We present a new measurement of the cosmic-ray positron fraction e+/(e+ + e-) obtained from the first balloon flight of the High Energy Antimatter Telescope (HEAT). Using a magnet spectrometer combined with a transition radiation detector, an electromagnetic calorimeter, and time-of-flight counters we have achieved a high degree of background rejection. Our results do not indicate a major contribution to the positron flux from primary sources. In particular, we see no evidence for the significant rise in the positron fraction at energies above ~10 GeV previously reported.
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