L.R. Turner

Problems and workshops for eddy current code comparison

Six problems have been proposed for testing eddy-current computer codes. The problems represent two-dimensional and three-dimensional geometries, steady-state and transient time variation, and near and far boundaries. Five regional workshops were held to compare solutions of the problems, followed by an international workshop at Graz, Austria. The workshops and problems are described. >

A volume integral formulation for nonlinear magnetostatics and eddy currents using edge elements

The properties of Whitney elements provide the basis of a novel integral formulation for solving three-dimensional magnetostatics and eddy-current problems. Using a tree structure reduces the number of unknowns to a few less than the number of nodes for the static case, a significant saving over earlier integral formulations. Interface conditions are satisfied exactly, but the material constitutive relations are satisfied only approximately. The resulting magnetostatics code, GFUNET, is attractive in terms of convenience, CPU time utilization, and accuracy. It realizes much of the speedup promised by parallel computing. Results for an accelerator sextupole magnet and for TEAM Workshop problem Hash 13 are presented. >

Magnetomechanics of internal-dipole, Halbach-array motor/generators

The magnetomechanical behavior of internal-dipole, Halbach-type magnet arrays is analyzed for application as a motor/generator (M/G) with an energy-storage flywheel that is suspended by low-stiffness bearings. Scaling laws for the maximization of torque are derived as a function of geometry. The optimal geometry is relatively insensitive to gap and stator design and occurs approximately at a ratio of inner to outer diameter of the array of 0.8. Values are found for the angular extent of each phase of the stator coil that minimize the stiffness. The negative stiffness of the internal-dipole array is calculated for several manufacturable configurations and is shown to provide an upper limit on the available torque of the M/G according to the positive stiffness of the bearings. Experimental results are reported for an internal-dipole array used as a M/G for a flywheel suspended by a bearing consisting of a permanent-magnet assembly levitated over an array of high-temperature superconductors. Results show that the system is stable and that idling losses are low.

Results from the Felix experiments on electromagnetic effects in hollow cylinders

The early experiments with the FELIX (Fusion Electromagnetic Induction eXperiments) facility have been devoted to obtaining data which can be used to validate eddy current computer codes. This paper describes experiments on field variation inside conducting cylinders.

An integral equation approach to eddy-current calculations

An integral-equation approach has been used to solve eddy current problems. The conducting material is represented by a network of current-carrying line elements. Consequently, Maxwells field equations can be replaced by Kirchhoffs circuit rules. The loop equations for voltages, supplemented by the node equations for the currents, comprise a set of linear equations that can be solved repeatedly to give the time development of the eddy currents. Currents, magnetic fields, and power are calculated at each step. For a two-dimensional geometry, either thin plates or infinite cylinders can be calculated. Rectangular and circular cross sections have been calculated with good agreement to analytical expressions. Thin curved shells have also been calculated.

The elliptical multipole wiggler project

The elliptical multipole wiggler (EMW) has been designed, constructed, and installed in the X13 straight section of the NSLS X-ray Ring. The EMW generates circularly polarized photons in the energy range of 0.1-10 keV with AC modulation of polarization helicity. The vertical magnetic field of 0.8 T is produced by a hybrid permanent magnet structure with a period of 16 cm. The horizontal magnetic field of 0.22 T is generated by an electromagnet, the core of which is fabricated from laminated iron to operate with a switching frequency up to 100 Hz. There are dynamic compensation trim magnets at the wiggler ends to control the first and second field integrals with very high accuracy throughout the AC cycle. The residual closed orbit motion due to the electromagnet AC operation is discussed.

Applications and further developments of the eddy current program EDDYNET

EDDYNET is a computer code for solving eddy current problems using an integral equation method and a network (wire mesh) approach. The code can be applied to infinitely long prisms, thin plates, and thin shell. Preliminary results with a three-dimensional version are described. Application to a tokamak limiter experiencing a plasma disruption is also described.

Developments in eddy current computation with EDDYNET

The eddy current computer code EDDYNET has been modified to incorporate, 2π/n symmetry, specification of current-crossing boundaries, a polar mesh generator, calculation of current density and temperature rise, calculation of forces and torques, a mesh with multiple sheets, and fields and fluxes from filamentary current rings. It has been successfully applied to find the forces and temperature rise of a conducting flat plate in a pulsed magnetic field and the currents in a hollow conducting torus.

Transient eddy current analysis for generalized structures using surface impedances and the fast Fourier transform

Surface impedances have primarily been utilized in eddy current problems, where the skin depth is small compared to the conductor thickness being modeled. Their use is extended to arbitrary-thickness conductors. In addition, the authors investigated modeling different shapes as combinations of slabs. In particular, a cylinder was emulated as a polygon of slabs to verify the versatility of the technique. The application to sinusoidal steady-state problems is straightforward. Of greater interest is the extension to the transient problem. A solution was sought via the fast Fourier transform. With the surface impedance method, the calculation of each frequency solution is fast; the overhead required in setting up the problem, albeit the integral or finite-element matrix is geometry-dependent only, and need be performed but once. The calculation of the transient response of a cylinder placed in an exponentially decaying field is computed and compared to analytic results. Some discussion is given on the benefits of breaking up the excitation field into parts that start and end at the same level. >

3-D field computation: the near-triumph of commercial codes

In recent years, more and more of those who design and analyze magnets and other devices are using commercial codes rather than developing their own. This paper considers the commercial codes and the features available with them. Other recent trends with 3-D field computation include parallel computation and visualization methods such as virtual reality systems.