高平均功率光学增益腔在多个领域有着广泛的应用，包括用于汤姆逊散射产生高平均通量的X或伽马射线、光腔增强的高次谐波产生、引力波探测、稳态微聚束光源以及聚变能源实验等。本论文的工作聚焦于以汤姆逊散射应用为背景的高平均功率光腔的理论与实验研究。以提高汤姆逊散射所产生光子的平均通量为目标，其要求光腔内激光场具有尺寸约为几十微米的束腰、脉冲长度为皮秒量级，并且具有稳定的几百千瓦的平均功率。为了在汤姆逊散射模拟中更精确并且更高效的描述光腔内强聚焦的激光场，通过使用一种推广型的 Lax 级数展开的方法给出了强聚焦、线偏振激光场的一组非傍轴近似的表达式。为了抑制在光腔内激光平均功率达到约 100 kW 时开始明显出现的影响光腔稳定性并且可能导致光腔失锁的模式不稳定性，使用将腔镜热弹性形变与腔内平均功率线性关联的 Winkler 模型较好的描述了引起光腔模式不稳定性的模式简并。我们提出并模拟证明了 D 型镜法可以成功抑制光腔内的模式不稳定性。在汤姆逊散射光源装置 ThomX 的原型光腔上安装 D 型镜并实现了小时时间尺度的 200 kW稳定的平均储存功率。针对影响光腔稳定性并阻碍腔内激光功率达到设计指标的光腔内功率快速下降现象进行了分析。这一现象表现为光腔内功率下降的幅度和时间尺度依赖于腔内的功率水平，进一步提升注入激光的功率最终导致光腔注入耦合镜表面的不可修复的损伤。通过对实验后已损伤的腔镜表面的成像和实验过程中采集的光腔的透射及反射数据的分析，发现主导这一现象的物理因素是腔镜表面的污染形成的热斑产生的表面形变所引起的散射损耗而导致的，并且通过模拟对这一现象进行了重现。这一分析可以帮助理解在多领域应用的高功率光腔上出现的此类功率快速下降现象背后的物理过程并起到损伤预警的作用。给出了清华汤姆逊散射光源装置 TTX 的原型光腔的完整设计并进行了初步实验，实现了将连续型激光器与光腔锁定的实验目标。对中心波长为 1064 nm 的连续型注入激光实现了 133 倍的增益。并且给出了 TTX 原型光腔高功率实验的设计以及将与电子储存环结合的 TTX 光腔的设计。
High-average-power optical enhancement cavities (OEC), have a wide range of applications including Thomson scattering producing high average flux quasimonochromatic X/?-rays, cavity-enhanced high-order harmonic generation (HHG), gravitational wave interferometers, steady-state microbunching (SSMB) light sources and fusion energy experiments etc.The works of this thesis focus on the theoretical and experimental studies of highaverage-power OEC dedicated to Thomson scattering light sources. With the purpose ofincreasing the average flux of Thomson scattering generated photons, it is demanded for the laser beam inside OEC to have small waist with radius size of few tens of microns, pulse length at the order of picosecond and stable intra-cavity average power of few hundreds of kilowatts.To precisely and effectively describe the highly focused laser field inside OEC to be used in simulations of Thomson scattering, a field expression of nonparaxial corrected highly focused linearly polarized laser field is derived with a generalized Lax series expansion method.To suppress the modal instabilities start to appear apparently on OEC with an intracavity average power reaching ～ 100 kW which affect cavity stability and could lead to lose of lock, the modal instabilities are well described with mode degeneracies induced by mirror surface thermoelastic deformation characterized by Winkler model. We brought up the D-shape mirror method for suppressing modal instabilities and proved its effectiveness with simulation. An hour-time-scale stable intra-cavity average power of 200 kW was realized on the prototype OEC of Thomson scattering light source ThomX with implementation of D-shape mirrors inside.Analysis is carried out for understanding the fast power drop phenomenon appearing on OEC which affects the cavity stability and hinders the intra-cavity power reaching thedesigned goal. Intra-cavity power drops appeared with magnitude and time scale depending on the power level. Increasing further the incident power led to irreversible damage of the cavity coupling mirror surface. The origin of this phenomenon is investigated with post mortem mirror surface imaging and analysis of the signals transmitted and reflected by the OEC. Scattering loss induced by mirror surface deformation due to a hot-spot con
