Geometric optics of thermal blooming in gases. Part 1.

Thermal blooming is considered for the cases of with and without wind transverse to the beam propagation from the point of view of fluid dynamics of a compressible gaseous system and the coupling of this with geometric optics using eikonal formalism. Full compressible fluid dynamic relationships are developed (first-order perturbation approximation) with kinetics of energy relaxation from vibrational levels into heat and with thermal conductivity of a compressible gas as a heat loss mechanism. Eikonal theory is examined from the point of view of paraxial treatmen t in rigorous form, and some analytical beam intensity relationships are derived. In the process, several questions on the formation of caustics and thick lens effects are resolved. As a consequence of the above, a general time dependent model for the interaction of a laser beam with a compressible absorbing medium in the presence of wind is developed, and certain time dependent analytical solutions are obtained. These solutions reduce to the plain hermal blooming case with no wind and for long times to steady state wind case that has been previously reported by others to various degrees of correctness [F. G. Gebhardt and D. C. Smith, Appl. Phys. Lett. 14, 52 (1969); D. C. Smith, IEEE J. Quantum Electron. QE-5, 600 (1969)].