I grew with time. For 200 pumping pulses, the photon density n had a maximum value just prior to the peak input. The input light pulse was then assumed to be proportional to sin2(27rt/10-4) up to 50 /is and thereafter to be constant. For p = 3 torr the calculations indicated a pulse of 350 p.s, and for p = 13 torr the duration was of order 10 ms with C = 5000. Plots of the other variables indicated a gradual depletion of IBr and a growth of I. The long time scale suggests that a gas flow system would be feasible for steady-state working provided the gas temperature was kept within limits. IX. TEMPERATURE EFFECTS As the absorbed photons have an average energy of several eV, and as the heat conduction of IBr is low, very high temperatures can occur. If the pressure/? of IBr is greater than 50 torr in a vessel 1 cm deep, then the temperature of the lasing gas can be roughly estimated assuming all the photon energy is deposited in the gas; ifp <50 torr, then roughly a fraction 10-2p is deposited. The heat produced travels an average distance x to the walls of the containing vessel by gaseous conduction. The walls are assumed at a temperature Tw and are thermally connected to a radiator into space. Above about 1000 °K, the gas would also act as a blackbody radiator. Estimates show that ifx = 0.5 cm, then for C = 2000 and p = 5 torr the gas temperature would be of order 1000 °K. If the pressure is increased (a requirement for high absorption efficiency) still higher temperatures are possible, as heat conduction in gases is independent of pressure. Cooling can be enhanced by reducing x by inserting fingers in the gas, or by admitting a noble gas with a high heat conductivity and a low quenching cross section. Assuming perfect conduction from the walls to a radiator the same size as the collector, then the radiator temperature would be somewhat less than 300 °K. High temperatures can have large effects on quenching, recombination and dissociation rates, and on exchange reactions. To our knowledge experimental data on the effect of temperature on the quenching of Br* by IBr or I2 are not available. The possible analogous case of quenching of I* by I2 was reported by Kartazaef et al. (31), whose measurements showed the quenching rates at 1000 °K were 20 times lower than at 300 °K. If a similar dependence occurred for the quenching coefficient of Br* by IBr or I2, the high temperatures would prove advantageous in this respect. Turner and Rapagnani (26) have reported measurements of the recombination rates for I + I + I2—» 2I2, where A = 1.1 x io10? 3 884. The coefficient is 1000 times smaller at 1000 °K than at 300 °K and is analogous to C6 used above where I recombined with Br and the third body was IBr. High temperatures cause thermal dissociation of IBr with the formation of I, Br, and Br2, which have large cross sections for the quenching of Br*. The depletion of the lower level by exchange reactions would also be reduced as the increase in I would enhance the reverse exchange reaction. On balance then, heating would seem to be very detrimental to IBr solar laser operation. X. CONCLUSIONS The time varying solutions of the species rate Eqs. 2 through 9 show that inversion
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