Fluid dynamics analysis of a gas attenuator for X-ray FELs under high-repetition-rate operation

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.