Investigations on collective behavior in radiation process with random walk model

Coherent radiation, e.g. synchrotron radiation, transition radiation and diffraction radiation etc. are widely used for electron bunch length and longitudinal profile characterizations. Incoherent synchrotron radiation and transition radiation are usually used for beam's transverse profile measurements. When the study for a whole bunch is to be performed, the collective behavior of electrons in the radiation process should be properly considered. In this paper, the collective behavior in radiation process is studied in detail with random walk model. It is found that the microscopic discreteness and randomness of electrons within the bunch plays a great role in the radiation process especially for the incoherent radiation component. Only when the discreteness and randomness of electrons is taken into account can the theoretical prediction for incoherent radiation intensity and angular distribution of a whole bunch coincide with experimental results. The results derived from random walk model are in good agreement with experimental results and show clearer physical picture in the radiation process.