Transonic thermal blooming due to an intense laser beam

According to the linearized solutions for thermal blooming, the density perturbations become infinite (i.e., 'castastrophic' defocusing) as the Mach number approaches unity. However, the nonlinearities in the transonic equations terminate the trend to infinity. The nonlinear equations, which are formulated in natural coordinates, with heat addition are transformed into simple linear algebraic equations through the specification of the streamline geometry in the heat release region. At a Mach number of unity, streamtube area variation was found to be directly proportional to the change in total temperature. A steady, two-dimensional, mixed flow solution has been obtained for the transonic thermal blooming problem. The solution for the density perturbations within a laser beam at a Mach number of precisely unity is given. For a Gaussian beam with an intensity of 33.3 MW/sq m and an atmospheric absorption of 0.8 millionths/cm the maximum fractional density perturbation is 0.0001028.