<title>Simplified Predictive Methodology For Nonlinear Repetitive Pulse And CW High Energy Laser Propagation</title>

Systems analysis studies frequently require simplified predictive methodology for determining nonlinear thermal blooming effects on a high energy laser beam propagating through the atmosphere. Because of the many variables, tens of thousands of propagation runs may be required in the course of a systems study. As a result, the wave optics codes are generally not practical due to excessive computation times. A methodology highly suitable for systems analysis has been constructed by observing that a phase integral can be defined which has the properties of a similarity variable. For a particular aperture plane beam shape, a high energy laser beam propagating through a convective medium experiences beam spread due to thermal blooming which can accurately be correlated as a simple function of the phase integral. A few well chosen wave optics calculations provide the data base for the correlation which then becomes a "scaling law". This scaling law expresses the dependence of the non-linear beam spread as a function of beam properties such as power, pulse repetition frequency, wavelength, Fresnel number and atmospheric properties such as absorption, transmission and wind speed. This correlation is combined with formulations for jitter and turbulence providing the basis for a simple yet highly accurate predictive methodology.