Magnetic Flux Loops Research Articles

Retraction Note: Comparative Measurements of the Asymmetry Factor in Tokamaks Using the Magnetic Probes, Poloidal and Toroidal Flux Loops

Retraction Note: Comparative Measurements of the Asymmetry Factor in Tokamaks Using the Magnetic Probes, Poloidal and Toroidal Flux Loops

Ion‐Scale Magnetic Flux Ropes and Loops in Earth's Magnetotail: An Automated, Comprehensive Survey of MMS Data Between 2017 and 2022

AbstractMagnetic reconnection is a critically important process in defining the dynamics and energy transport within plasma environments. In near‐Earth space we may track where and when reconnection occurs by identifying associated coherent magnetic structures. On a global scale these structures facilitate the flow of mass and magnetic flux into, within, and out of the magnetospheric system, whilst contributing to local plasma heating. In the Earth's magnetotail there are two similar structures we identify in this work: magnetic flux ropes and loops. We present a robust, automated and model independent method by which encounters with such structures may be identified using the Magnetospheric Multiscale (MMS) mission. The magnetic structures are first identified through their magnetic field signatures at a single spacecraft (MMS1), including checks on the local minimum variance coordinate system. Next, the local curvature of the magnetic field is evaluated with all four MMS spacecraft. Finally, the plasma conditions are checked to ensure that the interpretation is fully self‐consistent. We evaluate the data obtained by MMS between 2017 and 2022. In total we find 181 self‐consistent magnetic flux ropes and 263 magnetic loops, which fit an exponentially decaying size distribution with a scale size comparable to the ion gyroradius (∼0.23 RE/1,400 km). If we remove the requirements on the plasma properties of the structure, we locate 648 potential magnetic flux ropes and 1,073 magnetic loops. The magnetic structures are preferentially observed in the pre‐midnight region of the magnetotail, with most identifications occurring beyond 20 RE. All catalogs are provided to the community.

Topological Fracton Quantum Phase Transitions by Tuning Exact Tensor Network States.

Gapped fracton phases of matter generalize the concept of topological order and broaden our fundamental understanding of entanglement in quantum many-body systems. However, their analytical or numerical description beyond exactly solvable models remains a formidable challenge. Here we employ an exact 3D quantum tensor-network approach that allows us to study a Z_{N} generalization of the prototypical X cube fracton model and its quantum phase transitions between distinct topological states via fully tractable wave function deformations. We map the (deformed) quantum states exactly to a combination of a classical lattice gauge theory and a plaquette clock model, and employ numerical techniques to calculate various entanglement order parameters. For the Z_{N} model we find a family of (weakly) first-order fracton confinement transitions that in the limit of N→∞ converge to a continuous phase transition beyond the Landau-Ginzburg-Wilson paradigm. We also discover a line of 3D conformal quantum critical points (with critical magnetic flux loop fluctuations) which, in the N→∞ limit, appears to coexist with a gapless deconfined fracton state.

A model order reduction of hysteretic eddy-current fields in electric machines using Cauer ladder network method

This study aims to establish a hysteretic model order reduction method for electric machines using the Cauer ladder network (CLN) method. The first inductor of the CLN represents the hysteresis effect, which is computed using the scalar play model identified from the static I–ϕ (current–magnetic flux) loops. An iron-core inductor was analyzed, and pulse-width modulation (PWM) voltage input was applied to the coil. The proposed method yielded results that agreed with the transient finite element (FE) analysis and effectively reduced the computation time.

The rotation rate of solar active and ephemeral regions – II. Temporal variations of the rotation rates

ABSTRACT Systematic studies of the rotation rate of sunspot groups using white light images yield controversial results on the variations of the rotation rate: sunspot groups were found to either accelerate or decelerate systematically. This disagreement might be related to shortcomings of the method used to probe the rotation rate of sunspot groups. In contrast to previous works, in this study we use magnetic field maps to analyse the variations of the rotation rate of active regions. We found that an active region may exhibit either acceleration or deceleration during the emergence, while the rotation rate remains almost unchanged during decay. Hence, we suppose that there is no systematic geometrical inclination to the radial direction of the apex of the subsurface magnetic flux loop forming an active region. A thorough comparison of the rotation rate of unipolar and bi/multipolar active regions revealed no significant changes in the rotation rate of decaying active regions. In contrast to previous works, we presume the rotation rate to remain constant (within the expected uncertainties) during the evolution of an active region after emergence.

Design of Routing of In-Vessel Diagnostic Signals for RFXmod2

Reversed Field eXperiment modified 2 (RFXmod2) is the upgraded version of the experiment RFXmod, a toroidal fusion device that can be operated both as a Reversed Field Pinch and as a Tokamak. This experiment is hosted by Consorzio RFX, Padua, Italy, and has a major radius <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R=2$ </tex-math></inline-formula> m and a minor radius <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$a=0.5$ </tex-math></inline-formula> m. The upgrade of the previous machine consists mainly on a larger vacuum vessel and a more efficient active and passive plasma control system. Another important improvement involves the already wide set of in-vessel diagnostics, which includes now a large variety of sensors: electrostatic (single-pin, five-pin, 12-pin, ball pen), magnetic (flux loops, pick-up coils, saddle probes, halo shunts), mechanical (strain gauges), and thermal (thermocouples), for a total of about 5000 signals. The technological relevance of RFXmod2 is related indeed to the development of advanced plasma diagnostics and control systems. This work is focused on the integration of all the in-vessel diagnostics, especially from the point of view of electromagnetic compatibility and wire routing. In fact, the presence of several different families of sensors, having considerable differences in voltage and current output, together with the limited space in which those signal have to be routed, poses a challenging problem of electromagnetic compatibility. To solve this problem, the non-compatibilities between different types of signals were identified, and a series of criteria were drawn to design the cable routing of the whole machine. A preliminary and schematic routing map was developed, then a specific cable tray was designed and tested on a mock-up. This article describes all the activities related to the design of the wiring harness for the in-vessel diagnostics for RFXmod2: the signal classification, the electromagnetic compatibility problem, and the design of wire routing and cable trays.

Upgrade of the magnetic diagnostic system for restart of HT-6M operation

The HT-6M tokamak at the Thailand Institute of Nuclear Technology has been restarted. In order to ensure the smooth breakdown of plasma and obtain plasma discharge parameters, optimization of the poloidal field coils and upgrade of the magnetic diagnostics are described in this article. A perfect null field (stray field in the main chamber < 10 G) is obtained using an ohmic heating field. To obtain important information about the plasma, an external magnetic diagnostics system is designed and calibrated, including a Rogowski coil (measuring plasma current), a magnetic probe (measuring external field), diamagnetic loops (measuring β p) and so on. In order to realize high-frequency signal measurement and transmission, a series of frequency responses with the magnetic probe and transmission line are tested. Later, to verify the null field, a fitting code is developed to reconstruct the stray field in the vacuum chamber based on magnetic probe measurements and flux loops. The results show that the error is within 1.5%. This indicates the accuracy of the magnetic measurement system and ensures the preparation for the breakdown of plasma.

Evidence for 4e charge of Cooper quartets in a biased multi-terminal graphene-based Josephson junction

In a Josephson junction (JJ) at zero bias, Cooper pairs are transported between two superconducting contacts via the Andreev bound states (ABSs) formed in the Josephson channel. Extending JJs to multiple superconducting contacts, the ABSs in the Josephson channel can coherently hybridize Cooper pairs among different superconducting electrodes. Biasing three-terminal JJs with antisymmetric voltages, for example, results in a direct current (DC) of Cooper quartet (CQ), which involves a four-fermion entanglement. Here, we report half a flux periodicity in the interference of CQ formed in graphene based multi-terminal (MT) JJs with a magnetic flux loop. We observe that the quartet differential conductance associated with supercurrent exhibits magneto-oscillations associated with a charge of 4e, thereby presenting evidence for interference between different CQ processes. The CQ critical current shows non-monotonic bias dependent behavior, which can be modeled by transitions between Floquet-ABSs. Our experimental observation for voltage-tunable non-equilibrium CQ-ABS in flux-loop-JJs significantly extends our understanding of MT-JJs, enabling future design of topologically unique ABS spectrum.

Enthalpy-based modeling of tomographically reconstructed quiet-Sun coronal loops

The structure of the solar corona is made of magnetic flux tubes or loops. Due to the lack of contrast with their environment, observing and studying coronal loops in the quiet Sun is extremely difficult. In this work we use a differential emission measure tomographic (DEMT) technique to reconstruct, from a series of EUV images covering an entire solar rotation, the average 3D distribution of the thermal properties of the coronal plasma. By combining the DEMT products with extrapolations of the global coronal magnetic field, we reconstruct coronal loops and obtain the energy input required to keep them at the typical million-degree temperatures of the corona. We statistically study a large number of reconstructed loops for Carrington rotation (CR) 2082 obtaining a series of typical average loops of different lengths. We look for relations between the thermal properties and the lengths of the constructed typical loops and find similar results to those found in a previous work (Mac Cormack et al., 2020).. We also analyze the typical loop properties by comparing them with the zero-dimensional (0D) hydrodynamic model Enthalpy-Based Thermal Evolution of Loops (EBTEL, Klimchuk et al., 2008). We explore two heating scenarios. In the first one, we apply a constant heating rate assuming that typical loops are in quasi-static equilibrium. In the second scenario we heat the plasma in the loops using short impulsive events. We find that the reconstructed typical loops are overdense with respect to quasi-static equilibrium solutions of the hydrodynamic model. Impulsive heating, on the other hand, reproduces better the observed densities and temperatures for the shorter and approximately semicircular loops. The thermal properties of longer loops cannot be correctly reproduced with the EBTEL model. We suggest that to properly assess the physical characteristics of the analyzed loops in future works, it would be necessary to use a more sophisticated 1D model, with which to study the loop temperature and density profiles and test localized heating at different locations along the loops.

Global Non-ideal Magnetohydrodynamic Simulations of Protoplanetary Disks with Outer Truncation

Abstract It has recently been established that the evolution of protoplanetary disks is primarily driven by magnetized disk winds, requiring a large-scale magnetic flux threading the disks. The size of such disks is expected to shrink with time, as opposed to the conventional scenario of viscous expansion. We present the first global 2D non-ideal magnetohydrodynamic simulations of protoplanetary disks that are truncated in the outer radius, aiming to understand the interaction of the disk with the interstellar environment, as well as the global evolution of the disk and magnetic flux. We find that as the system relaxes, the poloidal magnetic field threading the disk beyond the truncation radius collapses toward the midplane, leading to a rapid reconnection. This process removes a substantial amount of magnetic flux from the system and forms closed poloidal magnetic flux loops encircling the outer disk in quasi-steady state. These magnetic flux loops can drive expansion beyond the truncation radius, corresponding to substantial mass loss through a magnetized disk outflow beyond the truncation radius analogous to a combination of viscous spreading and external photoevaporation. The magnetic flux loops gradually shrink over time, the rates of which depend on the level of disk magnetization and the external environment, which eventually governs the long-term disk evolution.

High-resolution Observations of Small-scale Flux Emergence by GST

Abstract Recent observations demonstrated that emerging flux regions, which constitute the early stage of solar active regions, consist of emergence of numerous small-scale magnetic elements. They in turn interact, merge, and form mature sunspots. However, observations of fine magnetic structures on photosphere with subarcsecond resolution are very rare due to limitations of observing facilities. In this work, taking advantage of the high resolution of the 1.6 m Goode Solar Telescope, we jointly analyze vector magnetic fields, continuum images, and Hα observations of NOAA AR 12665 on 2017 July 13, with the goal of understanding the signatures of small-scale flux emergence, as well as their atmospheric responses as they emerge through multiple heights in the photosphere and chromosphere. Under such a high resolution of 0.″1–0.″2, our results confirm two kinds of small-scale flux emergence: magnetic flux sheet emergence associated with the newly forming granules, and the traditional magnetic flux loop emergence. With direct imaging in the broadband TiO, we observe that both types of flux emergence are associated with darkening of granular boundaries, while only flux sheets elongate granules along the direction of emerging magnetic fields and expand laterally. With a life span of 10 ∼ 15 minutes, the total emerged vertical flux is on the order of 1018 Mx for both types of emergence. The magnitudes of the vertical and horizontal fields are comparable in the flux sheets, while the former is stronger in flux loops. Hα observations reveal transient brightenings in the wings in the events of magnetic loop emergence, which are most probably the signatures of Ellerman bombs.

Global Circulation of the Open Magnetic Flux of the Sun

Abstract The global circulation of the open magnetic flux of the Sun, the component of the solar magnetic field that opens into the heliosphere, and the consequences of the global circulation were proposed by Fisk and coworkers in the early 2000s. The Parker Solar Probe, on its initial encounters with the Sun, has provided direct confirmation of both the global circulation and the physical mechanism by which the circulation occurs, transport by interchange reconnection between open magnetic flux and large coronal loops. The implications of this confirmation of the global circulation of open magnetic flux and the importance of interchange reconnection is discussed.

Storing magnetic fields in pre-collapse cores of massive stars

We argue that the radiative zone above the iron core in pre-collapse cores of massive stars can store strong magnetic fields. To reach this conclusion we use the stellar evolutionary code MESA to simulate the evolution of two stellar models with initial masses of 15Mo and 25Mo, and reveal the entropy profile above the iron core just before core collapse. Just above the iron core there is a thin zone with convective shells. We assume that a dynamo in these convective shells amplifies magnetic fields and forms magnetic flux loops. By considering the buoyancy of magnetic flux loops we show that the steep entropy rise in the radiative zone above the dynamo can prevent buoyancy of flux loops with magnetic fields below about 10^{13}G. When this radiative zone collapses on to the newly born neutron star the converging inflow further amplifies the magnetic fields by a factor of about a hundred. After passing through the stalled shock at about a hundred kilometres from the center, these strong magnetic fields together with instabilities can facilitate the launching of jets that explode the star in the frame of the jittering jets explosion mechanism. Our study further supports the claim for the necessity to include magnetic fields in simulating the explosion of CCSNe.

3D simulations of rising magnetic flux tubes in a compressible rotating interior: The effect of magnetic tension

Context: Long-term variability in solar cycles represents a challenging constraint for theoretical models. Mean-field Babcock-Leighton dynamos that consider non-instantaneous rising flux tubes have been shown to exhibit long-term variability in their magnetic cycle. However a relation that parameterizes the rise-time of non-axisymmetric magnetic flux tubes in terms of stellar parameters is still missing. Aims: We aim to find a general parameterization of the rise-time of magnetic flux tubes for solar-like stars. Methods: By considering the influence of magnetic tension on the rise of non-axisymmetric flux tubes, we predict the existence of a control parameter referred as $\Gamma_{\alpha_1}^{\alpha_2}$. This parameter is a measure of the balance between rotational effects and magnetic effects (buoyancy and tension) acting on the magnetic flux tube. We carry out two series of numerical experiments (one for axisymmetric rise and one for non-axisymmetric rise) and demonstrate that $\Gamma_{\alpha_1}^{\alpha_2}$ indeed controls the rise-time of magnetic flux tubes. Results: We find that the rise-time follows a power law of $\Gamma_{\alpha_1}^{\alpha_2}$ with an exponent that depends on the azimuthal wavenumber of the magnetic flux loop. Conclusions: Compressibility does not impact the rise of magnetic flux tubes, while non-axisymmetry does. In the case of non-axisymmetric rise, the tension force modifies the force balance acting on the magnetic flux tube. We identified the three independent parameters required to predict the rise-time of magnetic flux tubes, that is, the stellar rotation rate, the magnetic flux density of the flux tube, and its azimuthal wavenumber. We combined these into one single relation that is valid for any solar-like star. We suggest using this generalized relation to constrain the rise-time of magnetic flux tubes in Babcock-Leighton dynamo models.

Magnetic flux surfaces and radial Shafranov shifts (ΔR) in SST-1 Tokamak Plasma

Magnetic flux surface contours of SST-1 tokamak plasma have been computed from the analytical solution of the Grad-Shafranov equation (GSE) by fitting experimental measurements obtained from magnetic probes and flux loops. The radial Shafranov shift (ΔR) has been calculated following these formulations. An optical imaging system has been employed to detect the boundary of the plasma column formed, from which the plasma center has been inferred. In this study, the radial shift obtained from the plasma flux surface contours computed from the Grad-Shafranov equations have been compared with the radial shift inferred from the optical imaging system. This comparison shows a good agreement between the plasma position shift from the flux surface contours and that from the imaging system.

Two-Dimensional Platform for Networks of Majorana Bound States.

We model theoretically a two-dimensional electron gas (2DEG) covered by a superconductor and demonstrate that topological superconducting channels are formed when stripes of the superconducting layer are removed. As a consequence, Majorana bound states (MBSs) are created at the ends of the stripes. We calculate the topological invariant and energy gap of a single stripe, using realistic values for an InAs 2DEG proximitized by an epitaxial Al layer. We show that the topological gap is enhanced when the structure is made asymmetric. This can be achieved either by imposing a phase difference (by driving a supercurrent or using a magnetic-flux loop) over the strip or by replacing one superconductor by a metallic gate. Both strategies also enable control over the MBS splitting, thereby facilitating braiding and readout schemes based on controlled fusion of MBSs. Finally, we outline how a network of Majorana stripes can be designed.

The Determination of Plasma Radial Shafranov Shift (ΔR) and Vertical Shift (ΔZ) experimentally using Magnetic probe and Flux loop Method for SST-1 Tokamak

The radial Shafranov shift (ΔR) and vertical shift (ΔZ) has been calculated for steady state superconducting tokamak (SST-1) experimentally using magnetic probes and flux loops. The SST-1 plasma at the present phases of operations is circular in shape and leans against the limiters. The radial and vertical shift formulated from Shafranov equation have been used for computation. We have selected best possible pairs of flux loops and magnetic probes location for the measurements. The comparison of results obtained from these two methods also has been performed for numerous numbers of shots for repeatability and reliability purpose. We have observed that the results of both the methods are in good agreement for almost all SST-1 experiment campaigns. Since the control of plasma position plays an important role in plasma confinement and optimizing tokamak operations, the computed ΔR and ΔZ could later on be used as a control parameter for feedback control of plasma position in SST-1.

Modeling the influence of varying magnetic properties in soft magnetic materials on the hysteresis shape using the flux tube approach

Magnetic properties can vary significantly inside soft magnetic steel sheets (SMSSs), both due to mechanical stresses and structural changes originating from different manufacturing processes. The integral consideration, i.e. averaging these effects over the SMSS, leads to a strong simplification of the underlying mechanisms. Such simplification is often inadequate when considering the influence of the varying magnetic properties on the hysteresis loop shape and its dynamic behavior. This paper presents a new approach to model irregular hysteresis loops of non-oriented SMSSs using the flux tube approach, where the SMSS is divided into several flux tubes having different magnetic properties. This enables to model non-homogeneous distributions of the magnetic flux and irregular hysteresis loops subject to varying magnetic properties.

Black hole jets without large-scale net magnetic flux

Abstract We propose a scenario for launching relativistic jets from rotating black holes, in which small-scale magnetic flux loops, sustained by disc turbulence, are forced to inflate and open by differential rotation between the black hole and the accretion flow. This mechanism does not require a large-scale net magnetic flux in the accreting plasma. Estimates suggest that the process could operate effectively in many systems, and particularly naturally and efficiently when the accretion flow is retrograde. We present the results of general-relativistic force-free electrodynamic simulations demonstrating the time evolution of the black hole's magnetosphere, the cyclic formation of jets, and the effect of magnetic reconnection. The jets are highly variable on time-scales ∼10–103rg/c, where rg is the black hole's gravitational radius. The reconnecting current sheets observed in the simulations may be responsible for the hard X-ray emission from accreting black holes.

Design and analysis of a compact synthetic-jet-based air pump for large airflow

In this paper, a compact synthetic jet actuator comprising a primary jet actuator and a synthetic jet chamber was proposed. This synthetic jet actuator can enhance the total airflow rate by combining the primary, and secondary flows synthesized by the synthetic jet. The oscillating diaphragm and valve parts of the synthetic jet actuator were designed as a closed magnetic flux loop to enhance the magnetic flux density in the coils. The primary jet actuator was designed with a separate inlet and outlet to serve as a heat-dissipation application and prevent the re-ingesting of heated air. Thus, a dynamic model of a synthetic jet actuator was constructed, and motion equations were subsequently derived using plate theory, the Lorentz law, and magnetic flux simulation. The behavior in association with the displacement of the oscillating diaphragm, oscillation frequency, and driving current is discussed in this paper. Finally, an experimental rig was constructed to verify the correctness of the airflow simulations. The synthetic jet actuator was integrated with flow channels, and achieved an airflow rate of 9.23 L/min at a 1.5 V driving voltage.