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The Alpha Magnetic Spectrometer (AMS) was flown on the space shuttle Discovery during flight STS-91 (June 1998) in a 51.7° orbit at altitudes between 320 and 390 km . A search for antihelium nuclei in the rigidity range 1–140 GV was performed. No antihelium nuclei were detected at any rigidity. An upper limit on the flux ratio of antihelium to helium of <1.1×10⁻⁶ was obtained. The high energy proton, electron, positron, helium, antiproton and deuterium spectra were accurately measured. For each particle and nuclei two distinct spectra were observed: a higher energy spectrum and a substantial second spectrum. Positrons in the second spectrum were found to be much more abundant than electrons. Tracing particles from the second spectra shows that most of them travel for an extended period of time in the geomagnetic field, and that the positive particles (p and e⁺) and negative ones (e⁻) originate from two …