Approximation of perturbations of an optical beam under thermal self-interaction conditions

An algorithm is proposed for the approximation of the parameters of a beam in which a quadratic polynomial, expressed in terms of coordinates transverse to the beam axis, is used to describe the phase front profile. The coefficients in this polynomial are related to the spatial moments of the intensity distribution and to their derivatives with respect to a coordinate along the beam axis. A system of approximate ordinary differential equations for the moments is derived for a convective gasdynamic thermal self-interaction. The use of this system of equations reduces significantly the computer time needed to analyse beam perturbations. The approximation quality is checked by comparing the results of rigorous and approximate calculations.