Three-dimensional Magnetic Field Structure Research Articles

Magnetic Fields in the Southern Coalsack and Beyond

Starlight polarimetry, when combined with accurate distance measurements, allows for exploration of the three-dimensional structure of local magnetic fields in great detail. We present optical polarimetric observations of stars in and close to the Southern Coalsack, taken from the Interstellar Polarization Survey. Located in five fields of view approximately 0.°3 × 0.°3 in size, these data represent the highest density of optical polarimetric observations in the Southern Coalsack to date. Using these data, combined with accurate distances and extinctions based on Gaia data, we are able to characterize the magnetic field of the Coalsack and disentangle contributions to the polarization caused by the Southern Coalsack and a background structure. For the Southern Coalsack, we find an average magnetic field orientation of θ ∼ 75° with respect to the Galactic north pole and an average plane-of-sky magnetic field strength of approximately B POS = 10 μG, using the Davis–Chandrasekhar–Fermi method. These values are in agreement with some earlier estimates of the Coalsack’s magnetic field. In order to study the distant structure, we introduce a simple method to separate and isolate the polarization of distant stars from foreground contribution. For the distant structure, which we estimate to be located at a distance of approximately 1.3–1.5 kpc, we find an average magnetic field orientation of θ ∼ 100° and estimate a field strength of B POS ∼ 10 μG, although this will remain highly uncertain until the precise nature of the distant structure can be uncovered.

Poloidal magnetic field in the dense plasma focus

Existence of an axial (poloidal) component of magnetic field in the dense plasma focus has been inferred using multiple diagnostics in many laboratories since 1979. It has not received much attention because its origin as well as role in plasma focus physics was unclear till recently. Recent discovery of long-lasting neutron emission perpendicular to the axis in PF-1000 and neutron fluence ratio (end/side) less than unity in Gemini shows that azimuthally accelerated and radially confined deuterons play an observable role in fusion reactions. A spontaneously generated poloidal magnetic field can provide both the azimuthal electric field necessary for acceleration and radial confinement of the ions being accelerated in the acceleration zone. A comprehensive survey of plasma focus research also confirms the role of spontaneously self-organized plasma objects in the fusion reaction process where their three-dimensional magnetic field structure provides a mechanism for accelerating and trapping ions making them repeatedly pass through a dense plasma target. With emerging appreciation of the likely role of the axial magnetic field in plasma focus neutron emission, it becomes imperative to consider models for its origin. This Letter proposes a partial theory of growth of the axial (poloidal) magnetic field via a simple dynamo, with the geomagnetic field as the seed, which converts the kinetic energy of the plasma into energy of the poloidal magnetic field. This theory leads to an experimentally testable proposition.

Three-dimensional simulation of electron extraction process and optimization of magnetic field based on multi-aperture structure of negative hydrogen ion source

In most of the simulations of the extraction region of negative hydrogen ion sources, the single-aperture simulation is often adopted by researchers to study the plasma phenomenon due to its small simulation domain and short calculation time. However, due to the complex three-dimensional magnetic field structure in the extraction region of the negative hydrogen ion source, the single aperture often does not meet the periodicity. In this paper, the complex three-dimensional magnetic field topology is established. The magnetic field includes the magnetic filter field and the magnetic deflection field. The influence of the plasma sheath is taken into account. The electron extraction process in the multi-aperture structure of the extraction region of a negative hydrogen ion source is numerically calculated using the PIC method. Besides, the magnetic field structure is optimized. Ultimately, the electron beam uniformity near the plasma grid is improved effectively, which has certain guiding significance for engineering application.

Formation of Solar Quiescent Coronal Loops through Magnetic Reconnection in an Emerging Active Region

Abstract Coronal loops are the building blocks of solar active regions. However, their formation mechanism remains poorly understood. Here we present direct observational evidence for the formation of coronal loops through magnetic reconnection as new magnetic fluxes emerge into the solar atmosphere. Extreme-ultraviolet observations by the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO) clearly show the newly formed loops following magnetic reconnection within a plasma sheet. Formation of the loops is also seen in the Hα line-core images taken by the New Vacuum Solar Telescope. Observations from the Helioseismic and Magnetic Imager on board SDO show that a positive-polarity flux concentration moves toward a negative-polarity one with a speed of ∼0.4 km s−1 before the formation of coronal loops. During the loop formation process, we found signatures of flux cancellation and subsequent enhancement of the transverse field between the two polarities. The three-dimensional magnetic field structure reconstructed through a magnetohydrostatic model shows field lines consistent with the loops in AIA images. Numerous bright blobs with an average width of 1.37 Mm appear intermittently in the plasma sheet and move upward with a projected velocity of ∼114 km s−1. The temperature, emission measure, and density of these blobs are about 3 MK, 2.0 × 1028 cm−5, and 1.2 × 1010 cm−3, respectively. A power spectral analysis of these blobs indicates that the observed reconnection is likely not dominated by a turbulent process. We have also identified flows with a velocity of 20–50 km s−1 toward the footpoints of the newly formed coronal loops.

Diagnostics of plasma jets in the solar corona

The paper discusses the diagnostics of plasma jets in the solar corona with the use of data from modern space- and ground-based telescopes observing the Sun in the extreme ultraviolet (EUV) and micro- wave bands. We examine observational parameters of EUV and radio emission in events associated with plasma jets, depending on the mechanism of formation, initiation conditions, and evolution of the jets. The opportunities provided by the study of plasma jets, which relies on simultaneous observations in different bands, are highlighted. For a number of jets, we have measured their primary parameters; and in this paper we present preliminary results of statistical processing of the data obtained. Microwave observations of several specific events, made by ground-based instruments RATAN-600, SRH, and Nobeyama Radioheliograph, are considered in detail. The diagnostic capabilities of these instruments for studying coronal jets are shown. To analyze the three-dimensional structure of the coronal magnetic field, we have used SDO/HMI data, which allowed for the reconstruction of the field in the lower corona. The information gained is compared with the results of diagnostics of the magnetic field at the base of the corona according to RATAN-600 data. The purpose of the methods developed is to determine the physical mechanisms responsible for the generation, collimation, and dynamics of plasma jets in the solar atmosphere.

Диагностика плазменных струй в короне Солнца

The paper discusses the diagnostics of plasma jets in the solar corona with the use of data from modern space- and ground-based telescopes observing the Sun in the extreme ultraviolet (EUV) and micro- wave bands. We examine observational parameters of EUV and radio emission in events associated with plasma jets, depending on the mechanism of formation, initiation conditions, and evolution of the jets. The opportunities provided by the study of plasma jets, which relies on simultaneous observations in different bands, are highlighted. For a number of jets, we have measured their primary parameters; and in this paper we present preliminary results of statistical processing of the data obtained. Microwave observations of several specific events, made by ground-based instruments RATAN-600, SRH, and Nobeyama Radioheliograph, are considered in detail. The diagnostic capabilities of these instruments for studying coronal jets are shown. To analyze the three-dimensional structure of the coronal magnetic field, we have used SDO/HMI data, which allowed for the reconstruction of the field in the lower corona. The information gained is compared with the results of diagnostics of the magnetic field at the base of the corona according to RATAN-600 data. The purpose of the methods developed is to determine the physical mechanisms responsible for the generation, collimation, and dynamics of plasma jets in the solar atmosphere.

Faraday Dispersion Function of Disk Galaxies with Axisymmetric Global Magnetic Fields. I.

Abstract Faraday tomography is a novel method to probe the three-dimensional structure of magnetic fields of polarized radio sources. In this paper, we investigate the intrinsic Faraday dispersion function (FDF) of disk galaxies extending a simple analytic model of galactic magnetic fields developed in Ideguchi et al. The model consists of axisymmetric coherent fields and turbulent fields, and we consider the effects of inclination, the relative amplitude of coherent and turbulent magnetic fields, and the pitch angle of coherent fields. Our simple model makes it easy to obtain a physical interpretation of FDFs and helps us understand observational results. We find that FDFs generally have two peaks when galaxies are observed with nonzero inclination and the gap between the two peaks, their relative heights, and their widths are dependent on the model parameters. In particular, the gap is strongly dependent on the inclination angle and typically varies by a factor of two when we consider the inclination of 10°–60°, while the relative height varies by less than 20%. These findings provide us with the important lesson that the presence of two peaks in intrinsic FDFs does not necessarily imply the presence of two separate radio sources within a beam and they allow us to estimate the galactic parameters.

Extrapolation of Three-dimensional Magnetic Field Structure in Flare-productive Active Regions with Different Initial Conditions

Abstract Nonlinear force-free field (NLFFF) modeling has been extensively used as a tool to infer three-dimensional (3D) magnetic field structure. In this study, the dependency of the NLFFF calculation with respect to the initial guess of the 3D magnetic field is investigated. While major parts of the previous studies used the potential field as the initial guess in NLFFF modeling, we adopt linear force-free fields with different constant force-free alpha as the initial guesses. This method enables us to investigate the uniqueness of the magnetic field obtained by the NLFFF extrapolation with respect to the initial guess. The dependence of the initial conditions on NLFFF extrapolation is smaller in the strong magnetic field region. Therefore, the magnetic field at lower heights (<10 Mm) tends to be less affected by the initial conditions (correlation coefficient C > 0.9 with different initial conditions); although, the Lorentz force is concentrated at lower heights.

Three-dimensional magnetic field structure of a flux-emerging region in the solar atmosphere

We analyze high-resolution spectropolarimetric observations of a flux-emerging region (FER) in order to understand its magnetic and kinematic structure. Our spectropolarimetric observations in the He I 10830 Å spectral region of a FER were recorded with GRIS at the 1.5 m aperture GREGOR telescope. A Milne–Eddington-based inversion code was employed to extract the photospheric information of the Si I spectral line, whereas the He I triplet line was analyzed with the Hazel inversion code, which takes into account the joint action of the Hanle and the Zeeman effects. The spectropolarimetric analysis of the Si I line reveals a complex magnetic structure near the vicinity of the FER, where a weak (350–600 G) and horizontal magnetic field was observed. In contrast to the photosphere, the analysis of the He I triplet presents a smooth variation of the magnetic field vector (ranging from 100 to 400 G) and velocities across the FER. Moreover, we find supersonic downflows of ∼40 km s−1 appearing near the foot points of loops connecting two pores of opposite polarity, whereas strong upflows of 22 km s−1 appear near the apex of the loops. At the location of supersonic downflows in the chromosphere, we observed downflows of 3 km s−1 in the photosphere. Furthermore, nonforce-free field extrapolations were performed separately at two layers in order to understand the magnetic field topology of the FER. We determine, using extrapolations from the photosphere and the observed chromospheric magnetic field, that the average formation height of the He I triplet line is ∼2 Mm from the solar surface. The reconstructed loops using photospheric extrapolations along an arch filament system have a maximum height of ∼10.5 Mm from the solar surface with a foot-point separation of ∼19 Mm, whereas the loops reconstructed using chromospheric extrapolations reach around ∼8.4 Mm above the solar surface with a foot-point separation of ∼16 Mm at the chromospheric height. The magnetic topology in the FER suggests the presence of small-scale loops beneath the large loops. Under suitable conditions, due to magnetic reconnection, these loops can trigger various heating events in the vicinity of the FER.

Multi-diagnostic analysis of plasma filaments in the island divertor

Filaments or blobs are well known structures in turbulence in magnetic fusion devices, they are considered to be the major cross-transport channel in the scrape off layer. They originate at the last closed magnetic flux surface and propagate out on the low field side of toroidal devices due to polarization in the curved magnetic field. The Wendelstein 7-X stellarator has a complex three-dimensional magnetic field structure and additionally the plasma is bounded by a chain of magnetic islands, forming an island divertor. After the first observation of filaments in Wendelstein 7-X with video cameras a multi-diagnostic study is presented in this paper to reveal their 3D structure and dynamics. Filaments are seen to be born at the edge and, at least in some cases, seen to extend to up to 4 toroidal turns. After moving radially out a few cm they enter the edge island. Here they disappear from the equatorial plane and about 200 microseconds later reappear on the outboard side of the island. A long-wavelength (∼20–30 cm) quasi coherent mode is observed in both regions where filaments appear. The similarities and differences between the filaments seen in W7-X and other devices are discussed. Possible explanations for this strange radial propagation are considered, together with the likely role of filaments in the edge and island density profile.

A new method to trace three-dimensional magnetic field structure within molecular clouds using dust polarization

Abstract The complete three-dimensional structure of the magnetic field within molecular clouds has eluded determination despite its high value in determining controlling factors in the star formation process, as it cannot be directly probed observationally. Considering that inclination of the magnetic field relative to the plane of sky is one of the major sources of depolarization of thermal emission from dust in molecular clouds, we propose here a new method to estimate the inclination angle of the cloud-scale magnetic field based on the statistical properties of the observed polarization fraction. We test this method using a series of Monte Carlo experiments and find that the method works well, provided that deviations of magnetic field direction from the averaged values are small. When applied to synthetic observations of numerical simulations of star-forming clouds, our method gives fairly accurate measurements of the mean magnetic field inclination angle (within 10°–25°), which can further be improved if we restrict our technique to regions of low dispersion in polarization angles ${\cal S}$. We tested our method on the BLASTPol polarimetric observations of the Vela C molecular cloud complex, which suggests that the magnetic field of Vela C has a high inclination angle (∼60°), consistent with previous analyses.

Distortion of Magnetic Fields in a Starless Core. III. Polarization–Extinction Relationship in FeSt 1-457

Abstract The relationship between dust polarization and extinction was determined for the cold dense starless molecular cloud core FeSt 1-457 based on the background star polarimetry of dichroic extinction at near-infrared wavelengths. Owing to the known (three-dimensional) magnetic field structure, the observed polarizations from the core were corrected by considering (a) the subtraction of the ambient polarization component, (b) the depolarization effect of inclined distorted magnetic fields, and (c) the magnetic inclination angle of the core. After these corrections, a linear relationship between polarization and extinction was obtained for the core in the range up to A V ≈ 20 mag. The initial polarization versus extinction diagram changed dramatically after the corrections of (a) to (c), with the correlation coefficient being refined from 0.71 to 0.79. These corrections should affect the theoretical interpretation of the observational data. The slope of the finally obtained polarization–extinction relationship is , which is close to the statistically estimated upper limit of the interstellar polarization efficiency. This consistency suggests that the upper limit of interstellar polarization efficiency might be determined by the observational viewing angle toward polarized astronomical objects.

Resolved magnetic dynamo action in the simulated intracluster medium

Faraday rotation and synchrotron emission from extragalactic radio sources give evidence for the presence of magnetic fields extending over ~Mpc scales. However, the origin of these fields remains elusive. With new high-resolution grid simulations we studied the growth of magnetic fields in a massive galaxy cluster that in several aspects is similar to the Coma cluster. We investigated models in which magnetic fields originate from primordial seed fields with comoving strengths of 0.1 nG at redshift z=30. The simulations show evidence of significant magnetic field amplification. At the best spatial resolution (3.95 kpc), we are able to resolve the scale where magnetic tension balances the bending of magnetic lines by turbulence. This allows us to observe the final growth stage of the small-scale dynamo. To our knowledge this is the first time that this is seen in cosmological simulations of the intracluster medium. Our mock observations of Faraday Rotation provide a good match to observations of the Coma cluster. However, the distribution of magnetic fields shows strong departures from a simple Maxwellian distribution, suggesting that the three-dimensional structure of magnetic fields in real clusters may be significantly different than what is usually assumed when inferring magnetic field values from rotation measure observations.

Investigation of heat flux deposition on divertor target on the Large Helical Device with EMC3-EIRENE modelling

The measured divertor heat flux profiles are compared to the EMC3-EIRENE simulations for two different times of an LHD discharge, corresponding to higher and lower edge temperatures. The relation between the three-dimensional magnetic field structure and the heat flux distributions on the divertor has been analysed. The modelled heat flux for the lower plasma temperature case has a better agreement with the experimental result obtained by the Langmuir probes, which shows a qualitative reproduction of the experimental profile shape. However, the heat flux distribution for the high plasma temperature case shows a different behaviour between the simulation results and the experimental measurements. The detailed analysis of the heat flux distribution for the higher temperature case which has a larger discrepancy has been performed, both quantitatively and qualitatively. The radiation of the eroded impurity from divertor target plates has a minor effect on the heat flux distribution. Non-uniform cross-field transport coefficients are used in the simulations and its impact on the heat flux distributions is discussed for the case of the high plasma temperature.

The magnetic field application for the gas discharge plasma control in processes of surface coating and modification

In this paper the method of magnetic field application to control the gas discharge plasma effect on the various surfaces in processes of surface coating and modification is considered. The magnetic field directed perpendicular to the direction of electric current in the gas discharge plasma channel is capable to reject this plasma channel due to action of Lorentz force on the moving electrically charged particles [1,2]. The three-dimensional spatial structure of magnetic field is created by system of necessary quantity of the magnets located perpendicular to the direction of course of electric current in the gas-discharge plasma channel. The formation of necessary spatial distribution of magnetic field makes possible to obtain a required distribution of plasma parameters near the processed surfaces. This way of the plasma channel parameters spatial distribution management is the most suitable for application in processes of plasma impact on a surface of irregular shape and in cases when the selective impact of plasma on a part of a surface of a product is required. It is necessary to apply automated computer management of the process parameters [3] to the most effective plasma impact.

Performance improvement of two-dimensional EUV spectroscopy based on high-frame-rate CCD and signal normalization method in Large Helical Device

In the Large Helical Device (LHD), two-dimensional (2D) distribution of edge impurity line emissions from the ergodic layer with a three-dimensional (3D) magnetic field structure has been observed in the wavelength range of 30–650 Å by horizontally scanning a space-resolved extreme ultraviolet (EUV) spectrometer during a steady phase in electron cyclotron heating (ECH) and ion cyclotron range of heating (ICRF) discharges with long pulse duration (τd ≥ 10 s). The 2D distribution of impurity line emissions can be measured at the upper or lower half in the full vertical range of LHD plasmas by a single horizontal scan. The performance of 2D EUV spectroscopy, however, was not sufficient for discussing the impurity transport in the ergodic layer from the viewpoints of the quality of 2D images and the requirement of long pulse discharges. The 2D EUV spectrometer is therefore modified by installing a high-frame-rate charge-coupled detector (CCD) and increasing its horizontal scanning speed. As a result, the quality of 2D images is significantly improved with increased horizontal spatial resolution, and then the 2D measurement is also possible for neutral beam injection (NBI) discharges with short pulse duration (τd ∼ 3 s). In addition, temporal and shot-by-shot intensity variations in the edge EUV emission are significantly reduced by applying a signal normalization method using another EUV spectrometer with high time resolution. A 0.5 µm poly(ethylene terephthalate) (PET) filter is also installed in front of an entrance slit of the space-resolved EUV spectrometer. The spike noise originating from high-energy neutral particles, which are enhanced in low-density NBI discharges, has been successfully reduced. Typical examples of the 2D distribution of impurity line emissions with improved quality are presented for several impurity species.

Electrodynamics of a ring-shaped spiral resonator

We present analytical, numerical, and experimental investigations of electromagnetic resonant modes of a compact monofilar Archimedean spiral resonator shaped in a ring, with no central part. Planar spiral resonators are interesting as components of metamaterials for their compact deep-subwavelength size. Such resonators couple primarily to the magnetic field component of the incident electromagnetic wave, offering properties suitable for magnetic meta-atoms. Surprisingly, the relative frequencies of the resonant modes follow the sequence of the odd numbers as f1:f2:f3:f4… = 1:3:5:7…, despite the nearly identical boundary conditions for electromagnetic fields at the extremities of the resonator. In order to explain the observed spectrum of resonant modes, we show that the current distribution inside the spiral satisfies a particular Carleman type singular integral equation. By solving this equation, we obtain a set of resonant frequencies. The analytically calculated resonance frequencies and the current distributions are in good agreement with experimental data and the results of numerical simulations. By using low-temperature laser scanning microscopy of a superconducting spiral resonator, we compare the experimentally visualized ac current distributions over the spiral with the calculated ones. Theory and experiment agree well with each other. Our analytical model allows for calculation of a detailed three-dimensional magnetic field structure of the resonators.

Probe measurements of the three-dimensional magnetic field structure in a rotating magnetic field sustained field-reversed configuration

A translatable three-axis probe was constructed and installed on the translation, confinement, and sustainment upgrade (TCSU) experiment. With ninety windings, the probe can simultaneously measure Br, Bθ, and Bz at 30 radial positions, and can be placed at any desired axial position within the field reversed configuration (FRC) confinement chamber. Positioning the probe at multiple axial positions and taking multiple repeatable shots allows for a full r-z map of the magnetic field. Measurements were made for odd-parity rotating magnetic field (RMF) antennas and even-parity RMF. The steady state data from applying a 10 kHz low pass filter used in conjunction with data at the RMF frequency yields a map of the full 3D rotating field structure. Comparisons will be made to the 3D magnetic structure predicted by NIMROD simulations, with parameters adjusted to match that of the TCSU experiments. The probe provides sufficient data to utilize a Maxwell stress tensor approach to directly measure the torque applied to the FRC's electrons, which combined with a resistive torque model, yields an estimate of the average FRC resistivity.

Magnetic fields and polarization in AGN jets

In the literature there is now a wealth of images of AGN in both linear and circular polarization at milliarcsecond resolution of many sources at multiple epochs and wavelengths. This review is a broad overview of our current state of knowledge of the polarization properties of AGN jets, and of what we can infer about the structure of their magnetic fields and the distribution of Faraday rotating material, and also what is premature to infer. We suggest that while many of the observations of transverse rotation measure gradients may be correct, they have in general been observed with neither enough resolution nor sensitivity to be incontrovertible. Fortunately, this could be remedied using the new broad-band receivers on the VLBA. We also argue that while a transverse rotation measure gradient is a strong indicator of a toroidal component of magnetic field, it does not necessarily imply a helical magnetic field. In jets where the dominant field component appears to be parallel to the jet, it more likely consists of sheared loops or compressed random fields that are not vector ordered. Finally, we draw attention to the power of imaging in all four Stokes parameters at multiple frequencies to constrain the three-dimensional magnetic field structure and the particle content of jets and measure fundamental physical properties. The linear polarization of the radio emission from AGN jets (assumed to be synchrotron radiation) tells us about the structure and order of the magnetic field. Especially on parsec scales, these are intimately related to the launching, acceleration and collimation of the jets (see the review by D. Meier, these proceedings). Monitoring reveals the evo- lution of the magnetic field, and the formation and dissi- pation of shocks. Faraday rotation measurements are an important diagnostic of thermal electrons (and lower en- ergy relativistic electrons) inside and outside the jet, and have revealed a torroidal component of the magnetic field in some sources. Observations of circular polarization can tell us about the positron fraction in the relativistic electron population and the vector-ordering of the magnetic field. The latter then permits an estimate of the net magnetic flux in the jet, and hence (because it is a conserved quantity) the magnetic flux at the central black hole-accretion disk system. It should be noted that none of the physical pa- rameters listed in this paragraph can be gleaned from total intensity images. With the advent of the VLBA in 1993, polarimetry at milliarcsecond resolution came of age. Earlier polariza- tion results, and some of the first polarization results from the VLBA, were discussed in the 1997 Annual Reviews article by Zensus (1). A conference celebrating the 10th birthday of the VLBA (2) featured 18 papers devoted to the polarization properties of AGN on parsec scales. These in- cluded observations of rotation measures, transverse gra-

Influence of frame-dragging on magnetic null points near rotating black holes

Understanding the mechanisms of particle acceleration from the vicinity of black holes poses a challenge. Electromagnetic effects are thought to be a prime suspect, but details still need an explanation. To this end, we study a three-dimensional structure of oblique magnetic fields near a rotating black hole in vacuum. It has been proposed that such a setup can lead to efficient acceleration when plasma is injected near a magnetic null point. We focus our attention especially on the magnetic field in the immediate neighborhood of the magnetic null point, which was previously shown to occur in the equatorial plane. By employing the line integral convolution method, we visualize the magnetic field lines and explore the electric lines rising out of the equatorial plane. We show the magnetic field structure near the boundary of ergosphere, depending on the spin of the black hole. Electric field develops a non-vanishing component passing through the magnetic null point and ensuring efficient acceleration of charged particles from this particular location near the horizon. We also examine the effect of translatory boost on the field lines. Similarly to the frame-dragging by rotation, the linear motion carries field lines along with the black hole. The position of the magnetic null point recedes from the black hole horizon as the spin parameter increases. For the extreme value of a = 1, the null point can occur outside the ergosphere.