Monte Carlo calculation of multi-electron effects on synchrotron radiation

The phase space distribution and time structure of an electron beam have fundamental influences on synchrotron radiation properties. These influences are due to the superposition of radiation from all electrons, each following a different trajectory. When the radiation wavelength is longer than the electron bunch length, coherent superposition occurs and results in the observed coherent synchrotron radiation. Usually the wavelength we use is much shorter, so incoherent superposition occurs and the emittance effect is the dominant multi-electron effect. The Monte Carlo simulation is a straightforward and generally valid approach to compute the multi-electron effects on synchrotron radiation. In this paper, we show how the Monte Carlo method can model these multi-electron effects systematically and discuss the statistical principles governing such simulation and their implication on the computing power requirement. We also describe the implementation of an efficient algorithm to calculate a single electron radiation spectrum, which is important to make the Monte Carlo simulation practical. Some calculated results are shown to demonstrate the methods. Comments on the usefulness and limitation of the Monte Carlo method are presented