Isotropy is a key assumption in many models of cosmic-ray electrons and positrons. We find that simulation results imply a critical energy of ~10-1000 GeV above which electrons and positrons can spend their entire lives in streams threading magnetic fields, due to energy losses. This would restrict the number of electron/positron sources contributing at Earth, likely leading to smooth electron and positron spectra, as is observed. For positrons, this could be as few as one, with an enhanced flux that would ease energetics concerns of a pulsar origin of the positron excess, or even zero, bringing dark matter into play. We conclude that ideas about electron/positron propagation based on either isotropic diffusion or turbulent fields must be changed.
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