Phase-alternated compositeπ/2 pulses for solid state quadrupole echo NMR spectroscopy

Phase-alternated compositeπ/2 pulses have been constructed for spinI=1 to overcome quadrupole interaction effects in solid state nuclear magnetic resonance (NMR) spectroscopy. Magnus expansion approach is used to design these sequences in a manner similar to the NMR coherent averaging theory. It is inferred that the symmetric phase-alternated compositeπ/2 pulses reported here are quite successful in producing quadrupole echo free from phase distortions. This effectiveness of the present composite pulses is due to the fact that most of them are of shorter durations as compared to the ones reported in literature. In this theoretical procedure, irreducible spherical tensor operator formalism is employed to simplify the complexity involved in the evaluation of Magnus expansion terms. It has been argued in this paper that compositeπ/2 pulse sequences for this purpose can also be derived from the broadband inversionπ pulses which are designed to compensate electric field gradient (efg) inhomogeneity in spinI=1 nuclear quadrupole resonance (NQR) spectroscopy.     

Recent Fourier and Laplace perspectives for multidimensional NMR in porous media

Multidimensional NMR techniques used in the measurement of molecular displacements, whether by diffusion or advection, and in the measurement of nuclear spin relaxation times are categorised. Fourier-Fourier, Fourier-Laplace and Laplace-Laplace methods are identified, and recent developments discussed in terms of the separation, correlation and exchange perspective of multidimensional NMR spectroscopy.     

A novel improved method for analysis of 2D diffusion-relaxation data--2D PARAFAC-Laplace decomposition

This paper demonstrates how the multi-linear PARAFAC model can with advantage be used to decompose 2D diffusion-relaxation correlation NMR spectra prior to 2D-Laplace inversion to the T(2)-D domain. The decomposition is advantageous for better interpretation of the complex correlation maps as well as for the quantification of extracted T(2)-D components. To demonstrate the new method seventeen mixtures of wheat flour, starch, gluten, oil and water were prepared and measured with a 300 MHz nuclear magnetic resonance (NMR) spectrometer using a pulsed gradient stimulated echo (PGSTE) pulse sequence followed by a Carr-Purcell-Meiboom-Gill (CPMG) pulse echo train. By varying the gradient strength, 2D diffusion-relaxation data were recorded for each sample. From these double exponentially decaying relaxation data the PARAFAC algorithm extracted two unique diffusion-relaxation components, explaining 99.8% of the variation in the data set. These two components were subsequently transformed to the T(2)-D domain using 2D-inverse Laplace transformation and quantitatively assigned to the oil and water components of the samples. The oil component was one distinct distribution with peak intensity at D=3 x 10(-12) m(2) s(-1) and T(2)=180 ms. The water component consisted of two broad populations of water molecules with diffusion coefficients and relaxation times centered around correlation pairs: D=10(-9) m(2) s(-1), T(2)=10 ms and D=3 x 10(-13) m(2) s(-1), T(2)=13 ms. Small spurious peaks observed in the inverse Laplace transformation of original complex data were effectively filtered by the PARAFAC decomposition and thus considered artefacts from the complex Laplace transformation. The oil-to-water ratio determined by PARAFAC followed by 2D-Laplace inversion was perfectly correlated with known oil-to-water ratio of the samples. The new method of using PARAFAC prior to the 2D-Laplace inversion proved to have superior potential in analysis of diffusion-relaxation spectra, as it improves not only the interpretation, but also the quantification.     

Clifford Algebras and the Dirac-Bohm Quantum Hamilton-Jacobi Equation

In this paper we show how the dynamics of the Schr?dinger, Pauli and Dirac particles can be described in a hierarchy of Clifford algebras, C_1,3, C_3,0{\mathcal{C}}_{1,3}, {\mathcal{C}}_{3,0}, and C_0,1{\mathcal{C}}_{0,1}. Information normally carried by the wave function is encoded in elements of a minimal left ideal, so that all the physical information appears within the algebra itself. The state of the quantum process can be completely characterised by algebraic invariants of the first and second kind. The latter enables us to show that the Bohm energy and momentum emerge from the energy-momentum tensor of standard quantum field theory. Our approach provides a new mathematical setting for quantum mechanics that enables us to obtain a complete relativistic version of the Bohm model for the Dirac particle, deriving expressions for the Bohm energy-momentum, the quantum potential and the relativistic time evolution of its spin for the first time.     

A practical and flexible implementation of 3D MRI in the Earth's magnetic field

The Earth's magnetic field, though weak, is appealing for NMR applications because it is highly homogeneous, globally available and free. However, the practicality of Earth's field NMR (EFNMR) has long been limited by the need to perform experiments in outdoor locations where the local field homogeneity is not disrupted by ferrous or magnetic objects and where ultra-low frequency (ULF) noise sources are at a minimum. Herein we present a flexible and practical implementation of MRI in the Earth's magnetic field that demonstrates that EFNMR is not as difficult as it was previously thought to be. In this implementation, pre-polarization and ULF noise shielding, achieved using a crude electromagnet, are used to significantly improve signal-to-noise ratio (SNR) even in relatively noisy environments. A three axis gradient coil set, in addition to providing imaging gradients, is used to provide first-order shims such that sub-hertz linewidths can routinely be achieved, even in locations of significant local field inhomogeneity such as indoor scientific laboratories. Temporal fluctuations in the magnitude of the Earth's magnetic field are measured and a regime found within which these variations in Larmor frequency produce no observable artefacts in reconstructed images.     

Quantitative analysis of Earth’s field NMR spectra of strongly-coupled heteronuclear systems

In the Earth’s magnetic field, it is possible to observe spin systems consisting of unlike spins that exhibit strongly coupled second-order NMR spectra. Such spectra result when the J-coupling between two unlike spins is of the same order of magnitude as the difference in their Larmor precession frequencies. Although the analysis of second-order spectra involving only spin-½ nuclei has been discussed since the early days of NMR spectroscopy, NMR spectra involving spin-½ nuclei and quadrupolar (I > ½) nuclei have rarely been treated. Two examples are presented here, the tetrahydroborate anion, , and the ammonium cation, . For the tetrahydroborate anion, ¹J(¹¹B,¹H) = 80.9 Hz, and in an Earth’s field of 53.3 μT, ν(¹H) = 2269 Hz and ν(¹¹B) = 728 Hz. The ¹H NMR spectra exhibit features that both first- and second-order perturbation theory are unable to reproduce. On the other hand, second-order perturbation theory adequately describes ¹H NMR spectra of the ammonium anion, , where ¹J(¹⁴N,¹H) = 52.75 Hz when ν(¹H) = 2269 Hz and ν(¹⁴N) = 164 Hz. Contrary to an early report, we find that the ¹H NMR spectra are independent of the sign of ¹J(¹⁴N,¹H). Exact analysis of two-spin systems consisting of quadrupolar nuclei and spin-½ nuclei are also discussed.     

Multiple echoes, multiple quantum coherence, and the dipolar field: demonstrating the significance of higher order terms in the equilibrium density matrix.

It is well known that dipolar field effects lead to multiple spin echoes in a simple two-RF pulse experiment (the MSE experiment). We show here that coherence transfer echoes (which identify the existence of multiple quantum coherences in liquid NMR) and multiple spin echoes have a common origin. Using density matrix theory we have calculated the phase and timing of multiple spin echoes from all quadrature phase combinations of RF pulses. We show for the MSE experiment that there is a one-to-one correspondence between the time domain echo order and the multiple quantum coherence order. The experimental confirmation of these phase predictions shows that multiple spin echoes provide independent evidence for the breakdown of the high temperature approximation as proposed by Warren et al. (Science 262, 2005 (1993)).     

用于 EAST 上低杂波平行波数测量的磁探针设计与测试

针对EAST上2.45GHz低杂波,完成了低杂波平行波数测量磁探针的设计、仿真与测试。利用有限元仿真软件COMSOL Multiphysics 5.2对磁探针尺寸进行仿真优化,确定了单匝环、矩形缝以及陶瓷片厚度等影响磁探针耦合性能的关键尺寸。测试结果表明,该磁探针对2.45GHz低杂波有良好的耦合性能和鉴别波极化的能力,与仿真结果一致。研究结果为EAST装置上低杂波平行波数测量诊断系统的建立提供重要的参考依据,从而为进一步开展高密度低杂波电流驱动实验研究提供必要的实验数据。