Highly responsive ac scalar atomic magnetometer with long relaxation time

We investigate the electrical response (0.1–1000 Hz) of reactive iron barriers by making measurements on zero valent iron (Fe0)-sand columns under the following conditions: (1) variable Fe0 surface area (0.1–100% by volume Fe0) under constant electrolyte chemistry; (2) variable electrolyte activity (0.01–1 mol/liter), valence (mono trivalent), and pH under constant Fe0-sand composition; and (3) forced precipitation of iron hydroxides and iron carbonates on the Fe0 surface. We model the measurements in terms of conduction magnitude, polarization magnitude, and polarization relaxation time. Our key findings are: Polarization magnitude exhibits a linear relation to the surface area of Fe0, whereas conduction magnitude is only weakly dependent on the Fe0 concentration below 30% by volume Fe0.Polarization magnitude shows a power law relation to electrolyte activity, with exponents decreasing from 0.9 for monovalent solutions to 0.7 for trivalent solutions.The relaxation time parameter depends on activity and valence in a manner that is partly consistent with the variation in double layer thickness predicted from theory.pH exerts minor control on the electrical parameters.Polarization magnitude and relaxation time both increase as a result of precipitation induced on the surface of Fe0. Our results show that induced polarization parameters systematically change in response to changes in the Fe0-electrolyte interfacial chemistry.

We report measurements of the real and imaginary part of the dielectric constant of liquid water in the far-infrared region from 0.1 to 2.0 THz in a temperature range from 271.1 to 366.7 K. The data have been obtained with the use of THz time domain reflection spectroscopy, utilizing ultrashort electromagnetic pulses generated from a photoconductive antenna driven by femtosecond laser pulses. A Debye model with an additional relaxation time is used to fit the frequency dependence of the complex dielectric constants. We obtain a fast (fs) and a Debye (ps) relaxation time for the macroscopic polarization. The corresponding time correlation functions have been calculated with molecular dynamics simulations and are compared with experimental relaxation times. The temperature dependence of the Debye relaxation time is analyzed using three models: Transition state theory, a Debye–Stoke–Einstein relation between the viscosity and the Debye time, and a model stating that its temperature dependence can be extrapolated from a singularity of liquid water at 228 K. We find an excellent agreement between experiment and the two latter models. The simulations, however, present results with too large statistical error for establishing a relation for the temperature dependence.

Atomic magnetometry is one of the most sensitive ways to measure magnetic fields. We present a method for converting a naturally scalar atomic magnetometer into a vector magnetometer by exploiting the polarization dependence of hyperfine transitions in rubidium atoms. First, we fully determine the polarization ellipse of an applied microwave field using a self-calibrating method, i.e., a method in which the light-atom interaction provides everything required to know the field in an orthogonal laboratory frame. We then measure the direction of an applied static field using the polarization ellipse as a three-dimensional reference defined by Maxwell's equations. Although demonstrated with trapped atoms, this technique could be applied to atomic vapors, or a variety of atomlike systems.

Vector field measurement is demonstrated with an all-optical scalar atomic magnetometer using intrinsic parameters related to its scalar operation. The Bell-Bloom type atomic magnetometer measures the Larmor precession of cesium atoms through on-resonant absorption of a probe beam. While the AC component of the probe signal is used for the field magnitude measurement, the probe DC signal contains information about the polar angle, defined as the angle between the magnetic field and the probe beam. Additional polar angle information is obtained from the light-shift-induced magnetic field caused by the frequency modulation of the probe beam. With a measurement time of 100 ms, better than 0.02° sensitivity has been achieved using a commercial miniaturized sensor at the optimal sensor orientation. The angle measurement accuracy is checked against an optical encoder over the entire polar angle range of 0°–180°. Better than 1° error is recorded over most set polar angles. Azimuthal angle measurement is also exhibited with two orthogonally oriented sensors.

Dielectric relaxation theory describes the complex permittivity of a material in an alternating field; in particular, Debye theory relates the time it takes for an applied field to achieve the maximum polarization and the electrical properties of the material. Although, Debye’s equations were proposed for electrical polarization, in this study, we investigate the correlation between the magnetic longitudinal relaxation time T1 and the complex electrical permittivity of tissue-mimicking phantoms using a 7 T magnetic resonance scanner. We created phantoms that mimicked several human tissues with specific electrical properties. The electrical properties of the phantoms were measured using bench-test equipment. T1 values were acquired from phantoms using MRI. The measured values were fitted with functions based on dielectric estimations, using relaxation times of electrical polarization, and the mixture theory for dielectrics. The results show that, T1 and the real permittivity are correlated; therefore, the correlation can be approximated with a rational function in the case of water-based phantoms. The correlation between index loss and T1 was determined using a fitting function based on the Debye equation and mixture theory equation, in which the fraction of the materials was taken into account. This phantom study and analysis provide an insight into the application relaxation times used for estimating dielectric properties. Currently, the measurement of electrical properties based on dielectric relaxation theory is based on an antenna, sometimes invasive, that irradiates an electric field into a small sample; thus, it is not possible to create a map of electrical properties for a complex structure such as the human body. This study could be further used to compute the electrical properties maps of tissues by scanning images and measuring T1 maps.

When using magnetic resonance tomography (MRT) for imaging 2-D or 3-D water-bearing structures in a subsurface, the transmitting frequency must be the same as the Larmor frequency. Due to the inhomogeneity and noise interference in a geomagnetic field, it is difficult to determine the precise Larmor frequency using a magnetometer, resulting in unknown frequency offsets and inaccurate estimations of water content and relaxation time ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T_{2}^{*}$ </tex-math></inline-formula> ). To solve the 2-D MRT imaging problem in the case of an unknown frequency offset, a frequency cycling method is proposed in this article. This method takes the estimated Larmor frequency as the center, uses two frequencies with the same offset for transmitting, then combines the acquired MRT signals to obtain frequency-cycled data, and finally uses the off-resonance kernel function for inversion. Based on MRT forward modeling and QT inversion, we conduct synthetic data experiments on a complex model with three water-bearing structures and test the 2-D imaging results of the frequency-cycled data. The results show that the water content and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T_{2}^{*}$ </tex-math></inline-formula> distribution obtained by the inversion of the frequency-cycled data can accurately reflect the water-bearing structure, which is better than the results of the assumed on-resonance case. In addition, the phase correction method presented in this article significantly improves the accuracy of 2-D MRT estimated aquifer properties under low resistivity conditions. Finally, the validity and accuracy of the frequency cycling method are verified by comparing the inversion results of the data with known drilling data collected in field measurements.

It is necessary to consider the TEM-mode, the higher TE and TM-mode and resonance phenomena in GIS to describe the propagation and detection characteristics for partial discharge measured with the UHF-method. Measurements on the non-reflection coaxial wave-guide simulating GIS were carried out with changing installation and shape of UHF sensor and wave-guide length. This paper describes the output characteristics of UHF sensor above cut-off frequencies, when reflection and resonance phenomena are taken into account. In the frequency region above the cut-off frequencies of the TE11 mode, the output characteristics of UHF sensor shows resonant by reason of the electromagnetic reflection of TE mode at the both ends of wave-guide. At the resonant frequency, the output characteristics of UHF sensor are different by wave-guide length, shape of sensor and sensor installation, distance from end of tank, angle at circumference. The resonant frequencies are function of tank-length and cut-off frequency of tank, and expressed with equation of cylindrical cavity resonator.

The growing demand for low-frequency, broadband vibration and noise suppression technologies in next-generation mechanical equipment has become increasingly urgent. Effective negative mass locally resonant structures represent one of the most paradigmatic classes of acoustic metamaterials. Their unique elastic wave bandgaps enable efficient suppression of low-frequency vibrations, while inherent nonlinear effects provide significant potential for the design and tunability of these bandgaps. To achieve ultra-low-frequency and ultra-broadband vibration attenuation, this study employs Duffing oscillators exhibiting negative-stiffness characteristics as structural elements, establishing a bistable nonlinear acoustic-metamaterial mechanical model. Subsequently, based on the effective negative mass local resonance theory, the perturbation solution for the dispersion curves is derived using the perturbation method. Finally, the effects of mass ratio, stiffness ratio, and nonlinear term on the starting and cutoff frequencies of the bandgap are analyzed, and key geometric parameters influencing the design of ultra-low vibration reduction bandgaps are comprehensively investigated. Subsequently, the influence of external excitation amplitude and the nonlinear term on bandgap formation is analyzed using numerical computation methods. Finally, effective positive mass, negative mass, and zero-mass phenomena within distinct frequency ranges of the bandgap and passband are examined to validate the theoretically derived results. The findings demonstrate that, compared to a positive-stiffness system, the bandgap of the bistable nonlinear acoustic metamaterial incorporating negative-stiffness Duffing oscillators shifts to higher frequencies and widens by a factor of 2. The external excitation amplitude F changes the bandgap starting frequency and cutoff frequency. As F increases, the starting frequency rises while the cutoff frequency decreases, resulting in a narrowing of the bandgap width. Within the frequency range bounded by the bandgap starting frequency and cutoff frequency, the region between the resonance frequency and cutoff frequency corresponds to an effective negative mass state, whereas the region between the bandgap starting frequency and resonance frequency exhibits an effective positive mass state. Critically, the bandgap encompasses both effective positive mass and negative mass regions, wherein vibration propagation is suppressed. Concurrently, a zero-mass state emerges within this structure, with its frequency precisely coinciding with the bandgap cutoff frequency. This study provides a theoretical foundation and practical guidelines for designing nonlinear acoustic metamaterials targeting ultra-low-frequency and ultra-broadband vibration and noise mitigation.

Nutation consists in monitoring the motion of nuclear magnetization under the application of a radiofrequency (rf) field. With an appropriate amplitude of the rf field, the nutation frequency depends on the NMR relaxation times. This property offers the possibility of differentiating species having the same Larmor frequency but differing by their relaxation times. This may occur for the composite proton NMR signal of water in complex systems. Separate nutation signals are thus observed with the possibility of measuring their longitudinal relaxation times by simply applying a saturation hard pulse, followed by an evolution interval, prior to the nutation sequence. This novel experiment has been used for studying the two sites existing for water in two kaolinite samples (one hydrated after stabilization of several months and the other nonhydrated). It turns out that water in these two sites differs essentially by its transverse relaxation time. Moreover, recovery is surprisingly biexponential for these two signals. A proper analysis of results obtained by this saturation-recovery nutation experiment provides not only the specific longitudinal relaxation rates of water in these two sites but also information about the averaging which occurs at long evolution times. This is discussed with regard of the structure and organization of the clay network. In particular, from relaxation rates at short evolution times, it is shown that this network is mainly constituted of ordered platelets, with a relatively weak proportion of randomly distributed platelets.

The nuclear magnetic double-resonance spectrum of a single nucleus of spin ½ is theoretically described by perturbation theory and by the Bloch equations. The perturbation theory correctly predicts all experimental features except line shapes and saturation effects. The description in terms of the Bloch equations provides a clear physical picture of the spin-½ problem. The analysis shows that the macroscopic moment is aligned with the effective field when the strong rf field is not in the immediate vicinity of the Larmor frequency. When the strong rf field is at the Larmor frequency, however, the macroscopic moment is perpendiclar to the effective field. This produces considerable changes in line shapes and intensities as the strong rf field approaches the Larmor frequency. The spectrum in this region is sensitive to the relaxation times, and provides a steady-state method for measurement of relatively short relaxation times. The theory is confirmed by frequency-sweep double-resonance experiments on chloroform saturated with oxygen.

To measure longitudinal (T(1)) and multi-echo transverse (T(2)) relaxation times of healthy breast tissue at 3 Tesla (T). High-resolution relaxation time measurements were made in six healthy female subjects. Inversion recovery images were acquired at 10 inversion times between 100 ms and 4000 ms, and multiple spin echo images were acquired at 16 echo times between 10 ms and 160 ms. Longitudinal relaxation times T(1) were measured as 423 ± 12 ms for adipose tissue and 1680 ± 180 ms for fibroglandular tissue. Multi-echo transverse relaxation times T(2) were measured as 154 ± 9 ms for adipose tissue and 71 ± 6 ms for fibroglandular tissue. Histograms of the voxel-wise relaxation times and quantitative relaxation time maps are also presented. T(1) and multi-echo T(2) relaxation times in normal human breast tissue are reported. These values are useful for pulse sequence design and optimization for 3T breast MRI. Compared with the literature, T(1) values are significantly longer at 3T, suggesting that longer repetition time and inversion time values should be used for similar image contrast.

Relationship between susceptibility induced field inhomogeneities, restricted diffusion, and relaxation in sedimentary rocks

Differential thermal analysis and the temperature dependence of broad‐line 1H NMR absorptions and of 1H spin‐lattice relaxation times in both laboratory and rotating frames were observed for (CH3)2NH2NO3, (CH3)ND2NO3, and (CH3)3NHNO3. A solid‐solid phase transition was located at 297 K for (CH3)2NH2NO3. while two phase transitions at 359 and 407 K were found for (CH3)3NHNO3. The 1H spin‐lattice relaxation times in the laboratory frame at different Larmor frequencies and those in the rotating frame at the rf field of 8 G observed for the above salts were analyzed by referring to the 1H NMR second moments determined. The motional parameters of the cations in each solid phase of the salts were evaluated by a fitting calculation to the relaxation times observed. In the highest‐temperature solid phase of (CH3)3NHNO3, the cation was found to perform self‐diffusion as well as overall rotation with the relatively low activation energy of 29 kJ mol−1. The motions of the cations in each newly found solid phase are characterized.

Improved determination of FID signal parameters in low-field NMR

The paper considers the preparation of potassium sodium niobate ceramics doped with titanium in an amount of 5 mol. %. The structure and dielectric properties were investigated in the temperature range 30–650 °C. It is shown that acceptor doping leads to a decrease in the grain size. Violation of stoichiometry in the anionic sublattice contributes to a decrease in the relaxation time of thermal ionic polarization compared to the case of nonstoichiometry in the cationic sublattice.