Floating orbit method in the synchrotron radiation theory

The effect of the electron betatron oscillations in soft focusing accelerators on the polarizational-angular distribution and synchrotron radiation spectrum is studied. The floating orbit technique utilizing specific features of the ultrarelativistic particles (short duration of the light pulse, small values of radiation angle PSI and relativistic factor 1/γ) is used in the analysis. It is found that both radial and vertical betatron oscillations contribute to the complete power of instantaneous radiation. The spectral-angular radiation energy distribution does not depend on the initial phase of radial oscillations and is connected with the initial phase of vertical oscillations only. The betatron oscillations do not affect the linear polarization components energy ratio. In the median plane only vertical oscillations contribute to the linear polarization component energy along the magnetic field. The radiation maximum is shifted to the high frequency domain