Large Toroidal Field Research Articles

Overview of JT-60U results for the development of a steady-state advanced tokamak scenario

Recent JT-60U experimental results towards the development of a steady-state advanced tokamak scenario are presented. The JT-60U experiments within the past two years emphasize the extension of the operation regimes and the development of active control for high bootstrap current fraction plasmas with a strong linkage between pressure and current profiles. Reduction of a toroidal magnetic field ripple by installing ferritic steel tiles decreases the fast ion loss and consequently enables one to access the new regimes due to an increase in net heating power. The decrease in the fast ion loss also contributes to access to the new regimes through confinement improvement attributed to the reduction of counter toroidal rotation. High βN (∼4.2) exceeding the no-wall ideal limit is achieved at li = 0.8–1 in the high βp ELMy H-mode plasmas with a weak positive shear at the large volume configuration close to the wall. The large volume configuration had so far suffered from the large toroidal field ripple. The value of βN reaches the ideal wall limit, where RWM is suppressed by the plasma rotation. Small critical rotation velocity about 0.3% of Alfvén velocity is found for suppressing RWM. High βN · HH98(y,2) of 2.2 with βN ∼ 2.3 and HH98(y,2) ∼ 1 is sustained for 23.1 s, significantly longer than the current diffusion time (∼12τR) in the high βp ELMy H-mode plasmas. This duration is extended to a time scale for enhancement of recycling owing to a decrease in the wall-pumping rate. Successful recycling and density control is demonstrated for ∼30 s in the enhanced recycling regime even with outgas from the wall by maximizing the divertor pumping rate in the high-density ELMy H-mode plasmas. With small effects of the toroidal field ripple reduction, the controllability is investigated in the reversed shear (RS) plasmas with a high bootstrap current fraction (fBS) of ∼0.7–1. It is difficult to sustain these plasmas using a feedback control scheme for global parameter such as stored energy and the duration is determined by the ideal limit or slow ITB degradation in the linkage of current and pressure profiles. Real time qmin control is demonstrated with MSE diagnostic and LHCD at fBS = 0.46 with the strong pressure and current profile linkage. Physics studies also progress towards burning plasma control. Semi-global change of the ITB structure is observed in both high βp mode and RS plasmas. Complete NTM suppression is demonstrated with misalignment of ECCD position less than about half of the island width. Fast ELM propagation to the main chamber wall is observed, and significant hydrogen retention in the main chamber wall is found. In the plasma-shadowed area underneath the divertor region, the averaged carbon deposition rate is significantly low, however the (H + D)/C retention rate is high (∼0.8).

The roles of plasma rotation and toroidal field ripple on the H-mode pedestal structure in JT-60U

By conducting power scan experiments in three cases of toroidal field ripple configurations (δr ≃ 0.4, 1.0 and 2.0%) with variation of the toroidal momentum source (co, balanced, counter) relative to the direction of the plasma current, the roles of the loss of fast ions and toroidal rotation on the H-mode pedestal structure were investigated. It was found that the pedestal pressure was increased with a decrease in fast ion loss power. On the other hand, the variation in toroidal rotation did not affect strongly the pedestal pressure, although the loss of fast ions due to existing large toroidal field ripple forced the toroidal rotation basically to the counter direction in JT-60U. Due to the enhanced counter toroidal rotation induced by the loss of fast ions, similar Vtor profiles were obtained for discharges with different toroidal momentum source and loss of fast ions. When the loss of fast ions became smaller, pedestal density was raised remarkably while there was no significant difference in the temperature profiles.

Comparison of rotamak plasmas in FRC and ST configurations

The results of experiments in a newly rebuilt rotamak are presented. A comparison is made for two types of operations: the common field-reversed configuration (FRC) produced by driving plasma current with a rotating magnetic field (RMF), and the spherical tokamak (ST) configuration when a steady toroidal magnetic field is added. In both cases the driven plasma current develops two current rings, but in the ST configuration the inner ring current density is about three times larger than that in the FRC case. The addition of the toroidal field enables the ST to overcome the current limit for a given radio-frequency power. The total plasma current is found to have a peak at an optimum value of the applied toroidal field; the optimum toroidal field depends on the value of the equilibrium magnetic field. With proper choice of the toroidal field magnitude, the plasma current can be enhanced two- or three-fold in comparison with the limits in the cases of too a small or too large toroidal field. In the rotamak–ST, the temperature of electrons is increased by at least 50%. The density profile is triangular-shaped in the ST case and almost uniform in the FRC. The measurements of the oscillating fields indicate that the penetration of RMF into plasma is greatly enhanced in the ST case. The analysis of RMF profiles in the plasma supports the hypothesis that the improved penetration is due to the excitation of a whistler wave mode.

Heat flux pattern on the toroidal pump limiter of Tore Supra: first observations and preliminary analysis

Tore Supra has re-started operation in 2001 with a partial toroidal pump limiter as the main plasma facing component. Assembled with actively cooled high heat flux elements, it has the shape of a toroidal ring. Thermal equilibrium is achieved within 4 s and the stabilised surface temperature is comparable to the design calculation. The observed heat flux pattern is similar to calculations realised beforehand with the heat deposition code TOKAFLU, and is dominated by the large toroidal field ripple. The power deposition is a combination of parallel convection and cross-field transport of similar magnitudes. The heat flux decay length is evaluated by three independent diagnostics to 10 mm. The excellent agreement between experiment and modelling indicates that the description of the power deposition mechanism is reasonable, although parameters such as the heat flux decay length and fraction of perpendicular power are still difficult to predict.

Properties ofrmodes in rotating magnetic neutron stars. II. Evolution of thermodes and stellar magnetic field

The evolution of the r-mode instability is likely to be accompanied by secular kinematic effects which will produce differential rotation with large scale drifts of fluid elements, mostly in the azimuthal direction. As first discussed by Rezzolla, Lamb and Shapiro 2000, the interaction of these secular velocity fields with a pre-existing neutron star magnetic field could result in the generation of intense and large scale toroidal fields. Following their derivation in the companion paper, we here discuss the numerical solution of the evolution equations for the magnetic field. The values of the magnetic fields obtained in this way are used to estimate the conditions under which the r-mode instability might be prevented or suppressed. We also assess the impact of the generation of large magnetic fields on the gravitational wave detectability of r-mode unstable neutron stars. Our results indicate that the signal to noise ratio in the detection of gravitational waves from the r-mode instability might be considerably decreased if the latter develops in neutron stars with initial magnetic fields larger than 10^10 G.

Joint Instability of Latitudinal Differential Rotation and Toroidal Magnetic Fields below the Solar Convection Zone. III. Unstable Disturbance Phenomenology and the Solar Cycle

We analyze additional solutions for the two-dimensional instability of coexisting differential rotation and toroidal magnetic fields, organized in families with fixed ratios ER of magnetic to kinetic energy in the unperturbed state. Solutions are found for a wide range of differential rotation amplitudes found in the solar tachocline, for toroidal fields that have a node that ranges in latitude from the pole to the equator, as we expect to exist in the Sun through a sunspot cycle. Fixed ER is a proxy for nonlinear saturation of the solar dynamo due to the reaction of electromagnetic body forces. Since the saturation ratio is not known from either theory or observations, we find solutions in the range 0.1 ≤ ER ≤ 30, corresponding to peak toroidal fields in the solar tachocline of between about 8 × 103 to 1.4 × 105 G. We focus on properties of the unstable disturbances that could test the hypothesis that such disturbances in the solar tachocline provide a template for surface features. We show that the symmetry of magnetic pattern about the equator could switch at one or more phases of the magnetic cycle, and for high ER a switch could also occur between two antisymmetric patterns of different latitudinal profiles. In the former case, the pattern rotation rate would be unchanged, but there would be a sudden longitudinal phase shift in one or both hemispheres. In the latter case, there would be no phase shift but instead a substantial change in the rotation rate of the observed magnetic pattern. For a given mode symmetry and type, the rotation rate is the same at all latitudes, with the rate being close to that of the local rotation of the plasma at the latitude where the disturbance amplitude peaks. For ER ≲ 1, the disturbance magnetic patterns have significant tilts upstream away from the equator, reminiscent of similar patterns in synoptic magnetograms. Sharp changes with latitude in the differential rotation and toroidal field are associated with "critical points" in the system, where the Doppler-shifted disturbance rotation equals the local (angular) Alfvén speed. These migrate toward the equator with the toroidal field node but increasingly lag it. The higher the magnetic energy for a given differential rotation, the closer the equator is approached. If these sharp changes in differential rotation and toroidal field are related to the torsional oscillations and latitudes of sunspots, then these solutions favor large toroidal fields in the tachocline, of peak amplitude at least 6 × 104 G.

MHD behaviour in a resistive-shell reversed-field pinch

The magnetic field on the external surface of the resistive shell has been measured in the T2 reversed-field pinch. Wall-locked internally-resonant modes, which produce toroidally localized , large quasi-stationary m = 1 radial field perturbations are observed. At the position of the wall-locked mode, m = 0 perturbations are generated in local dynamo events and produce a large stationary toroidal field perturbation. The m = 0 modes rotate toroidally from the location where they are produced and diminish within one toroidal turn. Numerical, resistive magnetohydrodynamic simulations verify the correlation between a m = 1 radial field and a toroidal field perturbation.

Tokamak formation and sustainment by coaxial helicity injection current drive

Experiments characterizing the coaxial helicity source and helicity injection current drive on the Prototype Helicity Injected Tokamak (Proto-HIT) have been performed. Toroidal currents over 30 kA can be sustained for times much greater than the plasma resistive time. The coaxial source operates with a large toroidal field that greatly enhances the source impedance, allowing a high rate of helicity injection (high source voltage) at a low source current (high efficiency), with results showing good agreement with a simple analytical model

Design of the Burning Plasma Experiment Vacuum Vessel

The Burning Plasma Experiment (BPX) is being designed to determine the physics behavior of self-heated fusion plasmas and demonstrate the production of substantial amounts of fusion power. The machine is designed to operate with a plasma current of 11.8 MA and a toroidal field of 9 T. The machine will have a major radius of 2.59 m and will have a fusion power of 100–500 MW. The interior surface area of the vessel is about 150 m2. The high power density on the divertor plates requires the use of pyrolytic graphite. Most of the remainder of the metallic surface of the vessel is covered with either carbon fiber composite or graphite tiles. The operating temperature of the vacuum vessel is chosen to be 350 °C because of the good experience of JET and JT-60 with graphite tiles and operation at similar temperatures. The high plasma current, large stored energy, and large toroidal field give rise to large forces on the vacuum vessel during plasma current disruptions. These forces, together with the operating temperature, require the use of Inconel for the vacuum vessel structure. Even with the high strength of Inconel, thicknesses of up to 90 mm are required to have acceptable stress in the vacuum vessel shell. The vacuum pumping speed on BPX is limited to about 7000 ℓ/s (N2) by the size of the access ports on the vessel and by remote handling considerations. The vacuum vessel can be baked to temperatures up to 550 °C without significant changes in the Inconel material properties. The requirements for outgassing of the vacuum vessel and the plasma facing components are discussed.

A Poloidal Field Coil System for a High Beta Ignited Tokamak Experiment

A conceptual design of a poloidal field coil system for an ignition and long pulse burn experiment is presented. The coil is located internal to the toroidal field coil and immediately adjacent to the plasma chamber. The advantages this system offers over alternate designs are: sufficient volt-sec to initiate and sustain plasma current for a 300 sec burn, plasma configurations with MHD beta limits in excess of 10%, and the operational flexibility to accommodate a number of different plasma configurations including diverted discharges. For equal ignition margin a divertor configuration requires a larger toroidal field and lower plasma current than a limiter configuration. Power requirements are modest, and technology developments required for construction are within the present state-of-the-art.

Experience highlights from the design and manufacture of U.S. LCT coils

The international Large Coil Task (LCT) is a major activity in the development of superconducting toroidal field (TF) coils for tokamak fusion reactors. The technical objective of this program is to design, build, and test six large TF coils, thereby producing information and data that can be used directly by program planners and designers of tokamak reactors. After an intensive competetive bidding cycle, contracts were awarded in 1977 to three U.S. industrial firms for the design and manufacture of test coils. Subsequently Japan, EURATOM, and Switzerland agreed to supply one coil each. External dimensions and minimum performance requirements are identical but freedom was allowed in the choice of internal design and manufacturing techniques. All six coils will be tested in a compact toroidal array in the Large Coil Test Facility (LCTF) in Oak Ridge, Tennessee. With the coil fabrication phase approaching completion, it is an appropriate time to review the major technical challenges and lessons from the design and manufacture of the three U.S. LCT coils.

The geomagnetic dynamo-elementary energetics and thermodynamics

This paper is a non-mathematical review, summarising the work in this field. Estimates are made of the power needed to maintain the electric currents which give the main geomagnetic field. The observed surface field needs at least 2×108 W, but unobservable fields may need much more; a toroidal field of peak value 10 or 50nT would need ∼1010 or 2.5×1011 W. Ways of obtaining this power from the Earth's rotation, particularly through precession, are considered and rejected. Thermal power sources have the disadvantages that there is inherent thermodynamic inefficiency in driving the dynamo, and that a significant fraction of the heat input will be carried away by conduction rather than convection. Radioactivity will only be important if there is a substantial amount of potassium in the core. If this is not the case the core might be cooling; cooling at 20K per 109 yr would release specific heat at a rate of ∼1012 W. If the cooling causes the inner core to grow by freezing from the liquid core, then an additional ∼1012 W would be released from the latent heat of freezing. These heat fluxes might support a dynamo having a small toroidal field. If, as seems likely, the solid inner core is significantly denser than the liquid, such cooling would also release ∼0.6×1012 W of gravitational energy, giving compositional convection which would drive the dynamo very efficiently and give a large toroidal field.

Sunspot index infers a small relict magnetic field in the Sun's core

Cowling1 long ago suggested the presence of a relict field in the Sun's core and argued that the bulk electrical conductivity was sufficient (provided that the field was dipolar) to prevent decay over the lifetime of the Solar System. Evidence for such a field is obtained by inference from the asymmetry in time of the solar sunspot number taken over many cycles2. As the Sun's dipole field reverses polarity approximately every 11 yr, if a core field of odd multipolarity (presumably dipolar) is present and in reasonable alignment with the oscillating dipole of the convective zone, it follows that in successive 11-yr periods, the two fields will tend first to be additive and then subtractive3,4. Because the net dipole field is the ‘seed’ field from which the much larger toroidal field arises5, the latter will vary in magnitude in alternating half cycles and correspondingly mediate the level of sunspot activity. Whether a fossil or relict field is present can be explored either by a search for the presence of a 22-yr line quintet in the Fourier spectrum of the sunspot index2, or alternatively the time sequence itself can be processed so as directly to bring out evidence for an offset. The latter involves a ‘demodulation’ of the sunspot sequence to emphasize the basic 22-yr Hale cycle. The latter is discussed here, but as the two are interrelated, the former is reviewed briefly first to provide the basis for the subsequent least squares (LS) analysis of the demodulated signal. As the solar cycle is unstable to drifts in frequency, the presence of frequency modulation can lead to a spurious relict field signal. A short summary of limits on frequency modulation (FM) contamination of the sunspot index spectrum is also given.

Magnetic reconnection driven by the coalescence instability

A detailed study of magnetic reconnection at an X point driven by the coalescence instability is presented. In particular, the effects of plasma compressibility and the magnitude of the toroidal field on the rate of reconnection are explored. For large toroidal fields, the plasma is almost incompressible and the destruction of magnetic flux proceeds linearly with time. However, when the attractive force between two neighboring islands is strong, and when the poloidal and the toroidal fields are comparable in magnitude, the reconnection rate is found to be faster. Implications for the steady-state models of magnetic reconnection are discussed.

Electric probe measurements in a tokamak with large magnetic field ripples

The cross-field diffusion coefficient, determined from the time evolution of the density profile near the edge of a tokamak with large toroidal field ripples, appears to agree better with a ripple enhanced diffusion coefficient than with either Bohm or Pfirsh-Schlüter diffusion rates.

On a uniformly rotating magnetic polytrope

The equilibrium structure of a uniformly rotating magnetic polytrope in the presence of a large toroidal field has been determined for polytropic indexn=1.0, 1.5, 2.0 and 3.0. It has been found that the contribution of higher-order nonspherical terms in the determination of equilibrium structure becomes significant for large magnetic field.

The dynamics of a toroidal magnetic ring

Solving the nonlinear partial differential equations of magnetohydrodynamics numerically, we examine (1) the time development of a purely toroidal magnetic field (a magnetic ring) and (2) the interaction of a magnetic ring with a poloidal magnetic field. Axisymmetry and incompressibility are assumed. Parameters are chosen to correspond to photospheric conditions. In case (1), the magnetic ring contracts to the axis and then splits in two with one ring travelling up along the axis and the other down. In case (2), a large toroidal velocity field is generated which has opposite direction of flow above and below the magnetic ring. The magnetic and flow patterns of case (2) may persist with little change for a relatively long time. We conjecture that toroidal magnetic fields may be involved in the bright rings of sunspots or in the dynamics of spicules.

Electromagnetic Core-mantle Coupling

Summary The work of Bullard (1950) and Rochester (1960) on the geomagnetic westward drift and its effects on the Earth’s rotation is extended to investigate the effects of assuming various distributions of electrical conductivity in the mantle. By a proper choice of conductivities, one is able to increase the theoretical value for the tightness of the coupling by a factor of at least six over that afforded by Rochester’s model, without sacrificing agreement with observations on the rapidity with which changes in the secular variation are established at the Earth’s surface. It is shown that it is reasonable to attribute the observed random changes in the length of the day to perturbations in the electromagnetic coupling. I. Introduction . The most significant hypotheses brought forward to date for the explanation of the existence and maintenance of the terrestrial magnetic field have been reviewed by Jacobs (1956). Of these, only the electromagnetic dynamo theory is able to stand in the light of present information. Elsasser (1956) has reviewed the models suggested for a dynamo mechanism in the core capable of maintaining the dipole part of the field. The analytical details of dynamo operation in the core are irrelevant to the theoretical development in this paper. We need only assume, as did Rochester (1960), that toroidal fields of the correct character are produced in the deep interior and manifest themselves at the core boundary. Convective motion (more or less radial) in the fluid core is fundamental to the maintenance of dynamo action in all current theories. Where the velocity of the convective motion possesses a radial component, conservation of angular momentum requires that the inner fluid core rotate more rapidly than the outer layers. Evidence for this differential rate of rotation is given by observation of a westward drift of the non-dipole part of the field and of the centres of secular change (Bullard & others 1950). Since the high electrical conductivity of the core requires that the magnetic field lines be forced to move bodily with the fluid, the average value of the geomagnetic westward drift can be interpreted as the rate of rotation of the outer layers of the fluid core relative to an observer stationed on the mantle. The non-uniform rotation, together with the high electrical conductivity of the core, leads to the conclusion that a large toroidal field must be induced at the core boundary from the poloidal fields observed at the Earth’s surface. The toroidal fields leak into the conducting part of the mantle, vanishing at the boundary between the conducting and insulating parfs. The existence of a 361