Stable Magnetic Field Research Articles

Unveiling complex magnetic field configurations in red giant stars

The recent measurement of magnetic field strength inside the radiative interior of red giant stars has opened the way toward full 3D characterization of the geometry of stable large-scale magnetic fields. However, current measurements, which are limited to dipolar (ℓ = 1) mixed modes, do not properly constrain the topology of magnetic fields due to degeneracies on the observed magnetic field signature on such ℓ = 1 mode frequencies. Efforts focused toward unambiguous detections of magnetic field configurations are now key to better understand angular momentum transport in stars. We investigated the detectability of complex magnetic field topologies (such as the ones observed at the surface of stars with a radiative envelope with spectropolarimetry) inside the radiative interior of red giants. We focused on a field composed of a combination of a dipole and a quadrupole (quadrudipole) and on an offset field. We explored the potential of probing such magnetic field topologies from a combined measurement of magnetic signatures on ℓ = 1 and quadrupolar (ℓ = 2) mixed mode oscillation frequencies. We first derived the asymptotic theoretical formalism for computing the asymmetric signature in the frequency pattern for ℓ = 2 modes due to a quadrudipole magnetic field. To access asymmetry parameters for more complex magnetic field topologies, we numerically performed a grid search over the parameter space to map the degeneracy of the signatures of given topologies. We demonstrate the crucial role played by ℓ = 2 mixed modes in accessing internal magnetic fields with a quadrupolar component. The degeneracy of the quadrudipole compared to pure dipolar fields is lifted when considering magnetic asymmetries in both ℓ = 1 and ℓ = 2 mode frequencies. In addition to the analytical derivation for the quadrudipole, we present the prospect for complex magnetic field inversions using magnetic sensitivity kernels from standard perturbation analysis for forward modeling. Using this method, we explored the detectability of offset magnetic fields from ℓ = 1 and ℓ = 2 frequencies and demonstrate that offset fields may be mistaken for weak and centered magnetic fields, resulting in underestimating the magnetic field strength in stellar cores. We emphasize the need to characterize ℓ = 2 mixed-mode frequencies, (along with the currently characterized ℓ = 1 mixed modes), to unveil the higher-order components of the geometry of buried magnetic fields and to better constrain angular momentum transport inside stars.

Effect of Nb-doping and AC annealing on the microstructure, magnetism and magnetoimpedance of metallic fibers

This paper systematically studies the changes in the microstructure and magnetic properties of CoFeSiBNb series metallic fibers before and after AC annealing. The influence of current intensity on the magneto-impedance (MI) effect of the fibers is analyzed and the mechanism of current annealing to improve the MI characteristics is further revealed. The results show that the surface of the CoFeSiBNb metallic fibers before and after AC annealing is smooth and continuous, the tensile strength of CoFeSiBNb3 fiber is 5.15 GPa and it is the most stable and fracture-reliable. After AC annealing, metallic fibers' general magnetic properties and MI ratio increase at first with current intensity and then decrease at higher intensities. Specifically, the 140 mA AC annealed metallic fiber shows excellent magnetic properties with Ms, μm, Hc, and Mr values reaching 94.38 emu/g, 0.4326, 34.36 Oe, and 13.94 emu/g, respectively. With an excitation frequency of f = 1 MHz, the fiber's [ΔZ/Zmax]max, ξmax, Hk, and Hp reached 216.81%, 31.04 %/Oe, 1 Oe, and 2 Oe, respectively. During the current annealing process, Joule heat eliminates residual stresses in the fibers while forming atomically ordered micro-domains, which improves the degree of its organizational order. Meanwhile, a stable toroidal magnetic field is generated, which promotes the distribution of the magnetic domain structure of the fibers, thereby improving the MI effect.

Near-zero magnetic field disturbance suppression method based on adaptive filtering and quasi-proportional resonance control

The cardiac magnetic field used for magnetocardiographic (MCG) imaging must be detected in a stable near-zero magnetic field environment. In the hospital environment, there are mainly two kinds of magnetic field disturbances that affect the signal-to-noise ratio of cardiac magnetic field detection. One is the magnetic field disturbance with high power spectral density at a specific frequency, and the other is the random magnetic field disturbance with low frequency. To suppress magnetic field disturbances, this paper proposed a near-zero magnetic field disturbance suppression method that combined a PI controller with adaptive filtering and quasi-proportional resonance control (PI-APF-QPR). The magnetic field disturbance with high amplitude and specific frequency was extracted by the adaptive filter (APF) and suppressed by the quasi-proportional resonance (QPR) controller. Additionally, the low-frequency random disturbance was suppressed by the PI controller. The experimental results showed that compared with the PI controller, the peak-to-peak value of the magnetic field by the PI-APF-QPR controller was reduced by 39.1%, and the suppression ratio of the magnetic field noise by the PI-APF-QPR controller was improved by 29.5%, which verified the effectiveness of the proposed magnetic field disturbance suppression method.

Separation and Evaluation of the Gradient Relaxation in the Atomic Comagnetometer

AbstractIn the atomic comagnetometer, nuclear spin relaxation is a core parameter that affects the magnetic field suppression ability and stability, and is influenced by various gradient fields. It is necessary to measure and separate the effects of different gradients on nuclear spin, which helps to effectively suppress them separately. This article proposes a periodic optical pumping method for separating and measuring polarization gradient relaxation and magnetic field gradient relaxation, considering the effects of pump light and applied magnetic field. The comprehensive influence model for pump light on transverse nuclear spin relaxation is established, and the measurement steps and parameter selection criteria for the proposed method considering signal decay characteristics are provided. Furthermore, the proportion of various gradient relaxations is quantified. This work provides an evaluation method for gradient relaxation suppression, supporting the improvement of the measurement sensitivity and stability of the atomic comagnetometer.

Effect of power supply parameters on discharge characteristics and sterilization efficiency of magnetically driven rotating gliding arc

Plasma sterilization is a new generation of high-tech sterilization method that is fast, safe, and pollution free. It is widely used in medical, food, and environmental protection fields. Home air sterilization is an emerging field of plasma application, which puts higher requirements on the miniaturization, operational stability, and operating cost of plasma device. In this study, a novel magnetically driven rotating gliding arc (MDRGA) discharge device was used to sterilize Lactobacillus fermentation. Compared with the traditional gas-driven gliding arc, this device has a simple structure and a more stable gliding arc. Simulation using COMSOL Multiphysics showed that adding permanent magnets can form a stable magnetic field, which is conducive to the formation of gliding arcs. Experiments on the discharge performance, ozone concentration, and sterilization effect were conducted using different power supply parameters. The results revealed that the MDRGA process can be divided into three stages: starting, gliding, and extinguishing. Appropriate voltage was the key factor for stable arc gliding, and both high and low voltages were not conducive to stable arc gliding and ozone production. In this experimental setup, the sterilization effect was the best at 6.6 kV. A high modulation duty ratio was beneficial for achieving stable arc gliding. However, when the duty ratio exceeded a certain value, the improvement in the sterilization effect was slow. Therefore, considering the sterilization effect and energy factors comprehensively, we chose 80% as the optimal modulation duty ratio for this experimental device.

Evaluation Method of Magnetic Field Stability for Robotic Arc Welding Based on Sample Entropy and Probability Distribution

In this study, we analyzed the arc magnetic field to assess the stability of the arc welding process, particularly in robotic welding where direct measurement of welding current is challenging, such as under water. The characteristics of the magnetic field were evaluated based on low-frequency fluctuations and the symmetry of the signals. We used double-wire pulsed MIG welding for our experiments, employing Q235 steel with an 8.0 mm thickness as the material. Key parameters included an average voltage of 19.8 V, current of 120 A, and a wire feeding speed of 3.3 m/min. Our spectral analysis revealed significant correlations between welding stability and factors such as the direct current (DC) component and the peak power spectral density (PSD) frequency. To quantify this relationship, we introduced a novel approach using sample entropy and mix sample entropy (MSE) as new evaluation metrics. This method achieved a notable accuracy of 88%, demonstrating its effectiveness in assessing the stability of the robotic welding process.

Development of a pulsed magnetic field power supply for small size Betatron

In this paper, we present a new structure of capacitor-inductor discharge circuit and develop a pulsed magnetic field power supply for small size Betatron, addressing the urgent need for adjustable pulsed radiation frequencies. The proposed power supply employs insulated gate bipolar transistors (IGBTs) to control the discharge of the energy storage capacitor to the excitation winding, thus generating a pulsed current, which produces a pulsed magnetic field and accelerates the electrons. By adjusting the operating frequency of the IGBTs, the frequency of the pulsed current, and consequently the accelerator pulsed radiation frequency, can be regulated. The proposed design employs dual sustained paths, which are formed by the energy storage capacitor and the excitation winding, as well as a loss-compensation capacitor with the excitation winding. By adjusting the loss-compensation time, the problem of the pulsed current amplitude attenuation due to losses can be overcome, ensuring the stability of the pulsed magnetic field. Experimental results show that the power supply produces a pulsed current up to 220 A, which accelerates the electrons to 6.2 MeV, allowing the accelerator pulsed radiation frequency to be adjusted within a 333-Hz range. The proposed power supply makes small size Betatron suitable for a wide range of applications and provides technical knowledge for other types accelerators.

Chemically peculiar stars on the pre-main sequence

Context. The chemically peculiar (CP) stars of the upper main sequence are defined by spectral peculiarities that indicate unusual elemental abundance patterns in the presence of diffusion in the calm, stellar atmospheres. Some of them have a stable local magnetic field of up to several kiloGauss. The pre-main-sequence evolution of these objects is still a mystery and contains many open questions. Aims. We identify CP stars on the pre-main sequence to determine possible mechanisms that lead to the occurrence of chemical peculiarities in the (very) early stages of stellar evolution. Methods. We identified likely pre-main-sequence stars by fitting the spectral energy distributions. The subsequent analysis using stellar spectra and photometric time series helped us to distinguish between CP and non-CP stars. Additionally, we compared our results to the literature to provide the best possible quality assessment. Results. Out of 45 candidates, about 70% seem to be true CP stars or CP candidates. Furthermore, 9 sources appear to be CP stars on the pre-main sequence, and all are magnetic. We finally report a possible CP2 star that is also a pre-main-sequence star and was not previously in the literature. Conclusions. The evolution of the peculiarities seems to be related to the (strong) magnetic fields in these CP2 stars.

Detectability of Axisymmetric Magnetic Fields from the Core to the Surface of Oscillating Post-main-sequence Stars

Magnetic fields in the stellar interiors are key candidates to explain observed core rotation rates inside solar-like stars along their evolution. Recently, asteroseismic estimates of radial magnetic field amplitudes near the hydrogen-burning shell (H-shell) inside about 24 red giants (RGs) have been obtained by measuring frequency splittings from their power spectra. Using general Lorentz-stress (magnetic) kernels, we investigated the potential for detectability of near-surface magnetism in a 1.3 M ⊙ star of supersolar metallicity as it evolves from a mid subgiant to a late subgiant into an RG. Based on these sensitivity kernels, we decompose an RG into three zones—deep core, H-shell, and near-surface. The subgiants instead required decomposition into an inner core, an outer core, and a near-surface layer. Additionally, we find that for a low-frequency g-dominated dipolar mode in the presence of a typical stable magnetic field, ∼25% of the frequency shift comes from the H-shell and the remaining from deeper layers. The ratio of the subsurface tangential field to the radial field in the H-burning shell decides if subsurface fields may be potentially detectable. For p-dominated dipole modes close to νmax , this ratio is around two orders of magnitude smaller in subgiant phases than the corresponding RG. Further, with the availability of magnetic kernels, we propose lower limits of field strengths in crucial layers in our stellar model during its evolutionary phases. The theoretical prescription outlined here provides the first formal way to devise inverse problems for stellar magnetism and can be seamlessly employed for slow rotators.

Superstrength permanent magnets with iron-based superconductors by data- and researcher-driven process design

Iron-based high-temperature (high-Tc) superconductors have good potential to serve as materials in next-generation superstrength quasipermanent magnets owing to their distinctive topological and superconducting properties. However, their unconventional high-Tc superconductivity paradoxically associates with anisotropic pairing and short coherence lengths, causing challenges by inhibiting supercurrent transport at grain boundaries in polycrystalline materials. In this study, we employ machine learning to manipulate intricate polycrystalline microstructures through a process design that integrates researcher- and data-driven approaches via tailored software. Our approach results in a bulk Ba0.6K0.4Fe2As2 permanent magnet with a magnetic field that is 2.7 times stronger than that previously reported. Additionally, we demonstrate magnetic field stability exceeding 0.1 ppm/h for a practical 1.5 T permanent magnet, which is a vital aspect of medical magnetic resonance imaging. Nanostructural analysis reveals contrasting outcomes from data- and researcher-driven processes, showing that high-density defects and bipolarized grain boundary spacing distributions are primary contributors to the magnet’s exceptional strength and stability.

Stability of the coronal magnetic field around large confined and eruptive solar flares

Context. The coronal magnetic field, which overlies the current-carrying field of solar active regions, straps the magnetic configuration below. The characteristics of this overlying field are crucial in determining if a flare will be eruptive and accompanied by a coronal mass ejection (CME), or if it will remain confined without a CME. Aims. In order to improve our understanding of the pre-requisites of eruptive solar flares, we study and compare different measures that characterize the eruptive potential of solar active regions – the critical height of the torus instability (TI) as a local measure and the helicity ratio as a global measure – with the structural properties of the underlying magnetic field, namely the altitude of the center of the current-carrying magnetic structure. Methods. Using time series of 3D optimization-based nonlinear force-free magnetic field models of ten different active regions (ARs) around the time of large solar flares, we determined the altitudes of the current-weighted centers of the non-potential model structures. Based on the potential magnetic field, we inspected the decay index, n, in multiple vertical planes oriented alongside or perpendicular to the flare-relevant polarity inversion line, and estimated the critical height (hcrit) of TI using different thresholds of n. The critical heights were interpreted with respect to the altitudes of the current-weighted centers of the associated non-potential structures, as well as the eruptive character of the associated flares, and the eruptive potential of the host AR, as characterized by the helicity ratio. Results. Our most important findings are that (i) hcrit is more segregated in terms of the flare type than the helicity ratio, and (ii) coronal field configurations with a higher eruptive potential (in terms of the helicity ratio) also appear to be more prone to TI. Furthermore, we find no pronounced differences in the altitudes of the non-potential structures prior to confined and eruptive flares. An aspect that requires further investigation is that, generally, the modeled non-potential structures do not really reside in a torus-instable regime, so the applicability of the chosen nonlinear force-free modeling approach when targeting the structural properties of the coronal magnetic field is unclear.

A novel joint-less second-generation high-temperature superconducting toroidal coil: Promise for fabricating compact toroidal magnetic fields

This paper presents a novel joint-less toroidal magnet made of second-generation high-temperature superconducting (2G-HTS) tapes. This approach effectively resolves the closed-loop issue for 2G-HTS magnets and has the potential to provide higher and more stable magnetic fields. Compared with traditional 2G-HTS toroidal magnets, while the current loops of the joint-less magnets have no resistance, a decrease in magnetic field still occurs, especially in coils with insulation. Therefore, this work focuses on the decrease of the magnetic field of this novel magnet using experimental and microanalytical methods. For the first time, it was verified that, by winding two coil groups, insulated and no-insulated, parallel charging does not cause interference between them. Furthermore, the magnetic field area was expanded by finite element analysis, and simulations showed that the magnetic field converged with increasing number of coils. Besides, we found that the decrease of the magnetic field was related to the damage of the tape during slitting and winding, where insulated coils were more susceptible to damage during winding. The damage usually occurred at the starting point of the tape slitting, because the copper layer was separated due to adhesion during the winding of insulated coils, which further caused the superconducting layer to detach, resulting in a decrease in the critical current. From our perspective, benefiting from the high critical field of the 2G-HTS tapes, this novel toroidal coil structure has significant implications for the construction of compact toroidal magnets.

Dynamic Magnetic Field Analysis and Delivery Strategy Optimization for Scanning Magnet in Proton Therapy System

In pencil beam scanning proton therapy, the regulation and stabilization of the scanning magnetic field between two spots should be completed as quickly as possible in order to reduce treatment time. Because of the eddy current effect, the dynamic magnetic field lags behind the excitation current. It is significant to analyze the dynamic field and reduce the field stability time to minimize the delivery time and improve the therapy efficiency. In this paper, dynamic magnetic field simulation is carried out with a full lamination model of the scanning magnet in the Huazhong University of Science and Technology Proton Therapy Facility. In addition, a single lamination model instead of a full lamination model is explored to reduce time cost and memory for lamination of no more than 1-mm thickness. The eddy current diffusion trend and the influence of lamination on the eddy current are investigated. Moreover, the effect of lamination thickness (ranging from 5 to 0.1 mm) and current ramp rate (ranging from 20 to 100 A/ms) on the magnetic field stability time is studied. In addition, the characteristic of magnetic stability time for various spot steps is analyzed. Considering two spot patterns with discrete or clustered spots, an optimized delivery strategy with various scanning dead times according to the step is presented. When the lamination is 1 mm, the scanning time can be reduced by 39.2% for a clustered pattern and 38.4% for a discrete pattern using a genetic algorithm based on the different scanning dead-time strategy instead of the fixed dead-time strategy. With a thinner 0.1-mm lamination, the scanning time can be reduced by 49.8% for the clustered pattern and 43.3% for the discrete pattern, compared to that of the 1-mm lamination.

Optimization stability and performance of the TPS storage ring dipole magnet power supply

This article focuses on the current status of the dipole magnet power supply (DMPS) and improvement in the Taiwan Photon Source (TPS) storage ring. The DMPS provides a stable and precise magnetic field for the storage ring operation. Appropriate wiring methods are employed to minimize magnetic field interference across the entire TPS area to meet the demands of high-energy output and overcome the challenges of operating at high currents. The target energy is set at 850 V and 750 A, utilizing a single-pole switching voltage regulator as a high-precision constant current source output structure. The system incorporates a closed control loop that uses the Direct Current Current Transducer (DCCT) to provide current signal feedback to the system. FPGA (Field-Programmable Gate Array) calculates PID (Proportional-Integral-Derivative) compensation values, generating a 2.1 kHz pulse width modulation (PWM) signal to regulate the output current. At the same time, insulated gate bipolar transistor (IGBT) modules are switching components. However, even after several years of practical operation, the stability and performance of the DMPS in the storage ring still require improvements. To enhance long-term output current stability and address peripheral issues, the current TPS utilizes the Beam Orbit Feedback (FOFB) system to suppress and fine-tune the magnetic field and compensate for the impact of temperature drift on the DMPS's output current. This improvement ensures a more stable circulation of the photon beam within the storage ring. By optimizing the temperature control circuit of the main control card, the long-term output current stability has been successfully enhanced to within ± 10 ppm. Simultaneously, the FOFB system reduces uncertainties in adjusting the X-axis beam position, improving beam stability and quality. Furthermore, relevant protective measures have been implemented to ensure robust system operation. Ultimately, these improvement measures have successfully met TPS's stringent requirements for the DMPS, enabling the synchrotron accelerator light source to operate at higher performance levels and fostering advanced scientific research. The results of these upgrades underscore the success of the power supply enhancements, making significant contributions to the overall improvement of the Taiwan Photon Source facility.

The astrophysical parameters of chemically peculiar stars from automatic methods

Context. The chemically peculiar (CP) stars of the upper main sequence are excellent astrophysical laboratories for investigating the diffusion, mass loss, rotational mixing, and pulsation in the presence and absence of a stable local magnetic field. For this, we need a homogeneous set of parameters, such as effective temperature (Teff) and surface gravity (log g), to locate the stars in the Hertzsprung-Russell diagram so that we can then estimate the mass, radius, and age. Aims. In recent years, the results of several automatic pipelines have been published; these use various techniques and data sets, including Teff and log g values for millions of stars. Because CP stars are known to have flux anomalies, these astrophysical parameters must be tested for their reliability and usefulness. If the outcome is positive, these can be used to analyse the new and faint CP stars published recently. Methods. I compared published Teff and log g values of a set of CP stars, which are mostly based on high-resolution spectroscopy, with values from four automatic pipeline approaches. In doing so, I searched for possible correlations and offsets. Results. I present a detailed statistical analysis of a comparison between the ‘standard’ and published Teff and log g values. The accuracy depends on the presence of a magnetic field and the spectral type of the CP subgroups. However, I obtain standard deviations of between 2% and 20%. Conclusions. Considering the statistical errors, the astrophysical parameters from the literature can be used for CP stars, although caution is advised for magnetic CP stars.

Instability analysis for MHD boundary layer flow of nanofluid over a rotating disk with anisotropic and isotropic roughness

The study focuses on the instability of local linear convective flow in an incompressible boundary layer caused by a rough rotating disk in a steady MHD flow of viscous nanofluid. Miklavčič and Wang's (Miklavčič and Wang, 2004) [9] MW roughness model are utilized in the presence of MHD of Cu-water nanofluid with enforcement of axial flows. This study will investigate the instability characteristics with the MHD boundary layer flow of nanofluid over a rotating disk and incorporate the effects of axial flow with anisotropic and isotropic surface roughness. The resulting ordinary differential equations (ODEs) are obtained by using von Kàrmàn (Kármán, 1921) [3] similarity transformation on partial differential equations (PDEs). Subsequently, numerical solutions are obtained using the shooting method, specifically the Runge-Kutta technique. Steady-flow profiles for MHD and volume fractions of nanoparticles are analyzed by the partial-slip conditions with surface roughness. Convective instability for stationary modes and neutral stability curves are also obtained and investigated by the formulation of linear stability equations with the MHD of nanofluid. Linear convective growth rates are utilized to analyze the stability of magnetic fields and nanoparticles and to confirm the outcomes of this analysis. Stationary disturbances are also considered in the energy analysis. The investigation indicates the correlation between instability modes Type I and Type II, in the presence of MHD, nanoparticles, and the growth rates of the critical Reynolds number. An integral energy equation enhances comprehension of the fundamental physical mechanisms. The factors contributing to convective instability in the system are clarified using this approach.

Compact remanence-free permanent magnet-based variable magnetic field source.

We demonstrate a simple and compact variable magnetic field source based on the permanent cube magnet array approximating a Halbach cylinder. The large air gap area accommodates standard cryostat tails while providing a high uniformity and magnetic field stability of up to 0.5T over regions of up to about a centimeter. It eliminates magnetic remanence effects and produces reproducible fields without the need for feedback. Thanks to the low cost and exceptional energy efficiency, it provides an accessible solution for modest magnetic field requirements in a wide range of research applications.

Intermittent Lobe Reconnection Under Prolonged Northward Interplanetary Magnetic Field Condition: Insights From Cusp Spot Event Observations

AbstractPrevious studies have suggested that lobe reconnection under stable northward interplanetary magnetic field (IMF) conditions should be continuous. However, to what extent it can be considered as continuous is unknown. Auroral cusp spots have been considered a signature of lobe reconnection. Here, we show that during a cusp spot event continuously observed by the Defense Meteorological Satellite Program for approximately 4 hr under stable IMF conditions, the ground radars recorded multiple intermittent equatorward‐moving radar forms (EMRFs) near local noon and multiple intermittent poleward‐moving radar forms (PMRFs) at post‐noon, each lasting ∼20–30 min. These intermittent EMRFs and PMRFs are suggested to correspond to intermittent lobe reconnections occurring at the cusp's poleward boundary near local noon and the duskside boundary at post‐noon, respectively. These findings challenge the previously held notion of continuous lobe reconnection under stable IMF conditions.

Achieving ultra-low and -uniform residual magnetic fields in a very large magnetically shielded room for fundamental physics experiments

High-precision searches for an electric dipole moment of the neutron (nEDM) require stable and uniform magnetic field environments. We present the recent achievements of degaussing and equilibrating the magnetically shielded room (MSR) for the n2EDM experiment at the Paul Scherrer Institute. We present the final degaussing configuration that will be used for n2EDM after numerous studies. The optimized procedure results in a residual magnetic field that has been reduced by a factor of two. The ultra-low field is achieved with the full magnetic-field-coil system, and a large vacuum vessel installed, both in the MSR. In the inner volume of ∼1.4m3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim 1.4~\\hbox {m}^3$$\\end{document}, the field is now more uniform and below 300 pT. In addition, the procedure is faster and dissipates less heat into the magnetic environment, which in turn, reduces its thermal relaxation time from 12h\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$12~\ ext {h}$$\\end{document} down to 1.5h\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1.5~\ ext {h}$$\\end{document}.

Magnetic field stabilization system designed for the cold-atom coherent population-trapping clock

Magnetic field stabilization system designed for the cold-atom coherent population-trapping clock