No 4 (2018)



To avoid complex computations based on wide Fourier expansions, the electromagnetic field of synchrotron radiation (SR) was analyzed using Lienard–Wiechert potentials in this work. The retardation equation was solved for ultrarelativistic movement of rotating charge at distances up to the trajectory radius. The radiation field was determined to be constricted into a narrow extended region with transverse sizes approximately the radius of trajectory divided by the particle Lorentz factor (characteristic SR length) cubed in the plane of trajectory and the distance between the observation and radiation emission point divided by the Lorentz factor in the vertical direction. The Lienard–Wiechert field of rotating charge was visualized using a parametric form to derive electric force lines rather than solving a retardation equation. The electromagnetic field of a charging point rotating at superluminal speeds was also investigated. This field, dubbed a superluminal synchrotron radiation (SSR) field by analogy with the case of a circulating relativistic charge, was also presented using a system of electric force lines. It is shown that SSR can arise in accelerators from “spot” of SR runs faster than light by outer wall of circular accelerator vacuum chamber. Furthermore, the mentioned characteristic lengths of SR in orbit plane and in vertical direction are less than the interparticle distances in real bunches in ultrarelativistic accelerators. It is indicating that this phenomenon should be taken into account when calculating bunch fields and involved at least into the beam dynamic consideration.


synchrotron radiation, Lienard–Wiechert, electrical field lines, superluminal, particle accelerator


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M.A. Aginian

S.G. Arutunian

E.G. Lazareva

A.V. Margaryan

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