Magnetic Field Calibration Research Articles

Flux Calibration of Coronal Magnetic Field

Romashets and Vandas (2024) derived a method for the determination of Euler potentials at a spherical surface and applied it to the geomagnetic field. Here, we apply it to find Euler potentials at the source surface. A regular mesh defined by Euler potentials divides the source surface to surface elements with the same magnetic flux. By tracing magnetic-field lines away from the source surface, Euler potentials can be extended into the heliosphere.

Magnetic field regression using artificial neural networks for cold atom experiments

Accurately measuring magnetic fields is essential for magnetic-field sensitive experiments in areas like atomic, molecular, and optical physics, condensed matter experiments, and other areas. However, since many experiments are often conducted in an isolated environment that is inaccessible to experimentalists, it can be challenging to accurately determine the magnetic field at the target location. Here, we propose an efficient method for detecting magnetic fields with the assistance of an artificial neural network (NN). Instead of measuring the magnetic field directly at the desired location, we detect fields at several surrounding positions, and a trained NN can accurately predict the magnetic field at the target location. After training, we achieve a below 0.3% relative prediction error of magnetic field magnitude at the center of the vacuum chamber, and successfully apply this method to our erbium quantum gas apparatus for accurate calibration of magnetic field and long-term monitoring of environmental stray magnetic field. The demonstrated approach significantly simplifies the process of determining magnetic fields in isolated environments and can be applied to various research fields across a wide range of magnetic field magnitudes.

A calibration method of ground-airborne frequency domain electromagnetic receving system based on magnetic source excitation

In the ground-airborne frequency domain electromagnetic detection, the receving system converts the magnetic field signal into an electrical signal representing the magnetic field signal. In order to accurately obtain the relationship between the magnetic field signal and the electrical signal, it is necessary to avoid the influence of environment and other factors on the system accuracy through on-site calibration. This requires high calibration accuracy, simple operation, portable equipment and strong adaptability to the environment. However, the existing calibration methods put forward higher requirements for instruments and environment. For example, the calibration of uniform magnetic field generated by Helmholtz coil needs to shield external magnetic field interference. In this paper, an overall calibration method of measurement system based on magnetic source excitation is proposed to meet the requirements of electromagnetic field accurate measurement in ground-airborne frequency domain. Firstly, based on the electromagnetic measurement method in ground-airborne frequency domain, the overall calibration method and principle of the detection system are introduced. Then, based on the computable standard magnetic field generated by the magnetic source transmitting coil, determine the measured voltage obtained by the receiving system, get the calibration coefficient of the receiving system. At last,the source of standard uncertainty related to calibration is analyzed, and the uncertainty is evaluated. In addition, the method is verified by comparing the calibration results with those obtained by Braunbeck coil calibration.

A method for estimating magnetic field of TEM objective lens

We propose a method for calibration of magnetic field in the objective lens of transmission electron microscope. The calibration process is based on classical Fresnel imaging of Permalloy disks and measuring the displacement of the magnetic vortex core when the sample is tilted at various excitations of the objective lens. We adopted the Carl Zeiss LIBRA 200 MC transmission electron microscope for Lorentz electron microscopy using this method. The objective lens magnetic field evaluation is tested on the Co/Pt multilayered films with known magnetic properties.

Regional quantification of cardiac metabolism with hyperpolarized [1-13C]-pyruvate CMR evaluated in an oral glucose challenge

BackgroundThe heart has metabolic flexibility, which is influenced by fed/fasting states, and pathologies such as myocardial ischemia and hypertrophic cardiomyopathy (HCM). Hyperpolarized (HP) 13C-pyruvate MRI is a promising new tool for non-invasive quantification of myocardial glycolytic and Krebs cycle flux. However, human studies of HP 13C-MRI have yet to demonstrate regional quantification of metabolism, which is important in regional ischemia and HCM patients with asymmetric septal/apical hypertrophy. MethodsWe developed and applied methods for whole-heart imaging of 13C-pyruvate, 13C-lactate and 13C-bicarbonate, following intravenous administration of [1-13C]-pyruvate. The image acquisition used an autonomous scanning method including bolus tracking, real-time magnetic field calibrations and metabolite-specific imaging. For quantification of metabolism, we evaluated 13C metabolite images, ratio metrics, and pharmacokinetic modeling to provide measurements of myocardial lactate dehydrogenase (LDH) and pyruvate dehydrogenase (PDH) mediated metabolic conversion in 5 healthy volunteers (fasting & 30 min following oral glucose load). ResultsWe demonstrate whole heart coverage for dynamic measurement of pyruvate-to-lactate conversion via LDH and pyruvate-to-bicarbonate conversion via PDH at a resolution of 6 × 6 × 21 mm3 (13C-pyruvate) and 12 × 12 × 21 mm3 (13C-lactate, 13C-bicarbonate). 13C-pyruvate and 13C-lactate were detected simultaneously in the RV blood pool, immediately after intravenous injection, reflecting LDH activity in blood. In healthy volunteers, myocardial 13C-pyruvate-SNR, 13C-lactate-SNR, 13C-bicarbonate-SNR, 13C-lactate/pyruvate ratio, 13C-pyruvate-to-lactate conversion rate, kPL, and 13C-pyruvate-to-bicarbonate conversion rate, kPB, all had statistically significant increases following oral glucose challenge. kPB, reflecting PDH activity and pyruvate entering the Krebs Cycle, had the highest correlation with blood glucose levels and was statistically significant. ConclusionsWe demonstrate first-in-human regional quantifications of cardiac metabolism by HP 13C-pyruvate MRI that aims to reflect LDH and PDH activity.

An AC magnetic compass based on magnetoelectric effect integrated with a calibration algorithm

Magnetoelectric (ME) composites are found to be sensitive to both the intensity and the orientation of external magnetic field, therefore, they have been developed as compasses for in-plane AC magnetic field detection. However, the angular sensitivity of ME compasses is still low compared to other compasses, due to their insensitive resonant mode and poor coupling structure. Here, we propose a ME compass working at L-T mode by using a Metglas/PZT composite that integrated with a calibration algorithm. Detection of the intensity and direction of in-plane AC magnetic field is demonstrated synchronously with intensity and angle sensitivities of 0.001 Oe and ± 0.1°, respectively. In addition, when the calibration algorithms are applied, the angular sensitivity is significantly enhanced to ± 0.02°, one order of magnitude higher than that of other reported ME compasses, demonstrating a great potential for applications in magnetic positioning, magnetic field calibration, and other magnetic detection technologies. A magnetoelectric compass made of Metglas/PZT composite is proposed, with intensity and angle sensitivities of 0.001 Oe and ± 0.1°, respectively. Integrated with a calibration algorithm, the angular sensitivity is significantly enhanced to ± 0.02°. • The properties are optimized by theoretical models and finite element analysis, giving a well guidance on similar devices. • A calibration algorithm is proposed, which is able to inexpensively and quickly increase the angular sensitivity. • The device shows intensity and angular sensitivities of 0.001 Oe and ± 0.1°, the latter is improved to ± 0.02° by calibration.

Deep learning for spin-orbit torque characterizations with a projected vector field magnet

Spin-orbit torque characterizations on magnetic heterostructures with perpendicular anisotropy are demonstrated on a projected vector field magnet via hysteresis loop shift measurement and harmonic Hall measurement with planar Hall correction. Accurate magnetic field calibration of the vector magnet is realized with the help of deep learning models, which are able to capture the nonlinear behavior between the generated magnetic field and the currents applied to the magnet. The trained models can successfully predict the applied current combinations under the circumstances of magnetic field scans, angle scans, and hysteresis loop shift measurements. The validity of the models is further verified, complemented by the comparison of the spin-orbit torque characterization results obtained from the deep-learning-trained vector magnet system with those obtained from a conventional setup comprised of two separated electromagnets. The damping-like spin-orbit torque (DL-SOT) efficiencies (|$\xi_{DL}$|) extracted from the vector magnet and the traditional measurement configuration are consistent, where |$\xi_{DL}$| $\approx$ 0.22 for amorphous W and |$\xi_{DL}$| $\approx$ 0.02 for $\alpha$-W. Our work provides an advanced method to meticulously control a vector magnet and to conveniently perform various spin-orbit torque characterizations.

Scandium dimetallofullerene with a single-electron metal-metal bond as a spectroscopic ruler for EPR measurements.

Measurements of electron paramagnetic resonance (EPR) close to the saturation region of iron-core electromagnets (ca. 1 Tesla) require precise magnetic field calibration due to nonlinear effects. Endohedral fullerenes Sc2@C80(CH2Ph) have unique spectral features due to the large hyperfine interaction (509 MHz) of the delocalized electron with two scandium nuclei (I = 7/2), resulting in a maximum spectral width of 0.25 Tesla. The spectrum consists of 64 well resolved lines divided into 15 groups, depending on the projection of the total spin of the scandium nuclei. Each group has a reference line with the largest possible total nuclear spin, located in the right edge of the group. These reference lines are shown to be equidistant in the low-field and high-field regions of the spectrum, and can therefore serve as a benchmark for magnetic field calibration. The calibration procedure is explained by theoretical calculations and verified on endofullerene spectra in Q-band EPR. To compare the spectral properties, measurements in the X- and W-bands were also performed. Absolute values of magnetic field strength were taken from standard Hall sensors of the spectrometer (X- and Q-bands) or on the measurements of the applied current (W-band); additional control of these values is carried out using a Gaussmeter at the sample location. The results show the high accuracy of the correction procedure for linear and nonlinear magnetic field offsets.

Design of the Stable Homogeneous Magnetic Field Calibration Device Generated by the Circular Coils

This research relates to manufacturing stable homogeneous magnetic field strength generating equipment. It refers to the stable homogeneous magnetic field device’s design method in the theoretical method, finite element method, and experimental method, which is beneficial for generating the high homogeneous magnetic field strength. The circular coils produce the uniform magnetic field strength for a given number of winding turns and distance between the pair of coils. The number of turns of each coil and gauge of the wire for the winding was adjusted by the theoretical calculations. The coil’s current carrying capacity determines the high magnetic field strength. The uniformity of the magnetic field is based on the size and current density of the coils. This paper emphasizes the theoretical formula to calculate a couple of values and then apply a finite element method for the verification. The finite element method values are compared with the theoretical values for proofreading. The different current values are applied, showing the increase in the magnetic field strength from low to high current values. The coils are made using the same theory and finite element method parameters. The experimental values are similar to the simulation values, with a maximum error percentage of 3.08. The magnetic field homogeneity distribution at the middle of the two coils is less than 1% of error. The magnetic flux density in the center of the two coils is measured using a High-precision Gauss meter.

Infrared diagnostics of the solar magnetic field with Mg I 12 μm lines: forward-model results

Context. The Mg I 12.32 and 12.22 μm lines are a pair of emission lines that present a great advantage for accurate solar magnetic field measurement. They potentially contribute to the diagnosis of solar atmospheric parameters through their high magnetic sensitivity. Aims. The goal of this study is to understand the radiation transfer process of these lines in detail and explore the ability of magnetic field diagnosis in the infrared. Methods. We calculated the Stokes profiles and response functions of the two Mg I 12 μm lines based on one-dimensional solar atmospheric models using the Rybicki-Hummer (RH) radiative transfer code. The integration of these profiles with respect to the wavelength was used to generate calibration curves related to the longitudinal and transverse fields. The traditional single-wavelength calibration curve based on the weak-field approximation was also tested to determine if it is suitable for the infrared. Results. The 12.32 μm line is more suitable for a magnetic field diagnosis because its relative emission intensity and polarization signal are stronger than that of the 12.22 μm line. The result from the response functions illustrates that the derived magnetic field and velocity with 12.32 μm line mainly originate from the height of 450 km, while that for the temperature is about 490 km. The calibration curves obtained by the wavelength-integrated method show a nonlinear distribution. For the Mg I 12.32 μm line, the longitudinal (transverse) field can be effectively inferred from Stokes V/I (Q/I and U/I) in the linear range below ∼600 G (∼3000 G) in quiet regions and below ∼400 G (∼1200 G) in penumbrae. Within the given linear range, the method is a supplement to the magnetic field calibration when the Zeeman components are incompletely split.

A nonlinear solar magnetic field calibration method for the filter-based magnetograph by the residual network

Context. The method of solar magnetic field calibration for the filter-based magnetograph is normally the linear calibration method under weak-field approximation that cannot generate the strong magnetic field region well due to the magnetic saturation effect. Aims. We try to provide a new method to carry out the nonlinear magnetic calibration with the help of neural networks to obtain more accurate magnetic fields. Methods. We employed the data from Hinode/SP to construct a training, validation and test dataset. The narrow-band Stokes I, Q, U, and V maps at one wavelength point were selected from all the 112 wavelength points observed by SP so as to simulate the single-wavelength observations of the filter-based magnetograph. We used the residual network to model the nonlinear relationship between the Stokes maps and the vector magnetic fields. Results. After an extensive performance analysis, it is found that the trained models could infer the longitudinal magnetic flux density, the transverse magnetic flux density, and the azimuth angle from the narrow-band Stokes maps with a precision comparable to the inversion results using 112 wavelength points. Moreover, the maps that were produced are much cleaner than the inversion results. The method can effectively overcome the magnetic saturation effect and infer the strong magnetic region much better than the linear calibration method. The residual errors of test samples to standard data are mostly about 50 G for both the longitudinal and transverse magnetic flux density. The values are about 100 G with our previous method of multilayer perceptron, indicating that the new method is more accurate in magnetic calibration.

Magnetic field sensor based on evanescent wave coupling effect of photonic crystal slab microcavity

In this study, a novel magnetic field sensor (MFS) based on 2D photonic crystal slab (2D PCS) microcavity is proposed. Magnetic fluid film (MFF) covers the surface of PCS and is coupled to high-Q microcavity by evanescent field. The slight disturbance of the refractive index of MFF can cause a larger response of the microcavity optical local field. The magnetic field calibration is realized by measuring the output power of W1 waveguide. The finite difference time domain (FDTD) method was used to analyze and optimize the sensing characteristics of MFS. The simulation results show that the PCS magnetic sensor has good linearity and sensitivity. When the MFF with a thickness of L = 0.4 μm completely covers the surface of PCS, the normalized sensitivity of W1 type waveguide-single microcavity coupling sensor structure can reach 2.52/T. Compared with the traditional photonic crystal magnetic sensor, the PCS magnetic sensor structure designed in this paper can adopt the existing MEMS processing technology and is easy to fabricate.

Fermi surface studies of the low-temperature structure of sodium

Sodium is the most abundant alkali-metal element and has one of the simplest electronic structures of any metal. At ambient conditions, sodium forms a body-centered-cubic lattice. However, during cooling, it undergoes a partial martensitic phase transition to a complex mixture of rhombohedral polytypes commencing from 36 K. Although the Fermi surface (FS) of bcc sodium has been extensively studied, not much attention has been given to the FS of the martensite structure. Here we report results for the Fermi surface and quantum oscillation (QO) frequencies of several energetically favorable crystal structures of Na at low temperature from first-principles calculations. Interestingly we find that despite drastic differences in the crystal structures of the candidate low-temperature phases of sodium, for all these phases the strongest quantum oscillation peak is centered at 28 kT. Our theoretical results are accompanied by experimental data of QO on a multigrain sodium sample at $T=0.3$ K and ${B}_{\mathrm{max}}=18$ T exhibiting a sharp peak at 28 kT, independent of the sample orientation. The persistence of this peak even in the presence of the structural transitions has an implication for using the quantum oscillations of polycrystalline sodium for high magnetic field calibration.

Research on vehicle attitude and heading reference system based on multi-sensor information fusion

To improve the accuracy of attitude and heading reference systems for moving vehicles, an effective orientation estimation method is proposed. The method uses an odometer, a low-cost magnetic, angular rate, and gravity sensor. This study addresses the problems of non-orthogonal error, carrier magnetic field interference and calibration to obtain accurate, long-term, stable magnetic field strength. A neural network fusion 12-parameter ellipse fitting method is proposed to eliminate the soft magnetic field and hard magnetic field interference. The interference to the accelerometer from linear acceleration is eliminated by using an odometer and a gyroscope, and the high-frequency noise from the accelerometer is eliminated by using a low-pass filter. An improved method to evaluate vehicle attitude is proposed and utilized to compensate for filtered accelerometer measurement when the vehicle is moving at a uniform, accelerate and steering state. The proposed method uses an effective adaptive Kalman filter based on the error state model to reduce dynamic perturbations. Filter gain is adaptively tuned under different moving modes by adjusting the noise matrix. The effectiveness of the algorithm is verified by experiments and simulations in multiple operating conditions.

Status of the Project 8 Phase II

The Project 8 collaboration aims to measure the absolute neutrino mass scale using cyclotron radiation emission spectroscopy on the beta decay of tritium. The second phase of the project will measure a continuous spectrum of molecular tritium beta decays and extract the tritium endpoint value with an eV or sub-eV scale precision. Monoenergetic electrons emitted by gaseous 83mKr atoms are used to determine the relationship between cyclotron frequency and electron energy. This study allows us to optimize both the event reconstruction algorithm and the hardware configuration, in preparation for measuring the tritium beta decay spectrum. Phase II will benefit from a gas system of krypton and tritium that will allow measurement of and offline correction for magnetic field fluctuations. We present the recent progress in understanding the electron kinematics and implementing the magnetic field calibration.

Nine-axis inertial fusion method based on dynamic magnetic field calibration

Nine-axis inertial fusion method based on dynamic magnetic field calibration

A Non-Linear Magnetic Field Calibration Method for Filter-Based Magnetographs by Multilayer Perceptron

For filter-based magnetographs, the linear calibration method under the weak-field assumption is usually adopted; this leads to magnetic saturation effect in the regions with strong magnetic field. This article explores a new method to overcome the above disadvantage using a multilayer perceptron network, which we call MagMLP, based on a back-propagation algorithm with one input layer, five hidden layers, and one output layer. We use the data from the \textit{Spectropolarimeter} (SP) on board \textit{Hinode} to simulate single-wavelength observations for the model training, and take into account the influence of the Doppler velocity field and the filling factor. The training results show that the linear fitting coefficient (LFC) of the transverse field reaches above 0.91, and that of the longitudinal field is above 0.98. The generalization of the models is good because the corresponding LFCs are above 0.9 for the test subsets. Compared with the linear calibration method, the MagMLP is much more effective on dealing with the magnetic saturation effect. Analyzing an active region, the results of the linear calibration present an evident magnetic saturation effect in the umbra regions; the corresponding systematic error reaches values greater than 1000 G in most areas, or even exceeds 2000 G at some pixels. However, the results of MagMLP at these locations are very close to the inversion results, and the systematic errors are basically within 300 G. In addition, we find that there are many "bright spots" and "dark spots" on the inclination angle images from the inversion results of \textit{Hinode}/SP with values of 180 and 0 degrees, respectively, where the inversion is not reliable and does not produce a good result; the MagMLP handles these points well.

Data reduction and calibration of the FMG onboard ASO-S

The Full-disk vectorMagnetoGraph (FMG) instrument will carry out polarization observations at one wavelength position of the Fe I 5324.179 °A spectral line. This paper describes how to choose this single wavelength position, the relevant data-processing and the magnetic field calibrations based on the measured polarization signals at one single wavelength position. It is found that solar radial Doppler velocity, which can cause the spectral line to shift, is a disadvantageous factor for the linear calibration at one wavelength position. Observations at two symmetric wavelength positionsmay significantly reduce the wavelength shift effect (∼ 75%), but simulations show that such polarization signals located at the solar limbs (e.g., beyond the longitude range of ±30°) are not free from the effect completely. In future work, we plan to apply machine learning techniques to calibrate vector magnetic fields, or employ full Stokes parameter profile inversion techniques to obtain accurate vector magnetic fields, in order to complement the linear calibration at the single wavelength position.

Real-time calibration algorithm of magnetometer for spinning projectiles

Purpose In spite of the vehicle, magnetic field interference can be reduced by some measures and techniques in ammunition design and manufacturing stage, the corruption of the vehicle magnetic field can still reach hundreds to thousands of nanoteslas. Besides, the magnetic field that the ferromagnetic materials generate in response to the strong magnetic field in the vicinity of the body. So, a real-time and accurate vehicle magnetic field calibration method is needed to improve the real-time measurement accuracy of the geomagnetic field for spinning projectiles. Design/methodology/approach Unlike the past two-step calibration method, the algorithm uses a linear model to calibrate the magnetic measurement error in real-time. In the method, the elliptical model of magnetometer measurement is established to convert the coefficients of hard and soft iron errors into the parameters of the elliptic equation. Then, the parameters are estimated by recursive least square estimator in real-time. Finally, the initial conditions for the estimator are established using prior knowledge method or static calibration method. Findings Studies show the proposed algorithm has remarkable estimation accuracy and robustness and it realizes calibration the magnetic measurement error in real-time. A turntable experiments indicate that the post-calibration residuals approximate the measurement noise of the magnetometer and the roll accuracy is better than 1°. The algorithm is restricted to biaxial magnetometers’ calibration in real-time as expressed in this paper. It, however, should be possible to broaden this method’s applicability to triaxial magnetometers' calibration in real-time. Originality/value Unlike the past two-step calibration method, the algorithm uses a linear model to calibrate the magnetic measurement error in real-time and the calculation is small. Besides, it does not take up storage space. The proposed algorithm has remarkable estimation accuracy and robustness and it realizes calibration the magnetic measurement error in real time. The algorithm is restricted to biaxial magnetometers’ calibration in real-time as expressed in this paper. It, however, should be possible to broaden this method’s applicability to triaxial magnetometers’ calibration in real-time.

Zero Magnetic Field Calibration for Single-Beam Atomic Magnetometers Using Second Harmonics

In this letter, we propose a simple and rapid method for zero field calibration of single elliptically polarized beam atomic magnetometers. This method uses a wobble adjustment that applies a small amplitude and low-frequency (70 Hz) ac magnetic field and sweeps the dc magnetic field. The second harmonic signal reaches its maximum when the dc magnetic field noise is zero. Our single-beam atomic magnetometer operates with elliptically polarized light, which has both circularly and linearly polarized light components. The wavelength of a single beam for a rubidium atom was determined to be 780.206 nm with a power of 2.72 mW.