Properties of an ultrarelativistic charged particle radiation in a constant homogeneous crossed electromagnetic field

The properties of radiation created by a classical ultrarelativistic scalar charged particle in a constant homogeneous crossed electromagnetic field are described both analytically and numerically with radiation reaction taken into account in the form of the Landau–Lifshitz equation. The total radiation naturally falls into two parts: the radiation formed at the entrance point of a particle into the crossed field (the synchrotron entrance radiation), and the radiation coming from the late-time asymptotics of a particle motion (the de-excited radiation). The synchrotron entrance radiation resembles, although does not coincide with, the ultrarelativistic limit of the synchrotron radiation: its distribution over energies and angles possesses almost the same properties. The de-excited radiation is soft, not concentrated in the plane of motion of a charged particle, and almost completely circularly polarized. The photon energy delivering the maximum to its spectral angular distribution decreases with increasing the initial energy of a charged particle, while the maximum value of this distribution remains the same at the fixed photon observation angle and entrance angle of a charged particle. The ultraviolet and infrared asymptotics of the total radiation are also described. - Highlights: • Properties of an electron radiation in a crossed electromagnetic field are studied. • Spectral angular distribution of the synchrotron entrance radiation is described. • Spectral angular distribution of the de-excited radiation is described. • De-excited radiation is almost completely circularly polarized. • Photon energy at the maximum of the de-excited radiation decreases with increasing the initial energy of an electron.