Time-dependent strain analysis of mirrors illuminated with intense femtosecond pulses in the soft x-ray spectral range

Abstract

We consider the three-dimensional time-dependent thermoelastic problem for a thin silicon blade illuminated by a single soft x-ray free-electron laser (FEL) pulse of fs duration. An exact analytical solution is given. It shows that the heat flow in the blade is very slow, which might pose problems for cooling if the FEL is operated to produce a train of pulses with short spacing. Surface mechanical oscillations are generated shortly after the FEL pulse is absorbed, and resonant enhancement by subsequent pulses in the pulse train is an issue. After the FEL pulse, but long before the heat front reaches the heat sink, the optical surface bulges outwards. The effects of a FEL pulse train with thousands of pulses need more detailed study, but experiments with single pulses at kHz rates are not expected to suffer from thermally induced surface figure distortion. The emphasis in this article is not on whether the blade will escape melting, but rather to what extent the profile of a high precision optical surface is preserved under FEL illumination, a question of major interest if focal spots with diameters in the micron range are needed.