In this paper we review a number of auxiliary space based preconditioners for the second order deflnite and semi-deflnite Maxwell problems discretized with the lowest order Nedelec flnite elements. We discuss the parallel implementation of the most promising of these methods, the ones derived from the recent Hiptmair-Xu (HX) auxiliary space decomposition (Hiptmair and Xu, SIAM J. Numer. Anal., 45 (2007), pp. 2483-2509). An extensive set of numerical experiments demonstrate the scalability of our implementation on large-scale H(curl) problems.

PARALLEL AUXILIARY SPACE AMG FOR H(curl) PROBLEMS

An instrument has been developed that reliably generates pulsed magnetic fields in the range 150-250 T for experimental applications. A 100 kJ, 40 kV capacitor bank with 18 nH internal inductance and 2.9 m Omega internal resistance is discharged into single turn coils made of copper sheet of 3 mm thickness. 150 T are obtained in 10 mm diameter with a rise time (quarter period) of 2.5 mu s, 200 T are obtained in 6 mm ID within 2 mu s and 250 T in 4 mm ID within 1.8 mu s. Although the coils explode violently and generate a strong axial blast, there is no movement towards the magnetic field volume and even delicate samples can easily be protected to survive an experiment unharmed. This is demonstrated with two experiments: infra-red cyclotron resonance in a GaAs-AlGaAs superlattice and Faraday rotation in GaP.

A laboratory instrument for generating magnetic fields over 200 T with single turn coils

A kilo-tesla level, quasi-static magnetic field (B-field), which is generated with an intense laser-driven capacitor-coil target, was measured by proton deflectometry with a proper plasma shielding. Proton deflectometry is a direct and reliable method to diagnose strong, mm3-scale laser-produced B-field; however, this was not successful in the previous experiment. A target-normal-sheath-accelerated proton beam is deflected by Lorentz force in the laser-produced magnetic field with the resulting deflection pattern recorded on a radiochromic film stack. A 610 ± 30 T of B-field amplitude was inferred by comparing the experimental proton pattern with Monte-Carlo calculations. The amplitude and temporal evolutions of the laser-generated B-field were also measured by a differential magnetic probe, independently confirming the proton deflectometry measurement results.

Direct measurement of kilo-tesla level magnetic field generated with laser-driven capacitor-coil target by proton deflectometry

A compact, self-contained magnetic-seed-field generator (5 to 16 T) is the enabling technology for a novel laser-driven flux-compression scheme in laser-driven targets. A magnetized target is directly irradiated by a kilojoule or megajoule laser to compress the preseeded magnetic field to thousands of teslas. A fast (300 ns), 80 kA current pulse delivered by a portable pulsed-power system is discharged into a low-mass coil that surrounds the laser target. A >15 T target field has been demonstrated using a <100 J capacitor bank, a laser-triggered switch, and a low-impedance (<1 Ω) strip line. The device has been integrated into a series of magnetic-flux-compression experiments on the 60 beam, 30 kJ OMEGA laser [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)]. The initial application is a novel magneto-inertial fusion approach [O. V. Gotchev et al., J. Fusion Energy 27, 25 (2008)] to inertial confinement fusion (ICF), where the amplified magnetic field can inhibit thermal conduction losses from the hot s...

Seeding magnetic fields for laser-driven flux compression in high-energy-density plasmas

Various types of explosive flux compression generators are illustrated and their relative advantages are compared. Experiments are described in which energy was supplied by these generators. The experiments were selected to show both versatility and limitations of the devices. Generator principles are derived from lumped parameter circuit theory. ,

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Introduction to explosive magnetic flux compression generators

An explosive‐driven magnetic‐field compression device can be used as a source of a large pulse of electrical energy. We describe a number of such systems, showing how their measured output currents compare with theoretical calculations. Both large‐inductance coil geometries and low‐inductance coaxial geometries are discussed. Energy losses due to resistive heating, wall compression, electrical breakdown, and gas compression are considered. A numerical calculation procedure for coaxial generators is also described. We have built and tested coaxial generators whose measured output current can be accounted for by calculations of resistive heating and wall compression. Coil geometry generators are measured to be less efficient than calculated. Our results also show that further investigations of electrical breakdown and gas compression effects are needed.

Explosive‐Driven Magnetic‐Field Compression Generators

We attempted to implode a conducting metal linear at high velocity, and our failure to do so led to switching, or rapidly transferring the field from pushing an aluminum conductor to snow-plowing a half-atmosphere of xenon gas. We successfully initiated convergent xenon gas shocks with the use of a magnetohydrodynamic switch and coaxial high-explosive, flux-compression generators. Principal diagnostics used to study the imploding xenon gas were /sup 133/Xe radioactive tracers, continuous x-ray absorption, and neutron output. We compressed the xenon gas about five to sixfold at a velocity of 10 cm/..mu..s at a radius of 4 cm. The snowplow efficiency was good; going from 13- to 4-cm radius, we lost only about 20% of the mass. The temperature of the imploded sheath was determined by mixing deuterium with the xenon and measuring the neutron output. Using reasonable assumptions about the amount, density, and uniformity of the compressed gas, we estimate that we reached temperatures as high as 155 eV. Energy-loss mechanisms that we encountered included wall ablation and Taylor instabilities of the back surface.

Converging xenon shock waves driven by megagauss magnetic fields

We summarize several years work aimed at utilizing high magnetic fields, produced by high-explosive flux-compression generators, for accelerating to high velocity a 1-cm-long metal liner in flat-plate geometry. The liner did not remain intact, even in a vaporized state, for more than a few centimeters of travel between two parallel conducting walls. We believe that liner bowing from pressure of the magnetic field prior to melt causes the liner to move to the walls rather than straight ahead between walls.

Flat-plate experiments on magnetically accelerated metal liners

High-explosive-driven, magnetic-field generators can routinely produce currents on the order of hundreds of megamperes and magnetic fields of several megagauss. However, for applications such as shock tubes, these generators compress the magnetic flux much too slowly. Using a relatively small and inexpensive high-explosive-driven generator, we have developed an aluminum switch which is opened by the pressure produced by the high magnetic field. While approximately 10% of the magnetic flux leaks through the switch early, most of the current is switched from the aluminum to a half-atmosphere of xenon gas in a time less than 2/3 of a microsecond. The xenon is compressed approximately 3-fold, and this compressed sheath reaches a velocity of nearly 4 cm/μs. However, the sheath is less dense and less uniformly compressed than similar, slightly slower-moving sheaths driven by fast capacitor banks.

D. J. Steinberg

Papers

Explosive‐Driven Magnetic‐Field Compression Generators

Converging xenon shock waves driven by megagauss magnetic fields

Flat-plate experiments on magnetically accelerated metal liners

Fast opening switches carrying multimegampere currents and their application to high velocity shock waves in xenon