Supernova Reverse Shocks and SiC Growth

We present new mechanisms by which the isotopic compositions of X-type grains of presolar SiC are altered by reverse shocks in Type II supernovae. We address three epochs of reverse shocks: pressure wave from the H envelope near t = 10$^6$s; reverse shock from the presupernova wind near 10$^8-10^9$s; reverse shock from the ISM near 10$^{10}$s. Using 1-D hydrodynamics we show that the first creates a dense shell of Si and C atoms near 10$^6$s in which the SiC surely condenses. The second reverse shock causes precondensed grains to move rapidly forward through decelerated gas of different isotopic composition, during which implantation, sputtering and further condensation occur simultaneously. The third reverse shock causes only further ion implantation and sputtering, which may affect trace element isotopic compositions. Using a 25M$_{\odot}$ supernova model we propose solutions to the following unsolved questions: where does SiC condense?; why does SiC condense in preference to graphite?; why is condensed SiC $^{28}$Si-rich?; why is O richness no obstacle to SiC condensation?; how many atoms of each isotope are impacted by a grain that condenses at time t$_0$ at radial coordinate r$_0$? These many considerations are put forward as a road map for interpreting SiC X grains found in meteorites and their meaning for supernova physics.Comment: 28 pages, 14 figures, animation for Figure 3 and machine-readable Table 3 can be found at http://antares.steelangel.com/~edeneau/supernova/DHC_2003, Submitted to Ap

Surface impedance of superconductors with magnetic impurities

Motivated by the problem of the residual surface resistance of the superconducting radio-frequency (SRF) cavities, we develop a microscopic theory of the surface impedance of s-wave superconductors with magnetic impurities. We analytically calculate the current response function and surface impedance for a sample with spatially uniform distribution of impurities, treating magnetic impurities in the framework of the Shiba theory. The obtained general expressions hold in a wide range of parameter values, such as temperature, frequency, mean free path, and exchange coupling strength. This generality, on the one hand, allows for direct numerical implementation of our results to describe experimental systems (SRF cavities, superconducting qubits) under various practically relevant conditions. On the other hand, explicit analytical expressions can be obtained in a number of limiting cases, which makes possible further theoretical investigation of certain regimes. As a feature of key relevance to SRF cavities, we show that in the regime of "gapless superconductivity" the surface resistance exhibits saturation at zero temperature. Our theory thus explicitly demonstrates that magnetic impurities, presumably contained in the oxide surface layer of the SRF cavities, provide a microscopic mechanism for the residual resistance.Comment: 9 pages, 3 figs; v2: published versio