The properties of radiation created by a classical ultrarelativistic scalarcharged particle in a constant homogeneous crossed electromagnetic field aredescribed both analytically and numerically with radiation reaction taken intoaccount in the form of the Landau-Lifshitz equation. The total radiationnaturally falls into two parts: the radiation formed at the entrance point of aparticle into the crossed field (the synchrotron entrance radiation), and theradiation coming from the late-time asymptotics of a particle motion (thede-excited radiation). The synchrotron entrance radiation resembles, althoughdoes not coincide with, the ultrarelativistic limit of the synchrotronradiation: its distribution over energies and angles possesses almost the sameproperties. The de-excited radiation is soft, not concentrated in the plane ofmotion of a charged particle, and almost completely circularly polarized. Thephoton energy delivering the maximum to its spectral angular distributiondecreases with increasing the initial energy of a charged particle, while themaximum value of this distribution remains the same at the fixed observationangle. The ultraviolet and infrared asymptotics of the total radiation are alsodescribed.
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