Newtonian fluid dynamics simulations were performed using the Navier-Stokes-Fourier formulations to elucidate the short time-scale (µs and longer) evolution of the density and temperature distributions in an argon-gas-filled attenuator for an X-ray free-electron laser under high-repetition-rate operation. Both hydrodynamic motions of the gas molecules and thermal conductions were included in a finite-volume calculation. It was found that the hydrodynamic wave motions play the primary role in creating a density depression (also known as a filament) by advectively transporting gas particles away from the X-ray laser-gas interaction region, where large pressure and temperature gradients have been built upon the initial energy deposition via X-ray photoelectric absorption and subsequent thermalization. Concurrent outward heat conduction tends to reduce the pressure in the filament core region, generating a counter gas flow to backfill the filament, but on an initially slower time scale. If the inter-pulse separation is sufficiently short so the filament cannot recover, the depth of the filament progressively increases as the trailing pulses remove additional gas particles. Since the rate of hydrodynamic removal decreases while the rate of heat conduction back flow increases as time elapses, the two competing mechanisms ultimately reach a dynamic balance, establishing a repeating pattern for each pulse cycle. By performing simulations at higher repetition rates but lower per pulse energies while maintaining a constant time-averaged power, the amplitude of the hydrodynamic motion per pulse becomes smaller, and the evolution of the temperature and density distributions approach asymptotically towards, as expected, those calculated for a continuous-wave input of the equivalent power.
Keywords: FEL; X-ray; attenuation; filamentation; fluid dynamics; gas; thermal conduction.