Ellinwood J W, Mirels H
Appl Opt. 1975 Sep 1;14(9):2238-42. doi: 10.1364/AO.14.002238.
A linearized theory is presented for density perturbations induced in a sluing laser beam as a function of time after beam turn-on and cross-flow Mach number M. The net local density perturbation is expressed as the sum of an isobaric and isentropic perturbation. A closed-form solution is obtained for M = 1, where the isentropic perturbations peak, and uniform heat addition in a circular beam. The results are compared with a corresponding one-dimensional beam. Poor agreement is found at large time, where the isentropic density perturbation varies as t and t((1/2)) for the one-dimensional and two-dimensional cases, respectively. An order-of-magnitude estimate for the final steady-state density perturbation, at M = 1, and the time scale in which it is achieved are obtained by consideration of nonlinear effects.
提出了一种线性化理论，用于描述在激光束开启后作为时间函数以及横流马赫数(M)的情况下，在斜置激光束中引起的密度扰动。净局部密度扰动表示为等压扰动和等熵扰动之和。对于(M = 1)（此时等熵扰动达到峰值）以及圆形光束中的均匀热添加情况，得到了一个封闭形式的解。将结果与相应的一维光束进行了比较。发现在较长时间时一致性较差，其中对于一维和二维情况，等熵密度扰动分别随时间(t)和(t^{\frac{1}{2}})变化。通过考虑非线性效应，得到了(M = 1)时最终稳态密度扰动的量级估计以及达到该稳态的时间尺度。
