LAW OF LARGE NUMBERS OF PROBABILITY THEORY AND FORMATION OF THE ENERGY SPECTRUM OF SYNCHROTRON RADIATION OF RELATIVISTIC ELECTRON IN THE STORAGE RING

The fluctuations of synchrotron radiation (SR) energy losses during the motion of relativistic electrons in the uniform magnetic field in a storage ring are considered. The influence on the formation of the energy spectrum of the SR photon flux of the duration of registration of SR relativistic electrons is analyzed. It has been established that with the increase in the duration of temporal registration, the energy spectrum of the SR photon flux is regularly transformed into the asymptotically normal density in accordance with the law of large numbers of probability theory. It is determined that the main mechanism in the formation of the energy spectrum is successive convolutions of the current spectra.