R.D. Pillsbury

A three dimensional eddy current formulation using two potentials: The magnetic vector potential and total magnetic scalar potential

A formulation of the three dimensional eddy current problem is presented. The magnetic vector potential is used in regions with source currents and conducting material and the total magnetic scalar potential is employed elsewhere. The continuity of the normal component of flux density and tangential component of field intensity are used to couple the two potentials on the interface between regions. The formulation leads to a symmetric system amenable to traditional solution techniques. The formulation is also valid for static problems with modification that are easily implemented.

A finite element/Fourier expansion technique for the design of a pulsed radial gradient system for magnetic resonance imaging (MRI)

A finite element/Fourier expansion technique is presented for use in the design of a coil system for producing pulsed radial gradients for Magnetic Resonance Imaging (MRI). The technique employs the high magnetic Reynolds number approximation and a Fourier expansion technique to the three dimensional eddy current problem to allow the solution of a sequence of two dimensional axisymmetric problems. The details of the algorithm will be presented along with examples of its application to the design of a radial gradient system for a whole-body MRI system.

TPX superconducting tokamak magnet system 1995 design and status overview

The TPX magnet preliminary design effort is summarized. Key results and accomplishments during preliminary design and supporting R&D are discussed, including conductor development, quench detection, TF and PF magnet design, conductor bending and forming, reaction heat treating, helium stubs, and winding pack insulation.

Superconducting magnet protection system for the Tokamak Physics Experiment

The TPX Tokamak must protect 30 superconducting magnets during a complex, pulsed physics scenario. 2.0 MA plasma vertical disruptions will occur at unpredictable intervals. These should not cause quench, but will be difficult to distinguish from quench. A redundant, multiple signal protection system combines conventional voltage taps with signals from cowound conductors, pressure and flow sensors. >

A 60 cm bore 2.0 tesla high homogeneity magnet for magnetic resonance imaging

A 60 cm warm bore imaging and spectroscopy magnet has been constructed and placed in operation at the Francis Bitter National Magnet Laboratory (FBNML). The magnet achieved its design central field of 2.0 T but is currently being operated at 1.5 T. It operates in the persistent mode with a measured decay rate of less than 0.03 ppm/hr. Employment of both 10 superconducting shims and small ferromagnetic shims located close to the warm bore has resulted in a homogencity of better than 3 ppm throughout the 25 cm diameter spherical volume (DSV). Room temperature shim coils have not been incorporated into the system. A novel form of compact shielded pulsed gradient coil system has been designed, constructed and tested. In such a system, appropriate configuration of an external shield coil results in cancellation of external flux without the introduction of impurity harmonics that degrade the linearity of the gradients. Six sets (X, Y, Z coils, and X, Y, Z shields) have been incorporated into a unit of 6 cm build. The all aluminum cryostat employs a 77 K nitrogen recondenser and a shield cooler operating at less than 20 K. Steady state helium consumption is about 50 ml/hour. The system is currently being used for both high resolution, in-vivo31P-NMR spectroscopy and a variety of MRI experiments including23Na imaging of eyes.

PQUENCH-A 3-D quench propagation code using a logical coordinate system

A computer program was developed to model the effects of normal region propagation in the longitudinal direction (along the conductor) and in the two transverse directions in a superconducting coil in a multicoil system. A simulation of 3-D quench propagation in real space was done using a logical coordinate system in which each magnet is transformed into a single long conductor which is divided into finite-length elements. Since an element can be associated with geometry-related information such as the element length, the local magnetic field influence coefficients, and the relationship to adjacent elements in 3-D, the quench propagation in any type of 3-D configuration can be simplified to a 1-D problem. As the growth of the normal region is determined, the transient current decay is calculated based on increases in conductor temperature and resistance. This calculation can be done for multiple, inductively coupled systems through the use of a circuit analysis subroutine. The code logic is described, and results are given for calculated versus measured quench times in a single-coil system.

Superconducting magnet system for the TPX Tokamak

The Tokamak Physics Experiment (TPX) will be the first Tokamak using superconducting magnets for both the poloidal and toroidal field. It is designed for advanced Tokamak physics experiments in steady-state and long-pulse operation. The TPX superconducting magnets use an advanced cable-in-conduit conductor (CICC) design similar to that developed in support of the International Thermonuclear Experimental Reactor (ITER). The toroidal field magnets provide 4.0 T at 2.25 m with a stored energy of 1.05 GJ. The poloidal field magnets provide 18.0 V-s to ohmically start and control long burns of a 2.0 MA plasma. >

Modelling of plasma start-up in ITER

A general eigenexpansion/least squares fit algorithm is described which can be used to determine the PF coil voltage waveforms required to break down, initiate, and ramp a plasma current in a tokamak. The technique is applied to ITER (International Thermonuclear Experimental Reactor). The technique includes the effects of passive structure eddy currents. In addition, the eigenexpansion technique does not require a time step size consistent with any numerical stability limits. The constant voltages during each time segment calculated on the basis of the procedure described produce the desired loop voltage and field quality during the three phases of start-up. >

NMLMAP-A two dimensional finite element program for transient or static, linear or nonlinear magnetic field problems

NMLMAP is a finite element program for the solution of two dimensional magnetic field problems. The problems may be transient or static, linear or nonlinear, and planar or axisymmetric. The program has features that include a coarse-to-fine rezone technique; an adaptive acceleration method for speeding the convergence of the nonlinear iteration; and a substructuring technique for decreasing solution times in certain non-linear problems. These features, the governing and finite element equations, and example problems are discussed

Eddy current heating in the cold structure in TPX

The toroidal field end cases and support structure for the TPX are at cryogenic temperatures. The time varying currents in the poloidal field coil system will induce eddy currents in these structures. The associated Joule dissipation will cause local heating and require heat removal which will show up as a load on the cryogenic system. Knowledge of the heat load distribution in both space and time is important to the design of the system. Analyses have been performed using programs EDDYCUFF and ANSYS and the results presented. >