Halo distribution is a key topic for background study. This paper has developed an analytical method to give an estimation of beam halo distribution in storage rings. This is a creative new theory. As an example, the equilibrium particle distribution of the beam tail in the Accelerator Test Facility damping ring is calculated analytically with different emittance and different vacuum degree. The analytical results agree the measurements very well. This is a general method, which can be applied to any electron rings.

High gain free electron laser devices, operating in the self amplified spontaneous emission regime, are under construction and was designed as the next generation of synchrotron radiation sources. In this paper we discuss the relevant physical aspects and derive simple relations for laser and higher order harmonic power, which can usefully be exploited in the preliminary design of these sources