Hybrid modelling of a high-power X-ray attenuator plasma

X-ray gas attenuators act as stress-free high-pass filters for synchrotron and free-electron laser beamlines to reduce the heat load in downstream optical elements without affecting other properties of the X-ray beam. The absorption of the X-ray beam triggers a cascade of processes that ionize and heat up the gas locally, changing its density and therefore the X-ray absorption. Aiming to understand and predict the behaviour of the gas attenuator in terms of efficiency versus gas pressure, a hybrid model has been developed, combining three approaches: an analytical description of the X-ray absorption; Monte Carlo for the electron thermalization; and a fluid treatment for the electron diffusion, recombination and excited-states relaxation. The model was applied to an argon-filled attenuator prototype built and tested at the European Synchrotron Radiation Facility, at a pressure of 200 mbar and assuming stationary conditions. The results of the model showed that the electron population thermalizes within a few nanoseconds after the X-ray pulse arrival and it occurs just around the X-ray beam path, recombining in the bulk of the gas rather than diffusing to the attenuator walls. The gas temperature along the beam path reached 850 K for 770 W of incident power and 182 W m^-1 of absorbed power. Around 70% of the absorbed power is released as visible and UV radiation rather than as heat to the gas. Comparison of the power absorption with the experiment showed an overall agreement both with the plasma radial profile and power absorption trend, the latter within an error smaller than 20%. This model can be used for the design and operation of synchrotron gas attenuators and as a base for a time-dependent model for free-electron laser attenuators.