Fig. 8. Critical propagation distance for thermal blooming as a function of altitude. hence, refractive index gradients which act as a distributed lens. In general, the explicit determination of the beam phase and intensity distributions at a target illuminated by a remote laser transmitter and separated by an inhomogeneous absorbing medium requires numerical solution. For the purposes of the present study, however, we wish only to determine the potential impact of thermal blooming on the present space-to-earth power transmission scenario. There exists a critical distance, zc, beyond which beam distortion caused by blooming is substantial. For the case of no kinetic cooling of the absorbing medium (a good approximation for CO-laser light absorption), the expression for the critical propagation distance, in meters, is (48) where p is the atmospheric density (g/m3), C„ is the specific heat of air at constant pressure (0.242 cal/g °K), v is the wind velocity (m/sec), n-1(dn/d7) is the refractive index gradient, and a, is the total molecular and aerosol absorption coefficient (nr1). Notice that p, v, and at are functions of altitude, h; hence, zc is implicitly a function of altitude. The refractive index gradient is also an implicit function of altitude because of the dependence of temperature on altitude. Now in Appendix A of Ref. (8), it was shown that
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