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Betatron oscillation refers to the oscillations of particles around their equilibrium orbits in cyclic particle accelerators. This phenomenon was first theorized in the context of the betatron, a type of particle accelerator designed for electrons.

In a betatron, electrons move in a circular path due to a magnetic field. An increasing magnetic field also induces an electric field that accelerates the electrons. The betatron's design includes a tapered magnet that weakens the field with increasing radius. This feature causes particles that stray from their orbit to experience forces that guide them back, thus focusing the beam. The theory explaining this focusing effect led to the naming of these particle oscillations as betatron oscillations.12

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