-supersaturated water by measuring its longitudinal relaxation rate (R₁), are also demonstrated.     

Delayed demagnetization jumps in (NdDy)(FeCo)B magnets in a steady-state magnetic field

Spontaneous demagnetization jumps are observed in sintered magnets (Nd_0.6Dy_0.4)₁₆(Fe_0.77Co_0.23)₇₈B₆ in a constant magnetic field after a sharp decrease in an external magnetic field from the value corresponding to the saturation to a value close to the coercive force. It is shown that the number of the magnetization jumps is proportional to their amplitudes. A low value of the autocorrelation coefficient between the jump amplitude and the time of its appearance (R < 0.1) demonstrate the stochasticity of the jumps. It is found that the spectral jump density is independent of the frequency, i.e., a white magnetic noise is observed. The distribution of the magnetic field gradient has been obtained near the sample surface that makes it possible to distinguish domains and the grain magnetization in the dependence on the direction of the texturing of the sintered magnet.

     

Optimizing magnetization orientation of permanent magnets for maximal gradient force

The force exercised on a permanent magnet (PM) in a nonuniform field (gradient force) is dependent on the magnetization orientation of the magnet. In this paper, it is shown theoretically that the gradient force is greatest when the magnetization through the magnet, or at least at its surface, is collinear with the external field. The formulae for calculating the force between an axis-symmetric optimal magnet and a coaxial axis-symmetric coil are presented. Using the finite element method (FEM), calculations of the magnetic field distribution of an optimal cylindrical magnet and some its approximations are performed. The forces between these magnets and a pancake coil are computed and compared. For a system consisting of a magnet with a height of 1 unit and a diameter of 2 units and magnetization invariant in field and an annular pancake coil with a diameter of 2.4 units, a thickness of 0.2 units, an inner diameter of 0.4 units and a distance from the magnet of 0.2 units, the force on the optimal magnet was 1.44 times greater than the force on an axially magnetized magnet of the same size and magnetization magnitude. The optimal magnetization may be approximated by magnetization inclined at a constant angle to the axis and by a combination of axially and radially magnetized sections. With magnetization at a constant angle to the axis in the axis plane, the force was greatest when the angle was about 45°, being 1.38-fold compared to the force on an axially magnetized magnet. When the magnet was composed of an axially magnetized cylindrical core and a radially magnetized outer ring, the force was greatest when the volume of the core was approximately equal to the volume of the ring, being 1.26-fold compared to the force on an axially magnetized magnet. The optimal magnet and its approximations also provided a reduced stray field. A short review of methods of the fabrication of permanent magnets (PMs) with a continuous variation of the magnetization orientation and with radial magnetization orientation is given.The results of this study can be used to design linear electromagnetic (micro)actuators.     

A unilateral NMR magnet for sub-structure analysis in the built environment: the Surface GARField

A new, portable NMR magnet with a tailored magnetic field profile and a complementary radio frequency sensor have been designed and constructed for the purpose of probing in situ the sub-surface porosity of cement based materials in the built environment. The magnet is a one sided device akin to a large NMR-MOUSE with the additional design specification of planes of constant field strength /B0/ parallel to the surface. There is a strong gradient G in the field strength perpendicular to these planes. As with earlier GARField magnets, the ratio G//:B0/ is a system constant although the method of achieving this condition is substantially different. The new magnet as constructed is able to detect signals 50mm (1H NMR at 3.2 MHz) away from the surface of the magnet and can profile the surface layers of large samples to a depth of 35-40 mm by moving the magnet, and hence the resonant plane of the polarising field, relative to the sample surface. The matching radio frequency excitation/detector coil has been designed to complement the static magnetic field such that the polarising B0 and sensing B1 fields are, in principal, everywhere orthogonal. Preliminary spatially resolved measurements are presented of cement based materials, including two-dimensional T1-T2 relaxation correlation spectra.     

An Efficacious Target-Field Approach to Design Shim Coils for Halbach Magnet of Mobile NMR Sensors

The main magnetic fields of mobile nuclear magnetic resonance (NMR) magnets differ from those of conventional NMR and magnetic resonance imaging (MRI) magnets. In the Halbach magnet, the main field B ₀ is perpendicular to the longitudinal axis, the symmetry of the current distribution with respect to the symmetry of the magnetic field differs from that in conventional target-field applications, and the current distribution on the coil surface cannot be expressed in terms of periodic basis functions. To obtain the winding pattern of the coil, an efficacious target-field approach. The surface of a coil is divided into small discrete elements, where each element is represented by a magnetic dipole. From the stream function of the elements, the resultant magnetic field is calculated. The optimization strategy follows an objective function defined by the power dissipation or efficiency of the coil. This leads to the optimum stream function on the coil surface, whose contour lines define the winding patterns of the coil. This paper shows winding patterns designed of shim coils for Halbach magnet and illustrates the craft of a shim coil using flexible printed circuit board. The performance of the coils is verified by simulating the fields they produce over the sensitive volume.     

On some consequences of an external magnetic field applied to HTS coils

A computational model which enables to evaluate the distribution of the critical currents, electric fields and the voltage in the winding of a solenoidal high temperature superconducting (HTS) magnets subjected to an external magnetic field parallel with the magnet axis, was developed. The model comes out from the well-known power law between the electric field and the transport current of the HTS tape short sample. It allows to predict the voltage–current V(I) characteristics of both the pancake coils and the complete magnet. The model was applied to the magnet system consisting of 22 pancake coils made of multifilamentary Bi(2223)/Ag tape at 20 K, which is subjected to an external uniform magnetic field parallel with the coil axis. A rather unexpected behavior of the magnet at different operating conditions (operating current and external magnetic field strength) is predicted, analyzed and reported together with a theoretical explanation. On one hand, the external uniform magnetic field parallel with the coil axis increases the resulting magnetic field strength, however, on the other hand it simultaneously decreases the angle between the resulting magnetic field and the tape surface. Thus, the effect of higher magnetic loading caused by the presence of an external magnetic field strength which is acting on individual turns located close to the coil’s flanges is compensated by more favorable orientation of the tape with respect to the resulting magnetic field. As a result, increase in the critical currents of these turns is expected. Further, the results indicate, that in case of the high field HTS insert coils the anisotropy in the I_c(B) characteristic does not play a substantial role. As a consequence, the technology of the production of the tapes for high field insert HTS coils should concentrate rather on the tapes having the current carrying capacity as high as possible, than on the attempt how to decrease the anisotropy in the I_c(B) by changing the architecture of the filaments in the tape.     

Evaluation of magnetic force distribution on a pair of superconducting bulk magnets

We study the construction of superconducting permanent magnets by RE123 bulk materials and the investigation of these industrial applications such as a magnetic separation. A bulk magnet can generate strong magnetic fields exceeding 2 T, which is the limit of ordinary iron-cored electromagnets, in a compact device with a low running cost. A magnetic field distribution of the bulk magnet is a cone shape, and it contributes to an increase of magnetic force which is proportional to the product of a magnetic field and its gradient. It is important to evaluate magnetic force when the application of the bulk magnet is discussed. In this paper, two Gd123 bulk materials of 65 mm in diameter were magnetized using a pair of superconducting bulk magnet system and three-axis components of magnetic flux density (B_x,⋅B_y, and B_z) in an open space between the magnetic poles were scanned with pitch of 2 mm in each direction. From these measured data, the axial and radial components of magnetic force factor, B_z⋅dB_z/dz and B_r⋅dB_r/dr, were calculated. At 10 mm gap, the B_z⋅dB_z/dz value reached 180.6 T²/m for a field of 2.33 T, which is comparable to B_z = 6.76 T for a common 10 T–100 mm∅ superconducting magnet.     

Effective-medium approach for surface-localized magnetic polaritons in magnetic (ferromagnetic and antiferromagnetic) superlattices

The general effective-medium dispersion relations are derived for surface-localized magnetic polaritons which propagate parallel to the surface between a superlattice and semi-infinite bulk material, as applied to ferromagnetic and antiferromagnetic superlattices, in the situation when a static magnetic field is applied in the plane of the layers and parallel to the magnetization. The dependence of the energy of the surface waves on the volume fraction of the ferromagnetic superlattice component and the influence of the external magnetic field on the spectrum of the surface magnetic polaritons for the antiferromagnetic superlattice are investigated. The spectrum of the surface-localized magnetic polaritons which appear at the junction of the magnetic (ferromagnetic and antiferromagnetic) superlattice with the magnetic material are more complex, in contrast to the cases of semi-infinite magnetic material or semi-infinite magnetic SL. It is essential that in all cases in the presence of the external magnetic field the spectrum of the magnetic polaritons are non-reciprocal. The properties of surface polaritons are discussed in detail for the system ferromagnetic superlattice (YIG/non magnet)/YAG and the antiferromagnetic superlattice (MnF₂/ZnF₂)/FeF₂.     

A design of novel type superconducting magnet for super—high field functional magnetic resonance imaging by using the harmonic analysis method of magnetic vector potentials

The approach of expanding the magnetic scalar potential in a series of Legendre polynomials is suitable for designing a conventional superconducting magnetic resonance imaging magnet of distributed solenoidal configuration. Whereas the approach of expanding the magnetic vector potential in associated Legendre harmonics is suitable for designing a single-solenoid magnet that has multiple tiers, in which each tier may have multiple layers with different winding lengths. A set of three equations to suppress some of the lowest higher-order harmonics is found. As an example, a 4T single-solenoid magnetic resonance imaging magnet with 4×6 layers of superconducting wires is designed. The degree of homogeneity in the 0.5m diameter sphere volume is better than 5.8 ppm. The same degree of homogeneity is retained after optimal integralization of turns in each correction layer. The ratio B_m/B₀ in the single-solenoid magnet is 30% lower than that in the conventional six-solenoid magnet. This tolerates higher rated superconducting current in the coil. The Lorentz force of the coil in the single-solenoid system is also much lower than in the six-solenoid system. This novel type of magnet possesses significant advantage over conventional magnets, especially when used as a super-high field functional magnetic resonance imaging magnet.     

Properties of superfine superconducting filaments embedded in normal matrix

The size-, surface- and proximity-effects are combined for calculating the critical temperature and some unusual electromagnetic properties of superfine superconducting NbTi filaments (i.e. with a diameterd _s < 0·1 μm) in the neighbourhood of normal metal (Cu). It is shown that the existence of the one-dimensional flux line lattice is responsible for the extremely large values of the critical current densities in low magnetic fields (B < 0·2B _c2,B _c2 — the upper critical magnetic field), for the maximum of the volume pinning force at low magnetic fields (B _m ≈ 0·1B _c2, comparing withB _m≈ 0·5B _c2 in usual macroscopic multifilamentary NbTi superconductors), as well as for the peculiar minimum of the magnetization after reversing the magnetic field direction. The possible role of the frozen-in flux lines in creating flux lines of opposite direction is sketched. It is proposed that for practical purposes the superconducting filaments should be coated with electrically insulating material (e.g. cupro-nickel or dielectric) to destroy the electro-magnetic coupling between the filaments and to ensure low ac losses in the composite.     

Finite size disc gradient coil set for open vertical field magnets

A new analytical approach is used in the design of disc-like gradient coils suitable for magnet geometries with main field direction perpendicular to the surface of the disc. An inverse procedure is used to optimize the coil's characteristics, subject to the restrictions imposed by the desired field behavior over a certain set of constraint points inside a predetermined imaging volume. Excellent agreement between the expected values of the gradient magnetic field and the numerical values generated by applying the Biot-Savart law to a discrete current pattern of the perspective disc coil was found. A Finite Element Analysis package was used to predict the fringe gradient field levels for a non-shielded axial disc coil and for a self-shielded transverse disc coil in the vicinity of the magnet poles. The numerical results indicate that for the self-shielded design the gradient fringe field is 1000 times smaller than the corresponding fringe field for the non-shielded disc case. Also no significant spatial dependence was noticed for the shielded coil's fringe field.     

Ultrasound velocimetry of ferrofluid spin-up flow measurements using a spherical coil assembly to impose a uniform rotating magnetic field

Ferrofluid spin-up flow is studied within a sphere subjected to a uniform rotating magnetic field from two surrounding spherical coils carrying sinusoidally varying currents at right angles and 90° phase difference. Ultrasound velocimetry measurements in a full sphere of ferrofluid shows no measureable flow. There is significant bulk flow in a partially filled sphere (1-14 mm/s) of ferrofluid or a finite height cylinder of ferrofluid with no cover (1-4 mm/s) placed in the spherical coil apparatus. The flow is due to free surface effects and the non-uniform magnetic field associated with the shape demagnetizing effects. Flow is also observed in the fully filled ferrofluid sphere (1-20 mm/s) when the field is made non-uniform by adding a permanent magnet or a DC or AC excited small solenoidal coil. This confirms that a non-uniform magnetic field or a non-uniform distribution of magnetization due to a non-uniform magnetic field are causes of spin-up flow in ferrofluids with no free surface, while tangential magnetic surface stress contributes to flow in the presence of a free surface.Recent work has fitted velocity flow measurements of ferrofluid filled finite height cylinders with no free surface, subjected to uniform rotating magnetic fields, neglecting the container shape effects which cause non-uniform demagnetizing fields, and resulting in much larger non-physical effective values of spin viscosity η′∼10⁻⁸−10⁻¹² N s than those obtained from theoretical spin diffusion analysis where η′≤10⁻¹⁸ N s. COMSOL Multiphysics finite element computer simulations of spherical geometry in a uniform rotating magnetic field using non-physically large experimental fit values of spin viscosity η′∼10⁻⁸−10⁻¹² N s with a zero spin-velocity boundary condition at the outer wall predicts measureable flow, while simulations setting spin viscosity to zero (η′=0) results in negligible flow, in agreement with the ultrasound velocimetry measurements. COMSOL simulations also confirm that a non-uniform rotating magnetic field or a uniform rotating magnetic field with a non-uniform distribution of magnetization due to an external magnet or a current carrying coil can drive a measureable flow in an infinitely long ferrofluid cylinder with zero spin viscosity (η′=0).     

Two-dimensional imaging with a single-sided NMR probe

A new low field unilateral NMR sensor equipped with a two-dimensional gradient coil system was built. A new NMR-MOUSE concept using a simple bar magnet instead of the classical U-shaped geometry was used to produce magnetic field profiles comparatively homogeneous in extended lateral planes defining a suitable field of view for 2D spatial localization. Slice selection along the depth direction is obtained by means of the highly constant static magnetic field gradient produced by this magnet geometry. Implementing a two-dimensional phase-encoding imaging method 2D cross sections of objects were obtained with high spatial resolution. By retuning the probe it was possible to change the depth of the selected slice obtaining a 3D imaging method. The details of the construction of the new device are presented together with imaging tests to show the quality of space encoding.     

The permanent magnet systems generating strong stray fields with large localization region

Three systems of permanent magnets, which produce strong magnetic stray fields (SFs) with H>B_r=4πM_r were studied in this work. Remarkable feature of the developed systems is localization of the strong fields in large region with linear dimension Δr comparable to characteristic magnet dimension a. The first system composed of uniformly magnetized magnets generates sufficiently homogeneous strong SFs, which amounts up to 1.5 of magnets induction B_r. The second system with nonuniform magnetization is represented by cylindrical and hemispheric magnets their magnetization vector directed at every point along the radius. Such distribution of magnetization is assumed to be the consequence of magnet radial crystal texture resulting in a high uniaxial anisotropy field H_K. It is shown that maximal SFs can exist on the flat surface of cylindrical magnet at the distance r from its axis and their limiting value equals to 4πM_r ln(2a/r). Here, the localization region of the fields is comparable to diameter of cylindrical magnet Δr≈2R. As for the hemisphere its SFs are less than corresponding SFs for the cylinder. The third so-called quasi-nonuniform system consists of uniformly magnetized cylindrical sectors their magnetization vector is directed along the sector bisectrix. The strong SFs and their localization region are calculated in details for this case. The passage to radial magnetized cylinder is considered.     

Magnetic properties of field-annealed FeCo thin films

Fe₅₀Co₅₀ thin films with thickness of 30 and 4 nm have been produced by rf sputtering on glass substrates, and their surface has been observed with atomic force microscopy (AFM) and magnetic force microscopy (MFM); MFM images reveal a non-null component of the magnetization perpendicular to the film plane. Selected samples have been annealed in vacuum at temperatures of 300 and 350 °C for times between 20 and 120 min, under a static magnetic field of 100 Oe. DC hysteresis loops have been measured with an alternating gradient force magnetometer (AGFM) along the direction of the field applied during annealing and orthogonally to it. Samples with a thickness of 4 nm display lower coercive fields with respect to the 30 nm thick ones. Longer annealing times affect the development of a harder magnetic phase more oriented off the film plane. The field applied during annealing induces a moderate magnetic anisotropy only on 30 nm thick films.     

Modeling the static fringe field of superconducting magnets

The resonance frequency-space and the frequency gradient-space relations are evaluated analytically for the static fringe magnetic field of superconducting magnets used in the NMR diffusion measurements. The model takes into account the actual design of the high-homogeneity magnet coil system that consists of the main coil and the cryoshim coils and enables a precise calibration of the on-axis magnetic field gradient and the resonance frequency inside and outside of the superconducting coil.     

Design considerations and coil comparisons for 7 T brain imaging

The development of 300 MHz radio-frequency (RF) head coils analogous to those used at field strengths of 1.5 and 3 T is complicated by increased dissipative losses in conductive tissue, effects arising from the short RF wavelength in biological tissue (about 13 cm at 300 MHz), and the constraints imposed by the use of head gradient sets desirable for mitigating increased static field susceptibility effects. In this study, five RF head coils were constructed and tested on a 7 T scanner including 2 TEM designs, 2 birdcage designs and a local receive-only array. Signal-to-noise ratio, coil reception profiles and interactions between the coil and dielectric head were examined. Particular attention was placed on the coil’s reception in the neck and shoulders, where the head gradient is unable to spatially encode the image. With the use of conductive shields and distributed capacitance, all of the coil designs could be made to image effectively at high field, but each design was found to have subtle differences in field distribution, interaction with the dielectric boundary conditions of the head and fringe fields in the neck and shoulders. In particular, the birdcage and array coils were found to have reducedB ₁ reception field profiles in the neck and shoulders which helped reduce signal detection outside the linear region of the head gradient coil. Although the TEM coils exhibited higher signal detection in the neck and shoulders, all the coils picked up enough signal from these regions to produce artifacts in the brain. These artifacts could be mitigated through use of a conductive shield or by small local dephasing shims sewn into the shoulders of a jacket worn by the subject. Although homogeneous in low-dielectric-constant phantoms, the volume coil’sB ₁ profile was strongly peaked in the center of the head, rendering them spatially complementary to that observed in the surface coil array. The image profile of the surface coil was found to be less dramatically changed from patterns observed at lower field strength. Its dielectric brightening pattern was found to depend on the orientation of the coil with respect to the head.     

Multiple Parallel Round Leg Design for Quadrature Birdcage Coil in Ultrahigh-Field MRI

Copper foil has been widely employed in conventional radio frequency (RF) birdcage coils for magnetic resonance imaging (MRI). However, for ultrahigh-field (UHF) MRI, current density distribution on the copper foil is concentrated on the surface and the edge due to proximity effect. This increases the effective resistance and distorts the circumferential sinusoidal current distribution on the birdcage coils, resulting in low signal-to-noise ratio (SNR) and inhomogeneous distribution of RF magnetic (B₁) field. In this context, multiple parallel round wires were proposed as legs of a birdcage coil to optimize current density distribution and to improve the SNR and the B₁ field homogeneity. The design was compared with three conventional birdcage coils with different width flat strip surface legs for a 9.4 T (T) MRI system, e.g., narrow-leg birdcage coil (NL), medium-leg birdcage coil (ML), broad-leg birdcage coil (BL) and the multiple parallel round wire-leg birdcage coil (WL). Studies were carried out in in vitro saline phantom as well as in vivo mouse brain. WL showed higher coil quality factor Q and more homogeneous B₁ field distribution compared to the other three conventional birdcage coils. Furthermore, WL showed 12, 10 and 13% SNR increase, respectively, compared to NL, ML and BL. It was proposed that conductor’s shape optimization could be an effective approach to improve RF coil performance for UHF MRI.     

Possible observation of the coexistence of superconductivity and long-range magnetic order in NdRh4B4

The ternary rare earth compound NdRh₄B₄ has been studied by means of critical field, low temperature heat capacity, and static magnetic susceptibility measurements. Features in the upper critical field and heat capacity data at 1.31 K and 0.89 K suggest the occurrence of long-range magnetic order in the superconducting state. The temperature dependence of the static magnetic susceptibility follows a Curie-Weiss law with an effective magnetic moment μ_eff = 3.58 ± 0.05 μ_B and a Curie-Weiss temperature θ_p = ?6.2 ± 1.0 K between 20 K and room temperature. However,, magnetization vs. applied magnetic field isotherms suggest the development of a ferromagnetic component in the Nd³⁺ magnetization at low temperatures.     

B1 transmit phase gradient coil for single-axis TRASE RF encoding

Purpose

TRASE (Transmit Array Spatial Encoding) MRI uses RF transmit phase gradients instead of B₀ field gradients for k-space traversal and high-resolution MR image formation. Transmit coil performance is a key determinant of TRASE image quality. The purpose of this work is to design an optimized RF transmit phase gradient array for spatial encoding in a transverse direction (x- or y- axis) for a 0.2 T vertical B₀ field MRI system, using a single transmitter channel. This requires the generation of two transmit B₁ RF fields with uniform amplitude and positive and negative linear phase gradients respectively over the imaging volume.

Materials and Methods

A two-element array consisting of a double Maxwell-type coil and a Helmholtz-type coil was designed using 3D field simulations. The phase gradient polarity is set by the relative phase of the RF signals driving the simultaneously energized elements.

Results

Field mapping and 1D TRASE imaging experiments confirmed that the constructed coil produced the fields and operated as designed. A substantially larger imaging volume relative to that obtainable from a non-optimized Maxwell-Helmholtz design was achieved.

Conclusion

The Maxwell (sine)–Helmholtz (cosine) approach has proven successful for a horizontal phase gradient coil. A similar approach may be useful for other phase-gradient coil designs.