Twisted Field Research Articles

Solar jet on 2014 April 16 modeled by Kelvin–Helmholtz instability

We study here the arising of Kelvin–Helmholtz Instability (KHI) in one fast jet of 2014 April 16 observed by the Atmospheric Imaging Assembly (AIA) on board Solar Dynamics Observatory (SDO) in different UV and EUV wavelengths. The evolution of jet indicates the blob like structure at its boundary which could be one of the observable features of the KHI development. We model the jet as a moving cylindrical magnetic flux tube of radius a embedded in a magnetic field Bi and surrounded by rest magnetized plasma with magnetic field Be. We explore the propagation of the kink MHD mode along the jet that can become unstable against the KHI if its speed exceeds a critical value. Concerning magnetic fields topology we consider three different configurations, notably of (i) spatially homogeneous magnetic fields (untwisted magnetic flux tube), (ii) internal (label ‘i’) twisted magnetic field and external homogeneous one (label ‘e’) (single-twisted flux tube), and (iii) both internal and external twisted magnetic fields (double-twisted magnetic flux tube). Electron number densities in the two media ni and ne are assumed to be homogeneous. The density contrast is defined in two ways: first as ne/ni and second as ne/(ni+ne). Computations show that the KHI can occur at accessible flow velocities in all the cases of untwisted and single-twisted flux tubes. It turns out, however, that in the case of a double-twisted flux tube the KHI can merge at an accessible jet speed only when the density contrast is calculated from the ratio ne/(ni+ne). Evaluated KHI developing times and kink mode wave phase velocities at wavelength of 4 Mm lie in the ranges of 1–6.2 min and 202–271 km s−1, respectively—all being reasonable for the modeled jet.

Probing Twisted Magnetic Field Using Microwave Observations in an M Class Solar Flare on 11 February, 2014

This work demonstrates the possibility of magnetic field topology investigations using microwave polarimetric observations. We study a solar flare of GOES M1.7 class that occurred on 11 February, 2014. This flare revealed a clear signature of spatial inversion of the radio emission polarization sign. We show that the observed polarization pattern can be explained by nonthermal gyrosynchrotron emission from the twisted magnetic structure. Using observations of the Reuven Ramaty High Energy Solar Spectroscopic Imager, Nobeyama Radio Observatory, Radio Solar Telescope Network, and Solar Dynamics Observatory, we have determined the parameters of nonthermal electrons and thermal plasma and identified the magnetic structure where the flare energy release occurred. To reconstruct the coronal magnetic field, we use nonlinear force-free field (NLFFF) and potential magnetic field approaches. Radio emission of nonthermal electrons is simulated by the GX Simulator code using the extrapolated magnetic field and the parameters of nonthermal electrons and thermal plasma inferred from the observations; the model radio maps and spectra are compared with observations. We have found that the potential magnetic field approach fails to explain the observed circular polarization pattern; on the other hand, the Stokes $V$ map is successfully explained by assuming nonthermal electrons to be distributed along the twisted magnetic structure determined by the NLFFF extrapolation approach. Thus, we show that the radio polarization maps can be used for diagnosing the topology of the flare magnetic structures where nonthermal electrons are injected.

Untwisting Jets Related to Magnetic Flux Cancellation

Abstract The rotational motion of solar jets is believed to be a signature of the untwisting process resulting from magnetic reconnection, which takes place between twisted closed magnetic loops (i.e., magnetic flux ropes) and open magnetic field lines. The identification of the pre-existing flux rope, and the relationship between the twist contained in the rope and the number of turns the jet experiences, are then vital in understanding the jet-triggering mechanism. In this paper, we will perform a detailed analysis of imaging, spectral, and magnetic field observations of four homologous jets, among which the fourth one releases a twist angle of 2.6π. Nonlinear force-free field extrapolation of the photospheric vector magnetic field before the jet eruption presents a magnetic configuration with a null point between twisted and open fields—a configuration highly in favor of the eruption of solar jets. The fact that the jet rotates in the opposite sense of handness to the twist contained in the pre-eruption photospheric magnetic field confirms the unwinding of the twist by the jet’s rotational motion. The temporal relationship between jets’ occurrence and the total negative flux at their source region, together with the enhanced magnetic submergence term of the photospheric Poynting flux, shows that these jets are highly associated with local magnetic flux cancellation.

The Effect of a Twisted Magnetic Field on the Nature of Kink MHD Waves

We consider a pressureless plasma in a thin magnetic-flux tube with a twisted magnetic field. We study the effect of twisted magnetic field on the nature of propagating kink waves. To do this, the restoring forces of oscillations in the linear ideal magnetohydrodynamics (MHD) were obtained. In the presence of a twisted magnetic field, the ratio of the magnetic-tension force to the gradient of the magnetic pressure increases for the mode with negative azimuthal wave number, but it decreases for the mode with positive azimuthal wave number. For the kink mode with positive azimuthal mode number, the ratio of the forces is more affected by the twisted magnetic field in dense loops. For the kink mode with negative azimuthal mode number, the perturbed magnetic pressure is negligible under some conditions. The magnetic twist increases (diminishes) the damping of the kink waves with positive (negative) azimuthal mode number due to resonant absorption. Our conclusion is that introducing a twisted magnetic field breaks the symmetry between the nature of the kink waves with positive and negative azimuthal wave number, and the wave can be a purely Alfvenic wave in the entire loop.

Magnetic cloud fit by uniform-twist toroidal flux ropes

Context. Detailed studies of magnetic cloud observations in the solar wind in recent years indicate that magnetic clouds are interplanetary flux ropes with a low twist. Commonly, their magnetic fields are fit by the axially symmetric linear force-free field in a cylinder (Lundquist field), which in contrast has a strong and increasing twist toward the boundary of the flux rope. Therefore another field, the axially symmetric uniform-twist force-free field in a cylinder (Gold-Hoyle field) has become employed to analyze magnetic clouds.Aims. Magnetic clouds are bent, and for some observations, a toroidal rather than a cylindrical flux rope is needed for a local approximation of the cloud fields. We therefore try to derive an axially symmetric uniform-twist force-free field in a toroid, either exactly, or approximately, and to compare it with observations.Methods. Equations following from the conditions of solenoidality and force-freeness in toroidally curved cylindrical coordinates were solved analytically. The magnetic field and velocity observations of a magnetic cloud were compared with solutions obtained using a nonlinear least-squares method.Results. Three solutions of (nearly) uniform-twist magnetic fields in a toroid were obtained. All are exactly solenoidal, and in the limit of high aspect ratios, they tend to the Gold-Hoyle field. The first solution has an exactly uniform twist, the other two solutions have a nearly uniform twist and approximate force-free fields. The analysis of a magnetic cloud observation showed that these fields may fit the observed field equally well as the already known approximately linear force-free (Miller-Turner) field, but it also revealed that the geometric parameters of the toroid might not be reliably determined from fits, when (nearly) uniform-twist model fields are used. Sets of parameters largely differing in the size of the toroid and its aspect ratio yield fits of a comparable quality.

Twofold twist defect chains at criticality

The twofold twist defects in the $D(\mathbb{Z}_k)$ quantum double model (abelian topological phase) carry non-abelian fractional Majorana-like characteristics. We align these twist defects in a line and construct a one dimensional Hamiltonian which only includes the pairwise interaction. For the defect chain with even number of twist defects, it is equivalent to the $\mathbb{Z}_k$ clock model with periodic boundary condition (up to some phase factor for boundary term), while for odd number case, it maps to $\mathbb{Z}_k$ clock model with duality twisted boundary condition. At critical point, for both cases, the twist defect chain enjoys an additional translation symmetry, which corresponds to the Kramers-Wannier duality symmetry in the $\mathbb{Z}_k$ clock model and can be generated by a series of braiding operators for twist defects. We further numerically investigate the low energy excitation spectrum for $k=3,~4,~5$ and $6$. For even-defect chain, the critical points are the same as the $\mathbb{Z}_k$ clock conformal field theories (CFTs), while for odd-defect chain, when $k\neq 4$, the critical points correspond to orbifolding a $\mathbb{Z}_2$ symmetry of CFTs of the even-defect chain. For $k=4$ case, we numerically observe some similarity to the $\mathbb{Z}_4$ twist fields in $SU(2)_1/D_4$ orbifold CFT.

Energetics of the Kelvin-Helmholtz instability induced by transverse waves in twisted coronal loops

Aims: We quantify the effects of twisted magnetic fields on the development of the magnetic Kelvin-Helmholtz instability (KHI) in transversely oscillating coronal loops. Methods: We modelled a fundamental standing kink mode in a straight, density-enhanced magnetic flux tube using the magnetohydrodynamics code, Lare3d. In order to evaluate the impact of an azimuthal component of the magnetic field, various degrees of twist were included within the flux tube's magnetic field. Results: The process of resonant absorption is only weakly affected by the presence of a twisted magnetic field. However, the subsequent evolution of the KHI is sensitive to the strength of the azimuthal component of the field. Increased twist values inhibit the deformation of the loop's density profile, which is associated with the growth of the instability. Despite this, much smaller scales in the magnetic field are generated when there is a non-zero azimuthal component present. Hence, the instability is more energetic in cases with (even weakly) twisted fields. Field aligned flows at the loop apex are established in a twisted regime once the instability has formed. Conclusions: The KHI may have implications for wave heating in the solar atmosphere due to the creation of small length scales and the generation of a turbulent regime. Whilst magnetic twist does suppress the development of the vortices associated with the instability, the formation of the KHI in a twisted regime will be accompanied by greater Ohmic dissipation due to the larger currents that are produced, even if only weak twist is present. The presence of magnetic twist will likely make the instability more difficult to detect in the corona, but will enhance its contribution to heating the solar atmosphere.

A Three-dimensional Magnetohydrodynamic Simulation of the Formation of Solar Chromospheric Jets with Twisted Magnetic Field Lines

Abstract This paper presents a three-dimensional simulation of chromospheric jets with twisted magnetic field lines. Detailed treatments of the photospheric radiative transfer and the equations of state allow us to model realistic thermal convection near the solar surface, which excites various MHD waves and produces chromospheric jets in the simulation. A tall chromospheric jet with a maximum height of 10–11 Mm and lifetime of 8–10 minutes is formed above a strong magnetic field concentration. The magnetic field lines are strongly entangled in the chromosphere, which helps the chromospheric jet to be driven by the Lorentz force. The jet exhibits oscillatory motion as a natural consequence of its generation mechanism. We also find that the produced chromospheric jet forms a cluster with a diameter of several Mm with finer strands. These results imply a close relationship between the simulated jet and solar spicules.

Anyonic Chains, Topological Defects, and Conformal Field Theory

Motivated by the three-dimensional topological field theory/two-dimensional conformal field theory (CFT) correspondence, we study a broad class of one-dimensional quantum mechanical models, known as anyonic chains, which can give rise to an enormously rich (and largely unexplored) space of two-dimensional critical theories in the thermodynamic limit. One remarkable feature of these systems is the appearance of non-local microscopic “topological symmetries” that descend to topological defects of the resulting CFTs. We derive various model-independent properties of these theories and of this topological symmetry/topological defect correspondence. For example, by studying precursors of certain twist and defect fields directly in the anyonic chains, we argue that (under mild assumptions) the two-dimensional CFTs correspond to particular modular invariants with respect to their maximal chiral algebras and that the topological defects descending from topological symmetries commute with these maximal chiral algebras. Using this map, we apply properties of defect Hilbert spaces to show how topological symmetries give a handle on the set of allowed relevant deformations of these theories. Throughout, we give a unified perspective that treats the constraints from discrete symmetries on the same footing as the constraints from topological ones.

Vacuum expectation value of twist fields

Twist fields emerge in a number of physical applications ranging from entanglement entropy to scattering amplitudes in four-dimensional gauge theories. In this work, their vacuum expectation values are studied in the path integral framework. By performing a gauge transformation, their correlation functions are reduced to field theory of matter fields in external Aharonov-Bohm vortices. The resulting functional determinants are then analyzed within the zeta function regularization for the spectrum of Bessel zeros and concise formulas are derived.

Toroidal–Poloidal Magnetic Field Generation in Neutron Stars by Spacetime Frame-dragging

Abstract Neutron star magnetic fields, particularly in magnetars, have strong poloidal and toroidal components, reaching magnitudes up to and extending into the magnetosphere, where they cause twisted magnetic fields and surface currents. Here, we show that to a large extent neutron star toroidal and poloidal magnetic fields are due to frame-dragging of spacetime in the stellar exterior. In the explicit case of linearized Kerr metric we show that general relativistic Maxwell equations admit a mixed poloidal and toroidal magnetic field configuration in which the toroidal field strength is comparable with the poloidal magnetic field. Calculations are performed to show that the frame-dragging-induced magnetic field has the observed order of magnitude at the stellar surface, and exhibits the flare-like phenomenon observed in magnetars.

Entanglement entropy and boundary renormalization group flow: Exact results in the Ising universality class

The entanglement entropy in one dimensional critical systems with boundaries has been associated with the noninteger ground state degeneracy. This quantity, being a characteristic of boundary fixed points, decreases under renormalization group flow, as predicted by the g-theorem. Here, using conformal field theory methods, we exactly calculate the entanglement entropy in the boundary Ising universality class. Our expression can be separated into the well known bulk term and a boundary entanglement term, displaying a universal flow between two boundary conditions, in accordance with the g-theorem. These results are obtained within the replica trick approach, where we show that the associated twist field, a central object generating the geometry of an $n$-sheeted Riemann surface, can be bosonized, giving simple analytic access to multiple quantities of interest. We argue that our result applies to other models falling into the same universality class. This includes the vicinity of the quantum critical point of the two-channel Kondo model, allowing to track in real space the presence of a region containing one half of a qubit with entropy $\frac{1}{2} \log (2)$, associated with a free local Majorana fermion.

The Effect of a Twisted Magnetic Field on the Phase Mixing of the Kink Magnetohydrodynamic Waves in Coronal Loops

Abstract There is observational evidence for the existence of a twisted magnetic field in the solar corona. This inspires us to investigate the effect of a twisted magnetic field on the evolution of magnetohydrodynamic (MHD) kink waves in coronal loops. With this aim, we solve the incompressible linearized MHD equations in a magnetically twisted nonuniform coronal flux tube in the limit of long wavelengths. Our results show that a twisted magnetic field can enhance or diminish the rate of phase mixing of the Alfvén continuum modes and the decay rate of the global kink oscillation depending on the twist model and the sign of the longitudinal (k z ) and azimuthal (m) wavenumbers. Also, our results confirm that in the presence of a twisted magnetic field, when the sign of one of the two wavenumbers m and k z is changed, the symmetry with respect to the propagation direction is broken. Even a small amount of twist can have an important impact on the process of energy cascading to small scales.

Successive Homologous Coronal Mass Ejections Driven by Shearing and Converging Motions in Solar Active Region NOAA 12371

Abstract We study the magnetic field evolution in AR 12371, related to its successive eruptive nature. During the disk transit of seven days, the active region (AR) launched four sequential fast coronal mass ejections (CMEs), which are associated with long duration M-class flares. Morphological study delineates a pre-eruptive coronal sigmoid structure above the polarity inversion line (PIL) similar to Moore et al.’s study. The velocity field derived from tracked magnetograms indicates persistent shear and converging motions of polarity regions about the PIL. While these shear motions continue, the crossed arms of two sigmoid elbows are being brought to interaction by converging motions at the middle of the PIL, initiating the tether-cutting reconnection of field lines and the onset of the CME explosion. The successive CMEs are explained by a cyclic process of magnetic energy storage and release referred to as “sigmoid-to-arcade-to-sigmoid” transformation driven by photospheric flux motions. Furthermore, the continued shear motions inject helicity flux with a dominant negative sign, which contributes to core field twist and its energy by building a twisted flux rope (FR). After a limiting value, the excess coronal helicity is expelled by bodily ejection of the FR, which is initiated by some instability as realized by intermittent CMEs. This AR is in contrast with the confined AR 12192 with a predominant negative sign and larger helicity flux, but much weaker (−0.02 turns) normalized coronal helicity content. While predominant signed helicity flux is a requirement for CME eruption, our study suggests that the magnetic flux normalized helicity flux is a necessary condition accommodating the role of background flux and appeals to a further study of a large sample of ARs.

Seismology of Oscillating Flux Tube with Twisted Magnetic Field and Plasma Flow

Transverse oscillations of a thin coronal loop in a zero-beta plasma in the presence of a twisted magnetic field and flow are investigated. The dispersion relation is obtained in the limit of weak twist. The twisted magnetic field modifies the phase difference and asymmetry of standing kink oscillations caused by the flow. Using data from observations the kink speed and flow speed have been determined. The presence of the twisted magnetic field can cause underestimation or overestimation of the flow speed in coronal loops depending on the direction of the flow and twisted magnetic field, but a twisted magnetic field has little effect on the estimated value of the kink speed.

Incompressible magnetohydrodynamic modes in the thin magnetically twisted flux tube

Context. Observations have shown that twisted magnetic fields naturally occur, and indeed are omnipresent in the Sun's atmosphere. It is therefore of great theoretical interest in solar atmospheric waves research to investigate the types of magnetohydrodynamic (MHD) wave modes that can propagate along twisted magnetic flux tubes. Aims. Within the framework of ideal MHD, the main aim of this work is to investigate small amplitude incompressible wave modes of twisted magnetic flux tubes with m more or equal 1. The axial magnetic field strength inside and outside the tube will be allowed to vary, to ensure the results will not be restricted to only cold plasma equilibria conditions. Methods. The dispersion equation for these incompressible linear MHD wave modes was derived analytically by implementing the long wavelength approximation. Results. It is shown, in the long wavelength limit, that both the frequency and radial velocity profile of the m = 1 kink mode are completely unaffected by the choice of internal background magnetic twist. However, fluting modes with m more or equal 2 are sensitive to the particular radial profile of magnetic twist chosen. Furthermore, due to background twist, a low frequency cut-off is introduced for fluting modes that is not present for kink modes. From an observational point of view, although magnetic twist does not affect the propagation of long wavelength kink modes, for fluting modes it will either work for or against the propagation, depending on the direction of wave travel relative to the sign of the background twist.

A Solar Blowout Jet Caused by the Eruption of a Magnetic Flux Rope

Abstract We investigate the three-dimensional (3D) magnetic structure of a blowout jet originating in the western edge of NOAA active region (AR) 11513 on 2012 July 2 by means of recently developed forced field extrapolation model. The results show that the blowout jet was caused by the eruption of the magnetic flux rope (MFR) consisting of twisted field lines. We further calculate the twist number and squashing factor Q of the reconstructed magnetic field and find that (1) the MFR corresponds well with the high region, and (2) the MFR outer boundary corresponds well with the high Q region, probably interpreting the bright structure at the base of the jet. The twist number of the MFR is estimated to be . Thus, the kink instability is regarded as the initiation mechanism of the blowout jet as reaches or even exceeds the threshold value of the kink instability. Our results also indicate that the bright point at the decaying phase is actually composed of some small loops that are heated by the reconnection occurring above. In summary, the blowout jet is mostly consistent with the scenario proposed by Moore et al., except that the kink instability is found to be a possible trigger.

MHD Simulations of the Eruption of Coronal Flux Ropes under Coronal Streamers

Abstract Using three-dimensional magnetohydrodynamic (MHD) simulations, we investigate the eruption of coronal flux ropes underlying coronal streamers and the development of a prominence eruption. We initialize a quasi-steady solution of a coronal helmet streamer, into which we impose at the lower boundary the slow emergence of a part of a twisted magnetic torus. As a result, a quasi-equilibrium flux rope is built up under the streamer. With varying streamer sizes and different lengths and total twists of the flux rope that emerges, we found different scenarios for the evolution from quasi-equilibrium to eruption. In the cases with a broad streamer, the flux rope remains well confined until there is sufficient twist such that it first develops the kink instability and evolves through a sequence of kinked, confined states with increasing height until it eventually develops a “hernia-like” ejective eruption. For significantly twisted flux ropes, prominence condensations form in the dips of the twisted field lines due to runaway radiative cooling. Once formed, the prominence-carrying field becomes significantly non-force-free due to the weight of the prominence, despite having low plasma β. As the flux rope erupts, the prominence erupts, showing substantial draining along the legs of the erupting flux rope. The prominence may not show a kinked morphology even though the flux rope becomes kinked. On the other hand, in the case with a narrow streamer, the flux rope with less than one wind of twist can erupt via the onset of the torus instability.

Finite flag-transitive affine planes with a solvable automorphism group

In this paper, we consider finite flag-transitive affine planes with a solvable automorphism group. Under a mild number-theoretic condition involving the order and dimension of the plane, the translation complement must contain a linear cyclic subgroup that either is transitive or has two equal-sized orbits on the line at infinity. We develop a new approach to the study of such planes by associating them with planar functions and permutation polynomials in the odd order and even order case respectively. In the odd order case, we characterize the Kantor–Suetake family by using Menichetti's classification of generalized twisted fields and Blokhuis, Lavrauw and Ball's classification of rank two commutative semifields. In the even order case, we develop a technique to study permutation polynomials of DO type by quadratic forms and characterize such planes that have dimensions up to four over their kernels.

Expectation values of twist fields and universal entanglement saturation of the free massive boson

The evaluation of vacuum expectation values (VEVs) in massive integrable quantum field theory (QFT) is a nontrivial renormalization-group ‘connection problem’—relating large and short distance asymptotics—and is in general unsolved. This is particularly relevant in the context of entanglement entropy, where VEVs of branch-point twist fields give universal saturation predictions. We propose a new method to compute VEVs of twist fields associated to continuous symmetries in QFT. The method is based on a differential equation in the continuous symmetry parameter, and gives VEVs as infinite form-factor series which truncate at two-particle level in free QFT. We verify the method by studying twist fields in free models, which are simply related to the branch-point twist fields. We provide the first exact formulae for the VEVs of such fields in the massive uncompactified free boson model, checking against an independent calculation based on angular quantization. We show that logarithmic terms, overlooked in the original work of Callan and Wilczek (1994 Phys. Lett. B 333 55–61), appear both in the massless and in the massive situations. This implies that, in agreement with numerical form-factor observations by Bianchini and Castro-Alvaredo (2016 Nucl. Phys. B 913 879–911), the standard power-law short-distance behavior is corrected by a logarithmic factor. We discuss how this gives universal formulae for the saturation of entanglement entropy of a single interval in near-critical harmonic chains, including corrections.