Mechanical-Stress Analytical Modeling for the Design of Coils in Power Applications

Abstract Modern electrical-power systems are often exploited for transmitting high-frequency carrier signals for communications purposes. Series-connected air-core coils represent the fundamental component allowing such applications by providing a proper filtering in the frequency domain. They must be designed, however, to withstand also the line short-circuit current. When a high-magnitude current flows through a coil, strong mechanical stresses are produced within the conductor, leading to possible damage of the coil. In this paper, an approximate analytical model is derived for the relationship between the maximum mechanical stress and the electrical/geometrical parameters of the coil. Such a model provides the guidelines for a fast and safe coil design, whereas numerical simulations are only needed for the design refinement. The presented approach can be extended to other applications such as, for example, the mechanical stress resulting from the inrush currents in the coils of power transformers

Motion and equilibrium of a spheromak in a toroidal flux conserver

A number of experiments have been performed on spheromaks injected into the empty vacuum vessel of the Caltech ENCORE tokamak (i.e., without tokamak plasma) [Phys. Rev. Lett. 64, 2144 (1990); Phys. Fluids B 2, 1306 (1990)]. Magnetic probe arrays (in a number of configurations) have been used to make single shot, unaveraged, in situ measurements of the spheromak equilibrium. These measurements are important because (i) they reveal for the first time the equilibrium structure of spheromaks in a toroidal geometry, (ii) they provide a reliable estimate of magnetic helicity and energy of spheromak plasmas used in injection experiments [Phys. Rev. Lett. 64, 2144 (1990)], and (iii) they constitute the first measurements of spheromak motion across and interaction with static magnetic fields (which are useful in corroborating recent theories). Probe measurements in the tokamak dc toroidal field show for the first time that the spheromak exhibits a ``double tilt.''The spheromak first tilts while in the cylindrical entrance region, emerging into the tokamak vessel antialigned to the dc toroidal field, then expands into the tokamak vacuum vessel, and finally tilts again to form an oblate (nonaxisymmetric, m=1) configuration. In addition, the spheromak drifts vertically in the direction given by Jcenter×Btok, where Jcenter is the unbalanced poloidal current that threads the center of the spheromak torus. Probe arrays at different toroidal locations show that the spheromak shifts toroidally (horizontally left or right) in the direction opposite that of the static toroidal field. In the absence of toroidal flux, the m=1 object develops a helical pitch, the sense of the pitch depending on the sign of the spheromak helicity. The spheromak equilibrium in the toroidal vessel is well fit by a pressureless infinite cylindrical model; however, there is evidence of deviation from m=1 symmetry because of toroidal effects, nonuniform J/B profile, and finite beta. Experiments performed in a test facility consisting of the spheromak gun and a replica of the entrance region (with a closed end) show that the spheromak is generated with its axis coaxial with that of the gun. Coherent, m=2 magnetic modes are observed during the formation stage rotating in the E×B direction at about 125 kHz (rotation velocity corresponding to 40% of the Alfvén speed)

Poincaré maps define topography of Vlasov distribution functions consistent with stochastic dynamics

In a recent paper [A. D. Bailey et al., Phys. Rev. Lett. 34, 3124 (1993)], the authors presented direct planar laser induced fluorescence measurements of the oscillatory ion fluid velocity field in the presence of a large amplitude drift-Alfven wave. Surprisingly, the measured speeds were an order of magnitude lower than predicted by standard fluid theory, yet the flow pattern was consistent with the fluid theory. A new model, based on the connection between stochasticity and bulk behavior, is presented which gives insights into the cause of this behavior. It is shown that when particle motion is stochastic, invariant sets of a 'Poincaré map' define a flat-topped particle distribution function consistent with both the electromagnetic field driving the Vlasov equation and the fine-scale single particle dynamics. The approach is described for the general case and explored for a slab model of the observed drift wave

Characterization of a spheromak plasma gun: The effect of refractory electrode coatings

In order to investigate the proposition that high-Z impurities are responsible for the anomalously short lifetime of the Caltech spheromak, the center electrode of the spheromak plasma gun has been coated with a variety of metals (bare steel, copper, nickel, chromium, rhodium, and tungsten). Visible light (230–890 nm) emitted directly from the plasma in the gun breech was monitored for each of the coated electrodes. Plasma density and temperature and spheromak lifetime were compared for each electrode. Results indicate little difference in gun performance or macroscopic plasma parameters. The chromium and tungsten electrodes performed marginally better in that a previously reported helicity injection effect [Phys. Rev. Lett. 64, 2144 (1990)] is only observed in discharges using these electrode coatings. There are subtle differences in the detailed line emission spectra from the different electrodes, but the spectra are remarkably similar. The fact that (1) contrary to expectations, attempts to reduce high-Z impurities had only marginal effect on the spheromak lifetime coupled with (2) an estimate of Zeff<2 based on a 0-D model suggests that it is not impurities but some other mechanism that limits the lifetime of small, cold spheromaks. We will discuss the general characteristics of the spheromak gun as well as effects due to the coatings

Wheels within wheels: Hamiltonian dynamics as a hierarchy of action variables

In systems where one coordinate undergoes periodic oscillation, the net displacement in any other coordinate over a single period is shown to be given by differentiation of the action integral associated with the oscillating coordinate. This result is then used to demonstrate that the action integral acts as a Hamiltonian for slow coordinates providing time is scaled to the ``tick-time'' of the oscillating coordinate. Numerous examples, including charged particle drifts and relativistic motion, are supplied to illustrate the varied application of these results.Comment: 7 pages, 3 figure

Spheromak formation and sustainment studies at the sustained spheromak physics experiment using high-speed imaging and magnetic diagnostics

A high-speed imaging system with shutter speeds as fast as 2 ns and double frame capability has been used to directly image the formation and evolution of the sustained spheromak physics experiment (SSPX) [E. B. Hooper et al., Nucl. Fusion 39, 863 (1999)]. Reproducible plasma features have been identified with this diagnostic and divided into three groups, according to the stage in the discharge at which they occur: (i) breakdown and ejection, (ii) sustainment, and (iii) decay. During the first stage, plasma descends into the flux conserver shortly after breakdown and a transient plasma column is formed. The column then rapidly bends and simultaneously becomes too dim to photograph a few microseconds after formation. It is conjectured here that this rapid bending precedes the transfer of toroidal to poloidal flux. During sustainment, a stable plasma column different from the transient one is observed. It has been possible to measure the column diameter and compare it to CORSICA [A. Tarditi et al., Contrib. Plasma Phys. 36, 132 (1996)], a magnetohydrodynamic equilibrium reconstruction code which showed good agreement with the measurements. Elongation and velocity measurements were made of cathode patterns also seen during this stage, possibly caused by pressure gradients or E×B drifts. The patterns elongate in a toroidal-only direction which depends on the magnetic-field polarity. During the decay stage the column diameter expands as the current ramps down, until it eventually dissolves into filaments. With the use of magnetic probes inserted in the gun region, an X point which moved axially depending on current level and toroidal mode number was observed in all the stages of the SSPX plasma discharge