Nonradiation condition

Classical nonradiation conditions define the conditions according to classical electromagnetism under which a distribution of accelerating charges will not emit electromagnetic radiation. According to the Larmor formula in classical electromagnetism, a single point charge under acceleration will emit electromagnetic radiation, i.e. light. In some classical electron models a distribution of charges can however be accelerated so that no radiation is emitted. The modern derivation of these nonradiation conditions by Hermann A. Haus is based on the Fourier components of the current produced by a moving point charge. It states that a distribution of accelerated charges will radiate if and only if it has Fourier components synchronous with waves traveling at the speed of light.

Finding a nonradiating model for the electron on an atom dominated the early work on atomic models. In a planetary model of the atom, the orbiting point electron would constantly accelerate towards the nucleus, and thus according to the Larmor formula emit electromagnetic waves. In 1910 Paul Ehrenfest published a short paper on "Irregular electrical movements without magnetic and radiation fields" demonstrating that Maxwell’s equations allow for the existence of accelerating charge distributions which emit no radiation. The need for a nonradiating classical electron was however abandoned in 1913 by the Bohr model of the atom, which postulated that electrons orbiting the nucleus in particular circular orbits with fixed angular momentum and energy would not radiate. Modern atomic theory explains these stable quantum states with the help of Schrödinger's equation.

...
Wikipedia