We theoretically show that a single free electron in circular/spiral motion radiates an electromagnetic wave possessing helical phase structure and carrying orbital angular momentum. We experimentally demonstrate it by double-slit diffraction on radiation from relativistic electrons in spiral motion. We show that twisted photons should be created naturally by cyclotron/synchrotron radiations or Compton scatterings in various situations in cosmic space. We propose promising laboratory vortex photon sources in various wavelengths ranging from radio wave to gamma-rays.
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