Magnetic Field Model Research Articles

Modeling and Simulation of Electric and Magnetic Fields of a Short Dipole Antenna at Low Frequencies in the Far Field

Modeling and Simulation of Electric and Magnetic Fields of a Short Dipole Antenna at Low Frequencies in the Far Field

Recovery of coronal dimmings

Context. Coronal dimmings are regions of reduced emission in the lower corona observed in the wake of coronal mass ejections (CMEs), representing their footprints. Studying the lifetime evolution of coronal dimmings helps us to better understand the recovery and replenishment of the corona after large-scale eruptions. Aims. We study the recovery of dimmings on different spatial scales to enhance our understanding of the replenishment and dynamics of the corona after CMEs. Methods. In order to investigate the long-term evolution of coronal dimming and its recovery, we propose two approaches that focus on both the global and the local evolution of dimming regions: the fixed mask approach and the pixel boxes approach. We present four case studies (September 6, 2011; March 7, 2012; June 14, 2012; and March 8, 2019) in which a coronal dimming is associated with a flare/CME eruption. We analyzed each event with the same methodology, using extreme-ultraviolet filtergrams from the Solar Dynamics Observatory’s Atmospheric Imaging Assembly (SDO/AIA) and Solar TErrestrial RElations Observatory’s Extreme UltraViolet Imager (STEREO/EUVI) instruments. We identified the dimming region by image segmentation, then restricted the analysis to a specific portion of the dimming and tracked the time evolution of the dimming brightness and area. In addition, we study the behavior of small subregions inside the dimming area, of about 3 × 3 pixels, to compare the recovery in different regions of the dimming. Results. Three out of the four cases show a complete recovery 24 hours after the flare/CME eruption. The primary recovery mechanism identified in the observations is the expansion of coronal loops into the dimming region. The recovery of the brightness follows a two-step trend, with a steeper and quicker segment followed by a slower one. In addition, some parts of the dimming, which may be core dimmings, are still present at the end of the analysis time and do not recover within 3 days, whereas the peripheral regions (secondary dimmings) show a full recovery. Conclusions. The high temporal and spatial resolution of SDO/AIA observations combined with multi-view data of the STEREO/EUV instrument reveal high-situated coronal loops expanding after CME eruptions, which cover dimming regions and gradually increase their intensity. Our developed approaches enable the analysis of dimmings alongside these bright structures, revealing different timescales of recovery for core and secondary or twin dimming regions. Combined with magnetic field modeling, these methods lay the foundation for further systematic analysis of dimming recovery and enhance the knowledge gained from already-analyzed events.

Development of a Permanent Magnet Magnetic System for an Energy-Saving Synchrotron Radiation Source

New technologies can be used to further improve the parameters of synchrotron radiation sources. One of them is the use of permanent magnets when creating elements of the magnetic storage system. This will help eliminate the influence of power supply instability and vibrations caused by the operation of the cooling system on the stability of the electron beam position. In addition, the use of permanent magnets will make it possible to increase the aperture of the vacuum chamber and, thus, simplify the vacuum and injection systems of the storage device, as well as increase the threshold instability currents. This work is devoted to the development of two bending magnets, focusing and defocusing, which make up the regular part of the magnetic system of an energy-saving compact synchrotron radiation source. The design and results of magnetic field modeling are presented.

The 540° Magnetic Buncher

Generation of short electron bunches with high peak current is of great importance for different research and technological applications. Such generation requires a special bunching magnetic system. The paper is an overview of the development of a new magnetic buncher. It consists of the buncher scheme description, the results of magnetic field modeling and reference particle trajectory calculation for the relativistic electrons, and of the description of bending magnets. The buncher provides a strong dependence of the time of flight on the particle energy and thus is capable to bunch relatively long bunches to short ones. Another feature of the buncher is that all electron-optical elements has been made of permanent magnets.

Testing the flux tube expansion factor

Context. The properties of the solar wind measured in situ in the heliosphere are largely controlled by energy deposition in the solar corona, which is in turn closely related to the properties of the coronal magnetic field. Previous studies have shown that long-duration and large-scale magnetic structures show an inverse relation between the solar wind velocity measured in situ near 1 au and the expansion factor of the magnetic flux tubes in the solar atmosphere. Aims. The advent of the Solar Orbiter mission offers a new opportunity to analyse the relation between solar wind properties measured in situ in the inner heliosphere and the coronal magnetic field. We exploit this new data in conjunction with models of the coronal magnetic field and the solar wind to evaluate the flux expansion factor and speed relation. Methods. We use a Parker-like solar wind model, the “isopoly” model presented in previous works, to describe the motion of the solar wind plasma in the radial direction and model the tangential plasma motion due to solar rotation with the Weber and Davis equations. Both radial and tangential velocities are used to compute the plasma trajectory and streamline from Solar Orbiter location sunward to the solar ‘source surface’ at rss. We then employed a potential field source surface (PFSS) model to reconstruct the coronal magnetic field below rss to connect wind parcels mapped back to the photosphere. Results. We found a statistically weak anti-correlation between the in situ bulk velocity and the coronal expansion factor, for about 1.5 years of solar data. Classification of the data by source latitude reveals different levels of anticorrelation, which is typically higher when Solar Orbiter magnetically connects to high latitude structures than when it connects to low latitude structures. We show the existence of a fast solar wind that originates in strong magnetic field regions at low latitudes and undergoes large expansion factor. We provide evidence that such winds become supersonic during the super-radial expansion (below rss) and are theoretically governed by a positive v–f correlation. We find that faster winds exhibit, on average, a flux tube expansion at a larger radius than slower winds. Conclusions. An anticorrelation between solar wind speed and expansion factor is present for solar winds originating in high latitude structures in solar minimum activity, typically associated with coronal hole-like structures, but this cannot be generalized to lower latitude sources. We have found extended time intervals of fast solar wind associated with both large expansion factors and strong photospheric magnetic fields. Therefore, the value of the expansion factor alone cannot be used to predict the solar wind speed. Other parameters, such as the height at which the expansion gradient is the strongest, must also be taken into account.

Magnetic fields in the outskirts of PSZ2 G096.88+24.18 from a depolarization analysis of radio relics

Context. Radio relics are diffuse, non-thermal radio sources present in a number of merging galaxy clusters. They are characterized by elongated arc-like shapes and highly polarized emission (up to ∼60%) at gigahertz frequencies, and are expected to trace shock waves in the cluster outskirts induced by galaxy cluster mergers. Their polarized emission can be used to study the magnetic field properties of the host cluster. Aims. In this paper, we investigate the polarization properties of the double radio relics in PSZ2 G096.88+24.18 using the rotation measure (RM) synthesis, and try to constrain the characteristics of the magnetic field that reproduce the observed depolarization as a function of resolution (beam depolarization). Our aim is to understand the nature of the low polarization fraction that characterizes the southern relic with respect to the northern relic. Methods. We present new 1–2 GHz Karl G. Jansky Very Large Array (VLA) observations in multiple configurations. We derived the RM and polarization of the two relics by applying the RM synthesis technique, and thus solved for bandwidth depolarization in the wide observing bandwidth. To study the effect of beam depolarization, we degraded the image resolution and studied the decreasing trend of polarization fraction with increasing beam size. Finally, we performed 3D magnetic field simulations using multiple models for the magnetic field power spectrum over a wide range of scales, in order to constrain the characteristics of the cluster magnetic field that can reproduce the observed beam depolarization trend. Results. Using RM synthesis, we obtained a polarization fraction of (18.6 ± 0.3)% for the northern relic and (14.6 ± 0.1)% for the southern one. Having corrected for bandwidth depolarization, and after noticing the absence of relevant complex Faraday spectrum, we inferred that the nature of the depolarization for the southern relic is external, and possibly related to the turbulent gas distribution within the cluster, or to the complex spatial structure of the relic. The best-fit magnetic field power spectrum, which reproduces the observed depolarization trend for the southern relic, was obtained for a turbulent magnetic field model, described by a power spectrum derived from cosmological simulations, and defined within the scales of Λmin = 35 kpc and Λmax = 400 kpc. This yields an average magnetic field of the cluster within 1 Mpc3 volume of ∼2 μG.

Unexpected major geomagnetic storm caused by faint eruption of a solar trans-equatorial flux rope

Some geomagnetic storms’ solar origins are ambiguous, making them hard to predict. On March 23, 2023, a severe geomagnetic storm occurred, however, forecasts based on remote-sensing observations failed to predict it. Here, we show clear evidence that this storm originates from the eruption of a trans-equatorial, longitudinal and low-density magnetic flux rope (FR) with weaker coronal emission and no chromospheric signs. The FR’s gentle eruption results in a faint full-halo coronal mass ejection (CME), which is missed by forecasters and not included in CME catalogs. Combining magnetic field modeling and in-situ measurements, we reveal the FR’s southward axial magnetic field as the main cause of the geomagnetic storm. This CME is the stealthiest one reported causing a severe geomagnetic storm. Our study highlights that erupting trans-equatorial FRs can generate major geomagnetic storms in a stealthy way. Characteristic observational signatures of similar eruptions are proposed to help in future forecasts.

Method for prediction magnetic silencing of uncertain energy-saturated extended technical objects in prolate spheroidal coordinate system

Aim. Development of method for prediction by energy-saturated extended technical objects magnetic silencing based on magnetostatics geometric inverse problems solution and magnetic field spatial spheroidal harmonics calculated in prolate spheroidal coordinate system taking into account of technical objects magnetic characteristics uncertainties. Methodology. Spatial prolate spheroidal harmonics of extended technical objects magnetic field model calculated as magnetostatics geometric inverse problems solution in the form of nonlinear minimax optimization problem based on near field measurements for prediction far extended technical objects magnetic field magnitude. Nonlinear objective function calculated as the weighted sum of squared residuals between the measured and predicted magnetic field COMSOL Multiphysics software package used. Nonlinear minimax optimization problems solutions calculated based on particle swarm nonlinear optimization algorithms. Results. Results of prediction extended technical objects far magnetic field magnitude based on extended technical objects spatial prolate spheroidal harmonics of the magnetic field model in the prolate spheroidal coordinate system using near field measurements with consideration of extended technical objects magnetic characteristics uncertainty. Originality. The method for prediction by extended technical objects magnetic cleanliness based on spatial prolate spheroidal harmonics of the magnetic field model in the prolate spheroidal coordinate system with consideration of magnetic characteristics uncertainty is developed. Practical value. The important practical problem of prediction extended technical objects magnetic silencing based on the spatial prolate spheroidal harmonics of the magnetic field model in the prolate spheroidal coordinate system with consideration of extended technical objects magnetic characteristics uncertainty solved. References 48, figures 2.

Modeling and analysis of non-circumferential symmetric permanent magnet spherical motor using genetic algorithm-based torque map method.

A permanent magnet spherical motor (PMSpM) is a typical multiple-degree-of-freedom apparatus. This paper proposes a torque map-based torque model and its counterpart using a genetic algorithm for the PMSpM with non-circumferential symmetric permanent magnets. The basic structure and operating principle of the PMSpM under study are presented. The analytic model of the 3D magnetic field is researched using the spherical harmonic method. The magnetic field model is verified via finite element method (FEM) analysis and an experiment of radial magnetic flux density. The analytic torque model is formulated using the Lorentz force method. The torque maps are established according to the principle, and the torque map-based torque model originates from the maps. FEM and the experimental results prove the correctness of the torque map-based torque model, and real-time performance of the torque model is also estimated. To solve the coil current calculation difficulty, the genetic algorithm is introduced for establishing the reversal torque model; MATLAB simulation is conducted for the convergence speed of the reversal torque model; and the real-time performance is studied on Qt 5.14/C++ upper software.

Effect of temperature anisotropy formed by fast electron beams moving in the flare loop on its excited electron-cyclotron maser instability

Context. The electron-cyclotron maser instability (ECMI) is a significant coherent radio emission mechanism widely utilized in various astrophysical radio phenomena. It is well known that the velocity anisotropic distribution of energetic electrons, which leads to an inverted perpendicular population in the vertical direction with ∂fb/∂v⊥ > 0, can provide the free energy necessary for the ECMI. Aims. The initial velocity distribution of energetic electrons leaving the acceleration region is typically isotropic or beam-like. However, as these energetic electrons travel along the magnetic field as fast electron beams (FEBs) in magnetic plasma, various velocity anisotropic distributions can emerge. In this paper, we examine the impact of temperature anisotropy formed by beam electrons traveling along a flare loop on the ECMI. Methods. By neglecting the energy loss of energetic electrons as they traverse the corona and invoking the conservation of energy and magnetic moments, we established the relationship between momentum dispersion and the magnetic field. Utilizing the magnetic field model of the flare loop, we calculated the evolution of momentum dispersion and the growth rates of the ECMI as FEBs precipitate along the flare loop. Results. The results demonstrate that the temperature anisotropy arising as FEBs descend along the flare loop significantly impacts the ECMI. The maximum growth rates of the excited modes exhibit a gradual increase initially and then decline rapidly after reaching a critical height for β0 = 0.2c and 0.15c. The results also show that the growth rates of the O2 mode are one order of magnitude smaller than those of the O1 and X2 modes. This indicates that the harmonic radiation is X-mode polarized. Notably, the temperature anisotropy of FEBs as they precipitate along the flare loop with different magnetic field models or at different heights has similar effects on the ECMI.

Disentangling the Faraday rotation sky

Context. Magnetic fields permeate the diffuse interstellar medium (ISM) of the Milky Way, and are essential to explain the dynamical evolution and current shape of the Galaxy. Magnetic fields reveal themselves via their influence on the surrounding matter, and as such are notoriously hard to measure independently of other tracers. Aims. In this work, we attempt to disentangle an all-sky map of the line-of-sight (LoS)-parallel component of the Galactic magnetic field from the Faraday effect, utilizing several tracers of the Galactic electron density, ne. Additionally, we aim to produce a Galactic electron dispersion measure map and quantify several tracers of the structure of the ionized medium of the Milky Way. Methods. The method developed to reach these aims is based on information field theory, a Bayesian inference framework for fields, which performs well when handling noisy and incomplete data and constraining high-dimensional-parameter spaces. We rely on compiled catalogs of extragalactic Faraday rotation measures and Galactic pulsar dispersion measures, a well as data on bremsstrahlung and the hydrogen α spectral line to trace the ionized medium of the Milky Way. Results. We present the first full sky map of the LoS-averaged Galactic magnetic field. Within this map, we find LoS-parallel and LoS-averaged magnetic field strengths of up to 4 µG, with an all-sky root mean square of 1.1 µG, which is consistent with previous local measurements and global magnetic field models. Additionally, we produce a detailed electron dispersion measure map that agrees with existing parametric models at high latitudes but suffers from systematic effects in the disk. Further analysis of our results with regard to the 3D structure of ne reveals that it follows a Kolmogorov-type turbulence for most of the sky. From the reconstructed dispersion measure and emission measure maps, we construct several tracers of variability in ne along the LoS. Conclusions. This work demonstrates the power of consistent joint statistical analysis including multiple datasets and physical quantities and defines a road map toward a full three-dimensional joint reconstruction of the Galactic magnetic field and the ionized ISM.

Assessment of the Weimer Geomagnetic Perturbation Model for High‐Latitude Positioning and Navigation

AbstractThe Geomagnetism Group at the National Centers for Environmental Information (NCEI), in collaboration with the Cooperative Institute for Research in Environmental Sciences (CIRES), along with various government and industry partners, specializes in developing and providing access to Earth's internal magnetic field models. These models are crucial for applications such as compass navigation and wellbore positioning, offering reference values for the geomagnetic field (total field, dip or inclination, and declination) at any location across the Earth. This study assesses the Weimer geomagnetic perturbation model, proposed by Weimer in 2013, which is an empirical model of magnetic field variations at high latitudes driven by solar wind measurements, as a candidate for capturing geomagnetic field variations in high‐latitude areas. We compare the geomagnetic field variations predicted by the Weimer model against data from the INTERMAGNET and SuperMAG observatory networks. Our findings indicate that the Weimer model achieves a reduction in the standard deviations of high‐latitude magnetic field variations by approximately 20%–30% once quiet‐time baselines are removed from the data set. Furthermore, we compare the performance of the Weimer model against the Space Weather Modeling Framework's Geospace model during specific geomagnetic storms in 2017 and 2018, and we find that the Weimer model is more effective in predicting magnetic variations at high latitudes than the Geospace model during these storms. Additionally, comparisons to magnetometer data collected from high‐latitude directional‐drilling operations align with the trends observed in comparisons with INTERMAGNET and SuperMAG observatory data, confirming the Weimer model's reliability and effectiveness for such applications.

Total Solar Eclipse White-light Images as a Benchmark for Potential Field Source Surface Coronal Magnetic Field Models: An In-depth Analysis over a Solar Cycle

Potential field source surface (PFSS) models are widely used to simulate coronal magnetic fields. PFSS models use the observed photospheric magnetic field as the inner boundary condition and assume a perfectly radial field beyond a “source surface” (R ss). At present, total solar eclipse (TSE) white-light images are the only data that delineate the coronal magnetic field from the photosphere out to several solar radii (R ⊙). We utilize a complete solar cycle span of these images between 2008 and 2020 as a benchmark to assess the reliability of PFSS models. For a quantitative assessment, we apply the Rolling Hough Transform to the eclipse data and corresponding PFFS models to measure the difference, Δθ, between the data and model magnetic field lines throughout the corona. We find that the average Δθ, 〈Δθ〉, can be minimized for a given choice of R ss depending on the phase within a solar cycle. In particular, R ss ≈ 1.3 R ⊙ is found to be optimal for solar maximum, while R ss ≈ 3 R ⊙ yields a better match at solar minimum. Regardless, large (〈Δθ〉 > 10°) discrepancies between TSE data and PFSS-generated coronal field lines remain regardless of the choice of source surface. However, implementation of solar-cycle-dependent R ss optimal values does yield more reliable PFSS-generated coronal field lines for use in models and for tracing in situ measurements back to their sources at the Sun.

Thrust ripple suppression analysis of moving-magnet-type linear synchronous motor based on independent coil

In this paper, a novel thrust ripple suppression method for multi-secondary permanent magnet synchronous linear motor based on independent coil structure is proposed. Independent coil structure can realize independent power supply for each coil by changing the driving mode of the coils. Combined with the new power supply strategy, the detent and electromagnetic force fluctuation can be suppressed. Firstly, the cogging and end force of moving-magnet-type linear motor are separated by periodic and vector boundary conditions and harmonic analysis is carried out. An analytical model of air gap magnetic field based on virtual magnetic poles is established to solve the back EMF and electromagnetic force fluctuation of the motor. The generation mechanism and harmonic of electromagnetic force fluctuation are analyzed. A multi-secondary PMLSM based on independent coil is proposed, the principle of suppressing motor thrust ripple is expounded, and the coupling effect between modules is analyzed. Finally, a zero-crossing power supply strategy is proposed. The simulation and experimental results show that multi-secondary independent coil PMLSM can effectively suppress the detent and electromagnetic force fluctuation.

Improvement of titanium film uniformity by magnetron sputtering with electromagnetic coil design

A novel magnetron assembly based on a combination of permanent magnet and adjustable electromagnetic coil is proposed for improved uniformity of the magnetron sputtering deposition process. The design of the magnetron sputtering system containing a rotating substrate and an off-axis arranged magnetron. A numerical framework has been developed to describe the evolution of the plasma density and distribution of sputtered particles. Specifically, the finite element method (FEM) was used to calculate the magnetic field and to model the magnetron sputtering discharge, and binary-collision Monte Carlo method was used to determine the transport of sputtered atoms to the substrate. Through parametric analyses, it was found that increasing the substrate-to-target distance, gas pressure, and coil current intensity benefits the uniform distribution of particles. The condition where the off-axis displacement of the magnetron effectively enhances uniformity. A strategy for optimizing deposition uniformity by combining adjustable current with an off-axis magnetron arrangement was proposed, which reduce the non-uniformity of film thickness by 77.6 % compared to the traditional fixed magnetic field model.

Study on Magnetic Field Modeling and Transmission Performance of Radial Solid Permanent Magnet Coupler

Study on Magnetic Field Modeling and Transmission Performance of Radial Solid Permanent Magnet Coupler

ОБЕРТАЛЬНИЙ МОМЕНТ БЕЗПАЗОВОГО МОМЕНТНОГО ДВИГУНА З ПОСТІЙНИМИ МАГНІТАМИ ТА МАСИВНИМ МАГНІТОПРОВОДОМ СТАТОРА

The properties of the solid magnetic core of the stator of a slotless torque motor with permanent magnets are considered. It is noted that the solid stator under the conditions of low rotation speed has some advantages over the traditional laminated magnetic circuit. These advantages consist in the cost reduction of the design, its compactness and the low time of production preparation. The mathematical model's assumptions and the input data's limitations are formulated. A model of a static magnetic field with a moving electrically conductive medium is chosen. The two-dimensional model is implemented in the "Magnetic fields" interface of the "COMSOL Multiphysics" software. The maximum torque values were obtained and the optimal number of pole pairs was found. The method of calculating the torque based on eddy current losses in the magnetic medium is used. The decrease in torque with increasing rotor speed is calculated. The correction coefficients of the maximum moment were obtained to correct the results of two-dimensional modelling using a three-dimensional model. References 5, figures 6, tables 1.

Development of Precision Controllable Magnetic Field-Assisted Platform for Micro Electrical Machining.

In order to introduce the magnetic field into micro electrical machining technology to explore the influence of magnetic field on micro electrical machining, the development of a precision controllable magnetic field-assisted platform is particularly important. This platform needs to precisely control the spatial magnetic field. This study first completes the hardware design and construction of the magnetic field generation device, using electromagnetic coils with soft iron cores as the sources of the magnetic field. Mathematical models of the magnetic field are established and calibrated. Since the magnetic dipole model cannot effectively describe the magnetic field generated by the electromagnetic coil, this study adopts a more precise description method: the spherical harmonic function expansion model and the magnetic multipole superposition model. The calibration of the magnetic field model is based on actual excitation magnetic field data, so a magnetic field sampling device is designed to obtain the excitation magnetic field of the workspace. The model is calibrated based on a combination of the theoretical model and magnetic field data, and the performance of the constructed setup is analyzed. Finally, a magnetic field-assisted platform has been developed which can generate magnetic fields in any direction within the workspace with intensities ranging from 0 to 0.2 T. Its magnetic field model arrives at an error percentage of 2.986%, a variance of 0.9977, and a root mean square error (RMSE) of 0.71 mT, achieving precise control of the magnetic field in the workspace.

Comparative study for heat transfer characteristics of many graphene hybrid nanofluids flow over a shrinking sheet

In this work, steady two-dimensional boundary layer flow of an electrically conductive hybrid nanofluids past a shrinking sheet, along with magnetic field, thermal radiation, suction/injection, heat source/sink and velocity slip model, has been investigated. Particularly, eight mixed hybrid graphene nanofluids of copper, silver, aluminium oxide and titanium dioxide were studied and compared with the classical graphene–water nanofluid. Appropriate similarity transformations have been used to convert the governing PDEs into a set of non-linear ODEs, then, we deduced exact solutions of the flow and temperature. In addition, possibility of obtaining no, unique and dual solutions for these functions were introduced as critical values and regions via graphs. Moreover, validation of the present solutions with those in the literature has been tabulated. Furthermore, asymptotic expression and local extremum for the most important equation were studied.On comparing with those results in the literature at some special values of the included parameters, excellent agreements were gotten. It was mentioned that two conditions have to be simultaneously applied to result the temperature dual solution with restrictions on choosing values of specific parameters. Further, in the injection case, the temperature distributions are larger by about 66.7% on comparing with those in the suction case, for all almost the investigated parameters. To get the highest temperature, it was deduced that the copper is to be firstly added to the water and then mixed with the graphene to produce the hybrid nanofluid. Graphene–copper/water employs as a heater on increasing the Eckert number, shrinking parameter and second velocity slip (for N<0). Furthermore, it acts as cooler with an increase of magnetic field, |heat source/sink parameter|, suction/injection parameter, solid volume fraction, first velocity slip and second velocity slip (for N>0).

Refinement of Global Coronal and Interplanetary Magnetic Field Extrapolations Constrained by Remote-sensing and In Situ Observations at the Solar Minimum

Solar magnetic fields are closely related to various physical phenomena on the Sun, which can be extrapolated with different models from photospheric magnetograms. However, the open flux problem (OFP), the underestimation of the magnetic field derived from the extrapolated model, is still unsolved. To minimize the impact of the OFP, we propose three evaluation parameters to quantitatively evaluate magnetic field models and determine the optimal free parameters in the models by constraining the coronal magnetic fields and the interplanetary magnetic fields (IMFs) with real observations. Although the OFP still exists, we find that magnetic field lines traced from the coronal models effectively capture the intricate topological configurations observed in the corona, including streamers and plumes. The OFP is lessened by using the Helioseismic and Magnetic Imager synoptic map instead of the Global Oscillation Network Group daily synoptic maps, and the potential field source surface + potential field current sheet (PFSS+PFCS) model instead of the current sheet source surface (CSSS) model. For Carrington Rotation 2231 at the solar minimum, we suggest that the optimal parameters for the PFSS+PFCS model are R ss = 2.2–2.5 R ☉ and R scs = 10.5–14.0 R ☉, as well as for the CSSS model, are R cs = 2.0–2.4 R ☉, R ss = 11.0–14.7 R ☉, and a = 1.0 R ☉. Despite the IMFs at 1 au being consistent with the measurements by artificially increasing the polar magnetic fields, the IMFs near the Sun are still underestimated. The OFP might be advanced by improving the accuracy of both the weak magnetic fields and polar magnetic fields, especially considering magnetic activities arising from interplanetary physical processes.