Total Stored Energy Research Articles

Overview of the initial NSTX experimental results

The main aim of the National Spherical Torus Experiment (NSTX) is to establish the fusion physics principles of the spherical torus (ST) concept. The NSTX device began plasma operations in February 1999 and theplasma current Ip was successfully brought up to the design value of 1 MA on 14 December 1999.The planned plasma shaping parameters, elongation κ = 1.6-2.2 and triangularity δ = 0.2-0.4, were achieved in inner walllimited, and single null and double null diverted configurations. The coaxial helicity injection(CHI) and high harmonic fast wave (HHFW) experiments were also initiated. CHI current of27 kA produced up to 260 kA toroidal current without using an ohmic solenoid. With theinjection of 2.3 MW of HHFW power, using 12 antennas connected to six transmitters, electrons were heated from a central temperature of 400 eV to 900 eV at acentral density of 3.5 × 1013 cm-3, increasing the plasma energy to 59 kJ and the toroidal β, βT, to 10%. The NBIsystem commenced operation in September 2000. The initial results with two ion sources (PNBI = 2.8 MW) show good heating, producing a total plasma stored energy of 90 kJ corresponding to βT ≈ 18% at a plasma current of 1.1 MA.

Optimum design of multi-ring composite flywheel rotor using a modified generalized plane strain assumption

A numerical method for calculating the stress and strength ratio distribution of the hybrid rim-type composite flywheel rotor is presented with a consideration of the thermally induced residual stresses. The axisymmetric rotor is divided into several rings and the stiffness matrix for each ring is derived by solving the radial equilibrium equation and the stress–strain–temperature relations. The ring stiffness matrices are assembled into a symmetric global matrix satisfying the continuity equations at each interface with the assumptions of a modified generalized plane strain (MGPS). In the MGPS, the z-directional axial strains are assumed to vary linearly along the radial direction; ε z = ε 0+ ε 1 r. The conditions that the z-directional force and the circumferential moment resultants vanish are thus used to solve the z-directional axial strains as well as the radial and circumferential strains. After solving the strain distributions, the on-axis stresses and the strength ratios are calculated at each ring. Three-dimensional finite element method (3D FEM) is then used to verify the accuracy of the present method. The results are also compared with those based on the assumption of a plane stress (PSS). In this case, the analysis of MGPS better matches with 3D FEM results than PSS. An optimum design is then performed maximizing total stored energy (TSE) with the thickness of each composite rim as design variables. The optimal design obtained in this study, which considers material sequence, provides a more effective way of maximizing TSE. It is found that the consideration of the residual stress in the design of the hybrid flywheel rotor is crucial. The result of the optimal designs shows that TSE with consideration of Δ T reduces by about 30%.

Numerical and experimental study on the solidification of PCM around a vertical axially finned isothermal cylinder

This paper presents the results of a numerical and experimental investigation realized on finned tubes with the objective of using them in thermal storage systems. The model is based upon the pure conduction mechanism of heat transfer, the enthalpy formulation approach and the control volume method. The finite difference approximation and the alternating direction scheme are used to discretize the basic equations and the associated boundary and initial conditions. The model was validated by comparison with available results and additional experimental measurements realized by the authors. The number of fins, fin length, fin thickness, the degree of super heat and the aspect ratio of the annular spacing are found to influence the time for complete solidification, solidified mass fraction and the total stored energy. The results confirm the importance of the fins in delaying the undesirable effects of natural convection during the phase change processes. Also, this study indicates the strong influence of the annular space size, the radial length of the fin and the number of fins on the solidified mass fraction and the time for complete phase change. Based upon experimental observations and the tendencies of the numerical results, a metallic tube fitted with four–five fins of constant thickness equal to the tube wall thickness and of radial length around twice the tube diameter should be a compromise solution between efficiency, increase in the heat flow rate and the loss of available storage capacity.

Effects of material properties on the total stored energy of a hybrid flywheel rotor

A numerical method based on the assumption of a generalized plane strain (GPS) state is presented for calculating the stress and strength ratio distributions of the rotating composite flywheel rotor of varying material properties in the radial direction. The rotor is divided into many rings and each ring has constant material properties. All the rings are assumed to expand and have the same axial strain. A three-dimensional finite element method is then used to verify the accuracy of the present method. This method gives a better solution for most of the rotors than other methods of a plane stress or plane strain state. After verification, the effects of material properties on the total stored energy (TSE) of the composite flywheel rotor are investigated. For this purpose, the material properties of the rotor, i.e. circumferential and radial Young's moduli, ply angles and mass densities are expressed by power functions of the radius, and the rotor is analyzed. The analysis shows that TSE can be most effectively increased by changing the circumferential Young's moduli along the radius, which amounts to over 300% of TSE of the constant material properties. The variation of ply angles along the radius can increase TSE by about 30% at most. The method of changing the mass densities along the radius could be also effective but its effects are not so noticeable in the rotor where the circumferential stiffness is properly arranged.

Monitoring of superconducting bus-line of LHD using fuzzy theorem

In the LHD (Large-scale Helical Device) system of National Institute far Fusion Science (NIFS), Toki, Gifu, Japan, the experiments using superconducting magnets with total stored energy of roughly 1.6 GJ are carried out. The LHD consists of nine coils those are fed by large-scale DC power supply. The superconducting bus-lines are connecting the power supply and coils with a length of about 50 m and a current capacity of 32 kA (rated current). As this bus-line has thick stabilizing barking metal (high purity Al), a resistive voltage generated at small normal-transitioned region is very small. Meanwhile, the inductive voltage noise induced by the external magnetic field or its own magnetic field is large because the length of the bus-line is large. Besides, the voltage detection leads cannot be attached directly just outside the conductors because of the thick thermal insulation and the care for electrical insulation. Therefore, it is difficult to decide the state of the superconducting bus-line only by the voltage signals, So, the authors proposed to introduce the Fuzzy theorem calculating the "dangerous rate" of the bus-line. In this system, not only the voltage signals of the bus-line but also the transport current and the liquid helium flow-rate in the bus-line are taken into consideration. The experimental result shows that the state of the bus-lines is well expressed by the "dangerous rate", and the bus-line has enough operation margin.

The superconducting magnet system for the ATLAS Detector at CERN

The superconducting magnet system for the ATLAS Detector for the Large Hadron Collider at CERN is under construction since 1997. The magnet system is a hybrid of 4 superconducting magnets, a 2.5 m bore, 5.3 m long 2 T central solenoid servicing the inner detector and three 4 T toroids with global dimensions of 20 m diameter, 25 m long providing the magnetic field of about 1 T for the muon detectors. The operating currents of the solenoid and toroids are 8 and 20 kA respectively with a total stored energy of 1.6 GJ. The realization of the system is challenging due to its unusual size and complexity. Last year the construction of the coils and cryostats commenced in industry. The manufacture of the solenoid cold mass is already finished and the delivery of the individual toroid coils will commence in 2001. An on-surface test of all magnets will occur. After installation in a new cavern 100 m underground this will start in 2003 leading to commissioning of the entire magnet system in early 2005. In the paper various magnets are introduced as well as the common infrastructure and services required. The status of the project is reviewed.

Multiple natural states for an elastic isotropic material with polyconvex stored energy

We show a necessary and sufficient condition for the undistorted reference configuration y(x)=x, with ∇y=F=1, to be a minimizer of the total stored energy for an isotropic elastic body. Polyconvexity of the stored energy function is not sufficient, and we give an example which possesses two distinct natural (i.e., unstressed) states to illustrate this point.

Design analysis of a cryostable sector magnet for superconducting separated-sector cyclotron

A full-scale prototype of a superconducting sector magnet is under construction at RIKEN to assess the magnet design conceived and to gain operational experiences of the magnet system. In this paper some design features of the prototype and viable alternatives are investigated chiefly through quench analysis. The coils are designed to be cryostable. The cryostability, however, may degrade when a helium vapor is trapped inside the coil vessel. Such an event is likely because the vessel is largely packed with supporting materials to elevate the coil stiffness, and because the vessel is configured horizontally flat. Assuming the existence of an uncooled conductor, critical lengths of a normal region and minimum quench energies were numerically studied. Another salient feature of the prototype is the use of iron pole pieces at 4.5 K to effectively enhance the magnetic fields and to reinforce the mechanical structure. However, due to close coupling of the pole pieces with the coils, AC losses are rather substantial. They were computed to quantify the energy shift during a quench and to look into the possibility of rapid spread of a normal region. The proposed high-field cyclotron comprises six superconducting separated-sector magnets in which the total stored energy amounts to 400 MJ at maximum excitation. An optimal arrangement of coil connection has been pursued in the design of the quench protection system.

Optimal Design of a Hybrid Composite Flywheel with a Permanent Magnet Rotor

A design method to optimize the dimensions of a hybrid composite flywheel rotor and a permanent magnet is presented. The flywheel rotor consists of multiple rims of advanced composite materials with a permanent magnetic rotor attached inside the flywheel. The pressure distribution at the inner surface from the centrifugal forces of the magnet is considered together with the centrifugal body forces in the flywheel rotor. The size of the magnet also maintains the required induced voltage. An analytical solution of the displacements and stresses for each ring has been obtained and expressed in terms of a symmetric stiffness matrix. Using the stiffness matrix, the continuity conditions between the rings and the pressure due to the magnet can be easily considered. An optimum design is thus performed maximizing the total stored energy (TSE) with the size of the magnet and the thickness of each composite ring as design variables. For that purpose, the sensitivities of TSE and the Tsai-Wu failure index with respect to the design variables are derived by using the global stiffness matrix and the relationship of the magnetic size and the induced voltage. As a result, the optimal design using the hybrid composite rims has significantly reduced the stresses in a rotor and attained about 2 times the total energy of cases of using each material alone. The present optimization approach can be used to develop an efficient flywheel rotor for various applications.

Time dependent transport simulations of JET H mode plasmas

A drift wave based transport model is used to self-consistently predict the time evolution of temperature and density profiles in JET H mode tokamak discharges. It is found that the same theoretically derived gyro-Bohm transport model previously used to simulate systematic scans of L mode discharges is equally successful in modelling JET ELMy H mode plasmas, implying that core transport is not intrinsically different from L mode confinement. The only difference between the L mode and H mode simulations results from the boundary conditions (i.e. density and temperature pedestals), which are taken from experimental data in both cases. Here, standardized experimental data from 16 JET H mode discharges in the ITER Profile Database are used, including dimensionless parameter scans in relative gyro-radius ρ*, collisionality ν and plasma β. Imperfections in dimensionless similarity for three pairs of scans in relative gyro-radius cause a purely gyro-Bohm transport model to exhibit worse than gyro-Bohm confinement. For the β scan, the model indicates a somewhat stronger β dependence than that observed with a thermal energy confinement scaling of Bτ ∝ β-0.7. More than half of the predicted β scaling is found to result from finite-β effects in the model. The model demonstrates a collisionality scaling of Bτ ∝ ν*-0.3 with some unfavourable dependence arising from neoclassical transport in the plasma core region. The overall goodness of fit obtained when comparing the global and local predictions results in a root mean square error averaging less than 13% for the total stored energy and averaging less than 9% for the density and temperature profiles relative to the maximum experimental values. When E × B shear effects are added to the model, the resulting change in the mean RMS error for the temperature profiles is less than 4%.

Overview of ITER physics deuterium-tritium experiments in JET

An overview of JET experimental results in DT plasmas directly relevant to ITER modes of operation is presented. Experiments in D:T mixtures varying from 100:0 to 10:90 and those carried out in hydrogen plasmas show that the H mode threshold power has an approximately inverse isotope mass dependence. Matching some of the key dimensionless parameters to the ITER values, the ITER similarity experiments with ITER shape and safety factor q show that the global energy confinement time is practically independent of isotopic mass (∼A0.03±0.08), where A is the atomic mass of the hydrogenic species. Subtracting the edge pedestal energy (which scales as ∼A0.57±0.2) from the total stored energy leads to a ∼A-0.17±0.1 dependence of confinement in the plasma core, very similar to that expected from the gyro-Bohm transport (∼ A-0.2) model. The observed scaling of the edge pedestal energy is consistent with a model in which the edge pressure gradient saturates at the ballooning limit over a region of width that scales as the ion poloidal Larmor radius governed by the average energy of the fast ions in the edge. The steady state total stored energy for a given input power in both ICRH and NBI discharges is the same despite the lower edge pedestal in the ICRH case, which is compensated for by more peaked power deposition profiles in ICRH. The ELM frequency is smaller with NBI; it decreases with isotopic mass in both NBI and ICRH discharges. A steady state, type I ELMy H mode discharge with ITER shape and q at 3.8 T/3.8 MA with an input power of 22 MW produced a Q ≈ 0.18 for 3.5 s and extrapolates well to ignition with ITER parameters. Here, Q is the ratio of fusion output power to input power. The thermal ELMy H mode confinement in both deuterium and tritium gas fuelled plasmas decreases significantly when the plasma density exceeds 0.75 of the Greenwald (nGW) limit, and the maximum density achieved is 0.85nGW. In L mode, the density limit decreases with increasing isotope mass roughly in accordance with code predictions. ITER reference ICRH scenarios have been evaluated. Second harmonic heating of tritium at the densities available in JET produces strong tails and heats electrons predominantly as expected. The 3He minority in 50:50 D:T and tritium dominated plasmas showed strong bulk ion heating leading to ion temperatures up to 13 keV with ICRH alone. Deuterium minority ion cyclotron heating in tritium plasmas at a power level of 6 MW produced steady state record values of Q ≈ 0.22 for more than 2.5 s.

Studies in JET divertors of varied geometry. II: Impurity seeded plasmas

In current large tokamaks, non-intrinsic seeded impurities have been used to produce divertor power loads which would be considered acceptable when extrapolated to ITER. Many devices have achieved the goals of high fractional radiated powers, small frequent ELMs and detachment which are characteristic of radiative H mode regimes. The influence of divertor geometry on these characteristics is described. It has been a matter of concern that the Zeff associated with the seeded impurities may exceed that allowable in ITER and also that the degradation in energy confinement may be unacceptable. Confidence can only be built in the prediction of these parameters in ITER if reliable scalings are available for impurity content and energy confinement which have a sound physics basis. Work is described at JET in this area whilst using multimachine data to characterize the size scaling and provide a context for the JET data. Predicted levels for the impurity content of seeded ITER plasmas appear to be of marginal acceptability. Discharges run in the JET Mark I, Mark IIA and Mark IIAP divertors are compared and indicate that increased divertor closure has brought relatively minor benefits in highly radiative discharges. The acceptability of the energy confinement of radiation for ITER remains unclear. Dimensionless parameter scaling experiments have been conducted in which β, q25, fractional radiated power and Zeff are held constant for a range of ρ*. The price paid for high edge radiation and small ELMs appears to be a 25% loss in total stored energy as a result of edge pedestal degradation. However, the underlying energy confinement scaling may still be consistent with gyro-Bohm scaling, which would give an adequate margin for ITER. This conclusion is, however, sensitive to the scaling of confinement with collisionality, which is difficult to determine due to the coupling between ρ* and ν* which is a consequence of radiation dominated regimes.

Cavity perturbation technique for the measurement of permittivity tensor of uniaxially anisotropic dielectrics

Based on microwave resonant perturbation theory, a bimodal TE/sub 112/ cylindrical cavity is developed for the measurement of permittivity tensor of uniaxially anisotropic dielectrics. The two perpendicular TE/sub 112/ degenerate modes in the cavity are used to measure the two complex components in the permittivity tensor of a uniaxial sample, respectively. In the measurement of each component, only the corresponding mode resonates in the bimodal cavity, and the real and imaginary parts of the complex component are deduced from the changes of the resonant frequency and the quality factor of the cavity due to sample insertion. In the present technique, the quality factors of the cavity before and after sample insertion are measured at the same frequency, so the uncertainties caused by the variation of the total stored energy in the cavity due to sample insertion are eliminated. Experimental results show that the present technique is accurate and reliable for the measurement of the permittivity tensor of uniaxial media. As an example, the dielectric properties of /spl alpha/-SiO/sub 2/ samples with different crystal orientations are characterized using the present technique.

On a Model of Nonlocal Continuum Mechanics Part I: Existence and Regularity

In this work we assume that the total stored energy functional for a body $\B$ depends not only on the local strain field, but also on the spatial average of the strain field over the body weighted with an influence kernel. We investigate the problem of minimizing the total stored energy subject to a given bulk displacement $\Delta\geq 0$. After the general setup for this problem is reviewed, we give sufficient conditions for an energy minimizing strain field $e(\cdot)$ to satisfy an integro-differential Euler--Lagrange equation. The result is general and applies to material energies that display a wide variety of singular behavior. Through analysis of this Euler--Lagrange equation for a special class of influence kernels, we arrive at a regularity theorem which ensures that energy minimizing strain fields must be periodic, piecewise smooth, and possess a finite number of simple discontinuities. We then combine this with a well-known existence result for relaxed minimization problems to arrive at a genera...

Various loss factors of a master harmonic oscillator coupled to a number of satellite harmonic oscillators

Three loss factors are defined for a master harmonic oscillator (HO); the I-loss factor, the U-loss factor, and the effective loss factor. A conductance (β) is conventionally defined as the ratio of the power imparted to a dynamic system by an external drive to the stored energy that this input power generates. The conductance (β) is related to the loss factor (η) by the frequency (ω); β=(ωη). In light of this definition, it is shown that all three loss factors are identical for an isolated master HO at resonance. Differences arise among these loss factors when the master HO is coupled to satellite harmonic oscillators (HO’s). The first two loss factors retain their definitive format in the sense that the stored energy is reckoned only in the master HO; the energy stored in the coupled satellite HO’s and in the couplings is discounted. The effective loss factor, on the other hand, is defined by accounting for the total stored energy that the external drive applied to the master HO generates in the complex. The complex here is composed of the master HO, the satellite HO’s, and the in situ couplings. In those situations in which the portion of the total energy stored in the satellite HO’s and in the couplings substantially exceeds the stored energy in the master HO, the I-loss factor and the U-loss factor may substantially exaggerate the true loss factor of the coupled master HO. Situations of this type are illustrated by data obtained in computational experiments, and it is argued that the true loss factor of the master HO in the complex as a whole is the effective loss factor.

Passive stress-strain measurements in the stage-16 and stage-18 embryonic chick heart.

The first stress-strain measurements on embryonic cardiovascular tissue are described here, obtained from cyclic uniaxial loading of the primitive ventricle. An excised ventricular segment from Hamburger/Hamilton stage-16 or stage-18 chicks (2-1/2 and 3 days of a 21-day incubation period) was mounted longitudinally between two small wires in oxygenated Krebs-Henseleit cardioplegia solution. One wire was attached to an ultrasensitive force transducer and the other to a Huxley micromanipulator controlled by remote motor drive. A real-time video tracking system calculated three myocardial surface strains based on the positions of three surface markers while the heart was deformed in a triangular wave pattern. Force transducer output was filtered, digitally sampled, and stored with strains and time. Results were plotted as strain (longitudinal, circumferential, shear, and principal) versus time, stress versus time, and stress versus longitudinal strain. The stress-strain curves were nonlinear, even at low strain levels. The hysteresis loops were large; mean hysteresis energy as a proportion of total cycle stored strain energy was 36 percent (stage 16) and 41 percent (stage 18). We created a finite element model of the ventricle and fit the model behavior to the experimental behavior to determine parameters for a stage-18 pseudoelastic strain-energy function of exponential form. The calculated exponential parameter is significantly lower than that found in corresponding uniaxial studies of mature myocardium, possibly indicating the lower fiber content of the immature tissue. The results of this study are the first step in characterizing material properties for comparisons with later developmental stages and with impaired and altered myocardium. The long-term goal is to aid in identifying the biomechanical factors regulating growth and morphogenesis.

Functional dependence of the lower hybrid power absorption coefficient in JET

The fraction of the coupled lower hybrid (LH) power absorbed in divertor plasmas in JET has been determined experimentally with a method utilizing the time derivative of the total stored energy (plasma and magnetic). This method can account for the power absorbed inside a normalized flux coordinate . The experimental LH absorption coefficient reaches 100% at low plasma densities, , and decreases to 25% at . The LH wave accessibility to the plasma core has been found to play an important role in determining the power absorption and the radial deposition profile. The decreasing absorption is correlated with a gradual shift of the LH power deposition profile, as determined by the hard x-ray profiles, towards the plasma periphery. Similar behaviour is found in ray-tracing + Fokker - Planck code calculations. The frequency spectrum of the LH pump wave, as determined by a probe outside the tokamak vessel, broadens strongly as the wave accessibility is reduced and the absorption drops.

The ITER magnet system

The main components of the ITER magnet system include 20 toroidal field (TF) coils, a central solenoid (CS), seven poloidal field (PF) coils and structural elements. The TF coils operate at a maximum field of 12.5 T with a total stored energy of about 100 GJ. These coils are enclosed in stainless steel cases that form the major part of an integrated mechanical structure and are bucked on the CS. The CS provides about 140 MA turns at a maximum field of 13 T. In the reference design, the CS is a monolithic, 12 m tall coil. An alternative segmented CS design is being considered to extend the range of operational flexibility and plasma control capability. The PF coil system comprises seven coils, with diameters up to 30 m, for plasma and shape control. The salient activity of the ITER R&D programme is the manufacture of model coils. The conductor production for these coils is well underway and construction of the coils has started. The initiation of the model coil test programme is scheduled for mid 1998.

Design and performance of a high-average-power flashlamp-pumped Ti:sapphire laser and amplifier

Design, performance and characterization of a high average-power flashlamp-pumped Ti:sapphire oscillator and amplifier are presented. The extensive design study, which covers the whole excitation process of the laser, focused on efficient laser operation at high average powers but also took into consideration the practicability of the laser device. For the first time, pumplight-induced absorptions in Ti:sapphire and their avoidance by appropriate filtering were investigated. The laser performance could be improved, firstly, due to the proper design of the discharge circuit, which resulted in an increased spectral overlap of the flashlamp-emission with the Ti:sapphire absorption. Secondly, the insight into the consequences of the flashlamp plasma reabsorption in conjunction with a small-spectral-band-transmitting pump-light filter led to a simple, experimentally confirmed transfer-efficiency reflector model and, based on this, to an improved reflector shape. As a result of the study, average powers of up to 220 W at a total laser efficiency of 2.25% have been achieved, Also, a single-pass small-signal gain of 3.1 and a total stored energy in the laser rod of 690 mJ at 100-Hz repetition rate could be demonstrated. This significant improvement over former flashlamp-pumped Ti:sapphire lasers and amplifiers for the first time opens up the possibility of femtosecond-pulse amplification to high average powers at 100 Hz repetition rate.

Confinement analysis in low-confinement mode of hydrogen isotope experiments on the Tokamak Fusion Test Reactor

The effect of isotope on confinement in high-recycling, L-mode plasmas is studied on the Tokamak Fusion Test Reactor (TFTR) [see D. M. Meade, J. Fusion Energy 7, 107 (1988)] by comparing hydrogen and deuterium plasmas with the same magnetic field and similar electron densities and heating power, with both Ohmic and deuterium-neutral-beam heating. Following a long operational period in deuterium, nominally hydrogen plasmas were created through hydrogen glow discharge and hydrogen gas puffing in Ohmic plasmas, which saturated the exposed limiter surface with hydrogen and raised the H/(H+D) ratio from 10±3% to 65±5%. Ohmic deuterium discharges obtained higher stored energy and lower loop voltage than hydrogen discharges with similar limiter conditions. Neutral-beam power scans were conducted in L-mode plasmas at minor radii of 50 and 80 cm, with plasma currents of 0.7 and 1.4 MA. To minimize transport differences from the beam deposition profile and beam heating, deuterium neutral beams were used to heat the plasmas of both isotopes. Total stored energy increased approximately 20% from nominally hydrogen plasmas to deuterium plasmas during auxiliary heating. Of this increase about half can be attributed to purely classical differences in the energy content of unthermalized beam ions. Kinetic measurements indicate a consistent but small increase in central electron temperature and total stored electron energy in deuterium relative to hydrogen plasmas, but no change in total ion stored energy. No significant differences in particle transport, momentum transport, and sawtooth behavior are observed. Overall, only a small improvement (∼10%) in global energy confinement time of the thermal plasma is seen between operation in hydrogen and deuterium.