Spectral Properties and High Brilliance Features of Two-Frequency Step Tapered Asymmetric Undulator Radiation

The theory of two frequency step tapered undulator radiation is developed with the help of generalized Bessel functions using an analytical transparent technique. In the approach, the radiation of a single electron on axis from the step sections of one-frequency and two-frequency undulator is derived as a sum of fields from the individual sections. It is shown that the radiation from the step sections superposes coherently and emits as proportional to the square of the number of step sections. This allows the undulator to behave as a high brilliance synchrotron radiation source. The analysis provides a simplest procedure to estimate the field taper in the tapered gap undulator.