A precision measurement of the cosmic-ray positron spectrum may help to solve the puzzle of the nature of dark matter. Pairwise annihilation of neutralinos, predicted by some supersymmetric extensions to the standard model of particle physics, may leave a distinct feature in the cosmic-ray positron spectrum. As the available data are limited both in terms of statistics and energy range, we are developing a balloon-borne detector (PEBS) with a large acceptance of 4000 cm^2 sr. A superconducting magnet creating a field of 0.8 T and a tracking device consisting of scintillating fibers of 0.25 mm diameter with silicon photomultiplier readout will allow rigidity and charge determination to energies above 100 GeV. The dominant proton background is suppressed by the combination of an electromagnetic calorimeter and a transition radiation detector consisting of fleece layers interspersed with straw-tube proportional counters. The calorimeter uses a sandwich of tungsten and scintillating fibers that are again read out by silicon photomultipliers.
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