Equilibrium Field Research Articles

Magnetohydrodynamic relaxation of AGN ejecta: radio bubbles in the intracluster medium

X-ray images of galaxy clusters often display underdense bubbles which are apparently inflated by AGN outflow. I consider the evolution of the magnetic field inside such a bubble, using a mixture of analytic and numerical methods. It is found that the field relaxes into an equilibrium filling the entire volume of the bubble. The timescale on which this happens depends critically on the magnetisation and helicity of the outflow as well as on properties of the surrounding ICM. If the outflow is strongly magnetised, the magnetic field undergoes reconnection on a short timescale, magnetic energy being converted into heat whilst the characteristic length scale of the field rises; this process stops when a global equilibrium is reached. The strength of the equilibrium field is determined by the magnetic helicity injected into the bubble by the AGN: if the outflow has a consistent net flux and consequently a large helicity then a global equilibrium will be reached on a short timescale, whereas a low-helicity outflow results in no global equilibrium being reached and at the time of observation reconnection will be ongoing. However, localised flux-tube equilibria will form. If, on the other hand, the outflow is very weakly magnetised, no reconnection occurs and the magnetic field inside the bubble remains small-scale and passive. These results have implications for the internal composition of the bubbles, their interaction with ICM -- in particular to explain how bubbles could move a large distance through the ICM without breaking up -- as well as for the cooling flow problem in general. In addition, reconnection sites in a bubble could be a convenient source of energetic particles, circumventing the problem of synchrotron emitters having a shorter lifetime than the age of the bubble they inhabit.

Linear transport in fully stratified discs

We consider the evolution of linear non-axisymmetric perturbations in discs with radially and vertically stratified equilibria. We work in the shearing sheet and Boussinesq approximations. We choose density and pressure equilibrium fields compatible with a background flow depending only on the radial pseudo-Cartesian coordinate x. We find that, for unstable vertical and radial stratifications, trailing waves can transport angular momentum outwardly. This occurs when entropy gradients with respect to x and z coordinates have the same sign and the wavenumbers ratio k z /k y is less than a critical value, which depends on the radial Richardson number and the shear parameter.

Investigation of the structure of compacts and sheets of an Al-Cu-Li alloy strengthened by Al2CuLi (T1) particles

X-ray diffraction and electron microscopy have been used to investigate structural states of the material of compacts and sheets of an aluminum-copper-lithium alloy with a lithium content corresponding to the field of equilibrium of a solid solution with the phase T 1 (Al2CuLi). In pressed strips, there arises a multicomponent texture (Bs “110”〈112〉, Cu “211”〈111〉, S “123”〈hkl〉) typical of pressed articles of aluminum-lithium alloys. Their microstructure was characterized by the presence of slip bands oriented in the rolling direction. The formation of lamellar precipitates of the T 1 phase at slip-band boundaries in the process of deformation is supposedly stimulated by Shockley partial dislocations. In hot-rolled sheets, there arose an unusually intense nearly single-component texture of the Ex 1 “011”〈111〉 type, whose appearance is mainly caused by the cross rolling of the sheets. The reduced strength characteristics of the sheets examined are connected with a sharply oriented character of the structure of both the matrix phase and the strengthening T 1 phase. A quasicrystalline phase T 2 present in the material and the precipitates of the δ′ phase exert no marked effect on the level of mechanical properties.

Electromagnetic energy, absorption, and Casimir forces: Uniform dielectric media in thermal equilibrium

The derivation of Casimir forces between dielectrics can be simplified by ignoring absorption, calculating energy changes due to displacements of the dielectrics, and only then admitting absorption by allowing permittivities to be complex. As a first step towards a better understanding of this situation we consider in this paper the model of a dielectric as a collection of oscillators, each of which is coupled to a reservoir giving rise to damping and Langevin forces on the oscillators and a noise polarization acting as a source of a fluctuating electromagnetic (EM) field in the dielectric. The model leads naturally to expressions for the quantized EM fields that are consistent with those obtained by different approaches, and also results in a fluctuation-dissipation relation between the noise polarization and the imaginary part of the permittivity; comparison with the Rytov fluctuation-dissipation relation employed in the well-known Lifshitz theory for the van der Waals (or Casimir) force shows that the Lifshitz theory is actually a classical stochastic electrodynamical theory. The approximate classical expression for the energy density in a band of frequencies at which absorption in a dielectric is negligible is shown to be exact as a spectral thermal equilibrium expectation value in the quantum-electrodynamical theory. Our main result is the derivation of an expression for the QED energy density of a uniform dispersive, absorbing media in thermal equilibrium. The spectral density of the energy is found to have the same form with or without absorption. We also show how the fluctuation-dissipation theorem ensures a detailed balance of energy exchange between the (absorbing) medium, the reservoir and the EM field in thermal equilibrium.

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Plant-to-plant direct competition for belowground resource in an overlapping depletion zone

In response to limited availability of soil resources in basal root zone, plant extends its roots into nearby resource-rich zones to fulfill essential resource demands for survival and repro- duction. This root proliferation into that enriched zones occupied by other plants constitutes inter- plant overlapping rooting zones and thereby the overlapping depletion zones, causing reduction in resource uptake by neighboring plants. By incorporating this mechanism into the classic resource competition model, we study interplant direct competition through their rooting system in an over- lapping depletion zone. The model results indicate an extension of Tilman's R* rule that has already been proved true when plants compete indirectly through their effect on shared resources. The results reveal that plant's direct competitive ability (i.e., the ability to occupy an overlapping deple- tion zone by excluding others) can be characterized by its R*-value, where a best competitor having lowest R*-value excludes others from an overlapping zone and occupies the zone by depleting the resource level to the lowest as in its non-overlapping depletion zone. By analyzing the model, we find a suite of traits that confers R* variation among directly competing plants. This suite of traits would be a useful proxy measure for R* that do not necessarily require to establish equilibrium field monoculture—a requirement for R* measurement in the field.

EFFECT OF SOLAR CHROMOSPHERIC NEUTRALS ON EQUILIBRIUM FIELD STRUCTURES

Solar coronal equilibrium fields are often constructed by nonlinear force-free field (NLFFF) extrapolation from photospheric magnetograms. It is well known that the photospheric field is not force-free and the correct lower boundary for NLFFF construction ought to be the top of the chromosphere. To compensate for this, pre-filtering algorithms are often applied to the photospheric data to remove the non-force-free components. Such pre-filtering models, while physically constrained, do not address the mechanisms that may be responsible for the field becoming force-free. The chromospheric field can change through, for example, field expansion due to gravitational stratification, reconnection, or flux emergence. In this paper, we study and quantify the effect of the chromospheric neutrals on equilibrium field structures. It is shown that, depending on the degree to which the photospheric field is not force-free, the chromosphere will change the structure of the equilibrium field. This is quantified to give an estimate of the change in a profiles one might expect due to neutrals in the chromosphere. Simple scaling of the decay time of non-force-free components of the magnetic field due to chromospheric neutrals is also derived. This is used to quantify the rate at which, or equivalent at which height, the chromosphere is expected to become force-free.

Coronal heating by magnetic reconnection in loops with zero net current

Context. The paper is concerned with heating of the solar corona by nanoflares: a superposition of small transient events in which stored magnetic energy is dissipated by magnetic reconnection. It is proposed that heating occurs in the nonlinear phase of an ideal kink instability, where magnetic reconnection leads to relaxation to a state of minimum magnetic energy. Aims. The aim is to investigate the nonlinear aspects of magnetic relaxation on a current loop with zero net axial current. The dynamical processes leading to the establishment of a relaxed state are explored. The efficiency of loop heating is investigated. Methods. A 3D magnetohydrodynamic numerical code is used to simulate the evolution of coronal loops which are initially in ideally unstable equilibrium. The initial states have zero net current. The results are interpreted by comparison both with linear stability analysis and with helicity-conserving relaxation theory. Results. The disturbance due to the unstable mode is strongly radially confined when the loop carries zero net current. Strong current sheets are still formed in the nonlinear phase with dissipation of magnetic energy by fast reconnection. The nonlinear development consists first of reconnection in a large scale current sheet, which forms near the quasi-resonant surface of the equilibrium field. Subsequently, the current sheet extends and then fragments, leading to multiple reconnections and effective relaxation to a constant α field. Conclusions. Magnetic reconnection is triggered in the nonlinear phase of kink instability in loops with zero net current. Initially, reconnection occurs in a single current sheet, which then fragments into multiple reconnection sites, allowing almost full relaxation to the minimum energy state. The loop is heated to high temperatures throughout its volume.

Rotational Brownian dynamics simulations of non-interacting magnetized ellipsoidal particles in d.c. and a.c. magnetic fields

The rotational Brownian motion of magnetized tri-axial ellipsoidal particles (orthotropic particles) suspended in a Newtonian fluid, in the dilute suspension limit, under applied d.c. and a.c. magnetic fields was studied using rotational Brownian dynamics simulations. The algorithm describing the change in the suspension magnetization was obtained from the stochastic angular momentum equation using the fluctuation-dissipation theorem and a quaternion formulation of orientation space. Simulation results are in agreement with the Langevin function for equilibrium magnetization and with single-exponential relaxation from equilibrium at small fields using Perrin's effective relaxation time. Dynamic susceptibilities for ellipsoidal particles of different aspect ratios were obtained from the response to oscillating magnetic fields of different frequencies and described by Debye's model for the complex susceptibility using Perrin's effective relaxation time. Simulations at high equilibrium and probe fields indicate that Perrin's effective relaxation time continues to describe relaxation from equilibrium and response to oscillating fields even beyond the small field limit.

Cohesive zone laws for void growth — II. Numerical field projection of elasto-plastic fracture processes with vapor pressure

Modeling ductile fracture processes using Gurson-type cell elements has achieved considerable success in recent years. However, incorporating the full mechanisms of void growth and coalescence in cohesive zone laws for ductile fracture still remains an open challenge. In this work, a planar field projection method, combined with equilibrium field regularization, is used to extract crack-tip cohesive zone laws of void growth in an elastic–plastic solid. To this end, a single row of void-containing cell elements is deployed directly ahead of a crack in an elastic–plastic medium subjected to a remote K-field loading; the macroscopic behavior of each cell element is governed by the Gurson porous material relation, extended to incorporate vapor pressure effects. A thin elastic strip surrounding this fracture process zone is introduced, from which the cohesive zone variables can be extracted via the planar field projection method. We show that the material's initial porosity induces a highly convex traction–separation relationship — the cohesive traction reaches the peak almost instantaneously and decreases gradually with void growth, before succumbing to rapid softening during coalescence. The profile of this numerically extracted cohesive zone law is consistent with experimentally determined cohesive zone law in Part I for multiple micro-crazing in HIPS. In the presence of vapor pressure, both the cohesive traction and energy are dramatically lowered; the shape of the cohesive zone law, however, remains highly convex, which suggests that diffusive damage is still the governing failure mechanism.

Prigogine theorem of minimum entropy production applied to the average-atom model

Thermodynamics of irreversible processes is applied to study the interaction of matter and a radiation field in non-local thermodynamic equilibrium within the framework of the average-atom model. The rate of entropy production of matter and the radiation field, in contact with a free electron reservoir in local thermodynamic equilibrium, is obtained using conjugates of the state variables. The average-atom one-electron populations are determined by minimizing the rate of entropy production at fixed electronic density, electronic temperature, and radiation field. Numerical results and comparisons with experiment for a photoionized iron plasma are presented and discussed. Our approach, which is based on first principles, can be used in a large variety of non-local thermodynamic equilibrium situations.

THE INTERNAL STRUCTURE OF CORONAL MASS EJECTIONS: ARE ALL REGULAR MAGNETIC CLOUDS FLUX ROPES?

In this Letter, we investigate the internal structure of a coronal mass ejection (CME) and its dynamics by invoking a realistic initiation mechanism in a quadrupolar magnetic setting. The study comprises a compressible three-dimensional magnetohydrodynamics simulation. We use an idealized model of the solar corona, into which we superimpose a quadrupolar magnetic source region. By applying shearing motions resembling flux emergence at the solar boundary, the initial equilibrium field is energized and it eventually erupts, yielding a fast CME. The simulated CME shows the typical characteristics of a magnetic cloud (MC) as it propagates away from the Sun and interacts with a bimodal solar wind. However, no distinct flux rope structure is present in the associated interplanetary ejection. In our model, a series of reconnection events between the eruptive magnetic field and the ambient field results in the creation of significant writhe in the CME's magnetic field, yielding the observed rotation of the magnetic field vector, characteristic of an MC. We demonstrate that the magnetic field lines of the CME may suffer discontinuous changes in their mapping on the solar surface, with footpoints subject to meandering over the course of the eruption due to magnetic reconnection. We argue that CMEs with internal magnetic structure such as that described here should also be considered while attempting to explain in situ observations of regular MCs at L1 and elsewhere in the heliosphere.

Temperature field of radiative equilibrium in a two-dimensional graded index medium with gray boundaries

In this paper, a numerical method is presented for the study of the radiative transfer in a two-dimensional graded index semitransparent medium with diffuse gray boundaries. The numerical method is a combination of the linear refractive index bar model, the discrete curved ray-tracing technique and the pseudo source adding method (LRIB-CRTP). In the traditional ray-tracing technique, it is difficult to deal with the diffuse gray boundary while solving the radiative transfer. Using the pseudo source adding method, the diffuse gray boundary of the medium can be treated as a black boundary. We have also studied the radiative equilibrium temperature field of the medium and analyzed the influence of some parameters involved. The results show that the directional discrete number is important for the medium having a large absorption coefficient. The results also show that the refractive index distribution greatly influences the temperature field, whereas the linear absorption coefficient distribution has little influence on the temperature field.

Upgrading the NIFS superconductor test facility for JT-60SA cable-in-conduit conductors

The superconductor test facility at the National Institute for Fusion Science (NIFS) was upgraded to test cable-in-conduit (CIC) conductors for the JT-60SA equilibrium field (EF) coil. Supercritical helium (SHe) lines were assembled with transfer tubes and a heat exchanger. The CIC conductor was covered with a thermal insulation vessel, filled with gas helium at atmospheric pressure. The temperature of the conductor was varied using a film heater attached to an inlet pipe. Critical current (Ic) and current sharing temperature (Tcs) measurements of the prototype CIC conductor were carried out successfully in the upgraded test facility. During the measurements, the conductor temperature was precisely controlled.

JT-60SA用超伝導マグネット

The upgrading of the JT-60U to the JT-60SA has started in a joint effort by the Japanese government (JA) and European commission (EU) under the framework of the Broader Approach (BA) Agreement. The superconducting magnet system for the JT-60SA consists of 18 toroidal field (TF) coils, a central solenoid (CS) with four modules, and six equilibrium field (EF) coils. The TF case encloses the winding pack and is the main structural component of the magnet system. The CS consists of independent winding pack modules, which are hung from the top of the TF coils through its pre-load structure. The six EF coils are attached to the TF coil case through supports with flexible plates that allow radial displacement. The CS modules operate at high field and use a Nb3Sn superconductor. The TF coils and EF coils use NbTi superconductors. This paper describes the technical requirements, operational interface and detailed manufacturing design outline of the superconducting magnet system for the JT-60SA.

Thermomagnetoelastic Stability of Ferromagnetic Cylindrical Shell Carrying Constant Electric Current

The modeling and study of the instability behavior of a magnetically active ferromagnetic cylindrical shell exposed to thermal and magnetic fields with a constant electric current is considered in this paper. It is assumed that the internal surface area of the shell is covered by the thin conductive cylindrical strip. The thickness of this metallic strip is small as compared to the total thickness of the shell and therefore its contribution to the elastic properties of the overall cylindrical shell can be considered negligible. The thermal and magnetic fields of the undisturbed state of the shell are determined assuming that the edges of the shell are thermo-isolated. Undisturbed state coincides with the equilibrium which was generated under the action of thermal field (in equilibrium the forces of magnetic origin are equal to zero). It is also assumed that the thermal exchanges shell-to-strip and shell-to-external media follow Newton-Rickman's law. Using the theory of thermo-magneto-elasticity of undisturbed state in conjunction with the predetermined thermal and magnetic fields the stresses of the undisturbed state are determined under the assumption that the deflection along the generators of the shell equals to zero. The solutions of the homogeneous boundary value problems are carried out and the buckling analysis of the shell is investigated. In particular, a close-form solution for the critical value of electric current for which the shell becomes statically unstable is presented.

Modeling Jupiter's cloud bands and decks: 1. Jet scale meridional circulations

We have investigated the formation of jet scale meridional circulation cells on Jupiter in response to radiative and zonal momentum forcing. In the framework of semi-geostrophic theory, the meridional streamfunction is described by an elliptic equation with a source term dependent on the sum of the latitudinal derivative of the radiative forcing and the vertical derivative of the zonal momentum forcing. Using this equation with analytic terms similar to the assumed forcing on Jupiter, we obtained two set of atmospheric circulations cells, a stratospheric and a tropospheric one. A possible shift in the overturning circulation of the high and deep atmosphere can be induced by breaking the latitudinal alignment of radiative heating with the enforced belt and zones. A series of numerical simulations was conducted with the Jovian GCM OPUS, which was initiated with observational data obtained from the Cassini CIRS temperature cross-section and a corresponding geostrophic zonal wind field. Newtonian forcing of potential temperature as well as zonal momentum was applied respectively towards latitudinally and vertically uniform equilibrium fields. In accordance with the analytic illustrations two rows of jet scale circulation cells were created. The stratospheric circulation showed the distribution of upwelling over zones and downwelling over belts, consistent with cloud observations. The tropospheric cells featured a partial reversal of the downward vertical velocity over the belts and a considerable reduction of the upward movement over the zones in the domain, consistent with recent detections of high water clouds and lightning in belts. We also used the modeled new forcing fields as source terms for the semi-geostrophic Poisson equation to attribute the origin of the modeled secondary circulation. In this analysis, the stratospheric circulation cells observed in the model are primarily generated in response to radiative forcing, while momentum forcing induces the shifted configurations in the deep atmosphere.

Compressional Alfvén Eigenmodes on MAST

Magnetic fluctuations at frequencies ω ≲ ωci driven by neutral-beam injection heating and identified as compressional Alfvén eigenmodes (CAEs) have been observed on MAST. The measured toroidal mode numbers are in the range 4 < |n| < 10 and waves rotate in both co- and counter-current directions. The frequency variation is consistent with an Alfvénic scaling, and modes are elliptically polarized with a significant magnetic field component aligned parallel to the equilibrium field. Frequency clustering of modes occurs on three frequency scales. At the finest scale there are multiple modes each separated by a constant frequency ∼10–20 kHz; this is shown to be a result of modulation by low-frequency tearing modes. A larger scale frequency splitting exists in the range 100–150 kHz; these have consecutive toroidal mode numbers and are in agreement with numerical modelling. Finally, modes exist at frequencies close to ω = ωci and ωci/2 consistently with previous observations on START and DIII-D suggesting that the CAEs exist in two distinct ranges of k∥. Calculations of CAEs suggest that the modes are localized at r/a ∼ 0.5. The modes form within a potential well due to the variation of (nq/κρ)2, and are not directly influenced by variations in vA. This is distinct from observations based on ion cyclotron emission in conventional aspect ratio tokamaks which indicate that CAE modes occur closer to the plasma edge and that their existence relies on a competition between k⊥ and 1/vA.

Influence of spatial variations in the lower critical field on the equilibrium field penetration into superconductors

The thermodynamic lower critical field ${H}_{c1}$ in ${\text{Bi}}_{2}{\text{Sr}}_{2}{\text{CaCu}}_{2}{\text{O}}_{8+y}$ crystals, in the presence of columnar defects, was determined using magneto-optical measurements combined with the shaking technique. We observe a downward shift in ${H}_{c1}$ due to columnar defects. Using partially irradiated samples, we show that small local variations in ${H}_{c1}$ dramatically affect the way the field penetrates into superconductors. We present a theoretical model which provides a quantitative fit to the experimental results and explains how the influence of small sample inhomogeneities is enhanced by geometrical effects and leads to significant variations in the local-field distribution and penetration.

Conceptual Design of Superconducting Magnet System for JT-60SA

The upgrade of JT-60U magnet system to superconducting coils (JT-60SA) has been decided by both parties of Japanese government (JA) and European commission (EU) in the framework of the Broader Approach (BA) agreement. The magnet system for JT-60SA consists of 18 toroidal field (TF) coils, a Central Solenoid (CS) with four modules, seven Equilibrium Field (EF) coils. The TF case encloses the winding pack and is the main structural component of the magnet system. The CS consists of independent winding pack modules, which is hung from the top of the TF coils through its pre-load structure. The seven EF coils are attached to the TF coil cases through supports which include flexible plates allowing radial displacements. The CS modules operate at high field and use Nb3 Sn type superconductor. The TF coils and EF coils use NbTi superconductor. The magnet system has a large heat load from nuclear heating from DD fusion and large AC loss. This paper describes the technical requirements, the operational interface and the outline of conceptual design of the superconducting magnet system for JT-60SA.