由包含弛豫作用的速率方程出发，建立了关于放大器能流密度空间分布最优问题的数学模型。采用最优问题求解方法，计算得到了多程放大器光束空间分布的优化设计，并分析了由此引起的对于放大器总体性能的影响。 Based on the rate equation including relaxation, a mathematical model about the optimal problem of spatial distribution of energy flux density in the amplifier is established. By using the optimal solution method, the optimal design of the spatial distribution of multi-pass amplifier was calculated and the effect on the overall performance of the amplifier was analyzed.