Series solution for transient thermal blooming of an axi-symmetric laser beam

Self-defocussing of an intense laser beam propagating through an initially quiescent compressible gas is investigated. The dependent variables are sought as Taylor series expansions involving the two space coordinates and the time, and the resulting recurrence relations are solved by digital computer. The beam is found to distort substantially as it propagates, but is not affected significantly by gravity when aimed vertically.