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We theoretically demonstrate for the first time that a single free electron in circular/spiral motion emits twisted photons carrying well defined orbital angular momentum along the axis of the electron circulation, in adding to spin angular momentum. We show that, when the electron velocity is relativistic, the radiation field contains harmonic components and the photons of l-th harmonic carry  l total angular momentum for each. This work indicates that twisted photons are naturally emitted by free electrons and more ubiquitous in laboratories and in nature than ever been thought.

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