Raman自由电子激光的半经典理论

采用Ｔｈｏｍａｓ-Ｆｅｒｍｉ近似势，将多电子系统简化为单电子问题，并用微扰论求解了Ｋｌｅｉｎ-Ｇｏｒｄｏｎ方程．由电子的零级波函数求得了电荷密度和电流密度的零级表达式．通过适当简化Ｋｌｅｉｎ-Ｇｏｒｄｏｎ方程，用分离变量和ＷＫＢ近似，求得了电子波函数及相应的电荷密度与电流密度的表达式 关键词：

SEMICLASSICAL THEORY OF RAMAN FREE-ELECTRON LASERS

In this paper, we point out that the problem of a system of many particles can be simplified into that of a single electron by using Thomas-Fermi potential in Raman free-electron lasers. Klein-Gordon equation is solved by using perturbation theory. The formula of the density of electric charge and current density are derived from the corresponding zero order wave function. If we simplify properly the Klein-Gordon equation, we can solved by using the methods of seperation of variables and WKB approximation. We also derived the formula of the electric charge and current density which correspond to the new wave function.