45 research outputs found

    Hypertiling -- a high performance Python library for the generation and visualization of hyperbolic lattices

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    Hypertiling is a high-performance Python library for the generation and visualization of regular hyperbolic lattices embedded in the Poincar\'e disk model. Using highly optimized, efficient algorithms, hyperbolic tilings with millions of vertices can be created in a matter of minutes on a single workstation computer. Facilities including computation of adjacent vertices, dynamic lattice manipulation, refinements, as well as powerful plotting and animation capabilities are provided to support advanced uses of hyperbolic graphs. In this manuscript, we present a comprehensive exploration of the package, encompassing its mathematical foundations, usage examples, applications, and a detailed description of its implementation.Comment: 52 pages, 20 figure

    Bright Coherent Ultrahigh Harmonics in the keV X-ray Regime from Mid-Infrared Femtosecond Lasers

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    High-harmonic generation (HHG) traditionally combines ~100 near-infrared laser photons to generate bright, phase-matched, extreme ultraviolet beams when the emission from many atoms adds constructively. Here, we show that by guiding a mid-infrared femtosecond laser in a high-pressure gas, ultrahigh harmonics can be generated, up to orders greater than 5000, that emerge as a bright supercontinuum that spans the entire electromagnetic spectrum from the ultraviolet to more than 1.6 kilo–electron volts, allowing, in principle, the generation of pulses as short as 2.5 attoseconds. The multiatmosphere gas pressures required for bright, phase-matched emission also support laser beam self-confinement, further enhancing the x-ray yield. Finally, the x-ray beam exhibits high spatial coherence, even though at high gas density the recolliding electrons responsible for HHG encounter other atoms during the emission process.The experimental work was funded by a National Security Science and Engineering Faculty Fellowship, and the NSF Center for EUV Science and Technology. A.G., A.J.-B., M.M.M., H.C.K. and A. Becker acknowledge support for theory from the U.S. Air Force Office of Scientific Research (grant no. FA9550-10-1-0561); A. Baltuška acknowledges support from Austrian Science Fund (FWF, grant no. U33-16) and the Austrian Research Promotion Agency (FFG, Project 820831 UPLIT); and C.H.-G. and L.P. acknowledge support from Junta de Castilla y León, Spanish MINECO (CSD2007-00013 and FIS2009-09522), and from Centro de Láseres Pulsados, CLPU. T.P., M.-C.C., A. Bahabad, M.M.M. and H.C.K. have filed for a patent on “Method for phase-matched generation of coherent soft and hard X-rays using IR lasers,” U.S. patent application 61171783 (2008)

    Lawson Criterion for Ignition Exceeded in an Inertial Fusion Experiment

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    Lawson criterion for ignition exceeded in an inertial fusion experiment

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    For more than half a century, researchers around the world have been engaged in attempts to achieve fusion ignition as a proof of principle of various fusion concepts. Following the Lawson criterion, an ignited plasma is one where the fusion heating power is high enough to overcome all the physical processes that cool the fusion plasma, creating a positive thermodynamic feedback loop with rapidly increasing temperature. In inertially confined fusion, ignition is a state where the fusion plasma can begin "burn propagation" into surrounding cold fuel, enabling the possibility of high energy gain. While "scientific breakeven" (i.e., unity target gain) has not yet been achieved (here target gain is 0.72, 1.37 MJ of fusion for 1.92 MJ of laser energy), this Letter reports the first controlled fusion experiment, using laser indirect drive, on the National Ignition Facility to produce capsule gain (here 5.8) and reach ignition by nine different formulations of the Lawson criterion
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