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 observation angle. The ultraviolet and infrared asymptotics of the total radiation are also described.
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GAP/Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等技术学院等离子体与核聚变研究所）；CEA, DAM, DIF（法国原子能及替代能源委员会）；Université Paris-Saclay, CEA, LMCE（巴黎萨克雷大学）；Helmholtz-Institut Jena（耶拿亥姆霍兹研究所）；Laboratoire d’Optique Appliquée (LOA), CNRS, École polytechnique, ENSTA, Institut Polytechnique de Paris（巴黎理工学院应用光学实验室）；Max-Planck-Institut für Kernphysik（马克斯·普朗克核物理研究所）
