热晕小尺度不稳定性解析理论的推导

ANALYTIC THEORY OF SMALL SCALE-SIZE THERMAL BLOOMING INSTABILITIES

本文在傍轴波近似和等压近似下推导出通过均匀介质传播的高能激光束小尺度不稳定性的线性解析理论。对扰动量方程在横向上进行傅里叶变换、在纵向和时间上进行各自的拉普拉斯变换,可以得到扰动量的解析表达式。最后,通过拉普拉斯反演后求得扰动量之傅里叶分量的解析解是用传播核(或格林函数)K_k(z,t)来表示的。

The linear analytic theory of small scale -size thermal blooming instabilities for a high energy laser propagating through a homogeneous medium is derived in paraxial scalar wave approximation and isobaric supposition. When we perform Fourier transforms in transversal coordinates and Laplace transforms in time and longitudinal coordinate, the fluctuations can be obtained in analytic form. In the real world the Fourier components of the fluctuations are written with the propagation kernal (or Green function) Kk (z,t), after the inverting Laplace transforms are performed.