HADES is a versatile magnetic spectrometer aimed at studying dielectron production in pion, proton and heavy-ion induced collisions. Its main features include a ring imaging gas Cherenkov detector for electron-hadron discrimination, a tracking system consisting of a set of 6 superconducting coils producing a toroidal field and drift chambers and a multiplicity and electron trigger array for additional electron-hadron discrimination and event characterization. A two-stage trigger system enhances events containing electrons. The physics program is focused on the investigation of hadron properties in nuclei and in the hot and dense hadronic matter. The detector system is characterized by an 85 % azimuthal coverage over a polar angle interval from 18• to 85• , a single electron efficiency of 50 % and a vector meson mass resolution of 2.5 %. Identification of pions, kaons and protons is achieved combining time-of-flight and energy loss measurements over a large momentum range. This paper describes the main features and the performance of the detector system.

The acoustic and entropy transfer functions of quasi-one-dimensional nozzles are studied analytically for both subsonic and choked flows with and without shock waves. The present analytical study extends both the compact nozzle solution obtained by Marble & Candel (1977) and the effective nozzle length proposed by Stow et al. (2002) and by Goh & Morgans (2011a) to non-zero frequencies for both modulus and phase through an asymptotic expansion of the linearized Euler equations. It also extends the piecewiselinear approximation of the velocity profile in the nozzle proposed by Moase et al. (2007) to any arbitrary profile or equivalently any nozzle geometry. The equations are written as a function of three variables, namely the dimensionless mass, total temperature and entropy fluctuations, yielding a first order linear system of differential equations with varying coefficients, which is solved using the Magnus expansion. The solution shows that both the modulus and the phase of the transfer functions of the nozzle have a strong dependence on the frequency. This holds for both choked flows and subsonic converging diverging nozzles. The method is used to compare two different nozzle geometries with the same inlet and outlet Mach numbers showing that, even if the compact solution predicts no differences between the transfer functions of the two nozzles, significant differences are found at non-zero frequencies. A parametric study is finally performed to calculate the indirect to direct noise ratio for a model combustor, showing that this ratio decreases at higher frequencies.

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