Equilibrium Field Research Articles

Nonaxisymmetric instabilities of neutron star with toroidal magnetic fields

Context.

Nontwist symplectic maps in tokamaks

We review symplectic nontwist maps that we have introduced to describe Lagrangian transport properties in magnetically confined plasmas in tokamaks. These nontwist maps are suitable to describe the formation and destruction of transport barriers in the shearless region (i.e., near the curve where the twist condition does not hold). The maps can be used to investigate two kinds of problems in plasmas with non-monotonic field profiles: the first is the chaotic magnetic field line transport in plasmas with external resonant perturbations. The second problem is the chaotic particle drift motion caused by electrostatic drift waves. The presented analytical maps, derived from plasma models with equilibrium field profiles and control parameters that are commonly measured in plasma discharges, can be used to investigate long-term transport properties.

Stability Margin of NbTi CIC Conductor for JT-60SA Equilibrium Field Coil

The equilibrium field (EF) coil conductors are designed with the NbTi cable in conduit (CIC) conductor because the maximum magnetic field of each conductor is up to 4.8 T for the EF-L conductor and 6.2 T for the EF-H conductor. The first EF conductor was manufactured and processed into the performance verification test sample. Then the performance verification tests had been operated before beginning the mass production. The current sharing temperature (Tcs) measurement tests and the quench tests were operated as the performance verification test to evaluate the Tcs and the minimum quench energy (MQE). The results of the Tcs measurement test indicate that both the Tcs of the EF-H conductor and the EF-L conductor are almost same as the expected value estimated by the strand characteristics. Additionally, the Tcs results satisfied the requirements of the EF coils, therefore the conductor design and the fabrication process are going well. The results of the quench test indicate that the EF conductors have enough stability marginuch as more than several hundred mJ/cc at the temperature margin of more than 0.5 K and the current of 20 kA. In addition, the supercritical helium (SHe) mass flow seldom influenced on the MQE. Thus the EF coil can be operated in stable condition even if the SHe mass flow will be decreased.

Design of JT-60SA Magnets and Associated Experimental Validations

In the framework of the JT-60SA project, aiming at upgrading the present JT-60U tokamak toward a fully superconducting configuration, the detailed design phase led to adopt for the three main magnet systems a brand new design. Europe (EU) is expected to provide to Japan (JA) the totality of the toroidal field (TF) magnet system, while JA will provide both Equilibrium field (EF) and Central Solenoid (CS) systems. All magnet designs were optimized trough the past years and entered in parallel into extensive experimentally-based phases of concept validation, which came to maturation in the years 2009 and 2010. For this, all magnet systems were investigated by mean of dedicated samples, e.g. conductor and joint samples designed, manufactured and tested at full scale in ad hoc facilities either in EU or in JA. The present paper, after an overall description of magnet systems layouts, presents in a general approach the different experimental campaigns dedicated to qualification design and manufacture processes of either coils, conductors and electrical joints. The main results with the associated analyses are shown and the main conclusions presented, especially regarding their contribution to consolidate the triggering of magnet mass production. The status of respective manufacturing stages in EU and in JA are also evoked.

Improved estimates and a limit case for the electrostatic Klein–Gordon–Maxwell system

We study the class of nonlinear Klein–Gordon–Maxwell systems describing a standing wave (charged matter field) in equilibrium with a purely electrostatic field. We improve some previous existence results in the case of an homogeneous nonlinearity. Moreover, we deal with a limit case, namely when the frequency of the standing wave is equal to the mass of the charged field; this case shows analogous features of the well-known ‘zero-mass case’ for scalar field equations.

A global structural and electromagnetic Fe model for the prediction of the mechanical behavior of the JT-60SA superconducting magnet system

The JT-60SA is a fusion experiment designed to contribute to the early realization of fusion energy by addressing key physics issues for ITER and by investigating how best to optimize the operation of the fusion power plants. The superconducting magnet system of JT-60SA consists of three sub-systems: a Central Solenoid split in four segments, a set of six Equilibrium Field coils and a set of eighteen Toroidal Field coils. Such systems are connected each other by means of a series of flexible and kinematic mechanical attachments, with the Toroidal Field magnet acting as the backbone of the whole magnet system. A detailed finite element model, representing a 40 degrees sector of the superconducting magnet system of JT-60SA, has been developed and a complete set of analyses were carried out to obtain the distribution of magnetic forces acting on the three magnet sub-systems, to predict the corresponding deformations, to estimate the stress levels in the magnets’ mechanical structures and to verify the integrity of the system and its fatigue life, in agreement with the applicable Codes and Standards and in consideration of the expected lifespan of the machine. This paper illustrates the details of the modeling strategy which lead to the production of the finite element model and provides a comprehensive report and a critical analysis of the most relevant results obtained in the calculations carried out so far.

Full orbit simulation of collisional transport of impurity ions in the MAST spherical tokamak

Transport analysis of MAST discharges indicates that collisions are an important loss mechanism in the core of a tight aspect ratio tokamak. In the strongly varying equilibrium fields of MAST many of the assumptions of drift kinetic and neoclassical theory (e.g. small plasma inverse aspect ratio and low ratio of toroidal Larmor radius to poloidal Larmor radius) are not met by all particle species and it becomes appropriate to use full orbit analysis to evaluate heat and particle fluxes. Collisional transport of impurity ions (C6+ and W20+) has been studied using a full orbit solver, CUEBIT, to integrate the test-particle dynamics. Electromagnetic fields in MAST plasma have been modelled using the cylindrical and toroidal two-fluid codes CUTIE and CENTORI. A detailed study of the scaling of the test-particle diffusivity with collisionality in the equilibrium field reveals deviations from the standard neoclassical theory, in both the Pfirsch–Schlüter and banana regimes, and difficulties in defining a local diffusivity at low collisionalities. The effect of electric and magnetic fluctuations is also briefly addressed. It is found that field fluctuations enhance the non-diffusive nature of transport. The full orbit analysis presented here predicts levels of transport and confinement times for the examined species broadly consistent with the experimental observations.

Fabrication and tests of EF conductors for JT-60SA

The conductors for plasma equilibrium field (EF) coils of JT-60SA are NbTi cable-in-conduit (CIC) conductor with stainless steel 316L jacket. The production of superconductors for actual EF coils started from February 2010. Nine superconductors with 444 m in length were produced up to July 2010. More than 300 welding of jackets were performed. Six nonconformities were found by inspections as go gauge, visual inspection and X-ray test. In order to shorten the manufacturing time schedule, helium leak test was conducted at once after connecting the long length jacket not just after the welding. The maximum force to pull the cable into jacket was about 7.6 kN on average. The mass flow rates of 9 conductors showed almost same values indicating that there are no blockages in the conductors. The measured current sharing temperature agreed with the expectation values from strand performance indicating that no degradation was caused by production process. The coupling time constants of conductors ranged from 80 to 90 ms which are much smaller than the design value of 200 ms.

Development of effective power supply using electric double layer capacitor for static magnetic field coils in fusion plasma experiments

A cost-effective power supply for static magnetic field coils used in fusion plasma experiments has been developed by application of an electric double layer capacitor (EDLC). A prototype EDLC power supply system was constructed in the form of a series LCR circuit. Coil current of 100 A with flat-top longer than 1 s was successfully supplied to an equilibrium field coil of a fusion plasma experimental apparatus by a single EDLC module with capacitance of 30 F. The present EDLC power supply has revealed sufficient performance for plasma confinement experiments whose discharge duration times are an order of several seconds.

ＪＴ‐６０ＳＡ真空容器の設計と試作試験

JT-60 is planned to be upgraded to a JT-60SA superconducting tokamak machine. This project is the JA-EU satellite tokamak program under both broader approach and Japanese domestic programs. The JT-60SA tokamak is composed of the following main components: vacuum vessel (VV), thermal shield, superconducting coils (toroidal field coil, equilibrium field coil, and central solenoid), cryostat, and heating facilities. The VV has a D-shaped poloidal cross section and a double-wall structure to ensure high rigidity and toroidal one-turn resistance simultaneously. The material of the VV is 316L stainless steel with a low cobalt content of <0.05 wt%. Before the start of manufacturing the VV, fundamental welding R&D was performed to study the manufacturing procedures. The manufacturing procedures were successfully established with a trial manufacturing of 20 degree upper half of the VV. Based on the results, the actual VV manufacturing has started in November 2009.

Equivalency principle for magnetoelectroelastic multiferroics with arbitrary microstructure: The phase field approach

A phase field method is proposed to determine the equilibrium fields of a magnetoelectroelastic multiferroic with arbitrarily distributed constitutive constants under applied loadings. This method is based on a developed generalized Eshelby’s equivalency principle, in which the elastic strain, electrostatic, and magnetostatic fields at the equilibrium in the original heterogeneous system are exactly the same as those in an equivalent homogeneous magnetoelectroelastic coupled or uncoupled system with properly chosen distributed effective eigenstrain, polarization, and magnetization fields. Finding these effective fields fully solves the equilibrium elasticity, electrostatics, and magnetostatics in the original heterogeneous multiferroic. The paper formulates a variational principle proving that the effective fields are minimizers of appropriate close-form energy functional. The proposed phase field approach produces the energy minimizing effective fields (and thus solving the general multiferroic problem) as a result of artificial relaxation process described by the Ginzburg–Landau–Khalatnikov kinetic equations.

On the accuracy of the symmetric ergodic magnetic limiter map in tokamaks

AbstractA new symmetric symplectic map for an ergodic magnetic limiter (EML) is proposed. A rigorous mapping technique based on the Hamilton–Jacobi equation is used for its derivation. The system is composed of the equilibrium field, which is fully integrable, and a Hamiltonian perturbation. The equilibrium poloidal flux function is a solution of the Grad–Schlüter–Shafranov equation. This equation is written in polar toroidal coordinate in order to take into account the outward Shafranov shift. The static perturbation field breaks the exact axisymmetry of the equilibrium field and creates a region of chaotic field lines near the plasma edge. The new symmetric EML map is compared with the conventional (asymmetric) EML map which is derived by applying delta-function method. The accuracy of the maps is considered through mean energy error criterion and maximal Lyapunov exponents. For asymmetric and symmetric maps the approximate location of the main cantorus near the edge of plasma is determined with high accuracy by using mean energy error. The forward–backward error criterion is applied to show the relation between the accuracy of the symmetric EML map and the number of EML rings. We also report on the effect of the number of EML rings on the maximal Lyapunov exponent of the symmetric EML map.

Relaxed equilibrium configurations to model fossil fields

Context. The understanding of fossil fields’ origin, topology, and stability is one of the corner stones of the stellar magnetism theory. On one hand, since they survive on secular time scales, they may modify the structure and the evolution of their host stars. On the other hand, they must have a complex stable structure since it has been demonstrated that the simplest purely poloidal or toroidal fields are unstable on dynamical time scales. In this context, the only stable configuration found today is the one resulting from a numerical simulation by Braithwaite and collaborators who studied the evolution of an initial stochastic magnetic field, which is found to relax on a mixed stable configuration (poloidal and toroidal) that seems to be in equilibrium and then diffuses. Aims. We investigate an equilibrium field in a semi-analytical way. In this first article, we study the barotropic magnetohydrostatic equilibrium states. Methods. The problem reduces to a Grad-Shafranov-like equation with arbitrary functions. These functions are constrained by deriving the lowest-energy equilibrium states for given invariants of the considered axisymmetric problem, in particular for a given helicity known to be one of the causes of such problems. These theoretical results were applied to realistic stellar cases, the solar radiative core and the envelope of an Ap star, and discussed. In both cases we assumed that the field is initially confined in the stellar radiation zone. Results. The generalization of the force-free Taylor’s relaxation states studied in laboratory experiments (in spheromaks) that become non force-free in the self-gravitating stellar case are obtained. The case of general baroclinic equilibrium states will be studied in Paper II.

SIMULATING MAGNETIC FIELDS IN THE ANTENNAE GALAXIES

We present self-consistent high-resolution simulations of NGC4038/4039 (the "Antennae galaxies") including star formation, supernova feedback and magnetic fields performed with the N-body/SPH code Gadget, in which magnetohydrodynamics are followed with the SPH method. We vary the initial magnetic field in the progenitor disks from 1 nG to 100 muG. At the time of the best match with the central region of the Antennae system the magnetic field has been amplified by compression and shear flows to an equilibrium field of approximately 10 muG, independent of the initial seed field. These simulations are a proof of the principle that galaxy mergers are efficient drivers for the cosmic evolution of magnetic fields. We present a detailed analysis of the magnetic field structure in the central overlap region. Simulated radio and polarization maps are in good morphological and quantitative agreement with the observations. In particular, the two cores with the highest synchrotron intensity and ridges of regular magnetic fields between the cores and at the root of the southern tidal arm develop naturally in our simulations. This indicates that the simulations are capable of realistically following the evolution of the magnetic fields in a highly non-linear environment. We also discuss the relevance of the amplification effect for present day magnetic fields in the context of hierarchical structure formation.

Recent Progress of the Design Activity for the Poloidal Field Coil System in JT-60SA

PA (procurement arrangement) for poloidal field (PF) coil system, which consists of the central solenoid (CS) and the equilibrium field (EF) coils, was agreed between Japan and EU. During this activity, design of PF coils system was continued to be modified. For CS, material for the jacket of this conductor was changed into stainless steel (316LN) to make providing easier. In the modified material, maximum stress at the jacket was kept within the allowable limit. Accompanying this modification, the amount of pre-compress had to be re-estimated. Therefore, it was clarified that designs of pre-compression and tie plates need not to be major modification. For EF coils, positions and the number of turns were modified since the progress of the research for the plasma operations required in JT-60SA. Due to this optimization, total amount of superconducting material was reduced. The detail designs of PF coils were also performed to reduce the materials of supports and to evaluate the mechanical strength considering the various events. Thickness of clamp plate of the EF coil which received relatively small electromagnetic force was able to be reduced. Regarding the design of support legs with flexible plate, deformation of toroidal field (TF) coil was considered that should be included the evaluation of stress at this parts because this parts are directly attached on the TF coil case. Therefore, the revised designs of supports with sufficient mechanical strength were obtained for EF1 and EF4.

Construction of the Jacketing Facility and First Production Results of Superconductor for JT-60SA

In order to fabricate the central solenoid (CS) and equilibrium field (EF) coil conductors for JT-60 Super Advanced (JT-60SA), the jacketing facility of 680 m was constructed at Naka site of Japan Atomic Energy Agency. The dummy copper conductors of 10 m and superconductors of 7 m were fabricated. The attachment sleeve to connect the cable and winch wire to pull cable through a 551 m jacket in maximum was developed. The sleeve attained the 30 kN of pulling force. In order to investigate the strand damage by the edge of central spiral through compaction and bending process, the measurements of strand critical current in prototype EF conductor with bending curvature radius of 150 mm was conducted. The degradation of was not observed.

MHD relaxation of fossil magnetic fields in stellar interiors

AbstractThe understanding of fossil fields origin, topology, and stability is one of the corner stones of the stellar magnetism theory. On one hand, since they survive on secular time scales, they may modify the structure and the evolution of their host stars. On the other hand, they must have a complex stable structure since it has been demonstrated that the simplest purely poloidal or toroidal fields are unstable on dynamical time scales. In this context, the only stable stellar configurations found today are those resulting from numerical simulations by Braithwaite and collaborators who studied the evolution of an initial stochastic magnetic field, which relaxes with a selective decay of magnetic helicity and energy, on mixed stable configurations (poloidal and toroidal) that seem to be in equilibrium and then diffuse. In this talk, we report the semi-analytical investigation of such an equilibrium field in the axisymmetric case. We use variational methods, which describe selective decay of magnetic helicity and energy during MHD relaxation, and we identify a supplementary invariant due to the stable stratification of stellar radiation zones. This leads to states that generalize force-free Taylor's relaxation states studied in plasma laboratory experiments that become non force-free in the stellar case. Moreover, astrophysical applications are presented and the stability of obtained configurations is studied.

Stability and Quench Test for NbTi CIC Conductor of JT-60SA Equilibrium Field Coil

The EF coil conductors of JT-60SA are designed with the NbTi cable in conduit conductor because the maximum magnetic field goes up to 6.2 T. The prototype NbTi conductor was developed and tested to confirm the capability of the real conductor. The prototype conductor was proven to have enough Tcs margin under the operating conditions investigated in previous test. In this study, the quench test was operated to measure the stability margin and the normal state propagation. Firstly, the MQE under the Tcs margin of 0.2 K was found to be 80 mJ/cc-strand which is almost the same as that of the previous CIC conductor to result in enough stability margins on EF coil operation. Secondly, the propagation velocity to upstream direction and downstream direction were found to be about 0.47 m/s and 0.54 m/s, respectively. Finally, the quench analysis was conducted to calculate the maximum temperature during quench. The analysis results showed that the maximum temperature reached about 70 K, which is within the permissible value of 150 K for the EF coils.

Development of JT-60SA superconducting magnet system

The upgrade of JT-60U magnet system to superconducting coils (JT-60SA) is progressing by both parties of Japanese government and European commission in the framework of the Broader Approach agreement. The magnet system for JT-60SA consists of 18 Toroidal Field (TF) coils, a Central Solenoid (CS) with four modules, six Equilibrium Field (EF) coils. The TF coil case encloses the winding pack and is the main structural component of the magnet system. The CS consists of four independent winding pack modules, which is support from the bottom of the TF coils. The six EF coils are attached to the TF coil cases through supports with flexible plates allowing radial displacements. The construction of CS and EF coils was started in 2008 by Japan Atomic Energy Agency (JAEA). The construction of TF coils will be started in 2009 by Fusion for Energy and European voluntary contributors. This paper introduces the design of the JT-60SA superconducting magnet system and activities for development of magnet components in Japan.

Dispersion characteristics of the electromagnetic waves in a relativistic electron beam guided by the ion channel

In this article, the dispersion characteristics of the paraxial (near axis) electromagnetic (EM) waves in a relativistic electron beam guided by the ion channel are investigated. Equilibrium fields such as ion-channel electrostatic field and self-fields of relativistic electron beam are included in this formalism. In accordance with the equilibrium field structure, radial and azimuthal waves are selected as base vectors for EM waves. It is shown that the dispersion of the radially polarized EM and space charge waves are influenced by the equilibrium fields, but azimuthally polarized wave remain unaffected. In some wave number domains, the radially polarized EM and fast space charge waves are coupled. In these regions, instability is analyzed as a function of equilibrium structure. It is shown that the total equilibrium radial force due to the ion channel and electron beam and also relativistic effect play a key role in the coupling of the radially polarized EM wave and space charge wave. Furthermore, some asymptotic behaviors such as weak and strong ion channel, nonrelativistic case and cutoff frequencies are discussed. This instability could be used as an amplification mechanism for radially polarized EM waves in a beam-plasma system where a relativistic electron beam is guided by the ion channel.