Gas dynamics of the pulsed emission of a perfect gas with applications to laser sputtering and to nozzle expansion

Abstract

Particles released from a target surface by laser-pulse bombardment normally collide with each other and, as a result, exhibit three limiting categories of gas-dynamic behavior. One possibility, (a), is that the particles pass directly into unsteady adiabatic expansion (UAE), a problem for which an analytical solution already exists. Alternatively, (b), the particles first form a Knudsen layer (KL), then pass into UAE, and are not subject to recondensing at the target surface if the release pulse terminates, or else, (c), the particles go through the same sequence of KL formation and UAE but are subject to recondensing. Closely related to (b) is the behavior of particles that escape into vacuum from a nozzle. We here present an analytical, one-dimensional, continuum solution for case (b) when the release is pulsed. The KL (like the throat of the nozzle) is treated as a boundary condition with a nonzero flow velocity. During the release pulse the solutions take on our previously derived forms for a planar UAE from an infinite reservoir. When the pulse ends (or the nozzle closes), there is an abrupt change of boundary condition from finite to zero flow velocity and from high to intermediate sound speed (thence density); at the same time the flow pattern breaks up into three regions. These analytical results are finally compared with the numerical solution of the flow equations by Knight [AIAA J. 20, 950 (1982)], with Monte Carlo solution of the Boltzmann equation by Sibold and Urbassek [Phys. Rev. A 43, 6722 (1991)], and with the explicit nanosecond-time-scale photography of Braren, Casey, and Kelly [Nucl. Instrum. Methods B 58, 463 (1991)]. The comparison with the Boltzmann equation is particularly important, as the generally good agreement with the flow equations suggests the latter to be useful in spite of being founded on the assumption of persistent local equilibrium.