考虑电子束横向发射度和电子β振荡, 将2005年国际上提出的单通过高增益自由电子激光饱和状态分析的统计物理方法发展到三维情形。首先建立一种描述电子三维运动的归一化简化模型, 推导了一维光场下包含电子横向运动的Vlasov方程。在螺旋型波荡器情形下通过引入横向运动守恒量发展了三维统计物理分析方法, 并编写了相应计算程序, 计算自由电子激光达到饱和时系统的光强增益、聚束因子。作为对比验证, 编写包含N个电子自由电子激光系统的三维直接数值模拟程序, 结果表明数值模拟和统计计算结果相一致。对比文献中一维模拟和一维统计理论计算结果, 所得结果反映了电子束横向发射度以及电子在波荡器中的横向β振荡对饱和点参数的影响。

Considering the transverse emittance of electron beam and electron beta oscillation, the statistical physics approach of the analysis to the single pass high-gain free electron laser at saturation is improved and extended to the three-dimensional case. Firstly, a three-dimensional, normalized and simplified model is conducted, then the Vlasov equation of one-dimensional light field including the transverse movement of electrons is derived. In the helical undulator case a three-dimensional statistical physics approach is developed by introducing the conserved quantities of transverse movement, and the relevant code is written for calculation of the saturation intensity, bunching factor and other parameters. For comparison and verification, a direct numerical simulation code of free electron laser which includes N particles is written. The results of numerical simulation and statistical theory are in well accordance with the original one-dimensional simulation and statistical physics approach, and the three-dimensional theory reveals the effect of saturation point parameters introduced by transverse emittance of electron beam and electron beta oscillation.