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.

J. R. Wilson

Papers

Explosive‐Driven Magnetic‐Field Compression Generators