Heat-transfer regimes in nuclear-reactor-pumped gas lasers

The flow induced in nuclear-reactor-pumped gas lasers by the competing effects of spatially nonuniform fission-fragment heating (pumping) and heat transfer to the walls is examined. The equations of motion are acoustically filtered (low Mach number approximation), and the resulting equations are seen to have three timescales: the duration of the heating, the time required by the heating to produce a pressure rise comparable to the initial pressure, and the time for the thermal boundary layer to grow into the center of the laser cell. Three distinct regimes emerge from consideration of the relative magnitudes of these timescales. In the negligible-conduction regime, thermal-conduction effects are small, and the motion is determined by the spatial nonuniformity of the heating. In the dominant-conduction regime, thermal-conduction effects govern the motion. In the mixed regime, the effects of thermal conduction and heating nonuniformity are comparable, but since they are oppositely directed, a complex gas motion results. Analytical solutions to the equations of motion are presented for the negligible-conduction and dominant-conduction regimes, and examples are given for all three regimes. Plots of the second spatial derivative of the density field (a quantity often used in optical analyses) are given for the negligible-conduction and the dominant-conduction regimes as functions of the appropriate similarity parameters.