Investigation of a method to calculate spontaneous radiation spectra from relativistic electrons in undulators

Undulators are key devices to produce brilliant synchrotron radiation at the synchrotron radiation facilities. In this paper we present a numerical computing method, including the computing program that has been developed to calculate the spontaneous radiation emitted from relativistic electrons in undulators by simulating the electrons＇ trajectory. The effects of electron beam emittance and energy spread have also been taken into account. Comparing with other computing methods available at present, this method has a few advantages with respect to several aspects. It can adopt any measured or arbitrarily simulated 3D magnetic field and arbitrary electron beam pattern for the calculation and it＇s able to analyze undulators of any type of magnetic structure. It＇s expected to predict precisely the practical radiation spectrum. The calculation results of a short period in-vacuum undulator and an Elliptically Polarized Undulator （EPU） at Shanghai Synchrotron Radiation Facility （SSRF） are presented as examples.

Unified Analysis for Calculating the Incoherent Spontaneous Emission of Cooperative Radiations

A unified analysis is presented to calculate the incoherent spontaneous power of cooperative radiations based on self-amplified spontaneous emission. Using quantum mechanical tools, we derive analytical expressions for the incoherent spontaneous power of undulator and Cherenkov free-electron lasers （FELs）. The undulator and Cherenkov FELs are considered as two different examples for the radiation that accumulate cooperatively. In the case of the undulator FEL, we show an excellent agreement between an expression for the incoherent radiation power derived in the present work and that obtained using a completely different approach [Phys. Ftev. E 65 （2002） 026501]. For the Cherenkov radiation, we demonstrate a satisfactory agreement between the incoherent power predicted in our analysis and previous experimental results.

Calculation and analysis of the number of return photons from sodium laser beacon excited by the long pulse laser with circular polarization

The number of return photons from sodium laser beacon（SLB） greatly suffers down-pumping, recoil, and geomagnetic field when the long pulse laser with circular polarization interacts with sodium atoms in the mesosphere. Considering recoil and down-pumping effects on the number of return photons from SLB, the spontaneous radiation rates are obtained by numerical computations and fittings. Furthermore, combining with the geomagnetic field effects, a new expression is achieved for calculating the number of return photons. By using this expression and considering the stochastic distribution of laser intensity in the mesosphere under different turbulence models for atmosphere, the number of return photons excited by the narrow-band single mode laser and that by the narrow-band three-mode laser are respectively calculated. The results show that the narrow-band three-mode laser with a specific spectrum structure has a higher spontaneous radiation rate and more return photons than a narrow-band single mode laser. Of note, the effect of the atmospheric turbulence on the number of return photons is remarkable. Calculation results indicate that the number of return photons under the HV5/7 model for atmospheric turbulence is much higher than that under the Greenwood and Mod HV models.