Static Field Configurations Research Articles

Coincident gauge for static spherical field configurations in symmetric teleparallel gravity

In symmetric teleparallel gravities, where the independent connection is characterized by nonmetricity while curvature and torsion are zero, it is possible to find a coordinate system whereby the connection vanishes globally and covariant derivatives reduce to partial derivatives – the coincident gauge. In this paper we derive general transformation rules into the coincident gauge for spacetime configurations where the both the metric and connection are static and spherically symmetric, and write out the respective form of the coincident gauge metrics. Taking different options in fixing the freedom in the connection allowed by the symmetry and the field equations, the Schwarzschild metric in the coincident gauge can take for instance the Cartesian, Kerr–Schild, and diagonal (isotropic-like) forms, while the BBMB black hole metric in symmetric teleparallel scalar–tensor theory a certain diagonal form fits the coincident gauge requirements but the Cartesian and Kerr–Schild forms do not. Different connections imply different value for the boundary term which could in principle be physically relevant, but simple arguments about the coincident gauge do not seem to be sufficient to fix the connection uniquely. As a byproduct of the investigation we also point out that only a particular subset of static spherically symmetric connections has vanishing nonmetricity in the Minkowski limit.

Spin-charge induced scalarization of Kerr-Newman black-hole spacetimes

It has recently been demonstrated that Reissner-Nordström black holes in composed Einstein-Maxwell-scalar field theories can support static scalar field configurations with a non-minimal negative coupling to the Maxwell electromagnetic invariant of the charged spacetime. We here reveal the physically interesting fact that scalar field configurations with a non-minimal positive coupling to the spatially-dependent Maxwell electromagnetic invariant mathcal{F} ≡ FμνFμν can also be supported in black-hole spacetimes. Intriguingly, it is explicitly proved that the positive-coupling black-hole spontaneous scalarization phenomenon is induced by a non-zero combination a ∙ Q ≠ 0 of both the spin a ≡ J/M and the electric charge Q of the central supporting black hole. Using analytical techniques we prove that the regime of existence of the positive-coupling spontaneous scalarization phenomenon of Kerr-Newman black holes with horizon radius r+(M, a, Q) and a non-zero electric charge Q (which, in principle, may be arbitrarily small) is determined by the critical onset line (a/r+)critical = sqrt{2} − 1. In particular, spinning and charged Kerr-Newman black holes in the composed Einstein-Maxwell-scalar field theory are spontaneously scalarized by the positively coupled fields in the dimensionless charge regime 0<frac{Q}{M}le sqrt{2sqrt{2}-2} if their dimensionless spin parameters lie above the critical onset line frac{a(Q)}{M}ge {left[frac{a(Q)}{M}right]}_{mathrm{critical}}=frac{1+sqrt{1-2left(2-sqrt{2}right){left(Q/Mright)}^2}}{2sqrt{2}} .

Exponentially generalized vortex

In this work, we propose an exponentially generalized Abelian model. We investigated the presence of vortex structures in models coupled to Maxwell and Chern-Simons fields. We chose to investigate the dynamics of the complex scalar field in models coupled separately to the Maxwell term and the Chern-Simons term. For this, we analyze the Bogomol'nyi equations in both cases to describe the static field configurations. An interesting result appears when we note that scalar field solutions generate degenerate minimum energy configurations by a factor of in Maxwell's case. On the other hand, in the Chern-Simons case, the solutions in this sector are degenerate by a factor of . Finally, we solve the Bogomol'nyi equations numerically and discuss our results.

Ring-like vortices in a logarithmic generalized Maxwell theory

We investigate the presence of vortex structures in a Maxwell model with a logarithmic generalization. This generalization becomes important because it generates stationary field solutions in models that describe the dynamics of a scalar field. In this work, we will choose to investigate the dynamics of the complex scalar field with the gauge field governed by the Maxwell term. For this, we will investigate the Bogomol'nyi equations to describe the static field configurations. Then, we show numerically that the complex scalar field solutions that generate minimum energy configurations have internal structures. Finally, assuming a planar vision, the magnetic field and the density energy show the interesting feature of the ring-like vortex.

Magnetoelectrostatics of axionically active systems: Induced field restructuring in magnetic stars

In the framework of the Einstein-Maxwell-axion theory, we consider a static field configuration in the outer zone of a magnetic star. We assume that this field configuration is formed by the following interacting quartet: a spherically symmetric gravitational field of the Reissner-Nordstr\"om type, pseudoscalar field, associated with an axionic dark matter, strong intrinsic magnetic field, and axionically induced electric field. Based on the analysis of the solutions to the master equations of the model, we show that the structure of the formed field configuration reveals the following triple effect. First, if the strong magnetic field of the star has the dipole component, the axionic halo around the magnetic star with spherically symmetric gravitational field is no longer spheroidal, and the distortion is induced by the axion-photon coupling. Second, due to the distortion of the axionic halo, the magnetic field is no longer pure dipolar, and the induced quadruple, octupole, etc., components appear, thus redistributing the magnetic energy between the components with more steep radial profiles than the dipolar one. Third, the interaction of the axionic and magnetic fields produces the electric field, which inherits their multipole structure. We attract attention to possible applications of the predicted field restructuring to the theory of axionic rotating magnetars.

NBImag: A Useful Tool in the Design of Magnetic Systems for the ITER Neutral Beam Injectors

NBImag is a code suitable for the design and optimization of complex magnetic field configurations, such as that of a multiaperture, multistage negative ion source and accelerator. The NBImag code has been developed for the design of the ITER neutral beam injector, whose full-size prototype, MITICA, is presently under construction in Padua, Italy. The ITER injector shall produce a focused beam of neutral particles (H or D) having an energy of about 1 MeV and a total power of 16.5 MW for 3600-s continuous operation. The NBImag code is based on an integral formulation and allows an efficient calculation of any static magnetic field configuration on the basis of the geometry of the magnetic sources, with linear material and permanent magnets. NBImag also includes magnetic force and inductance calculations, based on the same formulation. Thanks to the capability of efficiently describing a large number of permanent magnets with limited computational effort, NBImag has also been integrated with different automatic optimization procedures for the solution of inverse magnetic problems. This paper describes the formulation of the code and optimization algorithms, the validation against analytical models and experimental measurements, and the application to the design of MITICA.

Behavior of molten steel flow in continuous casting mold with different static magnetic field configurations

A three-dimensional mathematical model was established to investigate the behavior of molten steel flow and steel/slag interface with different processes and electromagnetic parameters under two different static magnetic field configurations [ruler-type electromagnetic brake (EMBr ruler) and vertical electromagnetic brake (V-EMBr)] in a continuous casting mold. The results showed that the brake effect of EMBr ruler is significantly influenced by its configuration parameters, the distance between the pole and bottom of the submerged entry nozzle (SEN), and the port angle of the SEN outlet; therefore, it is not helpful to depress the diffusion of jet flow along the thickness direction of mold. For a constant SEN depth and port angle, there is a reasonable pole position (P = 0 mm) where the pole simultaneously covers three key zones, i.e., the jet flow impact zone and the upward and downward backflow zones. For V-EMBr, the magnetic field can simultaneously cover the three key zones and depress the diffusion of jet flow along the casting and thickness directions of the mold. Both the meniscus height and the impact intensity of the jet flow can be obviously depressed by V-EMBr even if the SEN depth and port angle have changed in the continuous casting process.

Pulsed electron beam facility GESA-SOFIE for in-situ characterization of cathode plasma dynamics

A new pulsed electron beam facility was constructed, which is specially designed to investigate the cathode plasma on the microsecond timescale. The new triode type accelerator GESA-SOFIE is equipped with a large-area explosive emission cathode. The electron beam is focused on the target in a guiding magnetic field. Particle-in-cell code simulations were used to develop an enhanced and more flexible design compared with the previous facilities GESA I and GESA II. This concerned an improved adjustment of static electric field and magnetic field configurations, the possibility to tune shape and position of the electrodes, and an easy access for diagnostic tools to monitor the areas critical for operation. The performance of GESA-SOFIE was demonstrated for various operating conditions and the facility's versatile capabilities were shown. Typical values of GESA-SOFIE operation are electron energy 30-100 keV, beam current 50-180 A, beam cross-section 10-20 cm2 , and pulse duration up to 200 μs.

Onset of superradiant instabilities in rotating spacetimes of exotic compact objects

Exotic compact objects, horizonless spacetimes with reflective properties, have intriguingly been suggested by some quantum-gravity models as alternatives to classical black-hole spacetimes. A remarkable feature of spinning horizonless compact objects with reflective boundary conditions is the existence of a discrete set of critical surface radii, {rc(ā; n)}n = 1n = ∞, which can support spatially regular static (marginally-stable) scalar field configurations (here ā≡J/M2 is the dimensionless angular momentum of the exotic compact object). Interestingly, the outermost critical radius rcmax≡ maxn{rc(ā; n)} marks the boundary between stable and unstable exotic compact objects: spinning objects whose reflecting surfaces are situated in the region rc > rcmax(ā) are stable, whereas spinning objects whose reflecting surfaces are situated in the region rc < rcmax(ā) are superradiantly unstable to scalar perturbation modes. In the present paper we use analytical techniques in order to explore the physical properties of the critical (marginally-stable) spinning exotic compact objects. In particular, we derive a remarkably compact analytical formula for the discrete spectrum {rcmax(ā)} of critical radii which characterize the marginally-stable exotic compact objects. We explicitly demonstrate that the analytically derived resonance spectrum agrees remarkably well with numerical results that recently appeared in the physics literature.

Emerging Translational Variance: Vacuum Polarization Energy of the ϕ6 Kink

We propose an efficient method to compute the vacuum polarization energy of static field configurations that do not allow decomposition into symmetric and antisymmetric channels in one space dimension. In particular, we compute the vacuum polarization energy of the kink soliton in the ϕ6 model. We link the dependence of this energy on the position of the center of the soliton to the different masses of the quantum fluctuations at negative and positive spatial infinity.

Vacuum polarization energy for general backgrounds in one space dimension

For field theories in one time and one space dimensions we propose an efficient method to compute the vacuum polarization energy of static field configurations that do not allow a decomposition into symmetric and anti--symmetric channels. The method also applies to scenarios in which the masses of the quantum fluctuations at positive and negative spatial infinity are different. As an example we compute the vacuum polarization energy of the kink soliton in the $\phi^6$ model. We link the dependence of this energy on the position of the soliton to the different masses.

COSMIC-RAY PITCH-ANGLE SCATTERING IN IMBALANCED MHD TURBULENCE SIMULATIONS

Pitch-angle scattering rates for cosmic-ray particles in magnetohydrodynamic (MHD) simulations with imbalanced turbulence are calculated for fully evolving electromagnetic turbulence. We compare with theoretical predictions derived from the quasilinear theory of cosmic-ray diffusion for an idealized slab spectrum and demonstrate how cross helicity affects the shape of the pitch-angle diffusion coefficient. Additional simulations in evolving magnetic fields or static field configurations provide evidence that the scattering anisotropy in imbalanced turbulence is not primarily due to coherence with propagating Alfven waves, but an effect of the spatial structure of electric fields in cross-helical MHD turbulence.

Casimir energy of frequency dependent interactions

Vacuum polarization (or Casimir) energies can be straightforwardly computed from scattering data for static field configurations whose interactions with the fluctuating field are frequency independent. In effective theories, however,such interactions are typically frequency dependent. As a consequence, the relationship between scattering data and the Green's function is modified, which may or may not induce additional contributions to the vacuum polarization energy. We discuss several examples that naturally include frequency dependent interactions: (i) scalar electrodynamics with a static background potential, (ii) an effective theory that emerges from integrating out a heavy degree of freedom, and (iii) quantum electrodynamics coupled to a frequency dependent dielectric material. In the latter case, we argue that introducing dissipation as required by the Kramers-Kronig relations requires the consideration of the Casimir energy within a statistical mechanics formalism, while in the absence of dissipation we can work entirely within field theory, using an alternative formulation of the energy density.

Electronic dynamics and frequency effects in circularly polarized strong-field physics

We analyze, quantum mechanically, the dynamics of atomic ionization with a strong, circularly polarized, laser field. We show that the main source for non-adiabatic effects, defined as the deviations from the static-field configuration with corresponding instantaneous amplitude, is connected to an effective barrier lowering due to the laser frequency. Such non-adiabatic effects manifest themselves through ionization rates and yields that depart up to more than one order of magnitude from a static-field configuration which we take as a reference for comparison. As a rule of thumb, such non-adiabatic manifestations get stronger with increasing laser frequency. Beyond circular polarization and atomic targets, these results show the limits of standard instantaneous—static-field like—interpretation of laser–matter interaction and the great need for including time-dependent electronic dynamics.

Spin noise in a quantum dot ensemble: From a quantum mechanical to a semi-classical description

Spin noise spectroscopy is a promising technique for revealing the microscopic nature of spin dephasing processes in quantum dots. We compare the spin-noise in an ensemble of singly charged quantum dots calculated by two complementary approaches. The Chebyshev polynomial expansion technique (CET) accounts for the full quantum mechanical fluctuation of the nuclear spin bath and a semi-classical approach (SCA) is based on the averaging the electron spin dynamics over all different static Overhauser field configurations. We observe a remarkable agreement between both methods in the high-frequency part of the spectra, while the low-frequency part is determined by the long time fluctuations of the Overhauser field. We find small differences in the spectra depending on the distribution of hyperfine couplings. The spin-noise spectra in strong enough magnetic fields where the nuclear dynamics is quenched calculated by two complimentary approaches are in perfect agreement.

The source-sample stage of the new two-dimensional angular correlation of annihilation radiation spectrometer at Technische Universität München

Angular correlation of annihilation radiation (ACAR) is a well established technique for the investigation of the electronic structure. A major limitation of ACAR studies is the available positron flux at a small spot on the sample. For this reason, the focus of this work is put on the discussion of a newly developed source-sample stage of the new 2D-ACAR spectrometer at Technische Universität München which uses an optimized static magnetic field configuration to guide the positrons onto the sample. The achieved spot diameter is d(FWHM) = 5.4 mm, with a high efficiency over the whole energy spectrum of the (22)Na positron source. The implications of the performance of the source-sample stage are discussed with regard to 2D-ACAR measurements of single crystalline α-quartz, which serves as a model system for the determination of the total resolution. A value of (1.53 × 1.64) mrad(2) FWHM was achieved at room temperature.

Emergence of atomic semifluxons in optical Josephson junctions

We propose to create pairs of semifluxons starting from a flat-phase state in long, optical 0-$\ensuremath{\pi}$-0 Josephson junctions formed with internal electronic states of atomic Bose-Einstein condensates. In this optical system, we can dynamically tune the length $a$ of the $\ensuremath{\pi}$ junction, the detuning $\ensuremath{\delta}$ of the optical transition, or the strength ${\ensuremath{\Omega}}_{0}$ of the laser coupling to induce transitions from the flat-phase state to such a semifluxon-pair state. Similarly as in superconducting 0-$\ensuremath{\pi}$-0 junctions, there are two, energetically degenerate semifluxon-pair states. A linear mean-field model with two internal electronic states explains this degeneracy and shows the distinct static field configuration in a phase diagram of the junction parameters. This optical system offers the possibility to dynamically create a coherent superposition of the distinct semifluxon-pair states and observe macroscopic quantum oscillation.

Twinlike models in scalar field theories

This work deals with the presence of defect structures in models described by real scalar field in a diversity of scenarios. The defect structures which we consider are static solutions of the equations of motion which depend on a single spatial dimension. We search for different models, which support the same defect solution, with the very same energy density. We work in flat spacetime, where we introduce and investigate a new class of models. We also work in curved spacetime, within the braneworld context, with a single extra dimension of infinite extent, and there we show how the brane is formed from the static field configuration.

Current-Driven Kink Instability in Relativistic Jets

AbstractWe have investigated the development of current-driven (CD) kink instability in relativistic jets via 3D RMHD simulations. In this investigation a static force-free equilibrium helical magnetic field configuration is considered in order to study the influence of the initial configuration on the linear and nonlinear evolution of the instability. We found that the initial configuration is strongly distorted but not disrupted by the CD kink instability. The linear growth and nonlinear evolution of the CD kink instability depends moderately on the radial density profile and strongly on the magnetic pitch profile. Kink amplitude growth in the nonlinear regime for decreasing magnetic pitch leads to a slender helically twisted column wrapped by magnetic field. On the other hand, kink amplitude growth in the nonlinear regime nearly ceases for increasing magnetic pitch.

Interactions of massless monopole clouds

Some spontaneously broken gauge theories with unbroken non-Abelian gauge groups contain massless magnetic monopoles that are realized classically as clouds of non-Abelian field surrounding one or more massive monopoles. We use moduli space methods to investigate the properties of these massless monopole clouds. We show that the natural metric on the Nahm data for a class of $\mathrm{SU}(2M+2)$ solutions with $2M$ massive and $M(2M\ensuremath{-}1)$ massless monopoles can be obtained from that for a simpler class of $\mathrm{SU}(M+1)$ solutions. For the $M=1$ case, we show that the Nahm data metric is isomorphic to the metric for the moduli of the BPS solutions, thus verifying a previously conjectured result. For $M=2$ we use our results and the moduli space approximation to obtain an effective Lagrangian for an axially symmetric class of solutions. Using this Lagrangian, we study the interactions between the two types of clouds that appear. We show that, although the static spacetime field configurations suggest that the clouds might be rather diffuse, in scattering processes they behave as if they were relatively thin hard shells.