Untwisted Fields Research Articles

Understanding the Effects of Spacecraft Trajectories through Solar Coronal Mass Ejection Flux Ropes Using 3DCOREweb

This study investigates the impact of spacecraft positioning and trajectory on in situ signatures of coronal mass ejections (CMEs). Employing the 3DCORE model, a 3D flux rope model that can generate in situ profiles for any given point in space and time, we conduct forward modeling to analyze such signatures for various latitudinal and longitudinal positions, with respect to the flux rope apex, at 0.8 au. Using this approach, we explore the appearance of the resulting in situ profiles for different flux rope types, with different handedness and inclination angles, for both high- and low-twist CMEs. Our findings reveal that CMEs exhibit distinct differences in signatures between apex hits and flank encounters, with the latter displaying elongated profiles with reduced rotation. Notably, constant, nonrotating in situ signatures are only observed for flank encounters of low-twist CMEs, suggesting the existence of untwisted magnetic field lines within CME legs. Additionally, our study confirms the unambiguous appearance of different flux rope types in in situ signatures in all of the cases, barring some indistinguishable cases, contributing to the broader understanding and interpretation of observational data. Given the model assumptions, this may refute trajectory effects as the cause for mismatching flux rope types as identified in solar signatures. While acknowledging limitations inherent in our model, such as the assumption of constant twist and a nondeformable torus-like shape, we still draw relevant conclusions within the context of the global magnetic field structures of CMEs and the potential for distinguishing flux rope types based on in situ observations.

Detecting the massive bosonic zero-mode in expanding cosmological spacetimes

We examine a quantised massive scalar field in $(1+1)$-dimensional spatially compact cosmological spacetimes in which the early time and late time expansion laws provide distinguished definitions of Fock "in" and "out" vacua, with the possible exception of the spatially constant sector, which may become effectively massless at early or late times. We show, generalising the work of Ford and Pathinayake, that when such a massive zero mode occurs, the freedom in the respective "in" and "out" states is a family with two real parameters. As an application, we consider massive untwisted and twisted scalar fields in the $(1+1)$-dimensional spatially compact Milne spacetime, where the untwisted field has a massive "in" zero mode. We demonstrate, by a combination of analytic and numerical methods, that the choice of the massive "in" zero mode state has a significant effect on the response of an inertial Unruh-DeWitt detector, especially in the excitation part of the spectrum. The detector's peculiar velocity with respect to comoving cosmological observers has the strongest effect in the "in" vacuum of the untwisted field, where it shifts the excitation and de-excitation resonances towards higher values of the detector's energy gap.

Inquiring the Unruh–DeWitt detector about the global property of spacetime

We investigate the effect of spatial compactification on the transition rate of an inertial or accelerated Unruh–Dewitt detector coupled to an untwisted or twisted massless quantum scalar field. Four typical cases of the detector’s motion in the compactified Minkowski spacetime are considered respectively. Our results indicate that the detector’s transition rates are crucially dependent on the spatial compactification length, the magnitude and direction of detector’s velocity, the detector’s acceleration, and the field structure. As these factors change, the detector’s spontaneous emission and absorption processes can be enhanced or weakened at different degrees. In particular, when the compact length is small, the behavior of transition rate in the case of the twisted field is quite distinct from that of the untwisted field. Notably, when the detector moves at a constant velocity with nonzero components along the compact and non-compact directions, our study finds that the spontaneous emission rate depends on the component of velocity along the non-compact direction besides that along the compact direction. This is in sharp contrast with the case of the free Minkowski spacetime. Moreover, for the uniformly accelerated detector along the non-compact direction, the spatial compactification clearly modifies both the spontaneous emission and absorption rates, as the modifying factors depend on the compact length and the detector’s acceleration. Our work indirectly but comprehensively examines the nonequivalence of inertial frames in the compactified Minkowski spacetime, and meanwhile provides a theoretical way to identify the orientation and the size of the compact spatial dimension.

Induced fermionic current in AdS spacetime in the presence of a cosmic string and a compactified dimension

In this paper, we consider a massive charged fermionic quantum field and investigate the current densities induced by a magnetic flux running along the core of an idealized cosmic string in the background geometry of a 5-dimensional anti-de Sitter spacetime, assuming that an extra dimension is compactified. Along the compact dimension quasi-periodicity condition is imposed on the field with a general phase. Moreover, we admit the presence of a magnetic flux enclosed by the compactified axis. The latter gives rise to Ahanorov–Bohm-like effect on the vacuum expectation value of the currents. In this setup, only azimuthal and axial current densities take place. The former presents two contributions, with the first one due to the cosmic string in a 5-dimensional AdS spacetime without compact dimension, and the second one being induced by the compactification itself. The latter is an odd function of the magnetic flux along the cosmic string and an even function of the magnetic flux enclosed by the compactified axis with period equal to the quantum flux. As to the induced axial current, it is an even function of the magnetic flux along the string’s core and an odd function of the magnetic flux enclosed by the compactification perimeter. For untwisted and twisted field along compact dimension, the axial current vanishes. The massless field case is presented as well some asymptotic limits for the parameters of the model.

Chiral nematic liquid crystals in torus-shaped and cylindrical cavities.

We present a Monte Carlo simulation study of chiral nematic liquid crystals confined in torus-shaped and cylindrical cavities. For an achiral nematic with planar degenerate anchoring confined to a toroidal or cylindrical cavity, the ground state is defect free, with an untwisted director field. As chirality is introduced, the ground state remains defect free but the director field becomes twisted within the cavity. For homeotropic anchoring, the ground state for an achiral nematic within a toroidal cavity consists of two disclination rings, one large and one small, that follow the major circumference of the torus. As chirality is introduced and increased, this ground state becomes unstable with respect to twisted configurations. The closed nature of the toroidal cavity requires that only a half integer number of twists can be formed and this leads to the ground state being either a single disclination line that encircles the torus twice or a pair of intertwined disclination rings forming stable, knotted defect structures.

From Minkowski to de Sitter in multifield no-scale models

ABSTRACTWe show the uniqueness of superpotentials leading to Minkowski vacua of single-field no-scale supergravity models, and the construction of dS/AdS solutions using pairs of these single-field Minkowski superpotentials. We then extend the construction to two- and multifield no-scale supergravity models, providing also a geometrical interpretation. We also consider scenarios with additional twisted or untwisted moduli fields, and discuss how inflationary models can be constructed in this framework.

Induced current in high-dimensional AdS spacetime in the presence of a cosmic string and a compactified extra dimension

In this paper, we analyse the bosonic current densities induced by a magnetic flux running along the core of an idealized cosmic string in a high-dimensional AdS spacetime, admitting that an extra dimension coordinate is compactified. Additionally we admit the presence of a magnetic flux enclosed by the compactified axis. In order to develop this analysis we calculate the complete set of normalized bosonic wave-functions obeying a quasiperiodicity condition, with arbitrary phase $\beta$, along the compactified extra dimension. In this context, only azimuthal and axial currents densities take place. As to the azimuthal current, two contributions appear. The first one corresponds to the standard azimuthal current in high-dimensional AdS spacetime with a cosmic string without compactification while the second contribution is a new one, induced by the compactification itself. The latter is an even function of the magnetic flux enclosed by the compactified axis and is an odd function of the magnetic flux along its core with period equal to quantum flux, $\Phi_0=2\pi/e$. On the other hand, the nonzero axial current density is an even function of the magnetic flux along the core of the string and an odd function of the magnetic flux enclosed by the compactified axis. We also find that the axial current density vanishes for untwisted and twisted bosonic fields in the absence of the magnetic flux enclosed by the compactified axis. Some asymptotic expressions for the current density are provided for specific limiting cases of the physical parameter of the model.

Three-Dimensional Simulations of Tearing and Intermittency in Coronal Jets.

Observations of coronal jets increasingly suggest that local fragmentation and intermittency play an important role in the dynamics of these events. In this work we investigate this fragmentation in high-resolution simulations of jets in the closed-field corona. We study two realizations of the embedded-bipole model, whereby impulsive helical outflows are driven by reconnection between twisted and untwisted field across the domed fan plane of a magnetic null. We find that the reconnection region fragments following the onset of a tearing-like instability, producing multiple magnetic null points and flux-rope structures within the current layer. The flux ropes formed within the weak-field region in the center of the current layer are associated with "blobs" of density enhancement that become filamentary threads as the flux ropes are ejected from the layer, whereupon new flux ropes form behind them. This repeated formation and ejection of flux ropes provides a natural explanation for the intermittent outflows, bright blobs of emission, and filamentary structure observed in some jets. Additional observational signatures of this process are discussed. Essentially all jet models invoke reconnection between regions of locally closed and locally open field as the jet-generation mechanism. Therefore, we suggest that this repeated tearing process should occur at the separatrix surface between the two flux systems in all jets. A schematic picture of tearing-mediated jet reconnection in three dimensions is outlined.

Phenomenological aspects of no-scale inflation models

We discuss phenomenological aspects of inflationary models wiith a no-scale supergravity Kähler potential motivated by compactified string models, in which the inflaton may be identified either as a Kähler modulus or an untwisted matter field, focusing on models that make predictions for the scalar spectral index ns and the tensor-to-scalar ratio r that are similar to the Starobinsky model. We discuss possible patterns of soft supersymmetry breaking, exhibiting examples of the pure no-scale type m0 = B0 = A0 = 0, of the CMSSM type with universal A0 and m0 ≠ 0 at a high scale, and of the mSUGRA type with A0 = B0 + m0 boundary conditions at the high input scale. These may be combined with a non-trivial gauge kinetic function that generates gaugino masses m1/2 ≠ 0, or one may have a pure gravity mediation scenario where trilinear terms and gaugino masses are generated through anomalies. We also discuss inflaton decays and reheating, showing possible decay channels for the inflaton when it is either an untwisted matter field or a Kähler modulus. Reheating is very efficient if a matter field inflaton is directly coupled to MSSM fields, and both candidates lead to sufficient reheating in the presence of a non-trivial gauge kinetic function.

On the role of topological complexity in spontaneous development of current sheets

The computations presented in this work aim to asses the importance of field line interlacing on spontaneous development of current sheets. From Parker's magnetostatic theorem, such development of current sheets is inevitable in a topologically complex magnetofluid, with infinite electrical conductivity, at equilibrium. Relevant initial value problems are constructed by superposition of two untwisted component fields, each component field being represented by a pair of global magnetic flux surface. The intensity of field line interlacing is then specified by the relative amplitude of the two superposed fields. The computations are performed by varying this relative amplitude. Also to have a direct visualization of current sheet formation, we follow the evolution of flux surfaces instead of the vector magnetic field. An important finding of this paper is in the demonstration that initial field lines having intense interlacing tend to develop current sheets which are distributed throughout the computational domain with no preference for topologically favorable sites like magnetic nulls or field reversal layers. The onsets of these current sheets are attributed to favorable contortions of magnetic flux surfaces where two oppositely directed parts of the same field line or different field lines come to close proximity. However, for less intensely interlaced field lines, the simulations indicate development of current sheets at sites only where the magnetic topology is favorable. These current sheets originate as two sets of anti-parallel complimentary field lines press onto each other.

Induced vacuum bosonic current by magnetic flux in a higher dimensional compactified cosmic string spacetime

In this paper, we analyze the bosonic current densities induced by a magnetic flux running along an idealized cosmic string in a high-dimensional spacetime, admitting that the coordinate along the string's axis is compactified. Additionally we admit the presence of a magnetic flux enclosed by the compactification axis. In order to develop this analysis we calculate the complete set of normalized bosonic wave functions obeying a quasiperiodicity condition, with arbitrary phase β, along the compactified dimension. In this context, only azimuthal and axial currents densities take place. As to the azimuthal current, two contributions appear. The first contribution corresponds to the standard azimuthal current in a cosmic string spacetime without compactification, while the second contribution is a new one, induced by the compactification itself. The latter is an even function of the magnetic flux enclosed by the string axis and is an odd function of the magnetic flux along its core with period equal to quantum flux, Φ0 = 2π/e. On the other hand, the nonzero axial current density is an even function of the magnetic flux along the core of the string and an odd function of the magnetic flux enclosed by it. We also find that the axial current density vanishes for untwisted and twisted bosonic fields in the absence of the magnetic flux enclosed by the string axis. Some asymptotic expressions for the current density are provided for specific limiting cases of the physical parameter of the model.

ON THE HELICITY OF OPEN MAGNETIC FIELDS

We reconsider the topological interpretation of magnetic helicity for magnetic fields in open domains, and relate this to the relative helicity. Specifically, our domains stretch between two parallel planes, and each of these ends may be magnetically open. It is demonstrated that, while the magnetic helicity is gauge-dependent, its value in any gauge may be physically interpreted as the average winding number among all pairs of field lines with respect to some orthonormal frame field. In fact, the choice of gauge is equivalent to the choice of reference field in the relative helicity, meaning that the magnetic helicity is no less physically meaningful. We prove that a particular gauge always measures the winding with respect to a fixed frame, and propose that this is normally the best choice. For periodic fields, this choice is equivalent to measuring relative helicity with respect to a potential reference field. But for aperiodic fields, we show that the potential field can be twisted. We prove by construction that there always exists a possible untwisted reference field.

Kelvin-Helmholtz instability of twisted magnetic flux tubes in the solar wind

Solar wind plasma is supposed to be structured in magnetic flux tubes carried from the solar surface. Tangential velocity discontinuity near the boundaries of individual tubes may result in Kelvin-Helmholtz instability, which may contribute into the solar wind turbulence. While the axial magnetic field may stabilize the instability, a small twist in the magnetic field may allow to sub-Alfvenic motions to be unstable. We aim to study the Kelvin-Helmholtz instability of twisted magnetic flux tube in the solar wind with different configurations of external magnetic field. We use magnetohydrodynamic equations in the cylindrical geometry and derive the dispersion equations governing the dynamics of twisted magnetic flux tube moving along its axis in the cases of untwisted and twisted external fields. Then we solve the dispersion equations analytically and numerically and found thresholds for Kelvin-Helmholtz instability in both cases of external field. Both analytical and numerical solutions show that the Kelvin-Helmholtz instability is suppressed in the twisted tube by external axial magnetic field for sub-Alfvenic motions. However, even small twist in the external magnetic field allows the Kelvin-Helmholtz instability to be developed for any sub-Alfvenic motions. The unstable harmonics correspond to vortices with high azimuthal mode numbers, which are carried by the flow. Twisted magnetic flux tubes can be unstable to Kelvin-Helmholtz instability when they move with small speed relative to main solar wind stream, then the Kelvin-Helmholtz vortices may significantly contribute into the solar wind turbulence.

Fermionic current induced by magnetic flux in compactified cosmic string spacetime

In this paper, we investigate the fermionic current densities induced by a magnetic flux running along the idealized cosmic string in a four-dimensional spacetime, admitting that the coordinate along the string’s axis is compactified. In order to develop this investigation we construct the complete set of fermionic mode functions obeying a general quasiperiodicity condition along the compactified dimension. The vacuum expectation value of the azimuthal current density is decomposed into two parts. The first one corresponds to the uncompactified cosmic string geometry and the second one is the correction induced by the compactification. For the first part we provide a closed expression which includes various special cases previously discussed in the literature. The second part is an odd periodic function of the magnetic flux along the string axis with the period equal to the flux quantum and it is an even function of the magnetic flux enclosed by the string axis. The compactification of the cosmic string axis in combination with the quasiperiodicity condition leads to the nonzero axial current density. The latter is an even periodic function of the magnetic flux along the string axis and an odd periodic function of the magnetic flux enclosed by the string axis. The axial current density vanishes for untwisted and twisted fields in the absence of the magnetic flux enclosed by the string axis. The asymptotic behavior of the vacuum fermionic current is investigated near the string and at large distances from it. In particular, the topological part of the azimuthal current and the axial current are finite on the string’s axis.

Finite temperature current densities and Bose-Einstein condensation in topologically nontrivial spaces

We investigate the finite temperature expectation values of the charge and current densities for a complex scalar field with nonzero chemical potential in the background of a flat spacetime with spatial topology ${R}^{p}\ifmmode\times\else\texttimes\fi{}({S}^{1}{)}^{q}$. Along compact dimensions quasiperiodicity conditions with general phases are imposed on the field. In addition, we assume the presence of a constant gauge field which, due to the nontrivial topology of background space, leads to Aharonov-Bohm-like effects on the expectation values. By using the Abel-Plana-type summation formula and zeta function techniques, two different representations are provided for both the current and charge densities. The current density has nonzero components along the compact dimensions only and, in the absence of a gauge field, it vanishes for special cases of twisted and untwisted scalar fields. In the high-temperature limit, the current density and the topological part in the charge density are linear functions of the temperature. The Bose-Einstein condensation for a fixed value of the charge is discussed. The expression for the chemical potential is given in terms of the lengths of compact dimensions, temperature, and gauge field. It is shown that the parameters of the phase transition can be controlled by tuning the gauge field. The separate contributions to the charge and current densities coming from the Bose-Einstein condensate and from excited states are also investigated.

Towards matter ination in heterotic string theory

Recently, a class of inflation models in supergravity with gauge non-singlet matter fields as the inflaton has been proposed. It is based on a `tribrid' structure in the superpotential and on a Heisenberg symmetry for solving the eta-problem. We suggest that a generalization of this model class may be suitable for realising inflation in heterotic orbifold compactifications, where the Heisenberg symmetry is a property of the tree-level K"ahler potential of untwisted matter fields. We discuss moduli stabilization in this setup and propose a mechanism to stabilize the modulus associated to the inflaton, which respects the symmetry in the large radius limit. Inflation ends via a waterfall phase transition, as in hybrid inflation. We give conditions which have to be satisfied for realising inflation along these lines in the matter sector of heterotic orbifolds.

On spontaneous formation of current sheets: Untwisted magnetic fields

This is a study of the spontaneous formation of electric current sheets in an incompressible viscous fluid with perfect electrical conductivity, governed by the magnetohydrodynamic Navier–Stokes equations. Numerical solutions to two initial value problems are presented for a three-dimensional, periodic, untwisted magnetic field evolving, with no change in magnetic topology under the frozen-in condition and at characteristic fluid Reynolds numbers of the order of 500, from a nonequilibrium initial state with the fluid at rest. The evolution converts magnetic free energy into kinetic energy to be all dissipated away by viscosity so that the field settles into a minimum-energy, static equilibrium. The solutions demonstrate that, as a consequence of the frozen-in condition, current sheets must form during the evolution despite the geometric simplicity of the prescribed initial fields. In addition to the current sheets associated with magnetic neutral points and field reversal layers, other sheets not associated with such magnetic features are also in evidence. These current sheets form on magnetic flux surfaces. This property is used to achieve a high degree of the frozen-in condition in the simulations, by describing the magnetic field entirely in terms of the advection of its flux surfaces and integrating the resulting governing equations with a customized version of a general-purpose high-resolution (viz., nonoscillatory) hydrodynamical simulation code EULAG [J. M. Prusa et al., Comput. Fluids 37, 1193 (2008)]. Incompressibility imposes the additional global constraint that the flux surfaces must evolve with no change in the spatial volumes they enclose. In this approach, current sheet formation is demonstrated graphically by the progressive pressing together of suitably selected flux surfaces until their separation has diminished below the minimal resolved distance on a fixed grid. The frozen-in condition then fails in the simulation as the field reconnects through an effecting numerical resistivity. The principal results are related to the Parker theory of current-sheet formation and dissipation in the solar corona.

Induced fermionic current in toroidally compactified spacetimes with applications to cylindrical and toroidal nanotubes

The vacuum expectation value of the fermionic current is evaluated for a massive spinor field in spacetimes with an arbitrary number of toroidally compactified spatial dimensions in presence of a constant gauge field. By using the Abel-Plana type summation formula and the zeta function technique we present the fermionic current in two different forms. Non-trivial topology of the background spacetime leads to the Aharonov-Bohm effect on the fermionic current induced by the gauge field. The current is a periodic function of the magnetic flux with the period equal to the flux quantum. In the absence of the gauge field it vanishes for special cases of untwisted and twisted fields. Applications of the general formulae to Kaluz-Klein type models and to cylindrical and toroidal carbon nanotubes are given. In the absence of magnetic flux the total fermionic current in carbon nanotubes vanishes, due to the cancellation of contributions from two different sublattices of the graphene hexagonal lattice.

Topological complexity and tangential discontinuity in magnetic fields

This is a study of the topological magnetostatic problem. A magnetic field embedded in a perfectly conducting fluid and rigidly anchored at its boundary has a specific topology invariant for all time. Subject to that topology, the force-free state of such a field generally requires the presence of tangential discontinuities (TDs). This property proposed and demonstrated by Parker [Spontaneous Current Sheets in Magnetic Fields (Oxford University Press, New York, 1994)] is explained in terms of (i) the overdetermined nature of the magnetostatic partial differential equations nonlinearly coupled to the integral equations imposing the field topology and (ii) the hyperbolic nature of the partial differential equation for the twist function α of the force-free field. The mathematical analysis elucidates a basic incompatibility between preserving a complex field topology and attaining equilibrium, if analyticity is assumed. Physics avoids this incompatibility via TD formation as a natural consequence of perfect conductivity. The study relates TD formation to topological complexity in two-dimensional and three-dimensional fields, as well as the topological connectivity and geometric shape of the field domain. Mathematical points made are given physical interpretations, but important topological concepts for understanding spontaneous TDs have remained incomplete. As an application, examples are presented to define twisted and untwisted potential fields found in simply and multiply connected domains, clarifying a confusion in several recent publications. Appendix A treats the expression of the frozen-in condition by a continuum of conserved, total generalized helicities. Appendix B reports briefly on concurrent developments showing that a published objection to the theory of spontaneous TDs is based upon a misunderstanding of the theory.

DOES THE COMPRESSION OR THE EXPANSION OF A SIMPLE TOPOLOGY POTENTIAL MAGNETIC FIELD LEAD TO THE DEVELOPMENT OF CURRENT SHEETS?

Janse & Low have most recently addressed the following question. Consider a cylindrical domain containing a simple topology potential magnetic field threading its lower and upper horizontal faces, and a perfectly conducting plasma. Suppose that this domain is made to slowly contract or expand in the vertical direction, so driving the field into a quasi-static evolution through a series of force-free configurations. Then are these configurations smooth, or do they contain current sheets (CSs)? We reexamine here their three-step argument leading to the conclusion that CSs form most generally. We prove analytically that the field has to evolve through “topologically untwisted” and “nonpotential” configurations, thus confirming the first two steps. However, we find the third step—leading to the conclusion that a smooth untwisted force-free field is necessarily potential—to be very disputable.