Magnetic Field Observations Research Articles

Electron-scale Current Layers in the Martian Magnetotail: Spatial Scaling and Properties of Embedding

Abstract Current sheets (CSs) are widespread objects in space plasma capable of storing and, then, explosively releasing the accumulated magnetic energy. In planetary magnetotails the cross-tail CS plays an important role in the global dynamics of the tail and in the transformation of the magnetic energy into the kinetic and thermal energies of the ambient plasma. We have analyzed 114 crossings of the cross-tail CS by the MAVEN spacecraft at X MSO ∼ [−1.0, −2.8]R M. Magnetic field observations with high time resolution allowed the observation of the inner superthin CS (STCS) with a half-thickness L STCS ∼ (1–100)ρ e (ρ e is the gyroradius of thermal electrons) in 75 intervals of the CS crossings from our database. The STCS was embedded into a thicker ion-scale CS and provides 10%–50% of the total current density in the cross-tail CS. Our analysis has shown that the observed L STCS and the embedding parameter, σ emb, characterizing the contribution of the STCS to the total current density in the CS are well described by the novel analytical kinetic model of a multilayered CS with an inner embedded electron-scale layer: L STCS∼ (0.9–1.2)λ and σ emb ∼ (0.9–1.2) σ model, where the universal spatial scaling λ ∼ δ i 2/ρ P and the embedding parameter σ model ∼ δ i /ρ P are determined by the local ion inertial length (δ i ) and gyroradius of thermal protons (ρ P ) in the STCS.

Resonant Alfvén Waves in the Lower Auroral Ionosphere: Evidence for the Nonlinear Evolution of the Ionospheric Feedback Instability

AbstractDuring the “Auroral Jets” experiment from Poker Flat, Alaska on 2 March 2017, two NASA sounding rockets were simultaneously launched into the active auroral ionosphere. The rockets were equipped with instrumentation to measure DC and AC electric fields, magnetic fields, energetic electrons, plasma density, and neutral winds and achieved apogees of 190 and 330 km. A prominent feature of the electric and magnetic field observations is the presence of localized large‐amplitude (±40 mV/m and ±100 nT) small‐scale (λ⊥∼ 1 km) Alfvén wave structures at altitudes as low as 150 km in the vicinity of up‐ and down‐ward current regions. We interpret the oscillations as representing standing waves associated with the ionospheric Alfvén resonator formed between the ionosphere and the lower magnetosphere. The electric field components of the Alfvén waves show signatures of wave steepening in correlation with electron precipitation and large variations of the background plasma density. The signatures are discussed in the context of nonlinear evolution of the ionospheric feedback instability.

The “Singular” Behavior of the Solar Wind Scaling Features during Parker Solar Probe–BepiColombo Radial Alignment

Abstract At the end of 2020 September, the Parker Solar Probe (PSP) and BepiColombo were radially aligned: PSP was orbiting near 0.17 au and BepiColombo near 0.6 au. This geometry is of particular interest for investigating the evolution of solar wind properties at different heliocentric distances by observing the same solar wind plasma parcels. In this work, we use the magnetic field observations from both spacecraft to characterize both the topology of the magnetic field at different heliocentric distances (scalings, high-order statistics, and multifractal features) and its evolution when moving from near-Sun to far-Sun locations. We observe a breakdown of the statistical self-similar nature of the solar wind plasma with an increase in the efficiency of the nonlinear energy cascade mechanism when moving away from the Sun. We find a complex organization of large field gradients to dissipate the excess of kinetic energy across the inertial range near the Sun, whereas the topological organization of small fluctuations is still primarily responsible for the energy transfer rate at 0.6 au. These results provide, for the first time, evidence of the different roles of dissipation mechanisms near and far away from the Sun.

Evidence for Strong Intracluster Magnetic Fields in the Early Universe

Abstract The origin of magnetic fields in clusters of galaxies is still a matter of debate. Observations for intracluster magnetic fields over a wide range of redshifts are crucial to constrain possible scenarios for the origin and evolution of the fields. Differences in Faraday rotation measures (RMs) of an embedded double radio source, i.e., a pair of lobes of mostly Fanaroff–Riley type II radio galaxies, are free from the Faraday rotation contributions from the interstellar medium inside the Milky Way and the intergalactic medium between radio galaxies and us, and hence provide a novel way to estimate average magnetic field within galaxy clusters. We have obtained a sample of 627 pairs whose RMs and redshifts are available in the most updated RM catalogs and redshift databases. The RM differences of the pairs are derived. The statistically large RM differences for pairs of redshifts z > 0.9 indicate that intracluster magnetic fields are as strong as about 4 μG. Such strong magnetic fields in the intracluster medium at the half age of the universe, comparable to the intracluster field strength in nearby galaxy clusters, pose a challenge to the theories of the origin of cosmic magnetic fields.

The merging process of chromospheric fibrils into a filament

Context. Although solar filaments have been intensively studied, detailed observations that show an entire process of filament maintenance are rare. Aims. The aim of this paper is to study the whole process of the material supply and the magnetic flux injection from chromospheric fibrils to a nearby filament. Methods. Based on multiwavelength observations from the New Vacuum Solar Telescope and the Solar Dynamics Observatory (SDO), we tracked the evolution of the chromospheric fibrils involved in the process of filament maintenance and estimated the relevant kinetic parameters. The possible reconnection process was further analyzed in detail by using the SDO magnetic field and extreme ultraviolet observations. Results. In the southeast of the filament, two sets of chromospheric fibrils approach and interact with each other, accompanied by weak brightening at the interacting region. Subsequently, a long fibril is formed, keeps moving toward the filament, and finally merges into it. The mergence results in a disturbance in the filament, for example, some of the original filament fibrils move northward. Ten minutes later, a similar process occurs again. By checking the photospheric magnetograms, we find that the two sets of chromospheric fibrils are rooted in a pair of opposite-polarity magnetic patches, and magnetic cancellation takes place between them. We propose that magnetic reconnection could occur between chromospheric fibrils and that it plays an important role in the formation of the new longer fibrils. Conclusions. Magnetic reconnections between chromospheric fibrils produce new fibrils, which then merge into a nearby filament. Such observations imply that filament material and magnetic flux can be supplied from surrounding chromospheric fibrils.

A New Model of Jupiter's Magnetic Field at the Completion of Juno's Prime Mission

AbstractA spherical harmonic model of the magnetic field of Jupiter is obtained from vector magnetic field observations acquired by the Juno spacecraft during 32 of its first 33 polar orbits. These Prime Mission orbits sample Jupiter's magnetic field nearly uniformly in longitude (∼11° separation) as measured at equator crossing. The planetary magnetic field is represented with a degree 30 spherical harmonic and the external field is approximated near the origin with a simple external spherical harmonic of degree 1. Partial solution of the underdetermined inverse problem using generalized inverse techniques yields a model (“JRM33”) of the planetary magnetic field with spherical harmonic coefficients reasonably well determined through degree and order 13. Useful information regarding the field extends through degree 18, well fit by a Lowes' spectrum with a dynamo core radius of 0.81 Rj, presumably the outer radius of the convective metallic hydrogen region. This new model provides a most detailed view of a planetary dynamo and evidence of advection of the magnetic field by deep zonal winds in the vicinity of the Great Blue Spot (GBS), an isolated and intense patch of flux near Jupiter's equator. Comparison of the JRM33 and JRM09 models suggests secular variation of the field in the vicinity of the GBS during Juno's nearly 5 years of operation in orbit about Jupiter. The observed secular variation is consistent with the penetration of zonal winds to a depth of ∼3,500 km where a flow velocity of ∼0.04 ms−1 is required to match the observations.

Relativistic Electron Precipitation Near Midnight: Drivers, Distribution, and Properties

AbstractWe analyze the drivers, distribution, and properties of the relativistic electron precipitation (REP) detected near midnight by the Polar Orbiting Environmental Satellites (POES) and Meteorological Operational (MetOp) satellites, critical for understanding radiation belt losses and nightside atmospheric energy input. REP is either driven by wave‐particle interactions (isolated precipitation within the outer radiation belt), or current sheet scattering (CSS; precipitation with energy dispersion), or a combination of the two. We evaluate the L‐MLT distribution for the identified REP events in which only one process evidently drove the precipitation (∼10% of the REP near midnight). We show that the two mechanisms coexist and drive precipitation in a broad L‐shell range (4–7). However, wave‐driven REP was also observed at L < 4, whereas CSS‐driven REP was also detected at L > 7. Moreover, we estimate the magnetotail stretching during each REP event using the magnetic field observations from the Geostationary Operational Environmental Satellite (GOES). Both wave‐particle interactions and CSS drive REP in association with a stretched magnetotail, although CSS‐driven REP potentially shows more pronounced stretching. Wave‐driven REP events are localized in L shell and often occur on spatial scales of <0.3 L. Using either proton precipitation (observed by POES/MetOp during wave‐driven REP) as a proxy for electromagnetic ion cyclotron (EMIC) wave activity or wave observations (from GOES and the Van Allen Probes) at the conjugate event location, we find that ∼73% wave‐driven REP events are associated with EMIC waves.

A Study on Correcting the Effect of Polarization Crosstalk in Full-Disk Solar Photospheric Magnetic Field Observations

Magnetography using magnetic sensitive lines is regarded traditionally as the main instrument for measuring the magnetic field of the whole Sun. Full polarized Stokes parameters (\(I\), \(Q\), \(U\), \(V\)) can be used to deduce the magnetic field under specific theoretical models or inversion algorithms. Due to various reasons, there are often cross-talk effects among Stokes signals observed directly by magnetographs. Especially, the circularly polarized signal \(V\) usually seriously affects the linearly polarized \(Q\) and \(U\) signals, which is one of the main errors in the value of the transverse magnetic field (parallel to the solar surface) that is related to \(Q\) and \(U\). The full-disk magnetograph onboard the Advanced Space based Solar Observatory (ASO-S/FMG) is designed to observe Stokes parameters and deduce the magnetic-field vector. In this article, the methods for correcting the effects of cross-talk \(V\) on \(Q\) and \(U\) based on the assumption of perfectly symmetric \(Q\) and \(U\) and anti-symmetric Stokes \(V\) profiles and a new method for reducing the crosstalk effect under observation mode of the FMG are developed. Through the test, it is found that the two methods are effective in cross-talk removal in the sunspot region and have better consistency. Additionally, the developed method can be applied to remove the cross-talk effect by using only one group of \(Q\), \(U\) and \(V\) images observed at one wavelength position.

Tracing the large-scale magnetic field morphology in protoplanetary disks using molecular line polarization

Context. Magnetic fields are fundamental to the accretion dynamics of protoplanetary disks and they likely affect planet formation. Typical methods to study the magnetic field morphology observe the polarization of dust or spectral lines. However, it has recently become clear that dust-polarization in ALMA’s (Atacama Large (sub)Millimeter Array) spectral regime does not always faithfully trace the magnetic field structure of protoplanetary disks, which leaves spectral line polarization as a promising method for mapping the magnetic field morphologies of such sources. Aims. We aim to model the emergent polarization of different molecular lines in the ALMA wavelength regime that are excited in protoplanetary disks. We explore a variety of disk models and molecules to identify those properties that are conducive to the emergence of polarization in spectral lines and may therefore be viably used for magnetic field measurements in protoplanetary disks. Methods. We used POlarized Radiative Transfer Adapted to Lines in conjunction with the Line Emission Modeling Engine. Together, they allowed us to treat the polarized line radiative transfer of complex three-dimensional physical and magnetic field structures. Results. We present simulations of the emergence of spectral line polarization of different molecules and molecular transitions in the ALMA wavelength regime. We find that molecules that thermalize at high densities, such as HCN, are also the most susceptible to polarization. We find that such molecules are expected to be significantly polarized in protoplanetary disks, while molecules that thermalize at low densities, such as CO, are only significantly polarized in the outer disk regions. We present the simulated polarization maps at a range of inclinations and magnetic field morphologies, and we comment on the observational feasibility of ALMA linear polarization observations of protoplanetary disks. Conclusions. We conclude that those molecules with strong dipole moments and relatively low collision rates are most useful for magnetic field observations through line polarization measurements in high density regions such as protoplanetary disks.

Dynamics of variable dusk–dawn flow associated with magnetotail current sheet flapping

Abstract. We present Cluster spacecraft observations from 12 October 2006 of convective plasma flows in the Earth's magnetotail. Earthward flow bursts with a dawnward v⊥y component, observed by Cluster 1 (C1), are inconsistent with the duskward flow that might be expected at the pre-midnight location of the spacecraft. Previous observations have suggested that the dusk–dawn sense of the flow can be governed by the interplanetary magnetic field (IMF) By conditions, with the related “untwisting hypothesis” of magnetotail dynamics commonly invoked to explain this dependence, in terms of a large-scale magnetospheric asymmetry. In the current study, observations of the upstream solar wind conditions from OMNI, magnetic field observations by Cluster and ionospheric convection data using SuperDARN indicate a large-scale magnetospheric morphology consistent with positive IMF By penetration into the magnetotail. At the pre-midnight location of Cluster, however, the dawnward flow observed below the neutral sheet by C1 could only be explained by the untwisting hypothesis in a negative IMF By scenario. The Cluster magnetic field data also reveal a flapping of the magnetotail current sheet, a phenomenon known to influence dusk–dawn flow. Results from the curlometer analysis technique suggest that the dusk–dawn sense of the J×B force was consistent with localised kinks in the magnetic field and the flapping associated with the transient perturbations to the dusk–dawn flow observed by C1. We therefore suggest that the flapping overcame the dusk–dawn sense of the large-scale convection which we would expect to have been net duskward in this case. We conclude that invocation of the untwisting hypothesis may be inappropriate when interpreting intervals of dynamic magnetotail behaviour such as during current sheet flapping, particularly at locations where magnetotail flaring becomes dominant.

In situ observations of ions and magnetic field around Phobos: the mass spectrum analyzer (MSA) for the Martian Moons eXploration (MMX) mission

The mass spectrum analyzer (MSA) will perform in situ observations of ions and magnetic fields around Phobos as part of the Martian Moons eXploration (MMX) mission to investigate the origin of the Martian moons and physical processes in the Martian environment. MSA consists of an ion energy mass spectrometer and two magnetometers which will measure velocity distribution functions and mass/charge distributions of low-energy ions and magnetic field vectors, respectively. For the MMX scientific objectives, MSA will observe solar wind ions, those scattered at the Phobos surface, water-related ions generated in the predicted Martian gas torus, secondary ions sputtered from Phobos, and escaping ions from the Martian atmosphere, while monitoring the surrounding magnetic field. MSA will be developed from previous instruments for space plasma missions such as Kaguya, Arase, and BepiColombo/Mio to contribute to the MMX scientific objectives.

Multi-spacecraft observations of the structure of the sheath of an interplanetary coronal mass ejection and related energetic ion enhancement

Context. Sheath regions ahead of coronal mass ejections (CMEs) are large-scale heliospheric structures that form gradually with CME expansion and propagation from the Sun. Turbulent and compressed sheaths could contribute to the acceleration of charged particles in the corona and in interplanetary space, but the relation of their internal structure to the particle energization process is still a relatively little studied subject. In particular, the role of sheaths in accelerating particles when the shock Mach number is low is a significant open research problem. Aims. This work seeks to provide new insights on the internal structure of CME-driven sheaths with regard to energetic particle enhancements. A good opportunity to achieve this aim was provided by multi-point, in-situ observations of a sheath region made by radially aligned spacecraft at 0.8 and ∼1 AU (Solar Orbiter, the L1 spacecraft Wind and ACE, and BepiColombo) on April 19−21, 2020. The sheath was preceded by a weak and slowly propagating fast-mode shock. Methods. We apply a range of analysis techniques to in situ magnetic field, plasma and particle observations. The study focuses on smaller scale sheath structures and magnetic field fluctuations that coincide with energetic ion enhancements. Results. Energetic ion enhancements were identified in the sheath, but at different locations within the sheath structure at Solar Orbiter and L1. Magnetic fluctuation amplitudes at inertial-range scales increased in the sheath relative to the solar wind upstream of the shock, as is typically observed. However, when normalised to the local mean field, fluctuation amplitudes did not increase significantly; magnetic compressibility of fluctuation also did not increase within the sheath. Various substructures were found to be embedded within the sheath at the different spacecraft, including multiple heliospheric current sheet (HCS) crossings and a small-scale flux rope. At L1, the ion flux enhancement was associated with the HCS crossings, while at Solar Orbiter, the ion enhancement occurred within a compressed, small-scale flux rope. Conclusions. Several internal smaller-scale substructures and clear difference in their occurrence and properties between the used spacecraft was identified within the analyzed CME-driven sheath. These substructures are favourable locations for the energization of charged particles in interplanetary space. In particular, substructures that are swept from the upstream solar wind and compressed into the sheath can act as effective acceleration sites. A possible acceleration mechanism is betatron acceleration associated with a small-scale flux rope and warped HCS compressed in the sheath, while the contribution of shock acceleration to the latter cannot be excluded.

A Study of the Performances of Widely Used External Magnetic Field Models in the Outer Zone of the Earth's Radiation Belts by Comparing the Field Observations From Van Allen Probe‐A and the Model Estimations

AbstractUsing magnetic field observations from Van Allen Probe‐A (VAP‐A), we evaluated the performances of 13 widely used external magnetic field models in the Earth's outer radiation belt region in detail. It is shown that later models tend to match observations better than earlier models except for T03s, which has a top performance similar to the latest TA16_RBF model. Additionally, in its applicable domain from quiet to moderately disturbed geomagnetic conditions, T02 has comparable performance to T03s. In the dusk, dawn and night sectors, highly stretched magnetic fields are seen in both the observations and model output between LmIGRF ∼5.7 and 6.1, which suggests the existence of steep radial gradients in the plasma pressures inside the outer belt region. The contributions from the currents located in the dusk sector during a disturbed period, such as the partial ring current and the substorm current wedge, are not adequately accounted for by the models, and the contribution of field‐aligned currents may also be underestimated. The results of this study will help select reliable external field models for future radiation belt studies and help assess uncertainties caused by the selected models. In addition, detailed analysis of the field components depicted by the empirical models could shed light on understanding the contributions from different current systems in this region.

MMS Observation of the Hall Field in an Asymmetric Magnetic Reconnection with Guide Field

Abstract In this paper, we investigate the structure of out-of-plane magnetic field in the reconnection event observed by Magnetospheric Multiscale Mission at the magnetopause of the Earth magnetosphere on 2015 October 21. We find that the perturbation of out-of-plane magnetic field in this event is different from previous observations of the quadrupolar Hall magnetic field. The distinct out-of-plane magnetic field is interpreted as a part of the hexapolar Hall magnetic field obtained in a recent simulation of asymmetric reconnection with the guide field. This is significant evidence of the hexapolar Hall magnetic field in collisionless magnetic reconnection from the observations in the magnetosphere. High-resolution measurements of particle and field are used to provide a comprehensive description of the features of the hexapolar Hall magnetic field. The results from this study offer an insight into the Hall effect in collisionless magnetic reconnection.

Visualization of magnetic fields with cylindrical vector beams in a warm atomic vapor

We propose and demonstrate an experimental implementation for the observation of magnetic fields from spatial features of absorption profiles in a warm atomic vapor. A radially polarized vector beam that traverses atomic vapor will generate an absorption pattern with a petal-like structure by the mediation of a transverse magnetic field (TMF). The spatial absorption pattern rotates when the azimuthal angle of the TMF is changed, while its contrast decreases when the longitudinal component of the magnetic field increases. By analyzing the intensity distribution of the transmitted pattern, we can determine the magnetic field strength. Our work provides a framework for investigating 3D magnetic field distributions based on atoms.

Dawn‐Dusk Confinement of Magnetic Reconnection Site in the Near‐Earth Magnetotail and Its Implication for Dipolarization and Substorm Current System

AbstractThe dawn‐dusk confinement of magnetic reconnection site in the near‐Earth magnetotail is established on the basis of Geotail observations. Geotail has made more than 50 encounters with magnetic reconnection in association with the onset of substorms in the near‐Earth magnetotail at radial distances of 20–30 RE in the period of 1994–2019. Ground magnetic field observations are examined for these events, and geosynchronous spacecraft observations are investigated for a limited number of cases. The magnetic reconnection site is located in the upward (from the ionosphere to the tail) field‐aligned current part of large‐scale substorm current system derived from ground midlatitude magnetic variations. The site is confined to the localized dawn‐dusk extent of the 1‐hr local time, just west of the center of the large‐scale substorm current system. The short dawn‐dusk length of the X‐line implies that magnetic reconnection inherently proceeds as the two‐dimensional dynamics in the magnetotail meridional plane. Rapid dipolarization with upward field‐aligned currents occurs at geosynchronous altitude near the meridian of the magnetic reconnection site. This study demonstrates that rapid dipolarization in the inner magnetosphere is produced with earthward outflows from magnetic reconnection and that intense upward field‐aligned currents are a direct consequence of magnetic reconnection.

Improvements of the Longitudinal Magnetic Field Measurement from the Solar Magnetic Field Telescope at the Huairou Solar Observing Station

The weak-field approximation, implying a linear relationship between Stokes- $V/I$ and the longitudinal magnetic field [ $B_{\Vert }$ ], often suffers from saturation observed in strong magnetic-field regions such as sunspot umbrae. In this work, we seek to improve the magnetic-field observations carried out by the Solar Magnetic Field Telescope (SMFT) at the Huairou Solar Observing Station, China. We propose using a non-linear relationship between Stokes- $V/I$ and $B_{\Vert }$ to derive the magnetic field. To determine the form of the relationship, we perform a cross-calibration of the observed SMFT data and magnetograms provided by the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory. The algorithm for the magnetic-field derivation is described in detail. We show that using a non-linear relationship between Stokes- $V/I$ and $B_{\Vert }$ allows us to eliminate magnetic-field saturation inside the sunspot umbra. The proposed technique enables one to enhance the reliability of the SMFT magnetic-field data obtained even long before the space-based instrumentation era, since 1987.

Magnetic Structure in Successively Erupting Active Regions: Comparison of Flare-Ribbons With Quasi-Separatrix Layers

This paper studies the magnetic topology of successively erupting active regions (ARs) 11,429 and 12,371. Employing vector magnetic field observations from Helioseismic and Magnetic Imager, the pre-eruptive magnetic structure is reconstructed by a model of non-linear force-free field (NLFFF). For all the five CMEs from these ARs, the pre-eruptive magnetic structure identifies an inverse-S sigmoid consistent with the coronal plasma tracers in EUV observations. In all the eruption cases, the quasi-separatrix layers (QSLs) of large Q values are continuously enclosing core field bipolar regions in which inverse-S shaped flare ribbons are observed. These QSLs essentially represent the large connectivity gradients between the domains of twisted core flux within the inner bipolar region and the surrounding potential like arcade. It is consistent with the observed field structure largely with the sheared arcade. The QSL maps in the chromosphere are compared with the flare-ribbons observed at the peak time of the flares. The flare ribbons are largely inverse-S shape morphology with their continuity of visibility is missing in the observations. For the CMEs in the AR 12371, the QSLs outline the flare ribbons as a combination of two inverse J-shape sections with their straight parts being separated. These QSLs are typical with the weakly twisted flux rope. Similarly, for the CMEs in the AR 11429, the QSLs are co-spatial with the flare ribbons both in the middle of the PIL and in the hook sections. In the frame work of standard model of eruptions, the observed flare ribbons are the characteristic of the pre-eruptive magnetic structure being sigmoid which is reproduced by the NLFFF model with a weakly twisted flux rope at the core.

Three-Dimensional MHD Modeling of Interplanetary Solar Wind Using Self-Consistent Boundary Condition Obtained from Multiple Observations and Machine Learning

Three-dimensional (3-d) magnetohydrodynamics (MHD) modeling is a key method for studying the interplanetary solar wind. In this paper, we introduce a new 3-d MHD solar wind model driven by the self-consistent boundary condition obtained from multiple observations and the Artificial Neural Network (ANN) machine learning technique. At the inner boundary, the magnetic field is derived using the magnetogram and potential field source surface extrapolation; the electron density is derived from the polarized brightness (pB) observations, the velocity can be deduced by an ANN using both the magnetogram and pB observations, and the temperature is derived from the magnetic field and electron density by a self-consistent method. Then, the 3-d interplanetary solar wind from CR2057 to CR2062 is modeled by the new model with the self-consistent boundary conditions. The modeling results present various observational characteristics at different latitudes, and are in better agreement with both the OMNI and Ulysses observations compared to our previous MHD model based only on photospheric magnetic field observations.

Using Observations of Solar Vector Magnetic Field from Dual View Points to Remove the 180[formula omitted] Ambiguity

With Solar Orbiter (SO) being put into successful operational observation, solar magnetic observation has entered the era of remote sensing from dual view points. In this paper, we carried out a simulation of correcting the 180∘ ambiguity of transverse magnetic field with magnetograms from dual view points using an analytical formula as well as the observations made by the Helioseismic and Magnetic Imager (HMI). Magnetograms of a small mature sunspot at different times were used to simulate magnetograms from dual view points. We find that in order to correct the 180∘ ambiguity of the vector magnetograms, it is sufficient to have a line-of-sight magnetogram from another view point to help to judge the direction of the transverse magnetic field. For the measuring accuracy of HMI, we estimate that a ∼ 30∘ angle formed from two observational points is the smallest angle to correct the 180∘ ambiguity around the place with the magnetic field strength of < 50 Gs. Correction for weaker magnetic fields surely needs larger separation angles, but considering projection effect, we propose that separation angles of ∼ 30∘ are the optimal angles for future space missions with the scientific aim of correcting the 180∘ ambiguity of vector magnetograms.