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.

High-level Stark Effect and Spectrum of Spherical Nanometer System

In the electric field and layer-to-layer interaction energy, the law of split-level of high-level Stark effect of spherical nanometer system is explored as well as the frequency of spectrum, intensity and size effect of coefficient of spontaneous radiation. Taking three layers CdS/HgS spherical nanometer system as an example, the influence of the electric field and layer-to- layer interaction energy is explored on Stark effect and spectrum. The results show that in the Stark effect system, the energy level is split based on 1, 3, ..., （2n-1）, when it is in the electric field only, similar to the hydrogen atoms; and in the electric field and layer-to-layer interaction, it is split based on 1, 4, ~ -., n2; with the quantum transition, the frequency of the spectrum decreases with the increasing size of the system; apart from a few spectral lines, the intensity of most spectral lines will decreased as the size increases; while the coefficient of spontaneous radiation will increase with the increasing size; the electric field will cause the changes of spectrum frequency; its spectrum frequency shift is proportional to the square of the electric field intensity; apart from a few spectral lines, the frequency shift of spectral lines that is caused by the electric field and layer-to-layer interaction will decrease as the size increases; the interaction will make the level of electronic energy level lower slightly （the order of magnitude is between 10-7-10-9 eV）, the slightly increased spectrum intensity and the slightly increased value of coefficient of spontaneous radiation, but it will not influence the frequency of spectrum, intensity, and the trend that coefficient of spontaneous radiation changes with the size; when the size is smaller, the layer-to-layer interaction effect will be significant.

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.