On twisted Fourier analysis and convergence of Fourier series on discrete groups

We study norm convergence and summability of Fourier series in the setting of reduced twisted group $C^*$-algebras of discrete groups. For amenable groups, F{\o}lner nets give the key to Fej\'er summation. We show that Abel-Poisson summation holds for a large class of groups, including e.g. all Coxeter groups and all Gromov hyperbolic groups. As a tool in our presentation, we introduce notions of polynomial and subexponential H-growth for countable groups w.r.t. proper scale functions, usually chosen as length functions. These coincide with the classical notions of growth in the case of amenable groups.Comment: 35 pages; abridged, revised and update

X-ray Conversion Efficiency of high-Z hohlraum wall materials for indirect drive ignition

We measure the conversion efficiency of 351 nm laser light to soft x-rays (0.1-5 keV) for Au, U and high Z mixtures 'cocktails' used for hohlraum wall materials in indirect drive ICF. We use spherical targets in a direct drive geometry, flattop laser pulses and laser smoothing with phase plates to achieve constant and uniform laser intensities of 10{sup 14} and 10{sup 15} W/cm{sup 2} over the target surface that are relevant for the future ignition experiments on NIF. The absolute time and spectrally-resolved radiation flux is measured with a multichannel soft x-ray power diagnostic. The conversion efficiency is then calculated by dividing the measured x-ray power by the incident laser power from which the measured laser backscattering losses is subtracted. After {approx}0.5 ns, the time resolved x-ray conversion efficiency reaches a slowly increasing plateau of 95% at 10{sup 14} W/cm{sup 2} laser intensity and of 80% at 10{sup 15} W/cm{sup 2}. The M-band flux (2-5 keV) is negligible at 10{sup 14} W/cm{sup 2} reaching {approx}1% of the total x-ray flux for all target materials. In contrast, the M-band flux is significant and depends on the target material at 10{sup 15} W/cm{sup 2} laser intensity, reaching values between 10% of the total flux for U and 27% for Au. Our LASNEX simulations show good agreement in conversion efficiency and radiated spectra with data when using XSN atomic physics model and a flux limiter of 0.15, but they underestimate the generated M-band flux