An Electron Model with Synchrotron Radiation

Abstract

A classical model of the electron based on Maxwell's equations is presented in which the wave character is described by classical physics. Most properties follow from the description of a classical massless charge circulating with v\,=\,c. The magnetic moment of the electron yields the radius of this circulation and the generated synchrotron radiation removes the singularity of the Coulomb field and generates the mass of the electron. Quantum mechanics yields its size and the angular moment. The fine structure constant $\alpha$ compares this dynamic structure of the electron with the classical point-like static view. This configuration is not stable. It will decay by the emission of synchrotron radiation. The stability of this description is therefor investigated by extending this model to 3 dimensions. The field lines within the free electromagnetic fields of the creation process, solved in polar coordinates, yield possible tracks for a massless charge. Many possible circulating tracks are found but only a combination of background fields yield environments in which stable tracks for $\beta =1$ - charges may be created. Knotted toroidal tracks yield the stability. A knotted field line e.g. with T(3,2)-symmetry may describe a spin-1/3-particle and a field line with T(2,3)-symmetry in form of a knotted trefoil may belong to an electron as a stable spin-1/2-particle. With its fixed internal revolution frequency this electron appears to the external world as a standing wave with an amplitude propagating like the de Broglie wave. Keywords: - Electron - Classical wave model - Spherical wave field - Elementary charge - Mass - Knotted structure - Wave character